Category: Envision Math

Go through the enVision Math Common Core Grade 2 Answer Key Topic 7 More Solving Problems Involving Addition and Subtraction regularly and improve your accuracy in solving questions.

enVision Math Common Core 2nd Grade Answers Key Topic 7 More Solving Problems Involving Addition and Subtraction

Essential Question:
How can you solve word problems that use adding or subtracting?

envision STEM Project: Solving Problems
Find Out Find and share books that tell about ways to protect land from damage that wind or water can cause. Compare the different ways to protect the land.
Journal: Make a Book Show what you learn in a book. In your book, also:

• Show ways to solve problems caused by wind or water.
• Show ways to solve problems using addition or subtraction.

Review What You Know

Vocabulary
Question 1.
Write the subtraction problem below as an equation.

Answer:
The equation for the above subtraction problem is 75 – 30 = 45
Explanation:
Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtract 30 from 75 results 45. The problem can be written as an equation format is 75 – 30 = 45.

Question 2.
Complete the bar diagram to model 77 + 22 = ?

Answer:

77 + 22 = 99
Explanation:
The addition is taking two or more numbers and adding them together results sum. In the above bar diagram we can observe two numbers one is 77 and another one is 22. By adding these two numbers results sum which is 99. Place the result 99 above the box and place the addends in box.

Question 3.
Circle the two addends below that are compatible numbers.
18 + 6 + 4 = ?
Answer:

Explanation:
Compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally. Compatible numbers are close in value to the actual numbers that make estimating the answer and computing problems easier. We can round the numbers to the nearest ten, hundred, thousand or ten thousand to make them compatible numbers. In the above equation the two compatible numbers are 6 and 4. Draw a circle to the addends 6 and 4. Add 18 with 10 then we got 28.

Adding to Check Subtraction
Question 4.
Use addition to check if the subtraction equation is correct.
51 – 22 = 29
Is it correct? _________
Answer:
51 – 22 = 29
29 + 22 = 51
Yes, the above subtraction equation is correct by checking with the addition operation as we can observe in the above equation.
Explanation:
In the above subtraction equation we can observe the result as 29. Here we have to check whether the result is right or wrong by using addition operation. The result 29 is added to the smallest number in the equation. The smallest number is 22. ADD 29 with 22 then we got 51. The above subtraction equation is correct.

Subtracting to Check Addition
Question 5.
Use subtraction to check if the addition is correct.
37 + 26 = 53
Is it correct? _________
Answer:
37 + 26 = 53
53 – 37 = 16
No, the above addition equation is not correct by checking with the subtraction operation as we can observe in the above equation.
Explanation:
In the above addition equation we can observe the result as 53. Here we have to check whether the result is right or wrong by using subtraction operation. The result 53 is subtracted with the second biggest number in the equation. The second biggest number is 37. Subtract 37 from 53 then we got 16. In the above equation we can observe 26. So the above addition is not correct.

Number Story
Question 6.
Jim and Maria are counting birds. Jim counts 17 birds. Maria counts 33 birds. How many more birds does Maria count than Jim?
_________ more birds
Answer:
17 + ? = 33
17 + 10 = 27
27 + 6 = 33
10 + 6 = 16.
16 more birds does Maria count than Jim.
Explanation:
Jim and Maria are counting birds. Jim counts 17 birds and Maria counts 33 birds. By adding another 16 birds to the 17 birds results 33 birds.

Pick a Project

PROJECT 7A
How many points has your favorite hockey player scored?
Project: Design a Player Card

PROJECT 7B
How many floors do New York City skyscrapers have?
Project: Build a Skyscraper Model

PROJECT 7C
Where can you find caves in the United States?
Project: Create a Worksheet of Cave Problems

3-ACT MATH PREVIEW

Math Modeling
The Water Jug

Lesson 7.1 Represent Addition and Subtraction Problems

Solve & Share
Jenn has some red cubes and Il blue cubes. She has 24 red and blue cubes in all. She says the problem can be shown with the equation below.
? + 11 = 24
Draw what the ? represents. Explain your answer.
I can … model problems using equations with unknowns in any position.

Answer:

Answer:
? + 11 = 24
13 + 11 = 24
Jenn has 13 red cubes.
Explanation:
Jenn has some red cubes and 11 blue cubes. She has 24 red and blue cubes in all. Here we have to find how many red cubes does Jenn have. Subtract blue cubes from total number of cubes then we can get total number of red cubes. Subtract 11blue cubes from 24 total number of cubes then we got 13 red cubes.

Visual Learning Bridge

Convince Me! Could you show Robert’s robot problem with the equation below? Explain.
58 = 27 + ?
Answer:
58 – 27 = 31
Robert has 27 toy robots. He buys some more robots. Now he has 58 robots. Subtract 27 robots from 58 total number of robots then we got 31 robots.

Guided Practice

Write an equation with a ? for the unknown to model the problem. Then solve. Show your work.
Question 1.
Mary has some game tickets. She gives away 14 tickets and now has 17 tickets left. How many tickets did she have at first?

Answer:
? – 14 = 17 tickets
31 – 14 = 17 tickets
Explanation:
Mary has some game tickets She gave 14 tickets away and now she has 17 tickets left. Here we have to find the total number of tickets did she have at first. Perform addition operation on tickets left and gave away tickets then we can easily find total number of tickets did she have at first. ADD 17 with 14 then we got 31. Mary has 31 game tickets at first.

Question 2.
Tamara has $25. She earns $34 more by working. How much money does she have now?
Equation: ___________ $ ____________
Answer:
Tamara has $25. She earns $34 more by working. she has $59 now.
The equation is $25 + $34 = $59
Explanation:
Tamara has $25. She earned $34 more by working. Addition is a mathematical operation in which two or more numbers are added together to get the sum. Here we have to add the money which she had earned by working with actual money she have. Add $25 with $34 then we got $59.

Independent Practice

Write an equation with a ? for the unknown to model the problem. Then solve. Show your work.
Question 3.
Erin has 32 books on her bookshelf. She gives some to friends and now has 19 books left. How many books did she give away?
Equation: ___________
__________ books
Answer:
32 – ? = 19
32 – 19 = 13
32 – 13 = 19
Explanation:
Erin has 32 books on her bookshelf. She gave some to friends and now she has 19 books left. Perform subtraction on total number of books on her bookshelf and left over books then we get how many books does she gave away to her friends. Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtract leftover books from total number of books. Subtract 19 books from 32 books then we got 13 books. Erin gave 13 books to her friends.

Question 4.
A store sells 38 men’s bikes and 47 women’s bikes. How many bikes did the store sell in all?
Equation: ___________
________ bikes
Answer:
38 men’s bikes + 47 women’s bikes = ? bikes
38 men’s bikes + 47 women’s bikes = 85 bikes
Explanation:
A store sells 38 men’s bikes and 47 women’s bikes. Here we have to find the total number of bikes does store sell in all. So perform addition operation. Addition is a mathematical operation in which two or more numbers are combined together to get the sum. Add 38 men’s bikes with 47 women’s bikes then we got 85 bikes. 85 bikes does store is selling in all.

Question 5.
en Vision® STEM A field has 25 trees in it. 14 trees are new and the rest are old. How many trees are old? Write two different equations that represent the problem. Then solve.
Equation: ___________
Equation: ___________
__________ old trees
Answer:
14 + ? = 25
14 + 10 = 24
24 + 1 = 25
10 + 1 = 11
14 + 11 = 25
? = 25 – 14
11 = 25 – 14
11 trees are old.
Explanation:
STEM A field has 25 trees in it. 14 trees are new and the rest are old. Here we have to find how many trees are old. We can find old trees simply by adding 10 to the new tress. ADD 10 to the new tress which are 14 then we got the result as 24 trees. Here the total number of trees are 25. Add 1 to the 24 then we got total number of trees. Add 10 with one then we got 11 trees which are old.
Another way of solving the equation is performing subtraction operation. Subtract new trees from total number of trees then we get old trees. Subtract 14 from 25 then we got 11. 11 trees are old.

Question 16.
Number Sense Harry buys 22 fish. He has a round fish bowl and a rectangular fish tank. How could he place the fish in the bowl and tank?
Equation:
___________ fish in the bowl
___________ fish in the tank
Answer:
Equation: 11 + 11 = 22
11 fish in the bowl.
11 fish in the tank.
Explanation:
Harry buys 22 fish. He has a round fish bowl and a rectangular fish tank. He can place 11 fish in the round fish bowl and 11 fish in the rectangular fish tank. By adding 11 fish in the bowl and 11 fish in the tank results total number of fish. Total number of fish are 22.

Problem Solving

Write an equation with a ? for the unknown to model the problem. Then solve. Show your work.
Question 7.
Model Rodney collects 17 leaves and Sheila collects 23 leaves. How many more leaves does Sheila collect than Rodney?
Equation: ___________
___________ more leaves
Answer:
Equation: 23 – 17 = ?
23 – 17 = 6
6 more leaves does Sheila collected than Rodney.
Explanation:
Model Rodney collects 17 leaves and Sheila collects 23 leaves. Here we have to find how many more leaves does Sheila collect than Rodney. Subtract Rodney collected leaves from Sheila collected leaves. Subtract 17 leaves from 23 leaves then we got 6 leaves. Sheila collected 6 more leaves than Rodney.

Question 8.
Model Jun swims 18 laps and Mara swims 25 laps. How many fewer laps did Jun swim than Mara?
Equation: ___________
___________ fewer laps
Answer:
25 laps – 18 laps = 7 laps
Jun swim 7 fewer laps than Mara.
Explanation:
Model Jun swims 18 laps and Mara swims 25 laps. Here we have to find how many fewer laps did Jun swim than Mara. Subtract Jun swims laps from Mara swims laps. Subtract 18 laps from 25 laps ten we got 7 laps. Jun swim 7 fewer laps than Mara.

Question 9.
Higher Order Thinking Jim has 44 roses. 14 are white and the rest are red. How many are red? Write two different equations to model the problem. Then solve.
Equation: ___________
Equation: ___________
Answer:
Equation1: 14 white + ? red = 44 roses
14 + 10 = 24
24 + 10 = 34
34 + 10 = 44
10 + 10 + 10 = 30 red roses
Equation 2: 44 roses – 14 white = ? red
44 roses – 14 white = 30 red roses
Explanation:
Jim has 44 roses. 14 are white and the rest are red. Here we can find total number of red roses in two ways one is addition operation and another one is subtraction operation.
By adding 14 white roses with 30 red roses results 44 roses. Total number of red roses are 30.
Subtract 14 white roses from total number of roses are 44. Then we got 30 red roses.

Question 10.
Assessment Practice Some wolves howl in the woods. 12 wolves join them. Now 30 wolves howl. How many wolves howled at first?
Which equation models the problem? Choose all that apply.
☐ ? + 12 = 30
☐ 30 = 12 + ?
☐ 30 + 12 = ?
☐ 30 = ? + 12
Answer:

Below equations are correct
18 + 12 = 30
30 = 12 + 18
30 = 18 + 12
18 wolves howled at first.
Explanation:
Some wolves howl in the woods. 12 wolves join them. Now 30 wolves howl. Add 18 Wolves to the 12 wolves then we got 30 Wolves. 18 wolves howled at first.

Lesson 7.2 Mixed Practice: Solve Addition and Subtraction Problems

Solve & Share
Aiden has 27 fewer crayons this week than last week. Last week he had 56 crayons. How many crayons does Aiden have this week? Show your work.
I can … use drawings and equations to make sense of the words in problems.

Answer:

Aiden have 29 crayons this week.
Explanation:
Aiden has 27 fewer crayons this week than last week.  That means he has less crayons in this week. Last week he had 56 crayons. Here we have to perform subtraction operation. Subtract 27 crayons from 56 crayons then we got 29 crayons. Aiden have 29 crayons this week.

Visual Learning Bridge

Convince Me! How are these statements alike and different? Cal has 12 fewer blocks than Mia. Mia has 12 more blocks than Cal.
Answer :
Cal has 12 fewer blocks than Mia. Mia has 12 more blocks than Cal. These statements are alike in that both have a missing number of blocks. They are different in that one says how many more and the other how many less.

Guided Practice

Solve the problem any way you choose. Use drawings and equations to help.
Question 1.
Lakota has 11 fewer magnets than Jeffrey. Lakota has 25 magnets. How many magnets does Jeffrey have?

_________ magnets
Answer:

Jeffrey have 36 magnets.
Explanation:
Lakota has 11 fewer magnets than Jeffrey. Lakota has 25 magnets. That means Jeffrey have more magnets than Lakota. So we have to add the magnets. Add 25 magnets with 11 magnets then we got 36 magnets. Jeffrey have 36 magnets.

Independent Practice

Solve each problem any way you choose. Use drawings and equations to help. Show your work.
Question 2.
There are 28 more students than adults at 1 the school fair. There are 96 students at the school fair. How many adults are at the school fair?
_________ adults
Answer:

At the school fair there are 68 adults.
Explanation:
There are 28 more students than adults at 1 the school fair. There are 96 students at the school fair. Add 28 students with 68 adults results 96 students. At the school fair there are 68 adults.
Question 3.
Ellie the elephant has some peanuts. She eats 49 peanuts. Now Ellie the elephant has 31 peanuts. How many peanuts did she have before?
_________ peanuts
Answer:

Ellie have 80 peanuts before.
Explanation:
Ellie the elephant has some peanuts. She eats 49 peanuts. Now Ellie the elephant has 31 peanuts. Subtract 49 peanuts from 80 peanuts results 31 peanuts. Ellie have 80 peanuts before.

Question 4.
The blue team scores 16 fewer points than the green team. The blue team scores 41 points. How many points did the green team score?
_________ points
Answer:

Green Team score 57 points.
Explanation:
The blue team scores 16 fewer points than the green team. That means blue team score is less. The blue team scores 41 points. Here we have to perform addition operation. Add blue team fewer points with blue team score then we get green team score. Add 16 points with 41 points then we got 57 points. green team score is 57 points.

Question 15.
Higher Order Thinking Sean studies 16 fewer vocabulary words than Chris. Chris studies 10 fewer vocabulary words than Tia. Tia studies 34 words. How many words does Sean study? Explain your answer.
Answer:

Problem Solving

Solve the problem any way you choose. Use drawings and equations to help. Show your work.
Question 6.
Reasoning Kevin practices kicks for soccer. He kicks 13 times at recess. He kicks 14 times after school. Then he kicks 16 times before bed. How many practice kicks did Kevin take in all?

_________ kicks
Answer:

Question 7.
Higher Order Thinking There are 48 red tacks and blue tacks in a bag. There are fewer red tacks than blue tacks. There are at least 26 blue tacks but no more than 30 blue tacks. How many of each color could be in the bag?
Complete the chart to solve the problem.

Answer:

Explanation:
There are 48 red tacks and blue tacks in a bag. There are fewer red tacks than blue tacks. There are at least 26 blue tacks but no more than 30 blue tacks.
In first chance there are 22 red tacks and 26 blue tacks. Add 22 red tacks with 26 blue tacks then we got total number of red tacks and blue tacks in a bag are 48.
In second chance there are 21 red tacks and 27 blue tacks. Add 21 red tacks with 27 blue tacks then we got total number of red tacks and blue tacks in a bag are 48.
In third chance there are 20 red tacks and 28 blue tacks. Add 20 red tacks with 28 blue tacks then we got total number of red tacks and blue tacks in a bag are 48.
In fourth chance there are 19 red tacks and 29 blue tacks. Add 19 red tacks with 29 blue tacks then we got total number of red tacks and blue tacks in a bag are 48.
In fifth chance there are 18 red tacks and 30 blue tacks. Add 18 red tacks with 30 blue tacks then we got total number of red tacks and blue tacks in a bag are 48.

Question 18.
Assessment Practice Jim has 14 fewer baseball cards than Sara. Sara has 27 cards. How many baseball cards does Jim have?
Draw a line to show where each number and the unknown could be in the equation. Then solve.

_______ cards
Answer:

27 – 14 = 13
Jim have 13 baseball cards.
Explanation:
Jim has 14 fewer baseball cards than Sara. Sara has 27 cards. That means Jim have less cards then Sara. Here Sara have 27 baseball cards. Subtract fewer baseball cards from total number of baseball. Subtract 14 from 27 then we got 13 baseball cards. Jim have 13 baseball cards.

Lesson 7.3 Continue Practice with Addition and Subtraction Problems

Solve & Share
Erin has 17 more books than Isabella. Erin has 44 books. How many books does Isabella have?
Solve any way you choose. Show your work.
I can … use drawings and equations to make sense of the words in problems.
________ books
Answer:
44 – 17 = ?
44 – 17 = 27
Isabella have 27 books.
Explanation:
Erin has 17 more books than Isabella. That means Isabella have less books. Erin has 44 books. Here we have to perform subtraction operation. Subtract 17 more books of Erin from 44 books of Erin Then we get how many books does Isabella have. Subtract 17 from 44 then we got 27 books. Isabella have 27 books.

Visual Learning Bridge

Convince Me! Compare the two statements:
Sam has 18 more markers than Zoey.
Zoey has 18 fewer markers than Sam.
Answer:
Neither of the two statement say how many markers  does Sam has.

Guided Practice

Solve the problem any way you choose. Use drawings and equations to help.
Question 1.
The second grade has 19 more students than the first grade. The second grade has 68 students. How many students does the first grade have?

_________ students
Answer:

68 – 19 = ?
+1    +1
69 – 20 = 49
The first grade have 49 students.
Explanation:
The second grade has 19 more students than the first grade. That means first students are less. The second grade has 68 students. Subtract 19 more students from 68  second grade students then we get 49 students. The first grade have 49 students.

Independent Practice

Solve each problem any way you choose. Use drawings and equations to help. Show your work.
Question 2.
There are 11 more adults than children at a craft fair. There are 54 adults at the craft fair. How many children are at the craft fair?
_________ children
Answer:

There are 43 children at the craft fair.
Explanation:
There are 11 more adults than children at a craft fair. There are 54 adults at the craft fair. Subtract 11 adults from 54 adults then we get 43 children. There are 43 children at the craft fair.

Question 3.
Caleb is 17 years old. His sister is 12 years younger. How old is Caleb’s sister?
________ years old
Answer:

Caleb’s sister is 5 years old.
Explanation:
Caleb is 17 years old. His sister is 12 years younger. Subtract 12 years from 17 years then we got 5 years. Caleb’s sister is 5 years old.

Question 4.
Dylan and his friends had some blueberries. They ate 39 blueberries. They have 21 blueberries left. How many blueberries did Dylan and his friends have at first?
_________ blueberries
Answer:

At first Dylan and his friend have 60 blueberries.
Explanation:
Dylan and his friends had some blueberries. They ate 39 blueberries. They have 21 blueberries left. Add 39 blueberries with 21 blueberries then we got 60 blueberries. At first Dylan and his friend have 60 blueberries.

Question 5.
en Vision® STEM Addison made a dam with 18 more rocks than James. Addison’s dam had 42 rocks. How many rocks did James’s dam have? Explain your answer.
Answer:

James’s dam have 24 rocks.
Explanation:
Addison made a dam with 18 more rocks than James. Addison’s dam had 42 rocks. Subtract 18 rocks from 42 rocks then we got 24 rocks. James’s dam have 24 rocks.

Problem Solving

Solve the problem any way you choose. Use drawings and equations to help. Show your work.
Question 6.
Reasoning Connor has 39 sheets of green paper and some sheets of yellow paper. He has 78 sheets of paper in all. How many yellow sheets of paper does Connor have?

__________ yellow sheets
Answer:

Connor have 39 yellow sheets of paper.
Explanation:
Connor has 39 sheets of green paper and some sheets of yellow paper. He has 78 sheets of paper in all.  Subtract 39 sheets  of green paper from 78 sheets of paper in all then we get number of yellow sheets. By subtracting 39 from 78 results 39 yellow papers. Connor have 39 yellow sheets of paper.

Question 7.
Higher Order Thinking There are 58 red pens and blue pens in a bag. There are more red pens than blue pens. There are at least 36 red pens but no more than 40 red pens. How many of each color could be in the bag?
Complete the chart to solve the problem.

Answer:

Explanation:
There are 58 red pens and blue pens in a bag. There are more red pens than blue pens. There are at least 36 red pens but no more than 40 red pens.
In first chance red pens are 36 and blue pens are 22. Add red pens with blue pens then we got total number of pens in the bag. Add 36 red pens with 22 blue pens then we got 58 pens in the bag.
In second chance red pens are 37 and blue pens are 21. Add red pens with blue pens then we got total number of pens in the bag. Add 37 red pens with 21 blue pens then we got 58 pens in the bag.
In third chance red pens are 38 and blue pens are 20. Add red pens with blue pens then we got total number of pens in the bag. Add 38 red pens with 20 blue pens then we got 58 pens in the bag.
In fourth chance red pens are 39 and blue pens are 19. Add red pens with blue pens then we got total number of pens in the bag. Add 39 red pens with 19 blue pens then we got 58 pens in the bag.
In fifth chance red pens are 40 and blue pens are 18. Add red pens with blue pens then we got total number of pens in the bag. Add 40 red pens with 18 blue pens then we got 58 pens in the bag.

Question 18.
Assessment Practice Andrew has 63 more beanbags than Evan. Andrew has 92 beanbags. How many beanbags does Evan have?
The bar diagram models the problem. Which is the missing number?

A. 19
B. 29
C. 31
D. 39
Answer:

Evan bean bag   63 more bean bags
92 – 63 = ?
63 = 62 + 1
First we can subtract 62 and then 1
92 – 62 = 30
30 – 1 = 29
option B. 29 is correct.
Evan has 29 bean bags.
Explanation:
Andrew has 63 more beanbags than Evan. Andrew has 92 beanbags. That means Evan has less bean bags than Andrew. Here we have perform subtraction operation. Here 63 can be written as 62 + 1. So first subtract 62 bean bags from 92 bean bags then we got 30 bean bags. After that subtract 1 bean bag from 30 bean bags then we got 29 bean bags. Evan has 29 bean bags.

Lesson 7.4 Solve Two-Step Problems

Solve & Share
3 bees land on some flowers. 10 more bees join them. Then 4 bees fly away. How many bees are left?
Solve the problem any way you choose. Write equations to show how you solved each part of the problem.
I can model and solve two-step problems using equations.

Answer:

9 bees are left on flowers.
Explanation:
3 bees land on some flowers. 10 more bees join them. Here we have to perform addition operation. Add 3 bees with 10 more bees then we get 13 bees on flowers. Then 4 bees fly away. Here we have to perform subtraction operation. Subtract 4 bees from 13 bees then we get 9 bees. 9 bees are left on flowers.

Visual Learning Bridge

Convince Me! Read the problem below. What is the hidden question that you need to answer first?
Tom buys 15 pencils and then 7 more. He gives 10 pencils to Nyla. How many pencils does Tom have now?
Answer:
The hidden question is how many pencils does Tom buys in all.
15 + 7 = ?
15 + 7 = 22
Tom buys 22 pencils. Then he gave 10 pencils to Nyla.
22 – 10 = ?
22 – 10 = 12
Now Tom has 12 pencils.
Explanation:
Tom buys 15 pencils and then 7 more. He gives 10 pencils to Nyla. Here Tom buys total number of pencils is 22. After that he gave 10 pencils to Nyla. So subtract 10 pencils from total number of pencils are 22 then we got 12 pencils. Now Tom has 12 pencils.

Guided Practice

Solve any way you choose. Show your work. Write equations to solve both parts of the problem.
Question 1.
Carmen found 14 shells on Monday and 15 more shells on Tuesday. She found 6 more shells on Wednesday. How many shells did she have then?

_______ shells
Answer:

Carmen have 35 shells.
Explanation:
Carmen found 14 shells on Monday and 15 more shells on Tuesday. She found 6 more shells on Wednesday. First we have to add the shells that she had found in both Monday and Tuesday. She found 14 shells on Monday and 15 shells on Tuesday. Add 14 shells with 15 shells then she got 29 shells. She found 6 more shells on Wednesday. Add these 29 shells with 6 shells then we got 35 shells. Carmen have 35 shells now.

Independent Practice

Solve any way you choose. Show your work. Write equations to solve both parts of the problem.
Question 2.
There are 6 red birds and 17 brown birds in a tree. If 8 more brown birds come, how birds will there be in all?

________ birds
Answer:

There are 31 birds in all.
Explanation:
There are 6 red birds and 17 brown birds in a tree. 8 more brown birds came. First we have to add 6 red birds and 17 brown birds then we got 23 birds. There are 23 birds in a tree. After that 8 more brown birds came into a tree. Add 8 brown birds with 23 birds then we got 31 birds. There are 31 birds in all.

Question 3.
Erika saw 16 frogs on a lily pad and 8 frogs in the mud. If 7 of the frogs hop away, how many frogs will be left?

________ frogs
Answer:

There are 17 frogs left in the place.
Explanation:
Erika saw 16 frogs on a lily pad and 8 frogs in the mud. In that 7 of the frogs hop away. First we have to add16 frogs on a lily pad and 8 frogs in the mud then we get 24 frogs in total. In that 7 of the frogs hop away. So subtract 7 frogs from the total number of frogs then we got 17 frogs. There are 17 frogs left in that place.

Think: How can I break apart the problem into steps? What is the hidden problem that I need to solve first?

Question 4.
Higher Order Thinking Kevin has 15 photos in his scrapbook. He adds 21 photos. Then Kevin takes out some photos. Now he has 28 photos in the scrapbook. How many photos did Kevin take out?

________ photos
Answer:
The hidden question is how many photos in Kevin scrapbook.
15 + 21 = ?
15 + 21 = 36
Kevin has 36 photos in his scrapbook. Then Kevin takes out some photos. Now he has 28 photos in the scrapbook.
36 –  ? = 28
36 – 8 = 28

Kevin take out 8 photos from his scrapbook.
Explanation:
Kevin has 15 photos in his scrapbook. He adds 21 photos. Then Kevin takes out some photos. Now he has 28 photos in the scrapbook. First add 15 photos and 21 photos then we got 36 photos in his scrapbook. After that he take out some photos from his scrap book. We have to find out how many photos does he take out from the scrapbook. After taking out some photos from his scrap book he left with 28 photos. So subtract 8 photos from 36 photos then we got 28 photos. Kevin take out 8 photos from his scrap book.

Problem Solving

Solve each problem. Show your work.
Question 5.
Model There are 35 test questions. Kareem answers 10 of the questions. Then he answers 12 more questions. How many more questions does Kareem still need to answer?

__________ more questions
Answer:

Kareem still need to answer 13 questions.
Explanation:
There are 35 test questions. Kareem answers 10 of the questions. Then he answers 12 more questions. Perform addition operation on answered questions. Add 10 questions with 12 questions then we got 22 answered questions. Here we have to find out how many more questions does Kareem still need to answer. So subtract answered questions from total number of questions. Subtract 22 answered questions from total number of questions then we got 13 questions. Kareem still need to answer 13 questions.

Question 6.
Vocabulary Circle the equations that have a sum. Underline the equations that have a difference.
33 – 18 = 15
79 + 16 = 95
46 + 34 = 80
52 – 52 = 0
Answer:

Explanation:
In the above image we can observe 4 equations. Here we have to draw a circle for the equations that are having sum and we have to underline the equations that are having difference.

Question 7.
Algebra Find the missing numbers.

Answer:

The missing numbers are 65 and 82.
Explanation:
The missing number in first equation is 65.
The missing number in second equation is 82.

Question 8.
Higher Order Thinking There are 25 friends at a party. Another 20 friends arrive. Then some friends leave the party. Only 7 friends stay. How many friends leave the party?
Write two equations to solve the problem.
Answer:
25 + 20 = ?
25 + 20 = 45
45 – ? = 7
45 – 38 = 7
38 friends leave the party.
Explanation:
There are 25 friends at a party. Another 20 friends arrived. First add 25 friends and 20 friends then we got total number of friends in the party. The total number of friends in the party are 45. Then some friends leave the party. Only 7 friends stayed in the party. Subtract stayed friends in the party from total number of friends in the party then we get total number of friends left the party. Subtract 7 friends from 45 friends then we got 38 friends. 38 friends leave the party.

Question 9.
Assessment Practice Bill caught 22 fish and threw 6 fish back. He caught 8 more fish. How many fish does Bill have now? Which equations can be used to solve the problem?
A. 22 + 6 = 28 and 28 – 8 = 20
B. 22 – 6 = 16 and 8 – 6 = 2
C. 22 – 6 = 16 and 16 + 8 = 24
D. 22 + 6 = 28 and 28 + 8 = 36
Answer:
The equation in Option C is correct.
22 – 6 = 16 and 16 + 8 = 24
Bill have 24 fish now.
Explanation:
Bill caught 22 fish and threw 6 fish back. Here we have to perform subtraction operation first because he caught 22 fish and he threw 6 fish back. So subtract 6 fish from 22 fish then we got 16 fish. Bill caught 16 fish. He caught 8 more fish. Then we have to perform addition operation. Add 16 fish with 8 more fish then we got 24 fish. Bill have 24 fish now.

Lesson 7.5 Continue to Solve Two-Step Problems

Solve & Share
You have 26 library books. You return some books. Then you take out 15 more books. Now you have 27 books. How many books did you return? Solve any way you choose. Show your work.
I can … use different ways to solve two-step problems.

Answer:

I return 14 books.
Explanation:
I have 26 library books. I return some books. Then I take out 15 more books. Here I have to perform addition operation on 26 library books and 15 more books. Add 26 and 15 then I get 41 books. Here I return some books and now I have 27 books. So subtract 27 books from total number of books 41 then I got 14 books. Here I return 14 books to the library

Visual Learning Bridge

Convince Me! Why do you need two steps to solve the problem above?
Answer:
To solve above problem we need two steps in order to know how many birds there were in all and how many birds flew away.
First step is used to find the total number of birds does Mia can see. First we have to add 15 yellow birds with 16 red birds then we get total number of birds. Total number of birds are 31. Mia sees 31 birds in all.
Second step is used to find the how many birds flew away. Some birds flew away and now Mia sees only 14 birds. Here we have to perform subtraction operation. Subtract 14 birds from total number of birds are 31 then we got 17 birds. There are 14 birds left after 17 fly away.

Guided Practice

Complete the equations to solve.
Question 1.
There are some boys painting and 9 girls painting. In all, 17 children are painting. Then some more boys come to paint. Now there are 15 boys painting. How many more boys come to paint?

_________ more boys come to paint.
Answer:

7 more boys come to paint.
Explanation:
There are some boys painting and 9 girls painting. In all, 17 children are painting. In order to find how many boys are painting we need to perform subtraction operation on total number of children painting and number of girls painting. Subtract 9 girls from 17 children then we got 8 boys. 8 some boys are painting.
Then some more boys come to paint. Now there are 15 boys painting. Subtract 8 some boys painting from total number of boys painting in all then we get how many more number of boys added. Subtract 8 boys from 15 boys then we got 7 boys. 7 more boys come to paint.

Independent Practice

Solve each problem any way you choose. Show your work.
Question 2.
Jake has 16 toy cars. Lidia has 5 fewer toy cars than Jake. How many toy cars do they have in all?
They have __________ cars in all.
Answer:
Jake has 16 toy cars. Lidia has 5 fewer toy cars than Jake.
16 – 5 = ?
16 – 5 = 11
Lidia has 11 toy cars.
16 + 11 = 27
Jake and Lidia have 27 toy cars in all.
Explanation:
Jake has 16 toy cars. Lidia has 5 fewer toy cars than Jake. That means Lidia has less cars. Subtract 5 toy cars from 16 toy cars then we get 11 toy cars. Lidia has 11 toy cars. Then we have to find total number of toy cars. Add 16 toy cars of Jake with 11 toy cars of Lidia then we got 27 toy cars. Jake and Lidia have 27 toy cars in all.

Question 3.
Sandy has 12 balloons. Tom has 11 more balloons than Sandy. Some of Tom’s balloons popped and now he has 14 balloons. How many balloons popped?
___________ balloons popped.
Answer:
Sandy has 12 balloons. Tom has 11 more balloons than Sandy.
12 + 11 = ?
12 + 11 = 23
Tom has 23 balloons.
Some of Tom’s balloons popped and now he has 14 balloons.
23 – ? = 14
23 – 9 = 14
9 balloons popped.
Explanation:
Sandy has 12 balloons. Tom has 11 more balloons than Sandy. Perform addition operation on 12 balloons and 11 balloons then we get 23 balloons. Tom has 23 balloons. Some of Tom’s balloons popped and now he has 14 balloons. Subtract 14 balloons from 23 balloons then we got 9 balloons. 9 balloons popped.

Question 4.
25 wolves howl together in the woods. 14 wolves join them. Then 22 wolves run away. How many wolves are left?
_________ wolves are left.
Answer:
25 wolves howl together in the woods. 14 wolves join them.
25 + 14 = 39
Then 22 wolves run away.
39 – 22 = ?
39 – 22 =17
17 wolves are left.
Explanation:
25 wolves howl together in the woods. 14 wolves join them. Perform addition operation on wolves howl together in the woods and joined wolves. Add 25 wolves and 14 wolves then we get 39 wolves. Then 22 wolves run away. By Subtracting 22 wolves from 39 wolves we get total number of wolves left. 17 wolves are left.

Question 5.
Higher Order Thinking Explain how you solved Item 4.
Answer:
Item 4 is solved by using two equations.
25 wolves howl together in the woods. 14 wolves join them.
25 + 14 = 39
Then 22 wolves run away.
39 – 22 = ?
39 – 22 =17
17 wolves are left.
Explanation:
25 wolves howl together in the woods. 14 wolves join them. Perform addition operation on wolves howl together in the woods and joined wolves. Add 25 wolves and 14 wolves then we get 39 wolves. Then 22 wolves run away. By Subtracting 22 wolves from 39 wolves we get total number of wolves left. 17 wolves are left.

Problem Solving

Solve each problem. Show your work.
Question 6.
Make Sense Tim bakes 24 more muffins than Gina. Gina bakes 13 muffins. Lea bakes 16 fewer muffins than Tim.
How many muffins does Lea bake?

________ muffins
Answer:
Tim bakes 24 more muffins than Gina. Gina bakes 13 muffins.
13 + 24 = ?
13 + 24 = 37
Tim bake 37 muffins.
Lea bakes 16 fewer muffins than Tim.
37 – 16 = ?
37 – 16 = 21
Lea bake 21 muffins.
Explanation:
Tim bakes 24 more muffins than Gina. Gina bakes 13 muffins. Add 13 muffins with 24 muffins then we get 37 muffins. Tim bake 37 muffins. Lea bakes 16 fewer muffins than Tim. Subtract 16 muffins from 37 muffins then we got 21 muffins. Lea bake 21 muffins.

Question 7.
Higher Order Thinking Write a two-step number story using the numbers 36, 65, and 16. Then solve the problem. Write equations to show each step.

Answer:
Ram scores 36 points. Next, he scores 65 points. Then he loses 16 points. How many points does Ram have now?

Now Ram have 85 points.
Explanation:
Ram scores 36 points. Next, he scores 65 points. Add 36 points with 85 points then we get 101 points. Then he loses 16 points. Subtract 16 points from 101 points then we got 85 points. Now Ram have 85 points.

Question 8.
Assessment Practice There are 44 marbles in a jar. Some are red and 23 are blue. Julie adds 13 red marbles to the jar. How many red marbles are in the jar now?

Which equations show a way to solve the problem?
A. 44 – 23 = 21
21 + 13 = 34

B. 44 – 23 = 21
21 – 13 = 8

C. 23 + 21 = 44
44 – 13 = 31.

D. 23 + 44 = 67
67 + 13 = 80
Answer:
Option A is correct to solve the problem.
44 – 23 = 21
21 + 13 = 34
There are 34 red marbles in the jar now.
Explanation:
There are 44 marbles in a jar. Some are red and 23 are blue. First perform subtraction operation to find the red marbles in the jar. Subtract 23 blue marbles from total number of marbles in the jar are 44 then we got 21 red marbles. Julie adds 13 red marbles to the jar. Next perform addition operation because here Julie added 13 red marbles to the jar. Add 13 red marbles and 21 red marbles then we got 34 red marbles. Now there are 34 red marbles in the jar.

Lesson 7.6 Make True Equations

Solve & Share
What number goes in the blank to make this equation true? Show how you found out.
I can … fill in missing numbers in equations to make them true.

Answer:

17 – 9 = 6 + ?
8 = 6 + ?
8 = 6 + 2
8 = 8
The missing number in the above equation is 2.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first I can find 17 – 9 = 8. After that we have to find the remaining part 8 = 6 + ?. Here 8 is equal to 6 plus some number. By adding 2 to the 6 results 8. Here we have to check both sides of the equal sign have the same value or not.
Here 8 = 8
So 17 – 9 = 6 + 2
The missing number in the above equation is 2.

Visual Learning Bridge

Convince Me! What number goes in the blank to make this equation true? Explain how you know.
______ – 5 = 14 – 7
Answer:
12 – 5 = 14 – 7
The missing number in the above equation is 12.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first I can find 14 – 7 = 7. After that we have to find the remaining part ? – 5 = 7. Here 5 can be subtracted from what number to get 7. Subtract 5 from 12 then we get 7. Here we have to check both sides of the equal sign have the same value or not.
Here 7 = 7
So 12 – 5 = 14 – 7
The missing number that makes the above equation true is 12.

Guided Practice

Write the missing number that makes each equation true.
Question 1.
15 – ? = 2 + 4

Answer :
The missing number that makes the equation true is 9.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 2 + 4 = 6. After that we have to find the remaining part 15 – ? = 6. Here 6 is equal to the number 15 minus some number. By subtracting 9 from the 15 results 6. Here we have to check both sides of the equal sign have the same value or not.
Here 6 = 6
So 15 – 9 = 2 + 4
The missing number in the that makes the equation true is 9.

Question 2.
25 + 10 = 43 – ?
______ = 43 – ?
______ = 43 – ______
So,
25 + 10 = 43 – ______
Answer:
25 + 10 = 43 – ?
35 = 43 – ?
35 + 5 = 40
40 + 3 = 43
So add 5 and 3 the we got 8
35 = 43 – 8
35 = 35
So,
25 + 10 = 43 – 8
The missing number that makes the equation true is 8.
Explanation:
Here ‘=’ means the value on both sides is the same. First add 25 and 10 then we got 35. After that we have to find out what number we can subtract from 43 to get 35. Add 5 to the 35 then we got 40. Add 3 to the 40 then we got 43. So add 5 with 3 then we get 8. The missing number that makes the equation true is 8.

Independent Practice

Write the missing number that makes each equation true. Show your work.
Question 3.
9 + ______ = 8 + 8
Answer:
9 + ? = 8 + 8
9 + ? = 16
9 + 7 = 16
16 = 16
The missing number that makes the equation true is 7.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we can find 8 + 8 = 16. After that we have to find the remaining part 9 + ? = 16. Here 16 is equal to 9 plus some number. By adding 7 to the 9 results 16. Here we have to check both sides of the equal sign have the same value or not.
Here 16 = 16
So 9 + 7 = 8 + 8
The missing number that makes the equation true is 7.

Question 4.
16 – 8 = 10 – ______
Answer:
16 – 8 = 10 – ?
8 = 10 – 2
8 = 8
The missing number that makes the equation true is 2.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have to find 16 – 8 = 8. After that we have to find the remaining part 8 = 10 – ?. Here 8 is equal to 10 minus some number. By subtracting 2 from the 10 results 8. Here we have to check both sides of the equal sign have the same value or not.
Here 8 = 8
So 16 – 8 = 10 – 2
The missing number that makes the equation true is 2.

Question 5.
______ – 4 = 16 – 5
Answer:
? – 4 = 16 – 5
? – 4 = 11
15 – 4 = 11
11 = 11
The missing number that makes the equation true is 15.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have to find 16 – 5 = 11. After that we have to find the remaining part ? – 4 = 11. Here 11 is equal to the number 4 is subtracted from some number. By subtracting 4 from the 15 results 11. Here we have to check both sides of the equal sign have the same value or not.
Here 11 = 11
So 15 – 4 = 16 – 5
The missing number that makes the equation true is 15.

Question 6.
17 – 12 = 10 – ______
Answer:
17 – 12 = 10 – ?
5 = 10 – ?
5 = 10 – 5
5 = 5
The missing number that makes the equation true is 5.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have to find 17 – 12 = 5. After that we have to find the remaining part 5 = 10 – ?. Here 5 is equal to 10 minus some number. By subtracting 5 from the 10 results 5. Here we have to check both sides of the equal sign have the same value or not.
Here 5 = 5
So 17 – 12 = 10 – 5
The missing number that makes the equation true is 5.

Question 7.
______ – 3 = 5 + 12
Answer:
? – 3 = 5 + 12
? – 3 = 17
20 – 3 = 17
17 = 17
The missing number that makes the equation true is 20.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have to find 5 + 12 = 17. After that we have to find the remaining part ? – 3 = 17. Here 17 is equal to the number 3 is subtracted from some number. By subtracting 3 from 20 results 17. Here we have to check both sides of the equal sign have the same value or not.
Here 17 = 17
So 20 – 3 = 5 + 12
The missing number that makes the equation true is 20.

Question 8.
18 – ______ = 3 + 6
Answer:
18 – ? = 3 + 6
18 – ? = 9
18 – 9 = 9
9 = 9
The missing number that makes the equation true is 9.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have to find 3 + 6 = 9. After that we have to find the remaining part 18 – ? = 9. Here 9 is equal to 18 minus some number. By subtracting 9 from 18 results 9. Here we have to check both sides of the equal sign have the same value or not.
Here 9 = 9
So 18 – 9 = 3 + 6
The missing number that makes the equation true is 9.

Question 9.
27 + 20 = 17 + ______
Answer:
27 + 20 = 17 + ?
47 = 17 + ?
47 = 17 + 30
47 = 47
The missing number that makes the equation true is 30.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have to find 27 + 20 = 47. After that we have to find the remaining part 47 = 17 + ?. Here 47 is equal to the number 17 plus some number. By adding 17 with the 30 results 47. Here we have to check both sides of the equal sign have the same value or not.
Here 47 = 47
So 27 + 20 = 17 + 30
The missing number that makes the equation true is 30.

Question 10.
56 – 20 = 30 + ______
Answer:
56 – 20 = 30 + ?
36 = 30 + ?
36 = 30 + 6
36 = 36
The missing number that makes the equation true is 6.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have to find 56 – 20 = 36. After that we have to find the remaining part 36 = 30 + ?. Here 36 is equal to the 30 plus some number. By adding 6 to the 30 results 36. Here we have to check both sides of the equal sign have the same value or not.
Here 36 = 36
So 56 – 20 = 30 + 6
The missing number that makes the equation true is 6.

Question 11.
45 – 10 = 40 – ______
Answer:
45 – 10 = 40 – ?
35 = 40 – ?
35 = 40 – 5
35 = 35
The missing number that makes the equation true is 5.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have to find 45 – 10 = 35. After that we have to find the remaining part 35 = 40 – ?. Here 35 is equal to the number 40 minus some number. By subtracting 5 from the 40 results 35. Here we have to check both sides of the equal sign have the same value or not.
Here 35 = 35
So 45 – 10 = 40 – 5
The missing number that makes the equation true is 5.

Question 12.
Algebra Write the missing number in the equation below. Explain how you know.
I can solve the problem without adding!
______ + 5 + 6 = 6 + 9 + 5
Answer:
9 + 5 + 6 = 6 + 9 + 5
The missing number in the above equation is 9.
Explanation:
Here we can see both sides 3 addends are there. In that equation right side addends are 6, 9 , 5. In left side addends we can observe two addends are same in right side part. So the missing number is 9. We solved the problem without adding numbers.

Problem Solving

Write an equation to show each problem. Then solve. Show your work.
Question 13.
Reasoning Teresa has 4 daisies and 5 roses. Sam has 15 flowers. How many flowers would Sam need to give away so that he has the same number of flowers as Teresa?
_________ flowers
Answer:
4 + 5 = 15 – ?
9 = 15 – ?
9 = 15 – 6
9 = 9
Sam need to give away 6 flowers So that he has the same number of flowers as Teresa.
Explanation:
Teresa has 4 daisies and 5 roses. First add Teresa flowers. Add 4 daisies with 5 roses then we got 9 flowers. Here Sam has 15 flowers. Sam need to give away some flowers so that he has the same number of flowers as Teresa. So subtract 6 flowers from 15 flowers then we got 9 flowers. Now Sam has 9 flowers. Sam need to give away 6 flowers.

Question 14.
Reasoning Karen had $14 and spent $6. Larry had some money and spent $3. Now Karen and Larry have the same amount of money. How much money did Larry have before he spent $3?
$ _________
Answer:
$14 – $ 6 = ? – $ 3
$8 = ? – $3
$8 = $11 – $3
$8 = $8
Larry have $11 before he spent $3.
Explanation:
Karen had $14 and spent $6. So Subtract $6 from $14 then we got $8. Larry had some money and spent $3. Subtract $3 from $11 then we got $8. Now Karen and Larry have the same amount of money. Larry have $11 before he spent $3.

Question 15.
Higher Order Thinking Todd has the same number of fruits and vegetables. He has 3 apples and 7 oranges. He has 6 carrots and some onions. How many onions does Todd have? Tell how you know.
Answer:
3 apples + 7 oranges = 6 carrots + ? onions
Todd has the same number of fruits and vegetables.
3 + 7 = 6 +?
10 = 6 + ?
10 = 6 + 4
10 = 10
Todd have 4 onions.
Explanation:
Todd has the same number of fruits and vegetables. He has 3 apples and 7 oranges. First add fruits 3 + 7 = 10. There are 10 fruits. He has 6 carrots and some onions. Add 6 carrots with 4 onions then we got 10 vegetables. Todd have 4 onions.

Question 16.
Assessment Practice Match each number with the equation it is missing from.

Answer:

Explanation:
In first equation the missing number is 8. The equation is 1 + 3  = 12 – 8.
In second equation the missing number is 10. The equation is 10 + 2 = 6 + 6.
In third equation the missing number is 6. The equation is 4 + 7 = 5 + 6.
In fourth equation the missing number is 7. The equation is 7 – 2 = 12 – 7.

Lesson 7.7 Continue to Make True Equations

Solve & Share
Find the missing number to make the equation true. Show your work.
? – 9 = 22 – 7
How could you check your work? Is there a tool you could use? Explain.
I can … find the missing number in equations to make equations true.

Answer:

The missing number that makes the equation true is 24.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we can find 22 – 7 = 15. After that we have to find the remaining part ? – 9 = 15. Here 15 is equal to the number 9 subtracted from some number. By subtracting 9 from the 24  results 15. Here we have to check both sides of the equal sign have the same value or not.
Here 15 = 15
So 24 – 9 = 22 – 7
The missing number in the above equation is 24.

Visual Learning Bridge

Convince Me! What number goes in the blank to make this equation true? Explain how you know.
Answer:
Here ‘=’ means the value on both sides is the same. Here first we have find 45 + 10 + 10 = 65. After that we have to find the remaining part 65 = ? + 19. Here 65 is equal to the number 19 plus some number. By adding 46 to the 19 results 65. Here we have to check both sides of the equal sign have the same value or not.
Here 65 = 65
So 45 + 10 + 10 = 46 + 19
The missing number that makes the equation true is 46.

Guided Practice

Write the missing numbers to make the equations true.
Question 1.
8 + 10 + 12 = ? + 20

Answer:
The missing number that makes the equation true is 10.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 8 + 10 + 12 = 30. After that we have to find the remaining part 30 = ? +20. Here 30 is equal to the number 20 plus some number. By adding 10 to the 20 results 30. Here we have to check both sides of the equal sign have the same value or not.
Here 30 = 30
So 8 + 10 + 12 = 10 + 20
The missing number that makes the equation true is 10.

Question 2.
20 + 13 + 7 = 49 – ?
20 + 13 + 7 = _____
40 = 49 = ______
So,
20 + 13 + 7 = 49 – _______
Answer:
20 + 13 + 7 = 49 – ?
20 + 13 + 7 = 40
40 = 49 – ?
40 = 49 – 9
40 = 40
So,
20 + 13 + 7 = 49 – 9
The missing number that makes the equation true is 9.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 20 + 13 + 7 = 40. After that we have to find the remaining part 40 = 49 – ?. Here 40 is equal to the number 49 minus some number. By subtracting 9 from the 49 results 40. Here we have to check both sides of the equal sign have the same value or not.
Here 40 = 40
So 20 + 13 + 7 = 49 – 9
The missing number that makes the equation true is 9.

Independent Practice

Find the missing number that makes each equation true. Show your work.
Question 3.
25 + _______ = 6 + 20 + 4
Answer:
25 + ? = 6 + 20 + 4
6 + 20 + 4 = 30
25 + ? = 30
25 + 5 = 30
30 = 30
The missing number that makes the equation true is 5.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 6 + 20 + 4 = 30. After that we have to find the remaining part 25 + ? = 30. Here 30 is equal to the number 25 plus some number. By adding 25 to the 5 results 30. Here we have to check both sides of the equal sign have the same value or not.
Here 30 = 30
So 25 + 5 = 6 + 20 + 4
The missing number that makes the equation true is 5

Question 4.
10 + 3 + 27 = 30 + _______
Answer:
10 + 3 + 27 = 30 + ?
10 + 3 + 27 = 40
40 = 30 + ?
40 = 30 + 10
40 = 40
The missing number that makes the equation true is 10.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 10 + 3 + 27 = 40. After that we have to find the remaining part 40 = 30 + ?. Here 40 is equal to the number 30 plus some number. By adding 10 to the 30 results 40. Here we have to check both sides of the equal sign have the same value or not.
Here 40 = 40
So 10 + 3 + 27 = 30 + 10
The missing number that makes the equation true is 10.

Question 5.
48 – _______ = 12 + 12 + 4
Answer:
48 – ? = 12 + 12 + 4
12 + 12 + 4 = 28
48 – ? = 28
48 – 20 = 28
28 = 28
The missing number that makes the equation true is 20.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 12 + 12 + 4 = 28. After that we have to find the remaining part 48 – ? = 28. Here 28 is equal to the number 48 minus some number. By subtracting 20 from the 48 results 28. Here we have to check both sides of the equal sign have the same value or not.
Here 28 = 28
So 48 – 20 = 12 + 12 + 4
The missing number that makes the equation true is 20.

Question 6.
47 – 5 = 10 + 10 + _______
Answer:
47 – 5 = 10 + 10 + ?
47 – 5 = 42
42 = 10 + 10 + ?
42 = 10 + 10 + 22
42 = 42
The missing number that makes the equation true is 22.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 47 – 5 = 42. After that we have to find the remaining part 42 = 10 + 10 + ?. Here 42 is equal to the number 20 plus some number. By adding 20 to the 22 results 42. Here we have to check both sides of the equal sign have the same value or not.
Here 42 = 42
So 47 – 5 = 10 + 10 + 22
The missing number that makes the equation true is 22.

Question 7.
32 + 14 + 18 = 50 + _______
Answer:
32 + 14 + 18 = 50 + ?
32 + 14 + 18 = 64
64 = 50 + ?
64 = 50 + 14
64 = 64
The missing number that makes the equation true is 14.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 32 + 14 + 18 = 64. After that we have to find the remaining part 64 = 50 + ?. Here 64 is equal to the number 50 plus some number. By adding 50 to the 14 results 64. Here we have to check both sides of the equal sign have the same value or not.
Here 64 = 64
So 32 + 14 + 18 = 50 + 14
The missing number that makes the equation true is 14.

Question 8.
43 + 10 + 20 = 95 – _______
Answer:
43 + 10 + 20 = 95 – ?
43 + 10 + 20 = 73
73 = 95 – ?
73 = 95 – 22
73 = 73
The missing number that makes the equation true is 22.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 43 + 10 + 20 = 73. After that we have to find the remaining part 73 = 95 – ?. Here 73 is equal to the number 95 minus some number. By subtracting 22 from the 95 results 73. Here we have to check both sides of the equal sign have the same value or not.
Here 73 = 73
So 43 + 10 + 20 = 95 – 22
The missing number that makes the equation true is 22.

Question 9.
28 + 30 = 17 + 13 + _______.
Answer:
28 + 30 = 17 + 13 + ?
28 + 30 = 58
58 = 17 + 13 + ?
58 = 17 + 13 + 28
58 = 58
The missing number that makes the equation true is 28.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 28 + 30 = 58. After that we have to find the remaining part 58 = 17 + 13 + ?. Here 58 is equal to the number 30 plus some number. By adding 30 to the 28 results 58. Here we have to check both sides of the equal sign have the same value or not.
Here 58 = 58
So 28 + 30 = 17 + 13 + 28
The missing number that makes the equation true is 28.

Question 10.
56 – 20 = 18 + 12 + _______
Answer:
56 – 20 = 18 + 12 + ?
56 – 20 = 36
36 = 18 + 12 + ?
36 = 18 + 12 + 6
36 = 36
The missing number that makes the equation true is 6.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 56 – 20 = 36. After that we have to find the remaining part 36 = 18 + 12 + ?. Here 36 is equal to the number 30 plus some number. By adding 30 to the 6 results 36. Here we have to check both sides of the equal sign have the same value or not.
Here 36 = 36
So 56 – 20 = 18 + 12 + 6
The missing number that makes the equation true is 6.

Question 11.
21 + 5 + 19 = 65 – _______
Answer:
21 + 5 + 19 = 65 – ?
21 + 5 + 19 = 45
45 = 65 – ?
45 = 65 – 20
45 = 45
The missing number that makes the equation true is 20.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 21 + 5 + 19 = 45. After that we have to find the remaining part 45 = 65 – ?. Here 45 is equal to the number 65 minus some number. By subtracting 20 from the 65 results 45. Here we have to check both sides of the equal sign have the same value or not.
Here 45 = 45
So 21 + 5 + 19 = 65 – 20
The missing number in the that makes the equation true is 20.

Question 12.
Algebra Write the missing number in the equation. Explain how you know.
_______ + 25 + 18 = 18 + 20 + 25
I can solve the problem without adding.
Answer:
? + 25 + 18 = 18 + 20 + 25
20 + 25 + 18 = 18 + 20 + 25
The missing number in the above equation is 20.
Explanation:
In the above equation we can observe three addends on both sides. Right side addends are 18, 20, 25. The left side addends are also same. The left side addends are 20, 25, 18. we can solve the equation without addition operation.

Problem Solving

Write an equation to show each problem. Then solve. Show your work.
Question 13.
Reasoning Gemma had some game tokens and then earned 8 more. Ana had 32 tokens and lost 4. Now they have an equal number of tokens. How many tokens did Gemma have to start?
_______ tokens
Answer:
? + 8 = 32 – 4
? + 8 = 28
20 + 8 = 28
28 = 28
Gemma have 20 tokens to start the game.
Explanation:
Gemma had some game tokens and then earned 8 more. Ana had 32 tokens and lost 4. Subtract lost tokens from total number of tokens of Ana. Subtract 4 tokens from 32 tokens then we got 28 tokens. Now they have an equal number of tokens. Add 20 tokens with 8 tokens of Gemma then we got 28 tokens. Gemma have 20 tokens to start the game.

Question 14.
Reasoning Jill and Tim have the same number of toy cars. Tim has 10 red cars and 20 blue cars. Jill has 8 red cars, 15 blue cars, and some yellow cars. How many yellow cars does Jill have?
_________ yellow cars
Answer:
10 + 20 = 8 + 15 + ?
30 = 8 + 15 + ?
30 = 8 + 15 + 7
30 = 30
Jill have 7 yellow cars.
Explanation:
Jill and Tim have the same number of toy cars. Tim has 10 red cars and 20 blue cars. Perform addition operation on 10 red cars plus 20 blue cars results 30 cars. Jill has 8 red cars, 15 blue cars, and some yellow cars. Here we have to find yellow cars of Jill. By adding 8 red cars plus 15 blue cars results 23 cars of Jill. Add 23 cars with 7 cars results 30 cars. Jill have 7 yellow cars.

Question 15.
Higher Order Thinking Kate plays a card game with two friends. She gives 5 cards to each player. Ten plus what number is equal to the total number of cards Kate gives out?
Write an equation to show and solve the problem.
Answer:
10 + 0 = 10
Kate gives 10 cards.
Explanation:
Kate plays a card game with two friends. She gives 5 cards to each player. Total he gave 10 cards.

Question 16.
Assessment Practice Match each number with the equation it is missing from.

Answer:

Explanation
In first equation the missing number is 19. The equation is 8 +17 + 5 = 49 – 19.
In second equation the missing number is 20. The equation is 20 + 12 = 6 + 6 + 20.
In third equation the missing number is 32. The equation is 8 + 20 + 12 = 32 + 8.
In fourth equation the missing number is 22. The equation is 22 + 15 = 17 + 10 + 10.

Lesson 7.8 Problem Solving

Reasoning
Solve & Share
Write a number story that has an answer of 20. Then write an equation to match your story.
I can … use reasoning to write and solve number stories.

Answer:

There are 20 Aeroplanes in all at the airport.
Explanation:
There are 14 blue Aeroplanes and 6 red Aeroplanes at the airport. By adding 14 blue planes and 6 red planes results 20 aeroplanes. There are 20 Aeroplanes in all at the airport.

Thinking Habits
How are the numbers in the problem related?
How can I use a word problem to show what the equation means?

Visual Learning Bridge

Convince Me! Write a number story about comparing for 68 – 33 = ?.
Answer:
68 – 33 = ?
There are 68 second grade students. Some of them go to school on campus for a couple of days each week. The rest of the 33 students stay at home every day the whole week. How many students go to school on campus?
68 – 33 = 35

Guided Practice

Complete the number story. Then complete the equation to match the story. Draw a picture to help, if needed.
Question 1.
47 – 18 = _______
Blake collects 47 cans.
He recycles 18 cans.
How many cans does Blake have now?
________ cans
Answer:
47 – 18 = ?
Blake collects 47 cans. He recycles 18 cans. How many cans does Blake have now?
47 – 18 = ?
+2  + 2
49 – 20 = 29
Blake have 29 cans.
Explanation:
Blake collects 47 cans. He recycles 18 cans. Subtract 18 cans from 47 cans then we got 29 cans. Now Blake have 29 cans.

Independent Practice

Write a number story to show the problem. Complete the equation to match your story.
Question 2.
22 – 17 = _______
Answer:
Rosy have 22 grapes to her parrot. The parrot ate 17 grapes. How many grapes are left?
22 – 17 = ?
– 2  – 2
20 – 15 = 5
5 grapes are left.
Explanation:
Rosy have 22 grapes to her parrot. The parrot ate 17 grapes. Here we have to subtract 17 grapes from 22 grapes then we get number of grapes left. Total number of grapes left are 5.

Question 3.
84 – 62 = _______
Answer:
84 – 62 = ?
There are 84 birds on a tree. Then 62 birds flew away. How many birds are left on a tree?
84 – 62 = ?
-2   -2
82 – 60 = 22
22 birds are left on a tree.
Explanation:
There are 84 birds on a tree. Then 62 birds flew away. Subtract 62 birds from 84 birds then we get total number of birds left on a tree. There are 22 birds left on a tree.

Question 4.
28 + 12 = _________
Answer:
28 + 12 = ?
There are 28 brinjals in the basket. Mother put 12 more brinjals in the basket. How many brinjals are there altogether?
28 + 12 = 40
Altogether 40 brinjals are there.
Explanation:
There are 28 brinjals in the basket. Mother put 12 more brinjals in the basket. Perform addition operation on 28 brinjals and 12 more brinjals then we get 40 brinjals. There are 40 brinjals altogether.

Question 5.
39 + 47 = _________
Answer:
There are 39 red robots and 47 green robots on the building. How many robots are there in all?
39 + 47 = 86
There are 86 robots in all.
Explanation:
There are 39 red robots and 47 green robots on the building. perform addition operation on 39 red robots and 47 green robots then we get 86 robots. There are 86 robots in all.

Problem Solving

Performance Task
Toy Car Collection The picture at the right shows a toy car collection. Use the picture to write and solve number story problems.

Question 6.
Reasoning Write an addition story about the toy car collection.
Answer:
16 + 24 =?
In a room 16 green toy cars and 24 orange toy cars. How many toy cars are there in all ?
16 + 24 = 40
There are 40 toy cars in all.
Explanation:
In a room 16 green toy cars and 24 orange toy cars. Add 16 green toy cars and 24 orange toy cars then we get total number of toy cars are 40. There are 40 toy cars in all.

Question 7.
Reasoning Write a subtraction comparison story about the collection.
Answer:
There were 5 soccer balls and 9 footballs in the gym. How many fewer soccer balls were there than footballs?
9 – 5 = ?
9 – 5 = 4
There are 4 fewer soccer balls than footballs.
Explanation:
There were 5 soccer balls and 9 footballs in the gym. Subtract 5 soccer balls from 9 footballs then we get 4 balls. There are 4 fewer soccer balls than footballs.

Question 8.
Model Write an equation for each number story that you wrote in Item 6 and Item 7. Then solve any way you choose. Show your work.
Answer:
The equation for item 6 number story is 16 + 24 = ?
The equation for item 7 number story is 9 – 5 = ?

Explanation:
For item 6 In a room 16 green toy cars and 24 orange toy cars. Add 16 green toy cars and 24 orange toy cars then we get total number of toy cars are 40. There are 40 toy cars in all.
For item 7 there were 5 soccer balls and 9 footballs in the gym. Subtract 5 soccer balls from 9 footballs then we get 4 balls. There are 4 fewer soccer balls than footballs.

Topic 7 Fluency Practice Activity

Find a Match
Find a partner. Point to a clue. Read the clue.
Look below the clues to find a match. Write the clue letter in the box next to the match.
Find a match for every clue.
I can … add and subtract within 20.

Clues
A. is equal to 5 + 4
B. is equal to 8 + 7
C. is equal to 20 – 10
D. is equal to 12 – 7
E. is equal to 9 + 3
F. is equal to 13 – 9
G. is equal to 11 – 8
H. is equal to 7 + 6
I. Is equal to 2 + 4
J. Is equal to 5 +6
K. is equal to 14 – 7
L. is equal to 10 + 6

Answer:

Explanation:
A. 18 – 9 is equal to 5 + 4
B. 9 + 6 is equal to 8 + 7
C.19 – 9 is equal to 20 – 10
D.13 – 8 is equal to 12 – 7
E. 6 + 6 is equal to 9 + 3
F.12 – 8 is equal to 13 – 9
G. 10 – 7 is equal to 11 – 8
H. 4 + 9 is equal to 7 + 6
I. 13 – 7 is equal to 2 + 4
J. 8 + 3 is equal to 5 +6
K.15 – 8 is equal to 14 – 7
L. 8 + 8 is equal to 10 + 6

Topic 7 Vocabulary Review

Understand Vocabulary
Word List

• bar diagram
• compatible numbers
• difference
• equation
• open number line
• regroup
• sum

Write T for true or F for false.
Question 1.
________ An equation is a model you can use to help solve a problem.
Answer:
True (T)

Question 2.
________ 43 is the difference in the equation 43 – 16 = 27.
Answer:
False (F)

Question 3.
__________ Addition and subtraction can be shown using a bar diagram.
Answer:
True (T)

Question 4.
_________ An equation is a model you can use to represent a problem.
Answer:
True (T)

Question 5.
_________ A sum is the answer to a subtraction problem.
Answer:
False (F)

Draw a line from each term to its example.

Answer:

Explanation:
6. Regrouping in math is a term used to describe the process of changing groups of ones into tens to make adding and subtracting easier. In addition, we regroup when the numbers you are adding come out to two digit numbers if they are not in the furthermost left column. Here 15 ones = 1 ten and 5 ones.
7. Sum is the result of adding two or more numbers. Here the answer to 18 + 45 is called as sum.
8. A number line with no numbers or tick marks is called as open number line.

Use Vocabulary in Writing
Question 9.
Explain how you can count on to find 58 + 23. Use at least one term from the Word List.
Answer:

Topic 7 Reteaching

Set A

You can model problems.
A store has some rings. Then 34 rings are sold. Now the store has 47 rings. How many rings did the store have at first?

Write an equation with a ? for the unknown to represent the problem. Then solve using the bar diagram.
Question 1.
A store has 52 juice boxes. Then some juice boxes are sold. Now the store has 35 juice boxes. How many juice boxes were sold?
Equation: __________

_______ juice boxes
Answer:
52 – ? = 35
52 – 35 = 17
52 – 17 = 35

Sold juice  Store has
boxes         Juice boxes
17 juice boxes are sold.
Explanation:
A store has 52 juice boxes. Then some juice boxes are sold. Now the store has 35 juice boxes. Here 17 juice boxes are sold.

Set B

Will has 19 fewer crayons than Kari. Kari has 25 crayons. How many crayons does Will have?

Solve the problem any way you choose. Show your work.
Question 2.
A building kit has 26 fewer green blocks than blue blocks. The kit has 44 green blocks. How many blue blocks are there?
_________ blue blocks
Answer:
? – 26 = 44
? = 44 + 26
? = 70
70 – 26 = 44
There are 70 blue blocks.
Explanation:
A building kit has 26 fewer green blocks than blue blocks. That means green blocks are less. The kit has 44 green blocks. Add 44 green blocks with 26 fewer green blocks then we get total number of blue blocks. There are 70 blue blocks.

Set C

Trent has 29 more toy cars than Bill. Trent has 72 toy cars. How many toy cars does Bill have?

Solve the problem any way you choose. Show your work.
Question 3.
A game has 19 more red cards than blue cards. The game has 43 red cards. How many blue cards does the game have?
_________ blue cards
Answer:
43 – 19 = ?
+1   +1
44 – 20 = 24
There are 24 blue cards in a game.
Explanation:
A game has 19 more red cards than blue cards. That means blue cards are less. The game has 43 red cards. subtract 19 more red cards from 43 red cards then we get total number of blue cards. There are 24 blue cards in a game.

Set D

Lacie buys 28 peaches. She gives 12 to Ted. Then she buys 15 more. How many peaches does Lacie have now?

Use the bar diagrams to help solve both steps.
Question 4.
Craig scores 27 points. Next, he scores 33 points. Then he loses 14 points. How many points does Craig have now?

________ points
Answer:

Now Craig have 46 points.
Explanation:
Craig scores 27 points. Next, he scores 33 points. Add 27 points with 33 points then we get 60 points. Now he has 60 points. Then he loses 14 points. Subtract 14 points from 60 points then we get 46 points. Craig have 46 points.

Set E

Jess had 16 white eggs and 13 brown eggs. She broke some eggs and was left with 18 eggs to sell. How many eggs did she break?

Solve the problem any way you choose. Show your work.
Question 5.
There are 36 raspberries and 24 blueberries in the fruit salad. Ben eats some. Now there are 45 berries left. How many berries did Ben eat?
_________ berries
Answer:

Ben ate 15 berries.
Explanation:
There are 36 raspberries and 24 blueberries in the fruit salad. Add 36 raspberries and 24 blueberries then we get 60 berries. Ben eats some. Now there are 45 berries left. Subtract 45 berries from 60 berries then we get 15 berries. Ben ate 15 berries.

Set F

Write the missing number to make the equation true.
14 + 6 = ______ + 12
Both sides are equal.
14 + 6 = 20
So, 20 = 8 + 12.
The missing number is 8.

Find and write the missing numbers to make the equations true.
Question 6.
4 + 8 = 19 – 7 _____
Answer:
4 + 8 = 19 – ?
4 + 8 = 12
12 = 19 – ?
12 = 19 -7
The missing number is 7.
Explanation:
Here first we have to add these two numbers 4 and 8 then we got 12. Subtract 7 from 19 then we got 12. The missing number that makes the equation true is 7.

Question 7.
______ + 7 = 12 + 2
Answer:
? + 7 = 12 + 2
? + 7 = 14
7 + 7 = 14
14 = 14
The missing number that makes the equation true is 7.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 12 + 2 = 14. After that we have to find the remaining part ? + 7 = 14. Here 17 is equal to the number 7 plus some number. By adding 7 to the 7 results 14. Here we have to check both sides of the equal sign have the same value or not.
Here 14 = 14
So 7 + 7 = 12 + 2
The missing number that makes the equation true is 7.

Question 8.
15 + ______ = 10 + 8
Answer:
15 + ? = 10 + 8
15 + ? = 18
15 + 3 = 18
18 = 18
The missing number that makes the equation true is 3.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 10 + 8 = 18. After that we have to find the remaining part 15 + ? = 18. Here 18 is equal to the number 15 plus some number. By adding 3 to the 15 results 18. Here we have to check both sides of the equal sign have the same value or not.
Here 18 = 18
So 15 + 3 = 10 + 8
The missing number that makes the equation true is 3.

Question 9.
______ – 6 = 9 + 5
Answer:
? – 6 = 9 + 5
? – 6 = 14
20 – 6 = 14
14 = 14
The missing number that makes the equation true is 20.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 9 + 5 = 14. After that we have to find the remaining part ? – 6 = 14. Here 14 is equal to the some number minus 6. By subtracting 6 from 20 results 14. Here we have to check both sides of the equal sign have the same value or not.
Here 14 = 14
So 20 – 6 = 9 + 5
The missing number that makes the equation true is 20.

Question 10.
8 + 5 = ______ – 3
Answer:
8 + 5 = ? – 3
13 = ? – 3
13 = 16 – 3
13 = 13
The missing number that makes the equation true is 16.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 8 + 5 = 13. After that we have to find the remaining part 13 = ? – 3. Here 13 is equal to some number minus 3. By subtracting 3 from the 16 results 13. Here we have to check both sides of the equal sign have the same value or not.
Here 13 = 13
So 8 + 5 = 16 – 3
The missing number that makes the equation true is 16.

Set G

Find the missing number to make the equation true.
7 + 8 + ______ = 30 – 5
First, you can find the value of the side with no missing number.
30 – 5 = 25
The two sides are equal. So,
7 + 8 + _______ = 25

The missing number is 10.

Find and write the missing numbers to make the equations true.
Question 11.
13 + 7 + ______ = 27 + 8
Answer:
13 + 7 + ? = 27 + 8
First we have to find the value of the side with no missing number.
27 + 8 = 35
The two sides are equal. So,
13 + 7 + ? = 35
13 + 7 + 15 = 35
20 + 15 = 35
35 = 35
The missing number that makes the equation true is 15.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 27 + 8 = 35. After that we have to find the remaining part 13 + 7 + ? = 35. Here 35 is equal to some number plus 20. By adding 15 to the 20 results 35. Here we have to check both sides of the equal sign have the same value or not.
Here 35 = 35
So 13 + 7 + 15 = 27 + 8
The missing number that makes the equation true is 15.

Question 12.
10 + 8 + 12 = 33 – _______
Answer:
10 + 8 + 12 = 33 – ?
First we have to find the value of the side with no missing number.
10 + 8 + 12 = 30
30 = 33 – ?
30 = 33 – 3
30 = 30
10 + 8 + 12 = 33 – 3
The missing number that makes the equation true is 3.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 10 + 8 + 12 = 30. After that we have to find the remaining part 30 = 33 – ?. Here 30 is equal to 33 minus some number. By subtracting 3 from 33 results 30. Here we have to check both sides of the equal sign have the same value or not.
Here 30 = 30
So 10 + 8 + 12 = 33 – 3
The missing number that makes the equation true is 3.

Question 13.
_____ + 15 + 15 = 10 + 32
Answer:
? + 15 + 15 = 10 + 32
First we have to find the value of the side with no missing number.
10 + 32 = 42
? + 15 + 15 = 42
? + 30 = 42
12 + 30 = 42
42 = 42
12 + 15 + 15 = 10 + 32
The missing number that makes the equation true is 12.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 10 + 32 = 42. After that we have to find the remaining part ? + 30 = 42. Here 42 is equal to some number plus 30. By adding 12 to the 30 results 42. Here we have to check both sides of the equal sign have the same value or not.
Here 42 = 42
So 12 + 15 + 15 = 10 + 32
The missing number that makes the equation true is 12.

Question 14.
4 + 13 + 10 = ______ – 13
Answer:
4 + 13 + 10 = ? – 13
First we have to find the value of the side with no missing number.
4 + 13 + 10 = 27
27 = ? – 13
27 = 40 – 13
27 = 27
4 + 13 + 10 = 40 – 13
The missing number that makes the equation true is 40.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 4 + 13 + 10 = 27. After that we have to find the remaining part 27 = ? – 13. Here 27 is equal to some number minus 13. By subtracting 13 from 40 results 27. Here we have to check both sides of the equal sign have the same value or not.
Here 27 = 27
So 4 + 13 + 10 = 40 – 13
The missing number that makes the equation true is 40.

Set H

Thinking Habits
Reasoning
How are the numbers in the problem related?
How can I use a word problem to show what the equation means?

Write a number story for the problem. Complete the equation to match your story.
Question 15.
28 + 35 = ________
Answer:
28 + 35 = ?
There are 28 butterflies flying and 35 joined with them. How many butterflies are flying altogether?
28 + 35 = 63
Now 63 butterflies are flying altogether.
Explanation:
There are 28 butterflies flying and 35 joined with them. Perform addition operation on 28 butterflies flying and 35 more joined butterflies then we get total number of butterflies. Total number of butterflies flying together are 63.

Topic 7 Assessment Practice

Question 1.
Jodi has 28 apples. She buys some more. Now Jodi has 43 apples. How many apples did she buy?
Use the bar diagram to help you write an equation. Then use the open number line to solve.

Answer:

She buy 15 apples.
Explanation:
Jodi has 28 apples. She buys some more. Now Jodi has 43 apples. Add 15 apples to 28 apples then we get 43 apples. Jodi buy 15 apples.

Question 2.
Alayna draws 18 more stars than Pearl. Alayna draws 37 stars. How many stars does Pearl draw?
A. Can you use the equation to solve the problem? Choose Yes or No.

Answer:

B. How many stars does Pearl draw? _______ stars
Answer:
Pearl draw 19 stars.
Explanation:
Alayna draws 18 more stars than Pearl. That means pearl draw less stars. Alayna draws 37 stars. Subtract 18 stars from 37 stars then we get 19 stars. Pearl draw 19 stars.

Question 3.
Emily has 17 fewer ribbons than Piper. Piper has 48 ribbons. How many ribbons does Emily have?
Solve any way you choose. Show your work.
_________ ribbons
Answer:

Emily have 31 ribbons.
Explanation:
Emily has 17 fewer ribbons than Piper. Piper has 48 ribbons. Subtract 17 ribbons from 48 ribbons then we get 31 ribbons. Emily have 31 ribbons.

Question 4.
Write a number story for 72 – 36 = ?. Then solve the story problem.
72 – 36 = _______
Answer:
72 – 36 = ?
There were 72 tangerines in a tree. Some tangerines fell out of the tree. There are now 36 tangerines left. How many tangerines fell out?
72 – 36 = ?
+4  +4
76 – 40 = 36
36 tangerines fell out.
Explanation:
There were 72 tangerines in a tree. Some tangerines fell out of the tree. There are now 36 tangerines left. Subtract 36 tangerines from 76 tangerines then we get 36 tangerines. 36 tangerines fell out.

Question 5.
Joy needs 99 coats for children in need. She gets 54 coats from her school. She gets 22 coats from friends. How many more coats does Joy need?
Write equations to solve. Then write the answer.

Joy needs _________ more coats.
Answer:

Joy needs 23 more coats.
Explanation:
Joy needs 99 coats for children in need. She gets 54 coats from her school. She gets 22 coats from friends. Add 54 coats with 22 coats then we get 76 coats. Then subtract 76 coats from 99 coats then we get 23 coats. Joy needs 23 more coats for children.

Question 6.
Shane has 27 more cards than Tom. Shane has 62 cards. How many cards does Tom have?
Explain how you will solve the problem. Then solve.
Tom has ______ cards.
Answer:

Tom has 35 cards.
Explanation:
Shane has 27 more cards than Tom. That means Tom has less cards. Shane has 62 cards. Subtract 27 cards from 62 cards then we get 35 cards. Tom has 35 cards.

Question 7.
Grace collects cans to be recycled. The table shows the number of cans she has collected.

A. How many fewer cans did Grace collect on Thursday than on Saturday?
________ fewer cans
Answer:

Grace collects 25 fewer cans on Thursday than on Saturday.
Explanation:
On Thursday Grace collects 12 cans and he collects 37 cans on Saturday. Subtract 12 cans from 37 cans then we get 25 cans. Grace collects 25 fewer cans on Thursday than on Saturday.

B. Grace collects some more cans on Sunday. She now has 90 cans.
Find the missing number in the equation to find how many cans Grace collects on Sunday.
12 + 29 + 37 + ______ = 90
Answer:
12 + 29 + 37 + ? = 90
12 + 29 + 37 + 12 = 90
Grace collect 12 more cans on Sunday.
The missing number that makes the equation true is 12.
Explanation:
Grace collects 12 cans on Thursday, 29 cans on Friday and 37 cans on Saturday, and Some more cans on Sunday. Grace have 90 cans in all. Add 12 with 29, 37 and 12 then we got 90 cans. Grace collects 12 more cans on Sunday.

Question 8.
Find the missing number that makes each equation true.
18 – 10 = 9 – _______
35 + 30 = 45 + ________
Answer:
18 – 10 = 9 – ?
First we have to find the value of the side with no missing number.
18 – 10 = 8
8 = 9 – ?
8 = 9 – 1 
8 = 8
18 – 10 = 9 – 1
The missing number that makes the equation true is 1
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 18 – 10 = 8. After that we have to find the remaining part 8 = 9 – ?. Here 8 is equal to 9 minus some number. By subtracting 1 from 9 results 8. Here we have to check both sides of the equal sign have the same value or not.
Here 8 = 8
So 18 – 10 = 9 – 1
The missing number that makes the equation true is 1.

35 + 30 = 45 + ________
First we have to find the value of the side with no missing number.
35 + 30 = 65
65 = 45 + ?
65 = 45 + 20
65 = 65
35 + 30 = 45 + 20
The missing number that makes the equation true is 20.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 35 + 30 = 65. After that we have to find the remaining part 65 = 45 + ?. Here 65 is equal to 45 plus some number. By adding 20 to the 45 results 65. Here we have to check both sides of the equal sign have the same value or not.
Here 65 = 65
So 35 + 30 = 45 + 20
The missing number that makes the equation true is 20.
Question 9.
Find the missing number that makes each equation true.
24+ _______ = 7+ 15 + 8
46 – 5 = 10 + 10 + _________
Answer:
24+ _______ = 7+ 15 + 8
First we have to find the value of the side with no missing number.
7 + 15 + 8 = 30
24 + ? = 30
24 + 6 = 30
30 = 30
24 + 6 = 7 + 15 + 8
The missing number that makes the equation true is 6.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 7 + 15 + 8 = 30. After that we have to find the remaining part 24 + ? = 30. Here 30 is equal to 24 plus some number. By adding 6 to the 24 results 30. Here we have to check both sides of the equal sign have the same value or not.
Here 30 = 30
So 24 + 6 = 7 + 15 + 8
The missing number that makes the equation true is 6.

46 – 5 = 10 + 10 + _________
First we have to find the value of the side with no missing number.
46 – 5 = 41
41 = 10 + 10 + ?
41 = 10 + 10 + 21
41 = 41
46 – 5 = 10 + 10 + 21
The missing number that makes the equation true is 21.
Explanation:
Here ‘=’ means the value on both sides is the same. Here first we have find 46 – 5 = 41. After that we have to find the remaining part 41 = 10 + 10 + ?. Here 41 is equal to 20 plus some number. By adding 20 to the 21 results 41. Here we have to check both sides of the equal sign have the same value or not.
Here 41 = 41
So 46 – 5 = 10 + 10 + 21
The missing number that makes the equation true is 21.

Topic 7 Performance Task

School Fair Meadow School is having a school fair. The table shows the number of tickets Ms. Davis’s class has sold.

Question 1.
How many fewer tickets did Ms. Davis’s class sell on Wednesday than on Monday?
Complete the bar diagram to model the problem. Then solve.

_______ fewer tickets
Answer:

Ms. Davis’s class sold 21 fewer tickets on Wednesday than on Monday.
Explanation:
Ms. Davis’s class sold 42 tickets on Monday and 21 tickets on Wednesday. So Subtract 21 tickets from 42 tickets then we get 21 tickets. Ms. Davis’s class sold 21 fewer tickets on Wednesday than on Monday.

Question 2.
Ms. Davis says the class can have a party if they sell 95 tickets.
Part A
Write an equation to show how many tickets the class has sold.
Then solve the equation. Show your work.
_________ tickets sold
Answer:

42 + 17 + 21 = ?
42 + 17 + 21 = 80
The class has sold 80 tickets.
Explanation:
The class sold 42 tickets on Monday, 17 tickets on Tuesday and 21 tickets on Wednesday. Add the tickets sold on Monday, Tuesday, Wednesday. Add 42 with 17 and 21 then we get 80 tickets. The class has sold 80 tickets.

Part B
How many more tickets does the class have to sell to have a party? Explain.
________ tickets
Answer:
80 + ? = 95
95 – 80 = 15
The class needs to sell 15 more tickets to have a party.
Explanation:
The class can have a party if they sell 95 tickets. Here the class sold only 80 tickets. Subtract 80 tickets from 95 tickets then we get how many more tickets did the class need to have party. After subtracting 80 from 95 then we got 15 tickets. If they sell 15 more tickets then the class can have a party.

Question 3.
The table shows the number of tickets Mr. Rios’s class has sold.
How many more tickets did his class sell in all on Monday and Tuesday than on Wednesday?

Answer:

The class has to sell 14 more tickets in all on Monday and Tuesday than on Wednesday.
Explanation:
The class sold 24 tickets on Monday, 18 tickets on Tuesday and 28 tickets on Wednesday. Here we have to find how many more tickets his class has to sell in all on Monday and Tuesday than on Wednesday. First subtract 24 tickets from 28 tickets then we get 4 tickets. 4 more tickets that the class need to sell on Monday. Then Subtract 18 tickets from 28 tickets then we get 10 tickets. 10 more tickets that the class need to sell on Tuesday. Add 4 tickets on Monday with 10 tickets on Tuesday then we get 14 tickets. The class has to sell 14 more tickets in all on Monday and Tuesday than on Wednesday.

Question 4.
Part A
Write a number story about selling tickets for the school fair. Use numbers that you can add or subtract.
Answer:

Part B
Write an equation to match your story. Then solve any way you choose. Show your work.
Answer:

Go through the enVision Math Common Core Grade 3 Answer Key Topic 15 Attributes of Two-Dimensional Shapes regularly and improve your accuracy in solving questions.

enVision Math Common Core 3rd Grade Answers Key Topic 15 Attributes of Two-Dimensional Shapes

Essential Question:
How can two-dimensional shapes be described, analyzed, and classified?

enVision STEM Project: Forces and Motion
Do Research Use the Internet or other sources to find information about forces and the motion of an object. What does a balanced force mean? What happens when forces are unbalanced?

Journal: Write a Report Include what you found. Also in your report:

• Give examples of balanced and unbalanced forces on objects.
• Draw a picture that shows force acting on an object and the result.
• Describe the shapes in your drawing.

Review What You Know

Vocabulary
Choose the best term from the box. Write it on the line.

• circle
• hexagon
• pentagon
• triangle

Question 1.
A shape with exactly 6 sides is called a _________.

Answer:
The shape with exactly 6 sides is called a hexagon.

Explanation:
In the above-given question,
given that,
the terms are circle, hexagon, pentagon, and triangle.
6 sides = hexagon.
hexagon is one of the two-dimensional shapes.
for example:

Question 2.
A shape with exactly 3 sides is called a __________.

Answer:
The shape with exactly 3 sides is called a triangle.

Explanation:
In the above-given question,
given that,
the terms are circle, hexagon, pentagon, and triangle.
3 sides = triangle.
triangle is one of the two-dimensional shapes.
for example:

Question 3.
A shape with exactly 5 sides is called a ___________.

Answer:
The shape with exactly 5 sides is called a pentagon.

Explanation:
In the above-given question,
given that,
the terms are circle, hexagon, pentagon, and triangle.
5 sides = pentagon.
The pentagon is one of the two-dimensional shapes.
for example:

Name Shapes

Write the name of each figure.
Question 4.

Answer:
The name of the figure is a square.

Explanation:
In the above-given question,
given that,
the figure has four sides.
so square has four sides.
the area of the square = s x s.
where s = side.
so the name of the figure is a square.

Question 5.

Answer:
The name of the figure is a rectangle.

Explanation:
In the above-given question,
given that,
the figure has four sides.
so rectangle has the four sides.
the area of the rectangle = l x b.
where l = length, and b = breadth.
so the name of the figure is a rectangle.

Question 6.

Answer:
The name of the figure is a triangle.

Explanation:
In the above-given question,
given that,
the figure has three sides.
so triangle has three sides.
the area of the triangle =1/2( b x h).
where b = base, and h = height.
so the name of the figure is a triangle.

Question 7.

Answer:
The name of the figure is a hexagon.

Explanation:
In the above-given question,
given that,
the figure has six sides.
so hexagon has six sides.
the area of the pentagon = p x a/2.
where p = perimeter, and a = anotherm.
so the name of the figure is a hexagon.

Shapes

In 8-11 write the number of vertices each figure has.
Question 8.

Answer:
The number of vertices = 3.

Explanation:
In the above-given question,
given that,
the figure is a triangle.
the highest or the top point is called the vertex.
the number of vertices = 3.
triangle has 3 vertices.

Question 9.

Answer:
The number of vertices = 4.

Explanation:
In the above-given question,
given that,
the figure is a quadrilateral.
the highest or the top point is called the vertex.
A polygon that has exactly 4 sides is called a quadrilateral.
the number of vertices = 4.
quadrilateral has 4 vertices.

Question 10.

Answer:
The number of vertices = 4.

Explanation:
In the above-given question,
given that,
the figure is a rhombus.
the highest or the top point is called a vertex.
A polygon that has four equal sides is called a rhombus.
the number of vertices = 4.
rhombus has vertices.

Question 11.

Answer:
The number of vertices = 6.

Explanation:
In the above-given question,
given that,
the figure is a hexagon.
the highest or the top point is called a vertex.
a polygon that has 6 straight sides and angles is called a hexagon.
the number of vertices = 6.
hexagon has 6 vertices.

Question 12.
How many faces does a cube have?
A. 3
B. 4
C. 5
D. 6

Answer:
Option D is the correct answer.

Explanation:
In the above-given question,
given that,
a cube has 6 sides.
cube also has six faces.
they are top, bottom, left, right, up, and down.
so option D is the correct answer.

Question 13.
How are squares and triangles the same? How are they different?

Answer:
The square and the triangles are the same.
the square and the triangles are different.

Explanation:
In the above-given question,
given that,
the squares and triangles are the same:
when they both have common names that do not indicate the number of sides.
they have four right angles.
the squares and triangles are different:
when they both have different side lengths and angles in a triangle.
so both the squares and rectangles are the same and also different.

Pick a Project

PROJECT 15A
Where do professional baseball players play their games?
Project: Create Quadrilateral Riddles

Answer:
The professional baseball players play their games on baseball grounds.

Explanation:
In the above-given question,
given that,
the baseball players will play their games on baseball grounds.
baseball is a bat-and-ball game played between two opposing teams who take turns batting and fielding.
the game proceeds when a player on the fielding team, called the pitcher, throws a ball which a player on the batting team tries to hit with a bat.

PROJECT 15B
How are books measured?
Project: Collect Data about the Shapes of Books

Answer:
The books are measured in many ways.

Explanation:
In the above-given question,
given that,
the shape of the books is measured in many ways.
the square and the rectangle.
the area of the square = s x s.
where s = side.
the area of the rectangle = l x b.
where l = length, and b = breadth.
so the books are measured in many ways.

PROJECT 15C
Where are quadrilaterals around us in everyday life?
Project: Build a Quadrilateral Model

Answer:
The quadrilaterals around us in everyday life are tabletop, book, picture frame, door, baseball diamond, etc.

Explanation:
In the above-given question,
given that,
we found quadrilaterals in everyday life.
they are tabletop, book, photo frame, door, etc.
so we can also see quadrilaterals in many pictures.

3-ACT MATH PREVIEW

Math Modeling
Square It Up

I can … model with math to solve a problem that involves using attributes of 2-D shapes to compare weights.

Lesson 15.1 Describe Quadrilaterals

Solve & Share
Fold a square piece of paper to make the fold lines as shown below. Find as many different quadrilaterals as you can using the fold lines and the edges of the square paper. Sketch each quadrilateral you find and describe it.
I can … identify quadrilaterals and use attributes to describe them.

Look Back! Describe how you used what you know about quadrilaterals to identify the shapes.

Essential Question
What Are Some Attributes of Quadrilaterals?

Answer:
Some attributes of quadrilaterals are triangles, rhombus, and the square.

Explanation:
In the above-given question,
given that,
Fold a square piece of paper to make the fold lines.
if we fold the paper in an above-given way,
we can find some shapes.
the shapes are quadrilaterals, triangles, and rhombus.

Visual Learning Bridge
The welcome to Florida sign is a quadrilateral. How can you describe quadrilaterals?
An angle is formed when two sides of a polygon meet.

Some quadrilaterals have special names.

Convince Me! Make Sense and Persevere Draw a quadrilateral that is an example of one of the shapes listed in Box B. Name the shape. Then draw a quadrilateral that is NOT an example of a shape listed in Box B.

Answer:
The trapezoid is one example of the quadrilateral.

Explanation:
In the above-given question,
given that,
the shapes are trapezoid, parallelogram, rectangle, rhombus, and square.
among all these shapes,
a trapezoid is one example.

Another Example!
These are convex polygons. All angles point outward.

These are concave polygons. One or more angles point inward.

Guided Practice

Do You Understand?
Question 1.
This figure is a rectangle, but it is NOT a square. Why?

Answer:
The square has four right angles and all sides the same length.

Explanation:
In the above-given question,
given that,
the figure is a rectangle, but it is not a square because
the rectangle has four right angles or square corners.
but the square has four right angles and all sides the same length.
area of the square = s x s.
area of the rectangle = l x b.

Question 2.
Draw two different quadrilaterals that are NOT rectangles, squares, or rhombuses.

Answer:
The two different quadrilaterals are trapezoid and parallelogram.

Explanation:
In the above-given question,
given that,
the two different quadrilaterals that are not rectangles, squares, or rhombuses:
they are trapezoid and parallelogram.
a trapezoid has exactly one pair of sides on lines that never cross.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.

Do You Know How?
In 3-6, write as many special names as possible for each quadrilateral.
Question 3.

Answer:
The special name for the quadrilateral is a parallelogram.

Explanation:
In the above-given question,
given that,
the given figure is quadrilateral.
parallelogram is also a quadrilateral.
opposite sides are the same length.
opposite angles are the same size.

Question 4.

Answer:
The special name is a rectangle.

Explanation:
In the above-given question,
given that,
the shape is a rectangle.
the rectangle has four right angles or square corners.
area of the rectangle = l x b.
where l = length and b = breadth.
so the quadrilateral is a rectangle.

Question 5.

Answer:
The special name is a parallelogram.

Explanation:
In the above-given question,
given that,
the quadrilateral has two equal lengths and two equal breadths.
so the name is a parallelogram.
parallelogram is also a quadrilateral.
opposite sides are the same length.
opposite angles are the same size.

Question 6.

Answer:
The special name is square.

Explanation:
In the above-given question,
given that,
the quadrilateral has two equal lengths and two equal breadths.
so the name is square.
square is also a quadrilateral.
four right angles and all sides the same length.

Independent Practice

In 7-9, write as many special names as possible for each quadrilateral.
Question 7.

Answer:
The special name is a rectangle.

Explanation:
In the above-given question,
given that,
the quadrilateral has opposite sides that are the same length.
so the name is a rectangle.
the rectangle is also a quadrilateral.
opposite sides are the same length.
opposite angles are the same size.

Question 8.

Answer:
The special name is a trapezoid.

Explanation:
In the above-given question,
given that,
the quadrilateral has exactly one pair of sides.
so the name is a trapezoid.
trapezoid is also a quadrilateral.
exactly one pair of sides on lines that never cross.

Question 9.

Answer:
The special name is a parallelogram.

Explanation:
In the above-given question,
given that,
the quadrilateral has two equal lengths and two equal breadths.
so the name is a parallelogram.
parallelogram is also a quadrilateral.
opposite sides are the same length.
opposite angles are the same size.

In 10, name all the possible quadrilaterals that fit the rule.
Question 10.
Has 2 pairs of opposite sides that are equal _______________

Answer:
The 2 pairs of opposite sides that are equal are parallelogram and rectangle.

Explanation:
In the above-given question,
given that,
the quadrilateral that has 2 pairs of opposite sides that are equal is a parallelogram and rectangle.
opposite sides are the same length.
opposite angles are the same size.
four right angles, or square corners.
so rectangle and parallelogram have 2 pairs of opposite sides that are equal.

Problem Solving

In 11 and 12, write the name that best describes the quadrilateral. Draw a picture to help.
Question 11.
Vocabulary A rectangle with all sides the same length is a _________.

Answer:
A rectangle with all sides the same length is a rhombus.

Explanation:
In the above-given question,
given that,
a rhombus has all sides the same length.
rhombus is a special parallelogram.
so a rectangle with all sides the same length is a parallelogram.

Question 12.
Vocabulary A parallelogram with four right angles is a __________

Answer:
A parallelogram with four right angles is a rectangle.

Explanation:
In the above-given question,
given that,
the rectangle has four right angles or square corners.
a rectangle is a special parallelogram.
a parallelogram with four right angles is a rectangle.

Question 13.
I am a quadrilateral with opposite sides the same length. Which quadrilaterals could I be?

Answer:
The quadrilateral with opposite sides of th+e same length is a parallelogram.

Explanation:
In the above-given question,
given that,
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the quadrilateral with opposite sides of the same length is a parallelogram.

Question 14.
Higher Order Thinking Jae says that the figure on the left is a trapezoid. Carmen says that the figure on the right is a trapezoid. Who is correct? Explain.

Answer:
Yes, both of them are correct.

Explanation:
In the above-given question,
given that,
Jae says that the figure on the left is a trapezoid.
Carmen says that the figure o the right is a trapezoid.
a trapezoid has exactly one pair of sides on lines that never cross.
trapezoid is also a quadrilateral.
so both of them are correct.

Question 15.
Model with Math Sue bought a book for $12, two maps for $7 each, and a pack of postcards for $4. Use math you know, bar diagrams, equations, or properties of operations, to find Sue’s total cost.

Answer:
The total cost of Sue was $23.

Explanation:
In the above-given question,
given that,
Sue bought a book for $12, two maps for $7 each,
and a pack for $4.
12 + 7 + 4.
12 + 4 = 16.
16 + 7 = 23.
so the total cost of Sue was $23.

Question 16.
Algebra Angela drew 9 rhombuses and 6 trapezoids. She wants to find b, the total number of angles in her quadrilaterals. Explain how Angela can find b.

Answer:
The total number of angles in her quadrilaterals is

Explanation:
In the above-given question,
given that,
Algebra Angela drew 9 rhombuses and 6 trapezoids.

Assessment Practice

Question 17.
A square and a rhombus are shown at the right. Which attributes do these shapes always have in common? Select all that apply.

☐ Number of sides
☐ Side lengths
☐ Angle measures
☐ Right angles
☐ Number of angles

Answer:
The attributes of these shapes always have in common are the number of sides, side lengths, right angles.

Explanation:
In the above-given question,
given that,
A square and a rhombus are shown at the right.
rhombus has all sides the same length.
a rhombus is a special parallelogram.
a square has four angles and all sides the same length.
a square is a special parallelogram.
so the number of sides, side length, and right angles have the same attributes.

Lesson 15.2 Classify Shapes

Solve & Share
Sort the shapes below into two groups. Use colored pencils or crayons to color each group a different color. How did you sort the shapes? How are the shapes in both of your groups alike?
I can … classify shapes in several ways based on how they are alike and how they are different.

Look Back! What fraction of the triangles above have each attribute: all sides equal in length, no sides equal in length, exactly two equal angles, or one right angle?

Answer:
Triangle G, B, and I have all sides equal in length.
Triangle E, F, AND L have no sides equal in length.
Exactly one right angle is A, D, and K.
triangle B, C, I, and J have two equal angles.

Explanation:
In the above-given question,
given that,
there are 12 triangles.
the triangles are the names A, B, C, D, E, F, G, H, I, J, K, and L.
The triangles that have all sides equal in length are G, B.
the triangles that have no sides equal in length are E, F, and L.
the triangles that have exactly one right angle are A, D, and K.
the triangles have two equal angles is B, C, I, and J.

Essential Question
How Can You Describe Different Question Groups of Shapes?

Visual Learning Bridge
Ethan made two groups of polygons. How are the groups different? How are the groups alike?

Here is one way the two groups are different
In Group 1, each polygon has sides that all are the same length.
In Group 2, each polygon has sides that are not all the same length.

Here are some ways the two groups are alike.
In Group 1 and Group 2, all of the polygons have 4 sides.
In Group 1 and Group 2, all of the polygons have 4 angles.
In Group 1 and Group 2, all of the polygons are quadrilaterals.

Convince Me! Construct Arguments Draw a quadrilateral that does not belong to either Group 1 or Group 2. Explain why it does not belong to either group.

Answer:
The quadrilateral that does not belong to either group 1 and group 2 is a rectangle.

Explanation:
In the above-given question,
given that,
in group 1 each polygon has sides that all are the same length.
In Group 2, each polygon has sides that are not all the same length.
In Group 1 and Group 2, all of the polygons have 4 sides.
In Group 1 and Group 2, all of the polygons have 4 angles.
In Group 1 and Group 2, all of the polygons are quadrilaterals.
so the quadrilateral that does not belong to either group 1 and group 2 is a rectangle.

Guided Practice

Do You Understand?
Question 1.
Nellie drew a group of rectangles and a group of trapezoids. How are the shapes in each group different?

Answer:
The groups of rectangles and groups of trapezoids are different.

Explanation:
In the above-given question,
given that,
Nellie drew a group of rectangles and a group of trapezoids.
rectangles have four right angles or square corners.
a rectangle is a special parallelogram.
trapezoids have exactly one pair of sides on lines that never cross.
the trapezoid is also a quadrilateral.
so rectangles and trapezoids are different.

Question 2.
How are rectangles and trapezoids alike?

Answer:
The rectangles and trapezoids are alike.

Explanation:
In the above-given question,
given that,
rectangles have four right angles or square corners.
a rectangle is a special parallelogram.
trapezoids have exactly one pair of sides on lines that never cross.
the trapezoid is also a quadrilateral.
so rectangles and trapezoids are alike.

Question 3.
What larger group of polygons do all of Nellie’s shapes belong to?

Answer:
The larger group of polygons do Nellie’s shapes belong to rectangles and trapezoids.

Explanation:
In the above-given question,
given that,
Nellie drew a group of rectangles and a group of trapezoids.
rectangles have four right angles or square corners.
a rectangle is a special parallelogram.
trapezoids have exactly one pair of sides on lines that never cross.
the trapezoid is also a quadrilateral.
so rectangles and trapezoids belong to quadrilaterals.
Nellie’s shape belongs to quadrilaterals.

Do You Know How?
In 4-6, use the groups on the previous page.
Question 4.
Draw a shape that belongs to Ethan’s Group 1.

Answer:
The shape is a parallelogram, and square.

Explanation:
In the above-given question,
given that,
Ethan draws a shape that belongs to two groups.
in group 1 he draws 3 shapes.
they are parallelogram and square.

Question 5.
Draw a shape that belongs to Ethan’s Group 2.

Answer:
The shape is a trapezoid.

Explanation:
In the above-given question,
given that,
Ethan draws a shape that belongs to two groups.
in group 2 he draws 3 shapes.
they are different types of trapezoids.
the quadrilateral is also a trapezoid.

Question 6.
Why is there a square in Group 1?

Answer:
In group 1 there is a square because it has four right angles and all sides the same length.

Explanation:
In the above-given question,
given that,
Ethan draws a shape that belongs to two groups.
in group 1 he draws 3 shapes.
among the three shapes, one is square.
the area of the square = s x s.
where s = side.
square has four right angles and all sides the same length.

Independent Practice

In 7-11, use the groups below.

Question 7.
How are the shapes in Group 1 different from the shapes in Group 2?

Answer:
The shapes in group 1 different from the shapes in group 2.

Explanation:
In the above-given question,
given that,
in group 1 there are three pentagons.
the pentagons are the same with the edges have the same length.
in group 2 there are 3 pentagons.
the pentagons have different side lengths.

Question 8.
How are the two groups alike?

Answer:
The two groups are alike because they all are pentagons.

Explanation:
In the above-given question,
given that,
in group 1 all the pentagons have equal side lengths.
in group 1 there are 3 pentagons.
in group 2 all the pentagons have different side lengths.
in group 2 there are also 3 pentagons.

Question 9.
What larger group do all the shapes belong to?

Answer:
The shapes belong to the pentagons.

Explanation:
In the above-given question,
given that,
the larger group do all the shapes belong to pentagons.
there are 4 pentagons.
they have the same equal side lengths.
2 pentagons have different side lengths.

Question 10.
Draw a shape that could go in Group 2 but not Group 1.

Answer:
The shape is pentagon.

Explanation:
In the above-given question,
given that,
right pentagon belongs to group 2.
the polygon that has 5 sides is called a pentagon.

Question 11.
Draw a shape that could go in Group 1 but not Group 2.

Answer:
The shape that could go in group 1 is a trapezoid.

Explanation:
In the above-given question,
given that,
in group 1 there are 3 pentagons.
the 3 pentagons that have the same length.
i group 2 there are 3 trapezoids.
that have different side lengths.

Problem Solving

In 12-14, use the picture at the right.

Question 12.
How are the yellow shapes and the blue shapes different? How are they alike?

Answer:
The blue and the yellow shapes are same because they all are triangles.

Explanation:
In the above-given question,
given that,
in the given figure
there is one hexagon.
there are 6 equilateral triangles.
there is 6 isosceles triangles.
they are different because they are equilateral and isosceles triangles.

Question 13.
Which larger group of polygons do the yellow and blue shapes belong to?

Answer:
The larger group of polygons do the yellow and blue shapes belong to triangles.

Explanation:
In the above-given question,
given that,
in the given figure
there is one hexagon.
there are 6 equilateral triangles.
there are 6 isosceles triangles.
so the larger group of polygons do the yellow and blue shapes belong to triangles.
6 + 6 = 12.

Question 14.
Does the pink shape belong to the group identified in Exercise 13? Explain.

Answer:
Yes, the pink shape belongs to the group identified in exercise 13.

Explanation:
In the above-given question,
given that,
the pink shape is a hexagon.
hexagon has 6 sides.
the six sides have the same side lengths.
so the pink shape belong to the group identified in exercise 13.

Question 15.
Draw a quadrilateral that is NOT a rectangle, a rhombus, or a square.

Answer:
The quadrilateral is a parallelogram.

Explanation:
In the above-given question,
given that,
the quadrilateral is a parallelogram.
opposite sides are the same length.
opposite angles are the same size.
so the quadrilateral is a parallelogram.

Question 16.
Todd bought a jacket for $57 and two maps for $9 each. What was the total cost?

Answer:
The total cost is $66.

Explanation:
In the above-given question,
given that,
Todd bought a jacket for $57.
two maps for $9 each.
57 + 9 = $66.
so the total cost is $66.

Question 17.
Use Appropriate Tools Victoria wants to make two same-sized rhombuses. What tool can she use? Explain.

Answer:
The tool is scale.

Explanation:
In the above-given question,
given that,
Victoria wants to make two same-sized rhombuses.
rhombus has all the sides the same length.
rhombus is a special type of special parallelogram.

Question 18.
Higher Order Thinking Jessalyn needs to find 3 × 3,4 × 6, and 7 × 2. She draws area models to solve the problem. What polygon group do her area models all belong to? Explain.

Answer:
The area models belong to square and rectangle.

Explanation:
In the above-given question,
given that,
Jessalyn needs to find 3 × 3,4 × 6, and 7 × 2.
3 x 3 = 9.
where the area of the square = s x s.
where s = side.
the area of the rectangle = l x b.
where l = length and b = breadth.
4 x 6 = 24.
7 x 2 = 14.
so the area models belong to squares and rectangles.

Assessment Practice

Question 19.
What is the name of a shape that is NOT always a rectangle, but is a quadrilateral?
A. Square
B. Triangle
C. Hexagon
D. Parallelogram

Answer:
The name of a shape that is not always a rectangle is triangle.

Explanation:
In the above-given question,
given that,
the quadrilateral is a square, hexagon, and parallelogram.
the polygon that has three sides is called triangle.
a quadrilateral that is not always a rectangle is triangle.
opposite sides are the same length.
opposite angles are the same size.
square has four right angles and all sides the same length.

Question 20.
Which shape could be sorted into a group of parallelograms or a group of rhombuses?
A. Square
B. Rectangle
C. Trapezoid
D. Hexagon

Answer:
Option B and option C is correct.

Explanation:
In the above-given question,
given that,
The shapes are square, rectangle, trapezoid, and hexagon.
four right angles and all sides the same length is a square.
rectangle has four right angles or square corners.
a rectangle is a special parallelogram.
a trapezoid has exactly one pair of sides on lines that never cross.
option B and option C is correct.

Lesson 15.3 Analyze and Compare Quadrilaterals

Solve & Share
Describe at least two attributes that are the same in all or some of these shapes. Describe two attributes that are different.
I can … analyze and compare quadrilaterals and group them by attributes.

Look Back! Draw a quadrilateral that is different from all the quadrilaterals above. Tell how it is different.

Answer:
The quadrilateral that is different from all the quadrilaterals is diagram E.

Explanation:
In the above-given question,
given that,
the shapes are parallelogram and rhombus.
parallelogram has opposite sides are the same length.
opposite angles are the same size.
so the quadrilateral that is different from all the quadrilaterals is E.

Essential Question
How Can You Analyze bessed to Question and Compare Shapes?

Visual Learning Bridge
What are different ways you can classify the quadrilaterals shown below?

Shapes B, D, E, F, and G are also parallelograms. Each has two pairs of sides that have the same length.

Shapes D, E, and G are also rectangles. Each has 4 right angles.

Shapes B and D are parallelograms that are also rhombuses. Each has 4 equal-length sides.

Convince Me! Reasoning Which of the shapes above can you cover with whole unit squares and not have any gaps or overlaps? What attributes do these shapes have in common?

Guided Practice

Do You Understand?
Question 1.
Which shape on the previous page is a rhombus but not a rectangle? Explain.

Answer:
The shape D is the rhombus but not a rectangle.

Explanation:
In the above-given question,
given that,
the shapes are rhombus, parallelogram.
shapes D, E, G are also rectangles.
each has 4 right angles.

Question 2.
Can you have a square trapezoid? Explain.

Answer:
Yes, the shape D is a square trapezoid.

Explanation:
In the above-given question,
given that,
the shapes are B, D, E, F, and G.
the shape D is a square trapezoid.
D, E, and G are rectangles.
so the shape D is a square trapezoid.

Do You Know How?
Question 3.
Which shapes on the previous page are not a parallelogram, rectangle, rhombus, or square?

Answer:
The shapes belong to the parallelogram, rectangle, rhombus, and square.

Explanation:
In the above-given question,
given that,
the shapes are parallelogram, rectangle, rhombus, square.
shape D is a square.
shape B is a parallelogram.
shape G is a rectangle.
so all the shape belongs to the parallelogram, rectangle, rhombus, and a square.

Question 4.
What attributes does a square have because it is always a rectangle?

Answer:
The square has four right angles and all sides the same length.

Explanation:
In the above-given question,
given that,
the square has four right angles and all sides the same length.
the rectangle is four right angles or square corners.
a rectangle is a special parallelogram.
square is a rectangle.

Independent Practice

In 5-9, list all the polygons shown at the right that fit each description. If there could be no such polygon, tell why.

Question 5.
Is not a parallelogram

Answer:
The shape E is not a parallelogram.

Explanation:
In the above-given question,
given that,
a quadrilateral that has opposite sides are the same length.
opposite angles are the same size.
but the shape E does not have the opposite sides same length.

Question 6.
Is a quadrilateral but not a parallelogram or trapezoid

Answer:
The shapes B, F, A, and D are rectangle, rhombus, and square.

Explanation:
In the above-given question,
given that,
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
a trapezoid has exactly one pair of sides on lines that never cross.
so the shapes B, F, A, and D are rectangle, rhombus, and square.

Question 7.
Is a square and not a parallelogram

Answer:
The shapes A and D are square.

Explanation:
In the above-given question,
given that,
the square is the shape A and the shape D.
the shapes A and D are square and rhombus.

Question 8.
Is a rhombus and not a rectangle

Answer:
The shape D is a rhombus but not a rectangle.

Explanation:
In the above-given question,
given that,
the shape D is a rhombus.
but the shape D is not a rectangle.
so the shape D is a rhombus.

Question 9.
Is a parallelogram and not a rhombus

Answer:
The shape G is a parallelogram but not a rhombus.

Explanation:
In the above-given question,
given that,
the shape G is a parallelogram.
the shape G is not a rhombus.
the parallelogram has opposite sides that are the same length.
so the shape G is a parallelogram but not a rhombus.

Problem Solving

Question 10.
Cy put blocks 1 and 2 together to make a new shape. How are the blocks he used alike? How are they different?

Answer:
The new shape formed is a trapezoid.

Explanation:
In the above-given question,
given that,
Cy put blocks 1 and 2 together to make a new shape.
shape 1 is a parallelogram.
shape 2 is a trapezoid.
by joining the two shapes we will get the other shape.
so the new shape formed is a trapezoid.

Question 11.
Reasoning Explain which of the shapes at the right you can cover with whole unit squares and not have any gaps or overlaps.

Answer:
The shape rectangle can cover with whole unit squares.

Explanation:
In the above-given question,
given that,
the shape rectangle is filled with squares.
they have given the two shapes.
they are parallelogram and rectangle.
so the shape rectangle can cover with whole unit squares.

Question 12.
Higher Order Thinking Draw a quadrilateral with no sides the same length. Tell why it is not a parallelogram.

Answer:
The quadrilateral with no sides the same length is not a parallelogram is a trapezoid.

Explanation:
In the above-given question,
given that,
quadrilaterals have special names.
a trapezoid has exactly one pair of sides on lines that never cross.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the quadrilateral with no sides the same length is not a parallelogram is a trapezoid.

Question 13.
Sam needs 25 minutes to get ready and 15 minutes to bike to swim practice. Practice starts at 4:00 P.M. What time should Sam start getting ready?

Answer:
Sam starts getting ready at 3:20 P.M.

Explanation:
In the above-given question,
given that,
Sam needs 25 minutes to get ready and 15 minutes to bike to swim practice.
practice starts at 4:00 P.M.
25 + 15 = 40.
so Sam starts getting ready at 3:20 P.M.

Assessment Practice

Question 14.
Look at these polygons.

Part A
Name one attribute that all 4 polygons have.

Answer:
The 4 polygons that have the same attribute is the right angles.

Explanation:
In the above-given question,
given that,
The given polygons are rectangle, trapezoid, parallelogram.
the shape A and B are rectangles.
the shape C is trapezoid.
the shape D is a parallelogram.
so the 4 polygons that have the same attribute are the right angles.

Part B
Name an attribute that both A and D have that B and C do not.

Answer:
The attribute that both A and D have is the opposite sides have the same length.

Explanation:
In the above-given question,
given that,
the shape A is a rectangle.
the shape D is a parallelogram.
the rectangle has four right angles or square corners.
the rectangle has a special parallelogram.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the attribute that both A and D have is the opposite sides have the same length.

Lesson 15.4 Problem Solving

Precision
Solve & Share
Draw shapes that match all of these clues. Use math words and numbers correctly to name each shape and explain how your shapes match the clues. Clue 1: 1 am a polygon with 4 sides.
Clue 2: I am a polygon with 4 right angles.
Clue 3: My area is 12 square units.
I can … be precise when solving math problems.

Answer:
The 1st shape is a rectangle.
the 2nd shape is a square.
the 3rd shape is a rectangle.

Explanation:
In the above-given question,
given that,
the shape that has 4 sides is a rectangle.
the shape that has 4 right angles is the square.
the area is 12 sq units.
area of a rectangle = l x b.
where l = length, and b = breadth.
area = 3 x 4.
area = 12 sq units.
so the shape formed is a rectangle.

Thinking Habits
Be a good thinker! These questions can help you.

• Am I using numbers, units, and symbols appropriately?
• Am I using the correct definitions?
• Am I calculating accurately?
• Is my answer clear?
  

Look Back! Be Precise How did you use math terms or numbers to make your explanation clear?

Essential Question
How Can You Be Precise When Solving Math Problems?

Visual Learning Bridge
What shapes can you draw for this riddle?
I am a polygon with 4 sides.
I have 4 right angles.
My opposite sides are equal in length.

What do I need to do to solve this problem?
I will read the given information and use it to draw shapes that match the description.

Answer:
The shape formed is a rectangle.

Explanation:
In the above-given question,
given that,
I am a polygon with 4 sides.
I have 4 right angles.
My opposite sides are equal in length.
the rectangle has 4 right angles or square corners.
so the shape formed with the given polygon is a rectangle.

How can I be precise in solving this problem?
I can

• correctly use the information given.
• use pictures or objects to identify possible answers.
• decide if my answer is clear and appropriate.

Here’s my thinking…

I know that the shape is a 4-sided polygon with 4 right angles and opposite sides that are equal in length.

I can draw shapes that match all of the clues. Then I can name each shape.

Each of the shapes has 4 sides, 4 right angles, and opposite sides that are equal in length.

Convince Me! Be Precise Draw a shape for this riddle. Explain how it matches the clues.
I am a polygon with 4 sides.
None of my angles are right angles.
None of my sides is the same length.

Answer:
The shape is a trapezoid.

Explanation:
In the above-given question,
given that,
I am a polygon with 4 sides.
None of my angles are right angles.
None of my sides is the same length.
a trapezoid has exactly one pair of sides on lines that never cross.
so the shape formed is a trapezoid.

Guided Practice

Be precise. Carefully Students in Mr. Tesla’s class drew pictures of their favorite consider and use the shapes. Jackie made a polygon with 4 sides. It has 4 right information you are given angles, but not all of the shape’s sides are the same length.

Question 1.
What math words and numbers are important in this problem?

Answer:
The shape formed is a trapezoid.

Explanation:
In the above-given question,
given that,
Jackie made a polygon with 4 sides.
It has 4 right information you are given angles, but not all of the shape’s sides are the same length.
a trapezoid has exactly one pair of sides on lines that never cross.
so the shape formed is a trapezoid.

Question 2.
Draw and name the type of polygon Jackie made.

Answer:
The shape formed is a trapezoid.

Explanation:
In the above-given question,
given that,
Jackie made a polygon with 4 sides.
It has 4 right information you are given angles, but not all of the shape’s sides are the same length.
a trapezoid has exactly one pair of sides on lines that never cross.
so the shape formed is a trapezoid.

Question 3.
How can you check to make sure your answer is clear and correct?

Answer:
By using the formulas we can make sure.

Explanation:
In the above-given question,
given that,
Jackie made a polygon with 4 sides.
It has 4 right information you are given angles, but not all of the shape’s sides are the same length.
a trapezoid has exactly one pair of sides on lines that never cross.
so the shape formed is a trapezoid.

Independent Practice

Be Precise Students in Mrs. Edison’s class designed a mural to show what they have learned about quadrilaterals. Ethan made a shape with opposite sides that are the same length.

Question 4.
What math words and numbers are important in this problem?

Answer:
The shape Ethan formed is rectangle and parallelogram.

Explanation:
In the above-given question,
given that,
Students in Mrs. Edison’s class designed a mural to show what they have learned about quadrilaterals.
Ethan made a shape with opposite sides that are the same length.
a rectangle has 4 right angles or square corners.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the shape Ethan formed is a rectangle and a parallelogram.

Question 5.
Draw a possible polygon that Ethan could have made. Is there more than one type of quadrilateral that would correctly match the description? Explain.

Answer:
Yes, there is more than one type of quadrilateral is rectangle and parallelogram.

Explanation:
In the above-given question,
given that,
Students in Mrs. Edison’s class designed a mural to show what they have learned about quadrilaterals.
Ethan made a shape with opposite sides that are the same length.
a rectangle has 4 right angles or square corners.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the shape Ethan formed is a rectangle and a parallelogram.

Question 6.
How can you check to make sure your answer is clear and correct?

Answer:
By using the formulas we can make sure.

Explanation:
In the above-given question,
given that,
Ethan made a shape with opposite sides that are the same length.
a rectangle has 4 right angles or square corners.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the shape Ethan formed is a rectangle and a parallelogram.

Problem Solving

Performance Task
Crazy Quilts Each student in Ms. Beardon’s art class is designing a panel for a crazy quilt. Students can use different colors, but each panel will be the same shape. The attributes of the panel design are as shown at the right.

• 4 equal sides
• 4 right angles

Draw and name a shape to match this description. Answer Exercises 7-10 to solve the problem.
Question 7.
Make Sense and Persevere What do you know? What are you asked to do?

Answer:
The shape formed is square.

Explanation:
In the above-given question,
given that,
the polygon has 4 equal sides.
the polygon has 4 right angles.
square has 4 right angles and all sides the same length.
so the attributes match the given attributes.
so the shape formed is square.

Question 8.
Be Precise What math terms and numbers can help you solve the problem?

Answer:
Yes, we are using the correct answers.

Explanation:
In the above-given question,
given that,
we are using the correct answers.

Question 9.
Use Appropriate Tools Choose tools to help you solve this problem. Then draw and name a possible panel design.
Answer:

Question 10.
Critique Reasoning Tabby followed Ms. Beardon’s directions and made a quilt panel with the shape shown below. Did she follow directions correctly? Explain.

Answer:
Yes, she follows the directions correctly.

Explanation:
In the above-given question,
given that,
Ms. Beardon’s directions and make a quilt panel.
Ms. Beardon said to draw the rectangle.
so the tabby followed his instructions and draw the rectangle.
so she follows the directions correctly.

Topic 15 Fluency Practice Activity

Follow the path
Shade a path from START to FINISH. Follow the products and quotients that are even numbers. You can only move up, down, right, or left.
I can … multiply and divide within 100.

Topic 15 Vocabulary Review

Word List

• square rhombus
• angle
• parallelogram
• polygon
• quadrilateral
• rectangle
• rhombus
• right angle
• square
• trapezoid

Understand Vocabulary
Circle all the terms that match each description.
Question 1.
A quadrilateral
square
rectangle
trapezoid
polygon

Answer:
A quadrilateral is a polygon.

Explanation:
In the above-given question,
given that,
the terms are square, rectangle, trapezoid, and polygon.
a polygon is a closed shape that has only straight sides.
a quadrilateral is a polygon with four sides and four angles.
so a quadrilateral is a polygon.

Question 2.
A polygon
angle
quadrilateral
rectangle
square

Answer:
A polygon is a quadrilateral.

Explanation:
In the above-given question,
given that,
the terms are polygon, angle, quadrilateral, rectangle, and square.
a polygon is a closed shape that has only straight sides.
a quadrilateral is a polygon with four sides and four angles.
so a polygon is a quadrilateral.

Question 3.
A polygon with 4 right angles
square
trapezoid
rhombus
rectangle

Answer:
A polygon with 4 right angles is a square.

Explanation:
In the above-given question,
given that,
the terms are square, trapezoid, rhombus, and rectangle.
square has 4 right angles and all sides the same length.
area of a square = s x s.
where s = side.
so a polygon with 4 right angles is a square.

Question 4.
A parallelogram
rhombus
triangle
rectangle
trapezoid

Answer:
A parallelogram is a rhombus.

Explanation:
In the above-given question,
given that,
the terms are rhombus, triangle, rectangle, and trapezoid.
rhombus has all sides the same length.
rhombus is a special parallelogram.
so parallelogram is a rhombus.

For each term, draw an example and a nonexample.

Answer:
The example of the right angle is square.
Rectangle has 4 right angles or square corners.
A trapezoid has exactly one pair of sides on lines that never cross.

Explanation:
In the above-given question,
given that,
the terms are right angle, rectangle, trapezoid.
square has 4 right angles and all sides the same length.
the rectangle has 4 right angles or square corners.
a trapezoid has exactly one pair of sides on lines that never cross.

Use Vocabulary in Writing
Question 8.
Use at least 3 terms from the Word List to explain why a square is a rectangle.

Answer:
Yes, the square is a rectangle.

Explanation:
In the above-given question,
given that,
the terms are right angles, equal side lengths.
so the square is also a rectangle.
square has four right angles and all sides the same length.
rectangles have four right angles or square corners.

Topic 15 Reteaching

Set A pages 585-588

You can draw quadrilaterals and describe them by their attributes.

Remember that a polygon with 4 sides is a quadrilateral

In 1-3, draw the shapes named or described below and describe their attributes.
Question 1.
Trapezoid

Answer:
Attributes: exactly one pair of sides on lines that never cross.

Explanation:
In the above-given question,
given that,
a trapezoid has exactly one pair of sides on lines that never cross.
trapezoid is also a quadrilateral.

Question 2.
Rhombus

Answer:
Attributes: all sides the same length.

Explanation:
In the above-given question,
given that,
rhombus has all sides the same length.
a rhombus is a special parallelogram.

Question 3.
A quadrilateral that is NOT a trapezoid, parallelogram, rectangle, rhombus, or square.

Answer:
A quadrilateral is not a trapezoid, a parallelogram, rectangle, rhombus, and square is the triangle.

Explanation:
In the above-given question,
given that,
a shape that has 3 sides is a triangle.
area of the triangle = 2(l + b).
where l = length, and b = breadth.

Set B pages 589-592

How are the shapes in Groups 1 and 2 different? How are they alike?

The shapes in the groups are different because in Group 1, all shapes are convex. In Group 2, all shapes are concave.
The shapes in both groups are alike because they all have straight lines and are closed. Therefore, they all are polygons.

Remember that all of the shapes in these groups have something in common.

In 1 and 2, use the groups below.

Question 1.
How are the shapes in Groups 1 and 2 different?

Answer:
In group 1 the figures are triangles.
in group 2 the figures are hexagons.

Explanation:
In the above-given question,
given that,
in group 1 the shapes are triangles.
in group 2 the shapes are hexagons.
so triangles and hexagons are different.

Question 2.
How are the shapes in Groups 1 and 2 alike?

Answer:
The shapes in groups 1 and 2 are alike when the shapes are divided.

Explanation:
In the above-given question,
given that,
in group 1 the shapes are triangles.
in group 2 the shapes are hexagons.
when the shapes in group 2 are divided into parts.
they form triangles.
so the shapes in group 1 and group 2 are alike.

Set C pages 593-596

All of the shapes below have 4 sides, so they are quadrilaterals. Some quadrilaterals can be classified into multiple groups.

Parallelograms have 2 pairs of sides that have the same length. Shapes A, B, C, and D are parallelograms.

Rhombuses have 4 equal-length sides. Shapes A and C are rhombuses.

Rectangles have 2 pairs of sides that have the same length and 4 right angles. Shapes A, B, and D are rectangles.

Squares have 4 equal-length sides and 4 right angles. Shape A is a square.

Trapezoids have 1 pair of sides on lines that do not cross. Shape E is a trapezoid.

Remember that quadrilaterals with different names can have some of the same attributes.

In 1-4, list all the polygons that fit the given attributes.

Question 1.
Has at least 2 right angles but is not a rectangle

Answer:
The shape F is a square.

Explanation:
In the above-given question,
given that,
they have given the 7 polygons.
the polygons are rectangle, rhombus, square, and trapezoid.
square has 4 right angles.
so the shape F has 2 right angles.

Question 2.
Has pairs of sides the same length but is not a rectangle

Answer:
The shape D has the pairs of sides the same length but is not a rectangle.

Explanation:
In the above-given question,
given that,
they have given the 7 polygons.
the polygons are rectangle, rhombus, square, and trapezoid.
Rhombus has all sides the same length.
so the shape D has the pairs of sides the same length but is not a rectangle.

Question 3.
Is a quadrilateral with no right angles

Answer:
The shapes D and B are quadrilaterals with no right angles.

Explanation:
In the above-given question,
given that,
they have given the 7 polygons.
the polygons are rectangle, rhombus, square, and trapezoid
the shape D is a parallelogram.
the shape B is a rhombus.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.

Question 4.
Has 4 sides of the same length but is not a square

Answer:
The shape B has 4 sides of the same length but it not a square.

Explanation:
In the above-given question,
given that,
they have given the 7 polygons.
the polygons are rectangle, rhombus, square, and trapezoid.
The shape B is the rhombus.
rhombus has all sides the same length.
so the shape B has 4 sides of the same length.

Set D pages 597-600

Think about these questions to help you attend to precision.
Thinking Habits

• Am I using numbers, units, and symbols appropriately?
• Am I using the correct definitions?
• Am I calculating accurately?
• Is my answer clear?
  

Remember to consider all parts of the question.

Anton drew a quadrilateral with 4 sides the same length and 4 right angles.
Question 1.
What quadrilateral did he draw?

Answer:
Anton drew a quadrilateral that is a square.

Explanation:
In the above-given question,
given that,
Anton drew a quadrilateral with 4 sides of the same length and 4 right angles.
square has four right angles and all sides the same length.
so Anton draws the shape that is a square.

Question 2.
Is there any other shape that he could have drawn? Explain.

Answer:
No, he cannot draw.

Explanation:
In the above-given question,
given that,
Anton drew a quadrilateral with 4 sides of the same length and 4 right angles.
the rectangle has four right angles or square corners.
square has the four right and all sides the same length.

Topic 15 Assessment Practice

Question 1.
What other category does a parallelogram fall under?
A. Quadrilateral; because it has 4 right angles
B. Square; because it has 4 sides
C. Quadrilateral; because it has 4 sides
D. Rhombus; because all 4 sides are the same length

Answer:
Option D is correct.

Explanation:
In the above-given question,
given that,
a rhombus has all sides the same length.
because the rhombus has all 4 sides the same length.
rhombus comes under parallelogram.
so option D is correct.

Question 2.
Use the words in the box below. Write the names for the shapes in the correct columns.

Answer:
Quadrilateral comes under trapezoid.
rhombus, square, and rectangle come under parallelogram.

Explanation:
In the above-given question,
given that,
the shapes are rectangle, rhombus, square, and trapezoid.
the rectangle has four right angles or square corners.
rhombus has all sides the same length.
square has four right angles and all sides the same length.
so quadrilateral comes under trapezoid.

Question 3.
Name and draw a picture of a concave polygon with 4 sides.

Answer:
The trapezoid comes under a concave polygon.

Explanation:
In the above-given question,
given that,
concave polygon means that the sides come inside.
that means some of the sides come inside and also outside.
trapezoid comes under a concave polygon.

Question 4.
What are the possible shapes a parallelogram with 4 right angles could be?

Answer:
The possible shapes that come under a parallelogram with 4 right angles are a rectangle and a square.

Explanation:
In the above-given question,
given that,
the possible shapes a parallelogram with 4 right angles.
the rectangle has four right angles or square corners.
square has four right angles and all sides the same length.

Question 5.
The shapes are sorted into two groups, circled and not circled. How are the shapes in the two groups different?

Answer:
The circled shapes come under a parallelogram.
the not circled shapes come under quadrilateral.

Explanation:
In the above-given question,
given that,
the shapes are sorted into two groups.
the groups are circled and not circled.
the circled groups come under parallelogram.
the not circled shapes come under quadrilateral.

Question 6.
Select all true statements.
☐ A trapezoid is a parallelogram.
☐ A parallelogram is a quadrilateral.
☐ A square is a rhombus.
☐ A triangle is a quadrilateral.
☐ A square is a rectangle.

Answer:
A parallelogram is a quadrilateral.
A square is a rhombus.

Explanation:
In the above-given question,
given that,
the true statements are:
a parallelogram is a quadrilateral.
a square is a rhombus.
a parallelogram has opposite sides are the same length.
opposite angles are the same size.
rhombus has all sides the same length.
square has 4 right angles and all sides the same length.

Question 7.
What two quadrilaterals did Kim use to make the rug design? What do the shapes have in common?

Answer:
The two quadrilaterals are parallelogram and trapezoid.
the two shapes that have in common side lengths.

Explanation:
In the above-given question,
given that,
Kim uses to make the rug design.
the two quadrilaterals are parallelogram and trapezoid.
the parallelogram has opposite sides are the same length, opposite angles are the same size.
a trapezoid has exactly one pair of sides on lines that never cross.

Question 8.
Look at each group.

A. How are the two groups alike?

Answer:
The two groups are alike when the opposite sides are equal.

Explanation:
In the above-given question,
given that,
In group 1 the shapes are rhombus and parallelogram.
the parallelogram has opposite sides that are the same length.
in group 2 the shapes are square and rectangle.
square has four right angles and all sides the same length.
a square is a special parallelogram.
so the two groups are alike.

B. How are the two groups different?

Answer:
The two groups are different because rectangle and square have right angles.

Explanation:
In the above-given question,
given that,
In group 1 the shapes are rhombus and parallelogram.
the parallelogram has opposite sides that are the same length.
in group 2 the shapes are square and rectangle.
square has four right angles and all sides the same length.
rectangle and square have 4 right angles.
so they are different.

Question 9.
Which statement must be true about a rectangle?
A. It is a parallelogram.
B. It is a square.
C. It is a trapezoid.
D. It is a rhombus.

Answer:
Option A is correct.

Explanation:
In the above-given question,
given that,
the rectangle is a parallelogram.
the rectangle has four right angles or square corners.
so option A is correct.

Question 10.
Is a square always a rhombus? Explain.

Answer:
No, a square does not form a rhombus.

Explanation:
In the above-given question,
given that,
square has all 4 sides the same length and has 4 right angles.
rhombus has all 4 sides equal in length.
rhombus does not have the right angles.
so square does not form a rhombus.

Question 11.
Name and draw a quadrilateral that is NOT a rectangle or rhombus. Is there another shape you could have drawn? Explain.

Answer:
The other shape is a square.

Explanation:
In the above-given question,
given that,
the square has all four sides equal length.
all four sides have right angles.
so the quadrilateral that is not a rectangle or rhombus is a square.

Topic 15 Performance Task

Pet Tags Amelia and Bryce work at a pet store that sells pet identification tags in many shapes. The Pet Tags diagram shows the different shapes available.

Use the Pet Tags art to answer Questions 1-4.

Question 1.
A customer asks Amelia if the store has any pet tags that are concave. How should Amelia respond?

Answer:
The shape A is concave.

Explanation:
In the above-given question,
given that,
A customer asks Amelia if the store has any pet tags that are concave.
the concave shape has all the sides and one side come inside.
so the shape A is concave.

Question 2.
Another customer asks Bryce which pet tags have 2 pairs of equal-length sides and are quadrilaterals. Which tags have these attributes? Include the common name of each shape.

Answer:
The shapes B and D have 2 pairs of equal-length sides are parallelogram.

Explanation:
In the above-given question,
given that,
Another customer asks Bryce which pet tags have 2 pairs of equal length sides are quadrilaterals.
the shape B is a parallelogram.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the rectangle and parallelogram have 2 pairs of equal-length sides are parallelogram.

Question 3.
The store owner wants to mark for sale any pet tags that are not rectangles. Which tags should she mark for sale, and what shapes are they?

Answer:
The shapes are A, C, E, F, and H are not rectangles.

Explanation:
In the above-given question,
given that,
the store owner wants to mark for sale and any pet tags are not rectangles.
the shape A is a concave polygon.
the shape C is a pentagon.
the shape E is a hexagon.
the shape F is a triangle.
the shape H is a trapezoid.

Question 4.
The owner asks Bryce to group the tags to show which ones have at least 1 pair of equal-length sides. Complete the table with the pet tag labels.

Answer:
The shapes B and G have at least 1 pair of equal-length sides.

Explanation:
In the above-given question,
given that,
the shapes Rhombus, triangle, and square have equal side lengths.
the shapes trapezoid, parallelogram does not have equal side lengths.
the shape B is a parallelogram.
the shape G is a square.
so the shapes B and G have at least 1 pair of equal-length sides.

Question 5.
Use the Pet Tags diagram and the Tag Sort table to answer the questions in Part A and Part B.

Amelia sorts some of the pet tags into two different groups.

Part A
How are the groups different?

Answer:
The groups are different according to their shapes.

Explanation:
In the above-given question,
given that,
in group A the shapes are trapezoid, rectangle, rhombus, and square.
they have the sidelengths and right angles.
in group B the shapes are pentagon, hexagon, and trapezoids.
they are concave polygons.
so the groups are different according to their shapes.

Part B
How are the groups alike?

Answer:
The two groups are alike when they have the same angles.

Explanation:
In the above-given question,
given that,
in group A the shapes are trapezoid, rectangle, rhombus, and square.
they have the sidelengths and right angles.
in group B the shapes are pentagon, hexagon, and trapezoids.
they are concave polygons.
so the groups are alike when they have the same angles.

Use the Pet Tags diagram to answer Questions 6 and 7.
Question 6.
A customer says she wants to buy a pet tag that is a rhombus and a rectangle. What tag does she want? Explain.

Answer:
The tags B and D are rhombus and a rectangle.

Explanation:
In the above-given question,
given that,
A customer says she wants to buy a pet tag that is a rhombus and a rectangle.
the shape B is a rhombus.
the shape D is a rectangle.
rhombus has all sides the same length.
the rectangle has the opposite sides the same length and four right angles.
so the tags B and D are the rhombus and a rectangle.

Question 7.
Design a new pet tag that has 2 pairs of sides the same length, but that is not a rectangle or a rhombus. Explain the shape you drew.

Answer:
I draw the shape that is a square.

Explanation:
In the above-given question,
given that,
design a new pet tag that has 2 pairs of sides the same length, but is not a rectangle.
the shape is a square.
square has all the sides the same length and all four angles are right angles.
so the pet tag is G.