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: