## Envision Math 6th Grade Textbook Answer Key Topic 2.7 Using Expressions to Describe Patterns

Using Expressions to Describe Patterns

How can you write expressions to describe patterns?
Delvin saves a part of everything he earns. The table at the right shows Delvin’s savings pattern.
The INPUT column shows the money he has earned.
The OUTPUT column shows the money he has saved.

Question.
Write an expression to describe the pattern.

Guided Practice

Do you know HOW?
Use the input/output table for 1 and 2.

Question 1.
If the input number is 8, what is the output number?
11
Explanation:

Question 2.
Write an algebraic expression that describes the output pattern.
x + 3
Explanation:

Do you UNDERSTAND?
Question 3.
Suppose that Delvin earned $36 mowing lawns. What input and output entries would you add to his table? Answer: IN:$36; OUT: $18 Explanation: Question 4. Reasonableness Is it reasonable for an output to be greater than the input in the table above? Explain. Answer: See margin. Explanation: Question 5. What is the algebraic expression that describes the output pattern for the table above if the input is x? Answer: $$\frac{1}{2}$$x. Explanation: Independent Practice Use this table for 6 and 7. Question 6. What is the cost of 4 lb, 5 lb, and 10 lb of apples? Answer: Question 7. Write an algebraic expression that describes the output pattern if the input is a variable a. Answer: 2a Explanation: Use this table for 8 and 9. Question 8. Copy and complete the table. Answer: Question 9. Write an algebraic expression that describes the relationship between the input and output values. Answer: x ÷ 3 Explanation: An input/output table is a table of related values. Identify the pattern. What is the relationship between the values? $$\frac{1}{2}$$ (84) = 42 → 42 is half of 84 $$\frac{1}{2}$$ (66) = 33 → 33 is half of 66 $$\frac{1}{2}$$ (50) = 25 → 25 is half of 50. The pattern is: $$\frac{1}{2}$$ (INPUT) = OUTPUT Let x= INPUT. So, the pattern is $$\frac{1}{2}$$ x. Use the pattern to find the missing values. $$\frac{1}{2}$$ (22) = 11 $$\frac{1}{2}$$ (30) = 15 Problem Solving Use the input/output table at right for 10 and 11. Question 10. Hazem keeps $$\frac{1}{3}$$ of the tips he earns. Also, he gets$1 each night to reimburse his parking fee. This information is shown in the input/output table. Write an algebraic expression that describes the output pattern if the input is the variable k.
(k ÷ 3) + 1 or $$\frac{1}{3}$$ k + 1
Explanation:

Question 11.
How much money would Hazem keep in a night if he takes in $36 in tips? Answer:$13
Explanation:

Use the input/output table at right for 12 and 13.

Question 12.
Ms. Windsor’s classroom has a tile floor. The students are making stars to put in the center of 4-tile groups. This input/ output chart shows the pattern. Write an algebraic expression that describes the output pattern if the input is the variable t.
t ÷ 4
Explanation:

Question 13.
Writing to Explain There are 30 rows with 24 tiles in each row on a floor. Explain how to find the number of stars needed to complete the pattern for the floor.
See margin.
Explanation:

Use the table at right for 14.

Question 14.
Think About the Process Which algebraic expression shows the cost of a chosen number of books b?
A. b + $2.50 B.$2.50b
C. $b –$2.50
D. b + $2.50 Answer: B.$2.50b

## Envision Math 1st Grade Textbook Answer Key Topic 2.3 Ordering Numbers to 12 with a Number Line

Ordering Numbers to 12 with a Number Line

Home Connection Your child used a number line to order numbers to 12.
Home Activity Use only the first 12 pages of a book or magazine. Ask questions such as: What page comes after page 5? What page comes before page 3? What page comes between pages 7 and 9?

Question 1.

Question 2.

Question 3.

Question 4.

Guided Practice

Use the number line below.

Write the number that is before.
Question 1.

Question 2.
____ 9    10

Write the number that is after.
Question 3.
5     6 ____

Question 4.
10    11 ____

Write the number that is between.
Question 5.
8 ____ 10

Question 6.
9 ____ 11

Do you understand?
Question.
Do you look left or right to fi nd the number before 2?

Independent Practice

Use the number line below.
Write the missing numbers.
Question 7.
4    5    6 ____ 8    9 ____

Question 8.
2    3 ____ 5 ____ 7   8

Question 9.
1 ____ 3 ____ 5   6 ____

Algebra Use the clues. Write the number.
Question 10.
My secret number is between 4 and 9. It is after 7.

Problem Solving

Solve the problems below.

Question 11.
Kathy reads a book. She reads page 10. Then she skips a page. She reads page 12.
What page did Kathy skip?
___________

Question 12.
Yuko gets a number for a race.
His number is between 7 and 9.
What is Yuko’s number?
___________

Question 13.
Anita has some crayons. The number she has is between 5 and 8.
Which could be the number of crayons Anita has?

Question 14.
Journal Describe the number that comes after 8. Use pictures or words. Write the number.

## Envision Math 1st Grade Textbook Answer Key Topic 2.2 Ordering Three Numbers

Ordering Three Numbers

Home Connection Your child made cube towers and compared three numbers to put them in order from least to greatest.
Home Activity Have your child make a set of number cards from 1 through 12 on slips of paper. Mix up the cards. Have your child select three cards without looking and put them in order from least to greatest and greatest to least

Question 1.

Question 2.

Question 3.

Guided Practice

Count the cubes.
Write the numbers in order from least to greatest.
Question 1.

Question 2.

Do you understand?
Question.
How can you tell which number is least?

Independent Practice

Use cubes.
Write the numbers in order from least to greatest.
Question 3.

Question 4.

Question 5.

Question 6.

Reasoning Use cubes. Write who has the least.
Question 7.
Pat has 2 fewer cubes than Rosa. Jim has 4 cubes. Rosa has 1 more cube than Jim. ________ has the least

Problem Solving

Solve the problems below.
Question 8.
Jen draws 4 trees. Steve draws 8 trees. Luca draws 3 trees. Who draws the least number of trees? Draw a picture to solve.
______________

Question 9.
Stacy paints 6 pots. Yin paints 2 pots. Mario paints 4 pots. Which shows the number of pots from least to greatest?

Question 10.
Journal Choose three numbers less than 10. Put your numbers in order from greatest to least.

## Envision Math 1st Grade Textbook Answer Key Topic 2.1 Comparing Two Numbers

Review What You Know

Question 1.
Circle the group that has more.

Question 2.
Write the number that tells how many.

Question 3.
Count the cubes. Write the number.

Home-School Connection

Dear Family,
Today my class started Topic 2, Comparing and Ordering Numbers. I will learn ways to compare numbers and order them from least to greatest. Here are some of the new math words I will be learning and some things we can do to help me with my math.
Love, __________________

Reading math stories reinforces concepts. Look for this title in your local library:
Just Enough Carrots by Stuart J. Murphy (HarperTrophy, 1997)

Home Activity

Have your child compare two groups of items, such as forks and spoons, crayons and pencils, or shoes and socks. Have him or her determine which group has more items.

My New Math Words

more
the group with a greater number of objects

The group with 5 cars has more cars.

less than
number with a smaller value or quantity.

2 is less than 4.

greatest
a number or a group with the largest value.

5 is the greatest number.

Comparing Two Numbers

Home Connection Your child compared two groups of cubes to determine which group had more or which group had fewer.
Home Activity Put 12 small objects in each of 2 containers. Have your child take some objects from each container. Ask him or her to determine which group has more and then which group has fewer.

Question 1.

Question 2.

Question 3.

Question 4.

Guided Practice

Write each number.
Circle is less than or is greater than.
Question 1.

Question 2.

Question 3.

Question 4.

Do you understand?
Question.
How can you tell if a number is greater than or less than another number?

Independent Practice

Write each number.
Circle is less than or is greater than.
Question 5.

Question 6.

Question 7.

Question 8.

Algebra Use the clues. Write the number.
Question 9.
My number is greater than 9.
It is less than 11.
My number is ________ .

Problem Solving

Solve the problems below.
Question 10.
Jen has 10 grapes. Luca has 6 grapes. Who has more grapes? Draw a picture to show the story.

Question 11.
Jan read more than 7 books.
She read fewer than 10 books.
How many books did Jan read?

Question 12.
Journal Draw a picture of bugs.

Reteaching

Set A

You can draw counters to show the number.

Draw counters to show the number.
Question 1.

Question 2.

Set B

You can write the number to tell how many.

Write the number that tells how many.
Question 3.

Question 4.

Set C

You can use a ten-frame and counters to show and identify numbers.

There are 10 counters in the ten-frame. There is 1 counter outside. 10 and 1 more is 11.

Write the number that tells how many.
Question 5.

Question 6.

Set D

This side has 5 dots. This side has 1 dot.
There are 6 dots.

Write the number that tells how many.
Question 7.

Question 8.

Test

Oral Directions Say: Mark the correct answer. 1. Rover likes bones. How many bones does he have? 2. Bonnie drew 5 flowers. Then she drew 3 more. How many flowers did Bonnie draw in all? 3–4. Which number does the picture show?

Question 1.

Question 2.

Question 3.

Question 4.

Oral Directions Say: Mark the correct answer. 5–6. Which number does the picture show? 7. Chuck made 4 paper airplanes. Then he made 4 more. Which model shows how many airplanes Chuck made altogether? 8. Mel’s cat had 5 kittens. Which model shows the number of kittens

Question 5.

Question 6.

Question 7.

Question 8.

## Envision Math 1st Grade Textbook Answer Key Topic 1.6 Problem Solving

Problem Solving

Use Objects

Home Connection Your child used counters to model numbers and to solve problems.
Home Activity Tell your child the following story problem: Ken has 5 toys. Show the toys using objects
Question 1.
___________

Question 2.
___________

Question 3.
____________

Question 4.
____________

Guided Practice

Use counters to model the problem. Then draw a picture to show your counters.
Question 1.
Bo has 5 marbles. Show the marbles Bo has.

Question 2.

Do you understand?
Question.
How can you show a story problem with counters?

Independent Practice

Use counters to model the problem. Then draw a picture to show your counters.
Question 3.
Quan makes 9 paper hats. Show the paper hats Quan makes.

Question 4.
Ami sees 6 birds. Show the birds Ami sees.

Question 5.
Ann has 12 books. Show the books Ann has.

Problem Solving

Solve the problems below.
Question 6.
Jake puts 7 pencils on the table. Show the pencils Jake puts on the table. Use counters to model the problem. Then draw a picture to show your counters.

Question 7.
There are 4 frogs in the pond. Which shows the number of frogs?

Question 8.
Journal Write a story with the number 5. Ask a friend to draw a picture to show the problem.
________________________
________________________

## Envision Math 1st Grade Textbook Answer Key Topic 1.5 Spatial Patterns for Numbers to 10

Spatial Patterns for Numbers to 10

Home Connection Your child identified the number of dots in a pattern of two parts without counting.
Home Activity Draw a two-part pattern and ask your child to tell you the number of dots you drew.
Question 1.

Question 2.

Guided Practice

Write the number that tells how many.
Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Do you understand?
Question.
How can you show 6 as a pattern?

Independent Practice

Write the number that tells how many.
Question 7.

Question 8.

Question 9.

Question 10.

Algebra Draw the missing dots for 7.
Question 11.

Problem Solving

Solve the problems below.
Question 12.
First Mike had 3 puzzles. Now he has 5 puzzles. How many new puzzles did Mike get? Draw more dots. Write the number.

____ new puzzles

Question 13.
Jana had 2 pens. Her dad gave her 2 more pens. Which pattern shows how many pens Jana has now?

Question 14.
Journal Pick three numbers. Draw their patterns.

## Envision Math 1st Grade Textbook Answer Key Topic 1.4 Spatial Patterns for Numbers to 9

Spatial Patterns for Numbers to 9

Home Connection Your child recognized the number of dots in patterned arrangements without counting.
Home Activity Play a game using a dot cube or dominoes to help your child recognize the numbers 3 through 9 without counting.
Question 1.

Question 2.

Question 3.

Question 4.

Guided Practice

Write the number of dots.
Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Do you understand?
Question.
How is the 6 pattern like the 8 pattern? How are they different?

Independent Practice

Write the number of dots.
Question 7.

Question 8.

Question 9.

Question 10.

Question 11.

Question 12.

Algebra

Question 13.
Draw the missing dot pattern.

Problem Solving

Solve the problems below.
Question 14.
Jake uses fi ve counters. He makes a dot pattern. What pattern does Jake make? Draw a dot pattern to show your answer.

Question 15.
Melina draws six dots. She makes a pattern. What does the pattern look like?

Question 16.
Journal What is your age? Draw a dot pattern to show the number.

## Envision Math 1st Grade Textbook Answer Key Topic 1.3 10, 11, and 12

10, 11, and 12

Home Connection Your child used a ten-frame and counters to discover that 11 is 1 more than 10 and 12 is 2 more than 10.
Home Activity Use small objects such as pennies or buttons. Have your child arrange the objects so they are in a group of 10 and 1 or 2 more.

Question 1.

Question 2.

Question 3.

Guided Practice

Write the number that tells how many
Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Do you understand?
Question.
How can you use a ten-frame and counters to show 12?

Independent Practice

Write the number that tells how many.
Question 7.

Question 8.

Question 9.

Question 10.

Question 11.

Question 12.

Number Sense
Question 13.
Draw more counters to make 11.

Problem Solving

Solve the problems below.
Question 14.
Gena cooked 10 eggs. Then she cooked 1 more. How many eggs did Gena cook? Draw the counters. Write the number.