# 2.1 Adding, Subtracting, and Working with Data

## Unit Goals

• Students represent and solve story problems within 20 through the context of picture and bar graphs that represent categorical data. Students build toward fluency with addition and subtraction.

### Section A Goals

• Build toward fluency with adding within 100.
• Build toward fluency with subtracting within 20.

### Section B Goals

• Interpret picture and bar graphs.
• Represent data using picture and bar graphs.
• Solve one- and two-step problems using addition and subtraction within 20.

### Section C Goals

• Make sense of and interpret tape diagrams.
• Represent and solve Compare problems with unknowns in all positions within 100.
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### Problem 1

#### Pre-unit

Practicing Standards:  1.MD.C.4

The picture shows how Jada sorted the shapes on her table.

Use the picture to answer the questions:

1. How many squares were on the table?_______
2. How many triangles were on the table?_______
3. Which shape has the smallest number?_______

### Solution

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### Problem 2

#### Pre-unit

Practicing Standards:  1.MD.C.4

The table shows the favorite magical powers of some students.

• How many more students prefer being invisible to flying?
• How many fewer students prefer flying to reading minds?

### Solution

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### Problem 3

#### Pre-unit

Practicing Standards:  1.MD.C.4

Here are some shapes:

Fill out the chart showing the shapes.

### Solution

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### Problem 4

Find the value of each expression.

1. $$9 - 2$$
2. $$5 + 3$$
3. $$2 + 8$$
4. $$7 - 4$$
5. $$10 - 3$$
6. $$1 + 6$$

### Solution

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### Problem 5

Jada is playing “What’s Behind my Back?” with Han. Han has 10 cubes and shows Jada these connecting cubes.

1. How many connecting cubes are behind Han’s back?
2. What’s an addition equation that you can write that matches the game?
3. What’s a subtraction equation that you can write that matches the game?

### Solution

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### Problem 6

Find the number that makes each equation true. Show your thinking using drawings, numbers, or words.

1. $$20 - 10 = \underline{\hspace{0.9cm}}$$
2. $$17 + \underline{\hspace{0.9cm}} = 20$$
3. $$20 = 5 + \underline{\hspace{0.9cm}}$$
4. $$7 = 20 - \underline{\hspace{0.9cm}}$$

### Solution

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### Problem 7

Here are the numbers on seven cards:

• 1
• 2
• 3
• 5
• 6
• 7
• 9
1. Choose three of the numbers to add to get as close as you can to 20.
2. Write an equation to show your choice.

### Solution

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### Problem 8

Find the value of each sum. Show your thinking using drawings, words, or numbers.

1. $$31 + 15$$
2. $$17 + 8$$
3. $$26 + 17$$

### Solution

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### Problem 9

#### Exploration

Choose 3 of these 7 cards and get as close to 20 as possible.

• 1
• 3
• 4
• 5
• 7
• 8
• 9
1. Can you make 20?
2. Can you make 20 in more than 1 way?
3. Can you make 20 using the 1?

### Solution

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### Problem 10

#### Exploration

Clare has a set of cards numbered 1, 2, 3, 4, 5, 6, 7, 8, 9.
She picks out seven of the cards. Clare was NOT able to make 20 with 3 of her 7 cards. Which cards do you think she picked out if she was NOT able to make 20?

### Solution

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### Problem 1

Here is how Diego recorded his classmates’ favorite colors:

• yellow
• red
• red
• blue
• red
• blue
• purple
• yellow
• red
• red
• blue
• purple
• red
• blue
• blue
• yellow
• red
• red

Create a representation to show Diego’s data.

### Solution

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### Problem 2

The picture graph shows the favorite colors of some students.

Select 3 statements that are true about the data recorded in the graph.

A: More students like green than any of the other colors.
B: 5 students chose blue as their favorite color.
C: 2 more students chose blue than orange.
D: 22 students voted in all.
E: 3 fewer students chose blue than green.

### Solution

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### Problem 3

The picture graph shows the pattern blocks that were used to create a pattern.Select 3 questions that you can answer with the graph.

A: Are there more trapezoids than squares?
B: Are all of the triangles together in the pattern?
C: How many hexagons are there?
D: How many more triangles are there than rhombuses?
E: How many squares and trapezoids are there in the shape altogether?

### Solution

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### Problem 4

Use the bar graph to answer the questions about the trees in the park.

1. How many trees are there altogether?

2. How many more maple trees are there than willow trees?
3. Which kind of tree has the smallest number?

### Solution

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### Problem 5

The table shows the fish in a tank.

name number
goldfish 3
guppy 9
angel fish 4
molly 5

Make a bar graph showing the data from the table.

### Solution

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### Problem 6

The bar graph shows the favorite seasons of some students.

1. Write two questions that you can answer using the graph.

2. Answer your questions.

### Solution

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### Problem 7

#### Exploration

The data display about some shapes in a bag is not finished. It shows the kinds of shapes, but not how many of each are in the bag.

triangles squares circles
$$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$

Create a set of data about how many shapes are in the bag that makes all of these statements true:

1. There are more than 15 shapes altogether, but less than 25 shapes.
2. There are 6 more squares than circles.
3. There are 7 fewer circles than triangles.

### Solution

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### Problem 8

#### Exploration

1. Gather data at school or at home and make a graph showing the data.
2. Ask a math question that can be answered with the data.
3. Trade with a partner and answer each other’s questions.

### Solution

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### Problem 9

#### Exploration

Han made this bar graph showing the number of songs Elena and Noah listened to on Saturday.

1. How could Han improve the diagram?
2. If Noah listened to 7 songs, how many songs do you think Elena listened to? Explain your reasoning.

### Solution

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### Problem 1

The graph shows the number of friends these students had at their birthday parties.

1. How many fewer friends were at Elena’s party than at Jada’s party?
2. Write an equation to show how you found the difference.

### Solution

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### Problem 2

The bar graph shows the number of connecting cubes of different colors in a bag.

1. Use the bar graph to complete the tape diagram.
2. How many fewer green connecting cubes than brown connecting cubes are in the bag? Show or explain your reasoning.

### Solution

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### Problem 3

There are 25 crickets chirping in the front yard.

There are 16 fewer crickets chirping in the front yard than in the back yard.

1. Label the rectangles to match the story. Explain your reasoning.

2. Write an equation to represent the story problem.

### Solution

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### Problem 4

There are 35 cherries in the bowl. There are 17 more cherries in the bowl than on the plate. How many cherries are on the plate? Show your thinking using drawings, numbers, or words.

### Solution

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### Problem 5

There were 26 students in the cafeteria. There were 18 more students on the playground than in the cafeteria. How many students were on the playground? Show your thinking using drawings, numbers, or words.

### Solution

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### Problem 6

#### Exploration

Write a story to match the diagram. Explain why the story matches the diagram.

### Solution

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### Problem 7

#### Exploration

Write a Compare story problem.

Solve your problem. Include an equation and a tape diagram.

### Solution

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