FAMILY MATH Represent Data to Solve Problems

Your student begins the year by collecting and representing data in tables and graphs. These activities show that math is part of the world around them. Your student explores how the same data can be represented in different graphs, such as a picture graph and a bar graph, and then uses the information in the graphs to solve problems.

This table shows the number of students who voted for each subject.

In this picture graph, the categories are Reading, Writing, Math, and Science. The key shows that each check mark stands for 1 vote.

In a bar graph, the value of each category is represented by rectangular bars. The scale on this bar graph counts by 1. Each blue box represents 1 birthday.

Invite your student on a walk around your neighborhood or a park. Have them count or collect three or four types of objects they see, such as leaves, rocks, and sticks. Help your student make a table and use it to record the number of each object they saw. Consider asking questions about the data they’ve collected.

• “How many objects did you find in all?”

• “Which type of object did you find the most of?”

• “Which type of object did you find the least of?”

• “How many more leaves did you find than rocks?”

• “How many fewer sticks did you find than leaves?”

Encourage your student to collect data about something around their home or in their daily life (such as the number of different-colored cars that go by in 10 minutes or the number of plates, bowls, and cups in the kitchen). Use stickers or sticky notes to make a picture graph that includes a key. Then use the data to make a bar graph with a title and a scale.

1. Make a picture graph. Vegetables We Like

A table is a chart that shows information. Pieces of information are called data.

Key: Each stands for vote.

First, I give the graph a title. I can use the title from the table, “Vegetables We Like.”

Next, I write the categories at the bottom of the graph. I use the same categories as the table: Broccoli, Carrots, Celery, and Lettuce.

I draw 1 check mark for each vote.

I need to make a key to show the value of the unit in my graph. My key is “Each ✓ stands for 1 vote.”

2. Which vegetable has the fewest votes?

3. Which vegetable has the most votes?

I can use the data in the graph to answer the questions.

I know that 1 check mark stands for 1 vote.

I see that broccoli has the fewest check marks. So broccoli has the fewest votes.

Carrots has the most check marks. So carrots has the most votes.

Key: Each stands for vote.

The grasshopper is 3 centimeters long.

The bird is 13 centimeters long.

How much longer is the bird than the grasshopper?

I read the problem. I read again. I can use a 10 -stick and centimeter cubes to compare the lengths.

I see 3 centimeter cubes show the length of the grasshopper.

I see one 10 -stick and 3 centimeter cubes show the length of the bird.

I can draw a picture to match the cubes. I can draw 3 centimeter cubes to match the length of the grasshopper and a 10-stick and 3 centimeter cubes to match the length of the bird. I can see that the length of the bird is 10 centimeters longer than the grasshopper.

Sample:

Write 3 + 10 = 13

The bird is 10 centimeters longer than the grasshopper.

Key: Each stands for vote.

2. Which fruit has the fewest votes?

3. Which fruit has the most votes?

4. Read

The bee is 4 centimeters long.

The frog is 14 centimeters long.

How much longer is the frog than the bee ?

The frog is centimeters longer than the bee .

I give the bar graph a title. I use the title in the table, “Favorite Season.”

There are four categories: Spring, Summer, Fall, and Winter. I write these on the bar graph.

The scale is a number line that shows the value of each unit. Each box stands for 1 vote, so I fill in the scale along the bottom of the graph from 0 to 11 .

Spring has 3 votes. I color in 3 boxes on the graph. I color in 1 box for each vote for the rest of the seasons.

2. Which season got the most votes?

3. Which season got the fewest votes?

Summer

Winter

Summer has the longest bar.

Summer got the most votes.

Winter has the shortest bar.

Winter got the fewest votes.

2. Which snack has the most votes?

3. Which snack has the fewest votes?

Flip Flops

Dress Shoes

Boots

Tennis Shoes

1. How many votes are there in all? 18

Write a number sentence.

I count the votes for each category:

8 students voted for Flip Flops

1 student voted for Dress Shoes.

3 students voted for Boots.

6 students voted for Tennis Shoes.

2. Add 3 more votes for Flip Flops.

How many votes for Flip Flops are there now? 11

What is the new vote total? 21

The graph shows a total of 18 votes.

I add 3 more votes to the total.

18 + 3 = 21

3. Color the faces of the shape.

Rectangular Prism

The graph shows that 8 students like Flip Flops.

I add 3 more votes for Flip Flops.

8 + 3 = 11

A face is a flat surface.

A rectangular prism has six faces. The faces are squares and rectangles. I color the square and the rectangle. square rectangle

1. How many votes are there in all?

Write a number sentence.

2. Add 2 more votes for the ball .

How many votes are for the ball now?

How many votes are there in all now?

Animals at the Zoo

1. How many more frogs than lizards are there at the zoo? 5

I can match up the colored boxes, 1 frog to 1 lizard.

Then I count the extra boxes. There are 5 more frogs than lizards at the zoo.

2. How many fewer alligators than snakes are there at the zoo? 6

I can match up the colored boxes, 1 alligator to 1 snake.

Then I count the empty boxes. There are 6 fewer alligators than snakes at the zoo.

Strawberries

Cherries

Blueberries

1. How many more blueberries than cherries are there ?

2. How many more strawberries than pears are there ?

3. How many fewer pears than cherries are there ?