2nd Grade · 3rd Grade · 2.MD.D.10 · 3.MD.B.3

Bar graphs in 2nd and 3rd grade math

Bar graphs in school math show how many there are of each thing, with one bar for each group. In 2nd grade, your child draws bar graphs and picture graphs where each square or picture stands for 1. In 3rd grade, each square or picture can stand for more than 1, such as 5 or 10. The questions ask how many more or how many fewer, in one or two steps.

What the standards say

The official Common Core wording, quoted exactly. The plain version follows.

2.MD.D.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.

What it means, in plain words

2nd grade: one square for each 2.MD.D.10

A bar graph shows data with bars. Data is a set of counts, such as how many children in a class walk to school. Each bar stands for one group, called a category, and its height shows the count. Bar graphs in 2nd grade have up to 4 categories and a scale that counts by 1s, so each square on the grid is 1.

A picture graph shows the same counts with small pictures in a row, one picture for each. Children learn bar graphs and picture graphs together and turn a table of counts into either one.

Then they answer questions from the graph: how many in all, how many more and how many fewer. To find how many more children ride the bus than walk, they subtract the shorter bar from the taller one.

Your child should be able to:

Draw a bar graph and a picture graph from a table with up to 4 categories
Read the count for each bar
Find how many in all by adding the bars
Find how many more or how many fewer by comparing two bars

Example

A class bar graph shows how children get to school: 3 walk, 8 ride the bus, 6 come by car and 1 rides a bike. How many more ride the bus than walk, and how many children are on the graph?

The bus bar reaches 8 and the walk bar reaches 3.
How many more: $8 - 3 = 5$ .
In all: $3 + 8 + 6 + 1 = 18$ .
5 more children ride the bus than walk. The graph shows 18 children.

3rd grade: scaled bar graphs and picture graphs 3.MD.B.3

Bar graphs in 3rd grade use a scale. The scale is the amount each square or grid line stands for. On a graph with a scale of 10, the side of the graph counts 0, 10, 20, 30 and so on. A bar that ends halfway between 40 and 50 shows 45.

Scaled picture graphs work the same way. A key under the graph says what one picture stands for, such as "each book picture = 5 books". Six book pictures then mean $6 \times 5 = 30$ books.

The questions take one or two steps. A two-step question might ask how many more two categories have together than a third. Children add the two bars first, then subtract.

Your child should be able to:

Read a bar graph whose scale counts by 2s, 5s or 10s
Use the key to read a scaled picture graph
Draw a scaled bar graph or picture graph from a table
Solve one-step and two-step questions that ask how many more or how many fewer

Example

In a scaled picture graph, each book picture means 5 books. Room 1 has 9 pictures, Room 2 has 6 and Room 3 has 11. How many more books did Rooms 1 and 2 read together than Room 3?

Room 1: $9 \times 5 = 45$ books. Room 2: $6 \times 5 = 30$ books. Room 3: $11 \times 5 = 55$ books.
Step 1, add Rooms 1 and 2: $45 + 30 = 75$ .
Step 2, compare with Room 3: $75 - 55 = 20$ .
Rooms 1 and 2 read 20 more books together than Room 3.

Where children usually get stuck

On a graph with a scale of 5, your child counts 6 squares in a bar and says the count is 6.
In 2nd grade every square was 1, so counting squares worked. On this graph each square stands for 5. The numbers up the side of the graph show it.
What helps. Before reading any bar, have your child read the numbers up the side out loud. Then count the squares by 5s instead of by 1s.
Asked how many more children ride the bus than walk, your child answers "the bus" or gives the number for the bus bar.
"How many more" sounds like "which has more". The question asks for the difference between the two bars.
What helps. Build two towers of blocks to match the two bars. Stand them side by side and count only the blocks that stick up above the shorter tower.
On a graph that counts by 10s, your child draws the bar for 45 up to 40 or up to 50.
The child thinks a bar has to end on a grid line. The spot halfway between two lines is a real place on the graph.
What helps. Point to 40 and 50 and ask which number sits exactly in the middle. Then draw the bar up to that middle spot.

Try four practice questions

Real 2nd grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Ms. Park's class voted for their favorite fruit. Which picture graph matches the data?
Fruit Number of Students
Apples 3
Bananas 5
Strawberries 2
A
Apples
Bananas
Strawberries
Key:= 1 student
B
Apples
Bananas
Strawberries
Key:= 1 student
C
Apples
Bananas
Strawberries
Key:= 1 student
D
Apples
Bananas
Strawberries
Key:= 1 student
Show the answer and how to solve it
The correct picture graph shows 3 apples, 5 bananas, and 2 strawberries — exactly matching the table.
1. 1Look at the table to find the count for each fruit.
2. 2The table shows 3 apples, 5 bananas, and 2 strawberries. The correct picture graph must have a row with 3 apple icons, a row with 5 banana icons, and a row with 2 strawberry icons.
3. 3Count the icons in each picture graph row by row. The correct picture graph shows exactly 3 apples, 5 bananas, and 2 strawberries — matching every count in the table.
Common mistake. A common mistake is swapping two rows. Students may correctly see that bananas has the most icons, but mix up which row belongs to apples and which to bananas. Check each row label and count one by one.
The idea underneath. When 1 picture stands for 1 thing, the count in the table tells you exactly how many pictures to look for in that row of the graph. Match every row, not just one or two.
2On level
Mrs. Chen's class voted for their favorite snack. The table shows the number of votes for each snack.
Snack Votes
Pizza 10
Tacos 20
Salad 30
Burgers 40
On each bar graph below, the numbers on the vertical axis count by $5$ votes. Which bar graph correctly shows the data?
A
B
C
D
Show the answer and how to solve it
The correct graph shows Pizza at $10$ , Tacos at $20$ , Salad at $30$ , and Burgers at $40$ , with each bar reaching its labeled number of votes.
1. 1Read each snack and its number of votes from the table.
2. 2The numbers on the vertical axis count by $5$ votes. Find where each bar must reach.
3. 3Look for the graph where Pizza reaches $10$ , Tacos reaches $20$ , Salad reaches $30$ , and Burgers reaches $40$ . Only one graph shows all four bars at the correct heights — that is the answer.
Common mistake. Do not use the number of gaps as the count. Each gap is worth $5$ votes, so $2$ gaps above $0$ show $10$ votes.
The idea underneath. Use the numbers on the vertical axis to read bar heights. The numbers go up by $5$ votes. A bar for $10$ votes reaches the line labeled $10$ .
3On level
How many students chose Grapes?
A
5
B
7
C
8
D
6
Show the answer and how to solve it
There were 6 students who chose Grapes. The top of the Grapes bar lines up with 6 on the y-axis.
1. 1Look at the bar graph and find the bar labeled Grapes.
2. 2Look at where the top of the Grapes bar lines up with the y-axis. The top of the Grapes bar reaches the line at 6.
3. 3So 6 students chose Grapes.
Common mistake. A common mistake is reading the wrong bar. Find the bar labeled Grapes before counting how high it goes — looking at a neighbor bar like Apples or Bananas gives the wrong number.
The idea underneath. To read a bar graph, first find the bar with the right label, then trace the top of that bar across to the number axis.
4Stretch
Diego, Sofia, Noah, and Aria scored goals during soccer practice last week. The table shows how many goals each student scored.
Student Goals Scored
Diego 30
Sofia 10
Noah 50
Aria 20
Click each row of the picture graph to add soccer ball icons. Click an icon again to remove it. Each soccer ball icon represents 10 goals.
Tap or click a box to fill icons up to it; tap a filled icon to clear it and the ones after.
Number of goals scored
Diego
Sofia
Noah
Aria
Key:
= 10 goals
Show the answer and how to solve it
Diego's row has 3 soccer ball icons, Sofia's row has 1, Noah's row has 5, and Aria's row has 2. Each icon represents 10 goals, so the totals match the table: 30, 10, 50, and 20 goals.
1. 1First, read the data from the table. Diego scored 30 goals, Sofia scored 10 goals, Noah scored 50 goals, and Aria scored 20 goals.
2. 2The key tells us each soccer ball icon stands for 10 goals. Divide each student's total by 10 to find how many icons belong in that row.
3. 3Add 3 soccer ball icons to Diego's row, 1 soccer ball icon to Sofia's row, 5 soccer ball icons to Noah's row, and 2 soccer ball icons to Aria's row.
Common mistake. A common mistake is placing one soccer ball icon for each goal scored, ignoring the key. Because each icon stands for 10 goals, divide the total by 10 to find the correct number of icons per row.
The idea underneath. The key (1 soccer ball icon = 10 goals) is the multiplier that connects the icon count to the actual quantity — dividing each student's total by 10 gives the right number of icons for that row.

Fruit	Number of Students
Apples	3
Bananas	5
Strawberries	2

Snack	Votes
Pizza	10
Tacos	20
Salad	30
Burgers	40

Student	Goals Scored
Diego	30
Sofia	10
Noah	50
Aria	20