Bar Graph Worksheets

Bar graphs use bars of different heights to show how much there is in each group, so children can compare amounts at a glance. The five PDFs on this page ask children to read bar graphs, compare the bars and answer questions about them, with scales that count by 1s, 2s and 5s, and every sheet has an answer key. They follow standards 2.MD.D.10 and 3.MD.B.3 of the Common Core standards for grade 2 measurement and data, and the notes below show how to teach each step.

Reading a bar graph

Run your finger from the top of a bar straight across to the scale to read its value. To find “how many more”, read both bars and subtract. Some of these graphs count by 2s, so children must read the scale carefully rather than count the grid lines.

Bar graphs worksheets: what is in the set

There are 5 bar graphs worksheets on this page, and every one has an answer key except for any cut-out games. Two sets use a scale that counts by 2s, one set uses a scale of 5s, and the others mix questions about the most, the fewest and how many more.

Bar graphs: the parts of a graph

A bar graph has a few parts, and children who know them can read any graph. Wikipedia’s article on bar charts shows how old the idea is. The title says what the graph is about, the scale tells how much each line is worth, and the bars show the amounts. This table lists the five parts, with the example from the diagram above:

A good first step on every worksheet is to read the title and the labels aloud before looking at the questions. Children who skip this step often read the wrong scale, or answer a question about a different graph.

Bar graph worksheets: choosing and reading the scale

The bar graph worksheets in this pack use scales that count by 1, 2 and 5, and the scale is the most important thing to read. A scale that counts by 2 has labels 0, 2, 4, 6 and so on, and the lines between them are worth 1 each only if the grid shows them. Odd values land halfway between two labeled lines. This table shows what happens to the five bars of the survey data when the scale changes:

With a scale that counts by 5, none of the five bars end on a labeled line, so every value must be read by looking at how far a bar is between two lines. This is the reason why the scale of 5s is saved for the last worksheet. The skip counting worksheets page helps children count by 2s, 5s and 10s before they meet these scales.

Reading bar graphs: top of the bar, straight across

When reading bar graphs, children put a finger on the top of the bar and slide it straight across to the scale. The number at that level is the value of the bar. If the top of the bar is between two labeled lines, it is halfway between the two numbers, so a bar between 8 and 10 shows 9. This table turns the five votes into bars for a graph where each square is worth 2, and shows where each bar ends:

The second column is the number in the survey, and the third is the height of the bar in squares. A bar of 4 1/2 squares is half a square above the 8 line, which is the 9 on the scale.

Bar graph questions: most, least and how many more

Most bar graph questions ask for one of five things: the tallest bar, the shortest bar, the value of one bar, the difference between two bars, or the total of all the bars. This table shows eight questions for the survey, with how to find each one and the answer:

Questions about how many more or how many fewer are both subtractions. The gap between the top of one bar and the top of another is the difference, and children can see the gap if they draw a dotted line across from the taller bar. Every pair of bars gives two questions, so five bars give 10 pairs. This table lists all 10 differences for the survey:

Bar graph grade 2: the standards

For bar graph grade 2 the standard is 2.MD.D.10, which asks children to draw a picture graph and a bar graph with a single-unit scale for up to four categories, and to solve simple put-together, take-apart and compare problems using the graph. In grade 3, standard 3.MD.B.3 introduces scaled bar graphs, where each square is worth more than one, and one-step and two-step problems. The Common Core standards for grade 3 measurement and data describe the next step, and the tally charts and picture graphs page covers the way to collect the data first.

Every comparison in the table above is a compare problem, and every total is a put-together problem. The number of questions that can be asked grows quickly with the number of bars, as this table shows:

Interpreting graphs worksheets: from a table to a bar

Interpreting graphs worksheets use three skills: reading a value, comparing values and drawing conclusions. The last one is the hardest, and the answer is a sentence such as “Soccer is the most popular sport, and tennis is the least.” Children can start with a table of data and decide which kind of display fits best. This table compares five ways of showing data:

A bar graph is the best choice when the amounts are large or the categories are many, because a bar is quicker to read than a row of symbols. For a graph that shows how data changes over time, a line graph is used instead, and children meet this in grade 5.

A graph can mislead: where the scale starts

A fair bar graph starts its scale at 0. If the scale starts higher, a small difference looks big. For bars of 48 and 50, the shorter bar is 96% as tall as the taller one when the scale starts at 0, but only 80% when it starts at 40. This table shows what happens as the start moves up:

Children in grade 2 do not need this idea, but a short talk about it is a good way to show that graphs are made by people who choose the scale. A child who learns to check where the scale starts will read graphs in the news with more care.

Common mistakes with bar graphs

Most mistakes are about the scale or about the words in the question. This table shows five mistakes, what went wrong and the fix:

Bar graphs word problems

Story problems use the facts that a bar graph shows. Ask children to draw the bars first, and to say which bars they are comparing before they calculate:

Games and activities for bar graphs

Children learn bar graphs best when they play with it. These games use things that are found at home or in a classroom:

• Class survey: ask the class a question, record the answers with tally marks and draw the bar graph
• Graph detective: cover the labels of a bar graph and let a partner guess what it is about
• Human bar graph: children stand in lines by their favorite color to make a living bar graph
• Graph paper bars: color squares on graph paper to match a table of data
• Dice bars: roll a die 30 times, tally the results and draw a bar graph
• Spot the mistake: give a graph with an error in the scale and ask children to find it

Extra support and extra challenge with bar graphs

For children who need more support: start with a scale that counts by 1, and put a finger on the top of the bar and slide it across to the scale. Use a ruler or a strip of paper as a straight edge. Do the first set only, and say the question aloud before looking at the graph. Move to the scale of 2s when children read every bar correctly.

For children who need more challenge: ask for the total number of children without counting the bars one at a time, for a graph that is made from a table of their own data, and for a question that has two steps, such as how many more chose the top two sports than the bottom two. The scale of 5s worksheet is a good challenge.

How to tell that a child is ready to move on from bar graphs

1. The child reads the title, labels and scale before answering.
2. The child reads the value of a bar, including bars between two lines.
3. The child finds how many more or how many fewer by subtracting.
4. The child finds the total of all the bars.

When all four are true, move on to the tally charts and picture graphs page, or to the coordinate grids page.

A 20-minute lesson on bar graphs

A short lesson is the best way to introduce bar graphs. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where bar graphs fits across the grades

No skill stands alone. This table shows what children learn before and after bar graphs, with the standard that goes with each step:

This page is the main reading page for graphs. The whole sequence is on the graphing worksheets page.

Helping at home with bar graphs

Parents do not need to be experts to help with bar graphs. These suggestions work well, and each takes only a few minutes:

• Make a bar graph of the family’s favorite meals with a sheet of graph paper.
• Look for graphs in the newspaper and ask “what does the scale count?”.
• Ask “which is the most?” and “how many more?” when children look at a graph.
• Make a weather bar graph: count the sunny, cloudy and rainy days in a month.
• Check the answers with the answer key and ask the child to explain one.

How to check progress in bar graphs

A teacher or parent can check progress with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for bar graphs

Most children need about a week of short sessions for bar graphs. This plan follows the order of the worksheets on this page:

When the plan is complete, move on to the tally charts and picture graphs page. The whole sequence is on the graphing worksheets page.