Interpret a graph to find totals or differences. - ISEE Lower Level Mathematics Achievement

SECTION 1

Why Do We Use Graphs?

People have been drawing pictures to show numbers for a very long time! Long before computers, people needed ways to compare information quickly. A graph is a picture that shows data (numbers and facts) so you can understand them at a glance.

Think about it this way. If your teacher asked, "Which lunch is the most popular?" you could count every vote. But a bar graph lets you SEE the answer right away! That is the power of graphs.

1786 • The First Bar Graph

A man named William Playfair drew the very first bar graph. He used it to show how much money different countries made from trade.

1800s • Graphs in Schools

Teachers started using bar graphs and picture graphs in classrooms. Students learned to read data just like reading a story!

1900s • Graphs in Newspapers

Newspapers began printing graphs to help people understand big numbers, like how many people lived in each city.

Today • Graphs Are Everywhere

You see graphs on websites, in video games, and on the ISEE test! Knowing how to read them is a super useful skill.

On the ISEE, you will see graphs and need to answer questions about them. The big question is: can you find totals (adding numbers together) and differences (subtracting one number from another)? Let's learn how!

SECTION 2

Key Ideas for Reading Graphs

Before we dive into practice, let's learn the important parts of a graph. These ideas will help you answer every graph question on the ISEE.

Read the Title

The title tells you what the graph is about. Always read it first! It is like the name of the graph's story.

Check the Labels

Labels tell you what each bar or picture stands for. The bottom label names the groups. The side label shows the numbers.

Read the Scale

The scale is the set of numbers along the side. It might count by 1s, 2s, 5s, or 10s. Always check what each line means!

Find the Values

Look at where each bar ends. Match it to the number on the scale. That number is the value for that group.

Do the Math

To find a total, add values together. To find a difference, subtract the smaller number from the bigger number.

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KEY TAKEAWAY

Think of a graph like a scoreboard at a game. The scoreboard shows points for each team so you can quickly see who is winning. A graph shows numbers for each group so you can quickly compare them. Total means add all the scores together. Difference means subtract to find how far apart two scores are.

SECTION 3

See It! A Bar Graph Example

Let's look at a bar graph together. This graph shows how many books four students read during summer break. Study it carefully!

This bar graph shows that Ana read 6 books, Ben read 8, Cara read 4, and Dan read 7. The scale on the left counts by 2s from 0 to 10.

Notice how the tallest bar belongs to Ben. That means Ben read the most books. The shortest bar belongs to Cara, so she read the fewest. You can see this just by looking at the heights!

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ISEE Tip

Always check the scale before reading any bar! If the scale counts by 2s or 5s, a bar that lands between two lines means a number in between. For example, halfway between 4 and 6 would be 5.

SECTION 4

The Math: Finding Totals and Differences

Once you read the numbers from a graph, you need to do simple math. There are two main types of questions you'll see on the ISEE.

FINDING A TOTAL

Total = Value 1 + Value 2 + Value 3 + ...

A total means you add two or more values from the graph together. The question might say "how many in all" or "how many altogether" or "combined."

FINDING A DIFFERENCE

Difference = Bigger Number − Smaller Number

A difference means you subtract the smaller value from the bigger value. The question might say "how many more" or "how many fewer" or "how much less."

Let's use the book graph from above. If the question asks, "How many books did Ana and Cara read altogether?" you would add: 6 + 4 = 10 books.

If the question asks, "How many more books did Ben read than Cara?" you would subtract: 8 − 4 = 4 more books.

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Watch for Tricky Words!

"How many more" and "how many fewer" both mean SUBTRACT. "How many in all" and "how many combined" both mean ADD. Circle these clue words in the question to help you pick the right operation!

SECTION 5

Picture Graphs and Their Keys

Not all graphs use bars. A picture graph (also called a pictograph) uses small pictures or symbols to show data. Each picture stands for a certain number. The key tells you what each picture is worth.

In this picture graph, each apple symbol stands for 2 real apples. Room A has 5 symbols, so Room A picked 5 × 2 = 10 apples. Room B has 3 symbols = 6 apples. Room C has 6 symbols = 12 apples. Room D has 4 symbols = 8 apples.

Here is the most important thing about picture graphs: always check the key first! If each picture equals 2, you must multiply the number of pictures by 2. If each picture equals 5, you multiply by 5.

A common mistake is forgetting the key and just counting pictures. If you count 5 apples in Room A's row, the answer is NOT 5. It's 5 × 2 = 10. Don't fall into that trap!

SECTION 6

Worked Example: Step by Step

Let's solve a problem together using the "Books Read During Summer Break" bar graph from Section 3. Here's the question:

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Sample Question

How many more books did Ana, Ben, and Dan read combined than Cara read?

Solving the Combined-Difference Problem

1
Step 1 — Read Each Bar

Look at the graph and write down each student's number of books. Ana = 6, Ben = 8, Dan = 7, and Cara = 4.

Ana = 6, Ben = 8, Dan = 7, Cara = 4
2
Step 2 — Find the Total for Ana, Ben, and Dan

The question says "combined," so add these three together: 6 + 8 + 7. First, 6 + 8 = 14. Then, 14 + 7 = 21.

Combined total = 21 books
3
Step 3 — Find the Difference

The question asks "how many more" which means subtract. Take the combined total and subtract Cara's number: 21 − 4 = 17.

Difference = 17 books
4
Step 4 — Check Your Answer

Does 17 make sense? Cara only read 4 books, and the other three together read 21. Yes, 17 more sounds right! The answer is 17.

Answer: 17 more books

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REMEMBER THIS STRATEGY

For multi-step graph questions, break them into small pieces. First, read the values. Second, do one operation at a time. Third, check that your answer makes sense. Small steps lead to big success!

SECTION 7

Comparing Different Types of Graphs

On the ISEE, you might see different kinds of graphs. Let's compare the three main types so you know what to expect.

Graph Type	What It Looks Like	How to Read It
Bar Graph	Tall or short bars side by side	Match the top of each bar to the number on the scale
Picture Graph	Rows of small pictures or symbols	Count the pictures and multiply by the key value
Table	Numbers organized in rows and columns	Find the row and column you need, then read the number

The three most common data displays on the ISEE Lower Level

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ALL GRAPHS WORK THE SAME WAY

No matter which type of graph you see, the steps are the same: read the title, find the values, then add or subtract. It's like ordering food at different restaurants—the menus look different, but you always pick what you want and pay at the end!

SECTION 8

ISEE Test-Taking Strategies for Graph Questions

Knowing the math is important. But on test day, using smart strategies can help you answer faster and avoid mistakes. Here are some tips just for graph questions.

Strategy	What To Do
Read the question FIRST	Before studying the whole graph, read the question. Then you know exactly which bars or pictures to focus on. You save time!
Eliminate wrong answers	If you can tell a bar is around 6, cross out any answer choice that is way too big or too small. Then choose from what's left.
Check the scale	Don't assume the scale counts by 1s. It might count by 2s, 5s, or 10s. Reading the wrong scale is the most common mistake!
Always answer	There is NO penalty for wrong answers on the ISEE. If you're unsure, make your best guess. Never leave a question blank!

ISEE strategies for graph questions

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Process of Elimination

If the graph shows that a bar reaches about 8, and the answer choices are 3, 5, 8, and 15, you can quickly cross out 3 and 15 because they are way too far from 8. Even if you're not 100% sure, you've narrowed it down to two choices. That gives you a much better chance of getting it right!

SECTION 9

Practice Problems

Now it's your turn! Use the graph below to answer Problems 1 through 4. Problem 5 uses a different graph described in the question. Read carefully, and you've got this!

The bar graph shows: Soccer = 15 students, Basketball = 20, Baseball = 10, Tennis = 5, Swimming = 10. The scale counts by 5s.

Question 1: CONCEPTUAL

According to the bar graph above, which sport is the most popular among 4th graders?

A. Soccer
B. Basketball
C. Baseball
D. Swimming

Show answer (B)

The correct answer is B, Basketball. Looking at all five sports on the bar graph: Tennis reaches 5 students, Baseball and Swimming each reach 10 students, Soccer reaches 15 students, and Basketball reaches 20 students. Basketball has the tallest bar, which means it has the most students and is the most popular sport among 4th graders.

Question 2: BASIC CALCULATION

How many students chose Soccer and Tennis combined?

A. 10
B. 15
C. 20
D. 25

Show answer (C)

The correct answer is C, 20. Soccer = 15 students and Tennis = 5 students. The word "combined" means add: 15 + 5 = 20. Choice A (10) might come from subtracting instead of adding: 15 − 5 = 10. Choice B (15) is just Soccer alone. Choice D (25) would be too large — that would be every line on the scale.

Question 3: INTERMEDIATE

How many more students chose Basketball than chose Baseball?

A. 5
B. 10
C. 20
D. 30

Show answer (B)

The correct answer is B, 10. "How many more" means subtract. Basketball = 20 and Baseball = 10. So 20 − 10 = 10. Choice A (5) might come from reading the scale wrong. Choice C (20) is the value for Basketball alone, not the difference. Choice D (30) would be the two added together, but the question asks for the difference, not the total.

Question 4: APPLIED

How many 4th graders were surveyed in all?

A. 25
B. 50
C. 55
D. 60

Show answer (D)

The correct answer is D, 60. To find the total number of students surveyed, add all five bars: 15 + 20 + 10 + 5 + 10 = 60. Choice A (25) is just the highest number on the scale, not the total. Choice B (50) might come from forgetting one group. Choice C (55) might come from misreading one bar. Always add every bar when the question says "in all."

Question 5: CRITICAL THINKING

A picture graph shows how many stickers each child has. Each sticker symbol equals 3 real stickers. Maya's row has 4 symbols and Jake's row has 7 symbols. How many more stickers does Jake have than Maya?

A. 3
B. 9
C. 12
D. 21

Show answer (B)

The correct answer is B, 9. First, find each child's real sticker count using the key. Maya: 4 × 3 = 12 stickers. Jake: 7 × 3 = 21 stickers. Then subtract to find the difference: 21 − 12 = 9. Choice A (3) is the value of just one symbol, not the difference. Choice C (12) is Maya's total, not the difference. Choice D (21) is Jake's total. Remember: with picture graphs, always multiply by the key before doing any other math!

SUMMARY

Let's Review What You Learned!

Summary

Great work making it through this lesson! You learned how to read bar graphs and picture graphs by checking the title, labels, and scale first. For picture graphs, always multiply the number of symbols by the key value before doing anything else.

To find a total, add the values together — look for clue words like "in all," "combined," or "altogether." To find a difference, subtract the smaller number from the bigger number — look for "how many more" or "how many fewer." On test day, remember to read the question first, eliminate wrong answers, and never leave a question blank. You've got this!