Learn on PengiSaxon Math, Intermediate 4Chapter 6: Lessons 51–60, Investigation 6

Investigation 6: Displaying Data Using Graphs, Activity Displaying Information on Graphs

In this Grade 4 lesson from Saxon Math Intermediate 4, students learn to read and interpret four types of graphs: pictographs, bar graphs, line graphs, and circle graphs. Students practice identifying key graph components such as titles, labels, scales, units, and legends, and apply skills like using a key to calculate values in a pictograph. The lesson also introduces the concept of continuous data in line graphs and how circle graphs represent a whole divided into parts.

Section 1

📘 Displaying Data Using Graphs

New Concept

The four types of graphs we will study are pictographs, bar graphs, line graphs, and circle graphs.

Why it matters

Mastering graphs transforms you from just a calculator of numbers into a storyteller who can reveal hidden patterns and trends in data. This skill is fundamental not just in advanced math but in every scientific and economic field where making sense of complex information is critical for success.

What’s next

Next, you’ll analyze examples of each graph type and then practice creating your own to display different sets of data.

Section 2

Pictographs

Property

A pictograph uses pictures to display information. A legend, or key, tells what the symbols on the graph stand for, for example, ⚪ represents the choice of 2 students.

Example

If 🥤 represents 2 votes, then 🥤🥤🥤🥤 means 4×2=84 \times 2 = 8 students voted for juice.
If a key says 🍎 = 10 apples sold, a row with 🍎🍎🍎 shows 3×10=303 \times 10 = 30 apples were sold.
To show 15 votes where each ⚪ = 5 votes, you would draw three symbols: ⚪⚪⚪, since 15÷5=315 \div 5 = 3.

Explanation

These graphs tell a story with pictures! Each symbol stands for a certain number of items. Just count the symbols and use the key to find the real total. It’s data with personality!

Section 3

Bar Graphs

Property

Information can be shown in a bar graph where the bars can be vertical or horizontal. Labels on the sides of the graph tell what the other words or numbers along the sides mean.

Example

If the 'Pizza' bar reaches the line for 10 and the 'Chicken' bar reaches 6, then 10−6=410 - 6 = 4 more students chose pizza.
If a bar for 'Walk' and a bar for 'Car' both reach the line for 6, it means an equal number of students use each method.
A graph shows 7 students ride bikes and 3 use skateboards. The 'Bike' bar would be taller, representing a value of 77 students.

Explanation

It's a data showdown where taller bars mean bigger values! This graph makes it incredibly easy to compare different groups at a glance and see which category comes out on top.

Section 4

Line Graphs

Property

Line graphs are often used to show information or data that change over time. The data are continuous, which means that the data are assembled between the points on the graph.

Example

Jamil's height was 40 inches at age 4 and about 48 inches at age 8. The line connecting these points shows his growth over 4 years.
A runner's time is 6 minutes at mile 1 and 13 minutes at mile 2. The segment between these points shows their pace during that mile.
If a temperature graph shows 15°C on Monday and 20°C on Tuesday, the upward-sloping line shows it got warmer.

Explanation

Follow the line to see a story unfold over time! It connects data points to show how things like height or temperature change. A steep line means the change is happening fast!

Section 5

Circle Graphs

Property

A circle graph shows how a whole is divided into parts. A circle graph is sometimes called a pie graph, where the 'pie' is cut into 'slices' that show the size of the parts.

Example

In a 24-hour day, if sleeping takes up 9 hours, the 'Sleeping' slice covers 924\frac{9}{24} or 38\frac{3}{8} of the entire circle.
If school is 7 hours and homework is 2 hours, together they make up a single slice representing 7+2=97+2=9 hours of the day.
A budget shows 50% for rent, 30% for food, and 20% for fun. The 'Rent' slice would be half the entire circle.

Explanation

This is a 'pie' chart that shows how a whole is sliced up. Each piece represents a part of the total, like how you spend your 24-hour day or a monthly budget.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 6: Lessons 51–60, Investigation 6

  1. Lesson 1

    Lesson 51: Adding Numbers with More Than Three Digits, Checking One-Digit Division

    LearnPractice
  2. Lesson 2

    Lesson 52: Subtracting Numbers with More Than Three Digits, Word Problems About Equal Groups, Part 2

    LearnPractice
  3. Lesson 3

    Lesson 53: One-Digit Division with a Remainder, Activity Finding Equal Groups with Remainders

    LearnPractice
  4. Lesson 4

    Lesson 54: The Calendar, Rounding Numbers to the Nearest Thousand

    LearnPractice
  5. Lesson 5

    Lesson 55: Prime and Composite Numbers, Activity Using Arrays to Find Factors

    LearnPractice
  6. Lesson 6

    Lesson 56: Using Models and Pictures to Compare Fractions, Activity Comparing Fractions

    LearnPractice
  7. Lesson 7

    Lesson 57: Rate Word Problems

    LearnPractice
  8. Lesson 8

    Lesson 58: Multiplying Three-Digit Numbers

    LearnPractice
  9. Lesson 9

    Lesson 59: Estimating Arithmetic Answers

    LearnPractice
  10. Lesson 10

    Lesson 60: Rate Problems with a Given Total

    LearnPractice
  11. Lesson 11Current

    Investigation 6: Displaying Data Using Graphs, Activity Displaying Information on Graphs

    LearnPractice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Displaying Data Using Graphs

New Concept

The four types of graphs we will study are pictographs, bar graphs, line graphs, and circle graphs.

Why it matters

Mastering graphs transforms you from just a calculator of numbers into a storyteller who can reveal hidden patterns and trends in data. This skill is fundamental not just in advanced math but in every scientific and economic field where making sense of complex information is critical for success.

What’s next

Next, you’ll analyze examples of each graph type and then practice creating your own to display different sets of data.

Section 2

Pictographs

Property

A pictograph uses pictures to display information. A legend, or key, tells what the symbols on the graph stand for, for example, ⚪ represents the choice of 2 students.

Example

If 🥤 represents 2 votes, then 🥤🥤🥤🥤 means 4×2=84 \times 2 = 8 students voted for juice.
If a key says 🍎 = 10 apples sold, a row with 🍎🍎🍎 shows 3×10=303 \times 10 = 30 apples were sold.
To show 15 votes where each ⚪ = 5 votes, you would draw three symbols: ⚪⚪⚪, since 15÷5=315 \div 5 = 3.

Explanation

These graphs tell a story with pictures! Each symbol stands for a certain number of items. Just count the symbols and use the key to find the real total. It’s data with personality!

Section 3

Bar Graphs

Property

Information can be shown in a bar graph where the bars can be vertical or horizontal. Labels on the sides of the graph tell what the other words or numbers along the sides mean.

Example

If the 'Pizza' bar reaches the line for 10 and the 'Chicken' bar reaches 6, then 10−6=410 - 6 = 4 more students chose pizza.
If a bar for 'Walk' and a bar for 'Car' both reach the line for 6, it means an equal number of students use each method.
A graph shows 7 students ride bikes and 3 use skateboards. The 'Bike' bar would be taller, representing a value of 77 students.

Explanation

It's a data showdown where taller bars mean bigger values! This graph makes it incredibly easy to compare different groups at a glance and see which category comes out on top.

Section 4

Line Graphs

Property

Line graphs are often used to show information or data that change over time. The data are continuous, which means that the data are assembled between the points on the graph.

Example

Jamil's height was 40 inches at age 4 and about 48 inches at age 8. The line connecting these points shows his growth over 4 years.
A runner's time is 6 minutes at mile 1 and 13 minutes at mile 2. The segment between these points shows their pace during that mile.
If a temperature graph shows 15°C on Monday and 20°C on Tuesday, the upward-sloping line shows it got warmer.

Explanation

Follow the line to see a story unfold over time! It connects data points to show how things like height or temperature change. A steep line means the change is happening fast!

Section 5

Circle Graphs

Property

A circle graph shows how a whole is divided into parts. A circle graph is sometimes called a pie graph, where the 'pie' is cut into 'slices' that show the size of the parts.

Example

In a 24-hour day, if sleeping takes up 9 hours, the 'Sleeping' slice covers 924\frac{9}{24} or 38\frac{3}{8} of the entire circle.
If school is 7 hours and homework is 2 hours, together they make up a single slice representing 7+2=97+2=9 hours of the day.
A budget shows 50% for rent, 30% for food, and 20% for fun. The 'Rent' slice would be half the entire circle.

Explanation

This is a 'pie' chart that shows how a whole is sliced up. Each piece represents a part of the total, like how you spend your 24-hour day or a monthly budget.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 6: Lessons 51–60, Investigation 6

  1. Lesson 1

    Lesson 51: Adding Numbers with More Than Three Digits, Checking One-Digit Division

    LearnPractice
  2. Lesson 2

    Lesson 52: Subtracting Numbers with More Than Three Digits, Word Problems About Equal Groups, Part 2

    LearnPractice
  3. Lesson 3

    Lesson 53: One-Digit Division with a Remainder, Activity Finding Equal Groups with Remainders

    LearnPractice
  4. Lesson 4

    Lesson 54: The Calendar, Rounding Numbers to the Nearest Thousand

    LearnPractice
  5. Lesson 5

    Lesson 55: Prime and Composite Numbers, Activity Using Arrays to Find Factors

    LearnPractice
  6. Lesson 6

    Lesson 56: Using Models and Pictures to Compare Fractions, Activity Comparing Fractions

    LearnPractice
  7. Lesson 7

    Lesson 57: Rate Word Problems

    LearnPractice
  8. Lesson 8

    Lesson 58: Multiplying Three-Digit Numbers

    LearnPractice
  9. Lesson 9

    Lesson 59: Estimating Arithmetic Answers

    LearnPractice
  10. Lesson 10

    Lesson 60: Rate Problems with a Given Total

    LearnPractice
  11. Lesson 11Current

    Investigation 6: Displaying Data Using Graphs, Activity Displaying Information on Graphs

    LearnPractice