Learn on PengiSaxon Math, Intermediate 4Chapter 1: Lessons 1–10, Investigation 1

Lesson 11: Investigation 1 Number Lines, Activity Drawing Number Lines

In this Grade 4 lesson from Saxon Math Intermediate 4, students learn to draw and interpret number lines by placing equally spaced tick marks and labeling them using skip-counting intervals such as twos, fives, and tens. Students are introduced to positive and negative numbers, including how negative numbers represent values like temperatures below zero and debt. The lesson also covers using greater than and less than symbols to compare two numbers based on their positions on a number line.

Section 1

📘 Number Lines

New Concept

Numbers less than zero are called negative numbers.

What’s next

Next, you’ll use the number line as a tool to visualize these new numbers and compare their values.

Section 2

Number line

Property

A number line is a line with equally spaced tick marks labeled with numbers. The labels show the distance from zero. The space between tick marks, or the scale, can be ones, twos, fives, or any other number. This helps us visualize where numbers are located in relation to one another on an infinite line.

Example

To what number is the arrow pointing on a line from 0 to 20 with tick marks at every multiple of 2, and the arrow on 14?
The arrow points to 14.
To what number is the arrow pointing on a line from 0 to 100 with tick marks at every multiple of 10, and the arrow on 70?
The arrow points to 70.

Explanation

Think of a number line as a giant, endless ruler! It’s a map that shows exactly where every number lives, helping you see the distance and order between them easily. Just figure out the distance between tick marks, and you can find any number.

Section 3

Negative numbers

Property

Numbers less than zero are negative numbers, written with a minus sign to the left of the digit, like 5-5. Zero itself is neutral—neither positive nor negative. Negative numbers are super useful for describing things like very cold temperatures below zero, or when you owe someone money, which is also known as a debt.

Example

Use digits to write negative twenty: 20-20.
If the temperature starts at 6 degrees and drops 10 degrees, what is the new temperature? The new temperature is 4-4 degrees.
If you have 5 dollars but owe someone 8 dollars, your financial situation can be represented as 3-3 dollars.

Explanation

Negative numbers are the mirror image of positive numbers on the other side of zero. They represent opposites, like owing three dollars (3-3) instead of having three dollars (33), or a temperature drop!

Section 4

Comparing numbers

Property

To compare two numbers, we decide if one is greater than (>>), equal to (==), or less than (<<) the other. On a number line, numbers get greater as you move to the right and smaller as you move to the left. The comparison symbol always points to the smaller number, like a hungry alligator wanting the bigger meal!

Example

Compare 55 and 5-5. Since 55 is to the right of 5-5 on a number line, 5>55 > -5.
Compare 6-6 and 4-4. Since 4-4 is to the right of 6-6 on a number line, 4>6-4 > -6.
Arrange from least to greatest: 1,2,01, -2, 0. The correct order is 2,0,1-2, 0, 1.

Explanation

Comparing numbers is like figuring out who is further ahead in a race. The number further to the right on the number line is always the winner, or the greater number, no matter if it's positive or negative!

Book overview

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

Continue this chapter

Chapter 1: Lessons 1–10, Investigation 1

  1. Lesson 1

    Lesson 1: Review of Addition

  2. Lesson 2

    Lesson 2: Missing Addends

  3. Lesson 3

    Lesson 3: Sequences

  4. Lesson 4

    Lesson 4: Place Value, Activity Comparing Money Amounts

  5. Lesson 5

    Lesson 5: Ordinal Numbers, Months of the Year

  6. Lesson 6

    Lesson 6: Review of Subtraction

  7. Lesson 7

    Lesson 7: Writing Numbers Through 999

  8. Lesson 8

    Lesson 8: Adding Money

  9. Lesson 9

    Lesson 9: Adding with Regrouping

  10. Lesson 10

    Lesson 10: Even and Odd Numbers

  11. Lesson 11Current

    Lesson 11: Investigation 1 Number Lines, Activity Drawing Number Lines

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Number Lines

New Concept

Numbers less than zero are called negative numbers.

What’s next

Next, you’ll use the number line as a tool to visualize these new numbers and compare their values.

Section 2

Number line

Property

A number line is a line with equally spaced tick marks labeled with numbers. The labels show the distance from zero. The space between tick marks, or the scale, can be ones, twos, fives, or any other number. This helps us visualize where numbers are located in relation to one another on an infinite line.

Example

To what number is the arrow pointing on a line from 0 to 20 with tick marks at every multiple of 2, and the arrow on 14?
The arrow points to 14.
To what number is the arrow pointing on a line from 0 to 100 with tick marks at every multiple of 10, and the arrow on 70?
The arrow points to 70.

Explanation

Think of a number line as a giant, endless ruler! It’s a map that shows exactly where every number lives, helping you see the distance and order between them easily. Just figure out the distance between tick marks, and you can find any number.

Section 3

Negative numbers

Property

Numbers less than zero are negative numbers, written with a minus sign to the left of the digit, like 5-5. Zero itself is neutral—neither positive nor negative. Negative numbers are super useful for describing things like very cold temperatures below zero, or when you owe someone money, which is also known as a debt.

Example

Use digits to write negative twenty: 20-20.
If the temperature starts at 6 degrees and drops 10 degrees, what is the new temperature? The new temperature is 4-4 degrees.
If you have 5 dollars but owe someone 8 dollars, your financial situation can be represented as 3-3 dollars.

Explanation

Negative numbers are the mirror image of positive numbers on the other side of zero. They represent opposites, like owing three dollars (3-3) instead of having three dollars (33), or a temperature drop!

Section 4

Comparing numbers

Property

To compare two numbers, we decide if one is greater than (>>), equal to (==), or less than (<<) the other. On a number line, numbers get greater as you move to the right and smaller as you move to the left. The comparison symbol always points to the smaller number, like a hungry alligator wanting the bigger meal!

Example

Compare 55 and 5-5. Since 55 is to the right of 5-5 on a number line, 5>55 > -5.
Compare 6-6 and 4-4. Since 4-4 is to the right of 6-6 on a number line, 4>6-4 > -6.
Arrange from least to greatest: 1,2,01, -2, 0. The correct order is 2,0,1-2, 0, 1.

Explanation

Comparing numbers is like figuring out who is further ahead in a race. The number further to the right on the number line is always the winner, or the greater number, no matter if it's positive or negative!

Book overview

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

Continue this chapter

Chapter 1: Lessons 1–10, Investigation 1

  1. Lesson 1

    Lesson 1: Review of Addition

  2. Lesson 2

    Lesson 2: Missing Addends

  3. Lesson 3

    Lesson 3: Sequences

  4. Lesson 4

    Lesson 4: Place Value, Activity Comparing Money Amounts

  5. Lesson 5

    Lesson 5: Ordinal Numbers, Months of the Year

  6. Lesson 6

    Lesson 6: Review of Subtraction

  7. Lesson 7

    Lesson 7: Writing Numbers Through 999

  8. Lesson 8

    Lesson 8: Adding Money

  9. Lesson 9

    Lesson 9: Adding with Regrouping

  10. Lesson 10

    Lesson 10: Even and Odd Numbers

  11. Lesson 11Current

    Lesson 11: Investigation 1 Number Lines, Activity Drawing Number Lines