049. Integers on the Number Line

Learning Intentions

• To understand that integers can be negative, positive or zero
• represent integers on a number line
• compare two integers and decide which is greater

Pre-requisite Summary

• Understand that whole numbers can be ordered on a number line
• Know that zero can be used as a reference point
• Be able to count forwards and backwards by ones
• Understand that numbers to the right on a number line are greater
• Understand that numbers to the left on a number line are smaller
• Recognise that a negative sign indicates a value less than zero

Worked Examples

Worked Example 1

a) State whether each integer is negative, positive or zero: $5,-3,0$
b) Explain what an integer is.

Worked Example 2

a) Plot the integers $-4,0,3$ on a number line.
b) State which point is furthest to the left.
c) State which point is furthest to the right.

Worked Example 3

Compare the integers and decide which is greater:
a) $4$ and $-2$
b) $-3$ and $-7$
c) $0$ and $-5$

Worked Example 4

a) Write the integers in ascending order: $-1,4,0,-5,3$
b) Write the same integers in descending order.

Worked Example 5

a) Find the integer that is $2$ places to the left of $1$ on a number line.
b) Find the integer that is $4$ places to the right of $-3$.

Worked Example 6

a) A thermometer shows $-2^{\circ }\text{C}$ in the morning and $3^{\circ }\text{C}$ in the afternoon. Which temperature is greater?
b) Explain how the number line helps compare these integers.

Problems

Problem 1

a) State whether each integer is negative, positive or zero: $7,-6,0$
b) Explain what an integer is.

Problem 2

a) Plot the integers $-5,0,2$ on a number line.
b) State which point is furthest to the left.
c) State which point is furthest to the right.

Problem 3

Compare the integers and decide which is greater:
a) $6$ and $-1$
b) $-4$ and $-9$
c) $0$ and $-8$

Problem 4

a) Write the integers in ascending order: $-2,5,0,-6,1$
b) Write the same integers in descending order.

Problem 5

a) Find the integer that is $3$ places to the left of $2$ on a number line.
b) Find the integer that is $5$ places to the right of $-4$.

Problem 6

a) A lift is on level $-1$ and then moves to level $4$. Which level is greater?
b) Explain how the number line helps compare these integers.

Exercises

Understanding and Fluency

1. State whether each integer is negative, positive or zero:
   a) $9$
   b) $-2$
   c) $0$

2. State whether each integer is negative, positive or zero:
   a) $-11$
   b) $6$
   c) $0$

3. Plot these integers on a number line:
   a) $-3,0,4$
   b) $-6,2,5$
   c) $-1,-4,3$

4. Plot these integers on a number line:
   a) $-7,-2,0$
   b) $1,-5,6$
   c) $-8,4,2$

5. Compare the integers and choose the greater:
   a) $3$ or $-4$
   b) $-2$ or $-6$
   c) $0$ or $-1$

6. Compare the integers and choose the greater:
   a) $-5$ or $2$
   b) $-7$ or $-3$
   c) $4$ or $0$

7. Write in ascending order:
   a) $-3,2,0,-1$
   b) $4,-5,1,0$
   c) $-6,-2,3,5$

8. Write in descending order:
   a) $-4,3,0,2$
   b) $5,-1,-3,0$
   c) $-2,6,1,-5$

Reasoning

9. Explain why $-2$ is greater than $-5$.

10. A student says that $-8$ is greater than $-3$ because $8>3$. Explain the mistake.

11. Explain why every positive integer is greater than every negative integer.

12. A student places $-4$ to the right of $-1$ on a number line. Explain why this is incorrect.

Problem-solving

13. A diver is at $-6$ m and another diver is at $-2$ m. Which diver is at the greater integer position?

14. A temperature changes from $-4^{\circ }\text{C}$ to $2^{\circ }\text{C}$. Which temperature is greater?

15. A lift starts at floor $0$, goes down to floor $-3$, then up to floor $5$. List these floor numbers in ascending order.

16. A bank account record shows the integers $-7,-1,0,4$. Order these from greatest to least.

17. A game score changes through the integers $-2,3,-5,1$. Which score is the greatest and which is the least?

18. A submarine is at $-9$ m and rises to $-4$ m. Which position is greater on the number line?

Potential Misunderstandings

• Students may think integers are only positive whole numbers
• Students may forget that zero is an integer that is neither positive nor negative
• Students may compare negative integers by looking only at the digits and ignoring the sign
• Students may think the integer with the larger digit is always greater, even for negative numbers
• Students may place negative integers to the right of zero instead of to the left
• Students may not use the number line rule that numbers further right are greater
• Students may confuse ascending and descending order when negative integers are included
• Students may think that $-1$ is less than $-5$ because $1<5$, without considering position on the number line

Next: 050. Adding and Subtracting Integers on a Number Line