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:

b) Explain what an integer is.

Worked Example 2

a) Plot the integers 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) and

b) and

c) and

Worked Example 4

a) Write the integers in ascending order:

b) Write the same integers in descending order.

Worked Example 5

a) Solve the integer that is places to the left of on a number line.

b) Find the integer that is places to the right of .

Worked Example 6

a) A thermometer shows in the morning and 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:

b) Explain what an integer is.

Problem 2

a) Plot the integers 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) and

b) and

c) and

Problem 4

a) Write the integers in ascending order:

b) Write the same integers in descending order.

Problem 5

a) Find the integer that is places to the left of on a number line.

b) Find the integer that is places to the right of .

Problem 6

a) A lift is on level and then moves to level . Which level is greater?

b) Explain how the number line helps compare these integers.

Exercises

Understanding and Fluency

Exercise 1.

State whether each integer is negative, positive or zero:

a)

b)

c)

Exercise 2.

State whether each integer is negative, positive or zero:

a)

b)

c)

Exercise 3.

Plot these integers on a number line:

a)

b)

c)

Exercise 4.

Plot these integers on a number line:

a)

b)

c)

Exercise 5.

Compare the integers and Choose the greater:

a) or

b) or

c) or

Exercise 6.

Compare the integers and choose the greater:

a) or

b) or

c) or

Exercise 7.

Write in ascending order:

a)

b)

c)

Exercise 8.

Write in descending order:

a)

b)

c)

Reasoning

Exercise 9.

Explain why is greater than .

Exercise 10.

A student says that is greater than because . Explain the mistake.

Exercise 11.

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

Exercise 12.

A student places to the right of on a number line. Explain why this is incorrect.

Problem-solving

Exercise 13.

A diver is at m and another diver is at m. Which diver is at the greater integer position?

Exercise 14.

A temperature changes from to . Which temperature is greater?

Exercise 15.

A lift starts at floor , goes down to floor , then up to floor . List these floor numbers in ascending order.

Exercise 16.

A bank account record shows the integers . Order these from greatest to least.

Exercise 17.

A game score changes through the integers . Which score is the greatest and which is the least?

Exercise 18.

A submarine is at m and rises to 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 is less than because , without considering position on the number line

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