050. Adding and Subtracting Integers on a Number Line

Learning Intentions

• To understand the number line model for adding and subtracting positive integers
• Use a number line to add a positive integer to any integer
• use a number line to subtract a positive integer from any integer

Pre-requisite Summary

• Understand that integers can be negative, positive or zero
• Be able to locate integers on a number line
• Know that moving right on a number line means the value increases
• Know that moving left on a number line means the value decreases
• Be able to compare integers and Identify which is greater
• Understand that addition can be modelled as movement on a number line
• Understand that subtraction can be modelled as movement on a number line

Worked Examples

Worked Example 1

Use a number line to add a positive integer:

a) Start at and add

b) Start at and add

Worked Example 2

Use a number line to subtract a positive integer:

a) Start at and subtract

b) Start at and subtract

Worked Example 3

Use a number line to add a positive integer to any integer:

a)

b)

c)

Worked Example 4

Use a number line to subtract a positive integer from any integer:

a)

b)

c)

Worked Example 5

Describe the movement on the number line and Solve the result:

a) Start at , move right places

b) Start at , move left places

Worked Example 6

Explain whether each calculation should move left or right on a number line, then find the result:

a)

b)

c)

Problems

Problem 1

Use a number line to add a positive integer:

a) Start at and add

b) Start at and add

Problem 2

Use a number line to subtract a positive integer:

a) Start at and subtract

b) Start at and subtract

Problem 3

Use a number line to add a positive integer to any integer:

a)

b)

c)

Problem 4

Use a number line to subtract a positive integer from any integer:

a)

b)

c)

Problem 5

Describe the movement on the number line and find the result:

a) Start at , move right places

b) Start at , move left places

Problem 6

Explain whether each calculation should move left or right on a number line, then find the result:

a)

b)

c)

Exercises

Understanding and Fluency

Exercise 1.

Use a number line to add:

a)

b)

c)

Exercise 2.

Use a number line to add:

a)

b)

c)

Exercise 3.

Use a number line to subtract:

a)

b)

c)

Exercise 4.

Use a number line to subtract:

a)

b)

c)

Exercise 5.

Describe the movement and find the result:

a) start at , move right

b) start at , move left

c) start at , move right

Exercise 6.

Describe the movement and find the result:

a) start at , move left

b) start at , move right

c) start at , move left

Exercise 7.

Calculate Use a number line:

a)

b)

c)

Exercise 8.

Calculate using a number line:

a)

b)

c)

Reasoning

Exercise 9.

Explain why adding a positive integer means moving to the right on a number line.

Exercise 10.

A student says that means move left places. Explain the mistake.

Exercise 11.

Explain why ends at a negative integer.

Exercise 12.

A student starts at and solves by moving right places. Explain why this is incorrect.

Problem-solving

Exercise 13.

A lift is on floor and goes up floors. What floor does it reach?

Exercise 14.

A temperature is and then drops by . What is the new temperature?

Exercise 15.

A diver is at m and rises m. What is the diver’s new position?

Exercise 16.

A game score starts at and decreases by . What is the new score?

Exercise 17.

A submarine is at m and rises m. What integer represents its new position?

Exercise 18.

A bank account balance is represented by and then decreases by . What is the new integer balance?

Potential Misunderstandings

• Students may confuse adding with moving left instead of right on the number line
• Students may confuse subtracting with moving right instead of left on the number line
• Students may start from zero instead of from the given integer
• Students may count the starting point as the first jump incorrectly
• Students may think a negative starting number changes the direction of movement for adding a positive integer
• Students may not Recognise that subtracting a positive integer can move the result further into the negative numbers
• Students may make counting errors in the number of jumps on the number line
• Students may confuse the sign of the starting integer with the operation being performed

Next: 051. Adding and Subtracting Negative Integers