099r. Reviewing Integers and Integer Operations

Learning Intentions

• To understand that integers can be negative, zero or positive
• To understand how to Use a number line to add or subtract positive integers
• add a positive integer to a negative integer
• subtract a positive integer from a positive or negative integer

Pre-requisite Summary

• Know that whole numbers include
• Be able to read and mark values on a number line. See 049. Integers on the Number Line
• Understand that moving right on a number line increases value
• Understand that moving left on a number line decreases value
• Recall basic addition and subtraction facts with positive whole numbers. See 050. Adding and Subtracting Integers on a Number Line
• Know that subtraction can be interpreted as moving back a number of steps
• Be familiar with comparing numbers as greater than or less than. 002. Place Value and Comparing Numbers
• Understand that zero separates positive and negative numbers on a number line

Worked Examples

Worked Example 1

Identify each integer as negative, zero or positive:

a)

b)

c)

Worked Example 2

Use a number line to Solve each answer:

a)

b)

Worked Example 3

Add a positive integer to a negative integer:

a)

b)

Worked Example 4

Subtract a positive integer from a positive integer:

a)

b)

Worked Example 5

Subtract a positive integer from a negative integer:

a)

b)

Worked Example 6

Use a number line to Solve:

a)

b)

c)

Problems

Problem 1

Classify each integer as negative, zero or positive:

a)

b)

c)

Problem 2

Use a number line to find each answer:

a)

b)

Problem 3

Add a positive integer to a negative integer:

a)

b)

Problem 4

Subtract a positive integer from a positive integer:

a)

b)

Problem 5

Subtract a positive integer from a negative integer:

a)

b)

Problem 6

Use a number line to solve:

a)

b)

c)

Exercises

Understanding and Fluency

Exercise 1.

State whether each integer is negative, zero or positive:

a)

b)

c)

d)

Exercise 2.

Place these integers in order from least to greatest:

a)

b)

c)

Exercise 3.

Use a number line to Evaluate:

a)

b)

c)

Exercise 4.

Add a positive integer to a negative integer:

a)

b)

c)

Exercise 5.

Subtract a positive integer from a positive integer:

a)

b)

c)

Exercise 6.

Subtract a positive integer from a negative integer:

a)

b)

c)

Exercise 7.

Use a number line to solve:

a)

b)

c)

Exercise 8.

Complete each statement:

a) is neither ______ nor ______

b) Integers to the right of are ______

c) Integers to the left of are ______

d) Subtracting a positive integer means moving ______ on the number line

Reasoning

Exercise 9.

Explain why is less than Use a number line.

Exercise 10.

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

Exercise 11.

Noah says that because he added and and kept the negative sign. Explain why this is incorrect.

Exercise 12.

Explain why subtracting a positive integer from a negative integer always gives a smaller number.

Exercise 13.

A student says . Describe what the student has forgotten about the number line.

Problem-solving

Exercise 14.

The temperature is in the morning. It rises by . What is the new temperature?

Exercise 15.

A diver is at m relative to sea level. She moves up m. What is her new position?

Exercise 16.

A lift starts on floor and goes down floors. What floor does it reach?

Exercise 17.

A submarine is at m and then descends m more. What is its new position?

Exercise 18.

A game score starts at . A player loses points and then gains points. What is the final score?

Exercise 19.

At night the temperature is . It drops by . What is the new temperature?

Potential Misunderstandings

• Students may think integers are only negative numbers
• Students may forget that is an integer
• Students may think is positive or negative
• Students may confuse the size of a negative number with the size of its digits, for example thinking
• Students may move the wrong direction on a number line when subtracting
• Students may think subtracting always makes a number stay positive
• Students may add the digits correctly but Choose the wrong sign for the answer
• Students may think subtracting a positive integer from a negative integer makes the number closer to zero
• Students may ignore the starting point on the number line and only count the jumps
• Students may confuse moving left and right with increasing and decreasing values

Next: 100. Multiplying and Dividing Integers