Year 7 Negative Numbers

Dr J Frost (jfrost@tiffin.kingston.sch.uk)

Last modified: 18th July 2015

Objectives: Add, subtract, multiply and divide negative numbers, as well as raise a negative number to a power.

For Teacher Use:

Recommended lesson structure:

Lesson 1: Adding, subtracting negative numbers.Lesson 2: Multiplying, dividing and mixed questions.

Visualising negatives with a number line

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

For any addition/subtraction of numbers, you should ALWAYS visualise a number line. How would we visualise the following?

3−7=−𝟒Click>

−3−4=−𝟕Click>

Bro Tip: Notice that the answer is always either the sum of the two numbers (ignoring sign) or the difference.

−6+10=𝟒Click>

−7+5=−𝟐Click>

Test Your Understanding

Copy and complete the following.

[JMC 2014 Q7] What is

a

bc

d

e

f

g

h

N

???

??

???

?

Adding/subtracting negative numbers

9+−3=?What is the answer. How could we show it?

9+2=𝟏𝟏???

Adding/subtracting negative numbers

5−−2=?What is the answer. How could we show it?

5−2=𝟑???

! A plus and a minus become a minus Two minuses become a plus.

Common Misunderstanding:

−4−10=14“Two minuses make a plus!”

What did they do wrong?Two minuses only become a plus when they’re next to each other.If we think about a number line can see the above doesn’t make sense.

Quickfire Questions:

?

????????

Check Your Understanding:

????????

Exercise 1Calculate the following.

Fill in the missing value.

Find two numbers which have a sum of -2 and a difference of 8. Solution: 3 and -5

[JMC 2010 Q1] What is ? Solution: 2010

[JMC 2013 Q6] What is the value of? Solution: -2

[JMO 2007 A1] What is the value of ? Solution: 1

[IMC 2001 Q1] Between which of the following pairs of numbers is there the greatest difference?A -3, 8 B -5, -13 C 1, 11 D 4, -5 E -6, -15

Solution: A

[SMC 2009 Q3] What is the value of Solution: 5

[Kangaroo Grey 2004 Q5] What is the value of the expression Solution: 48

??

??

??

?????

??

?

??????

?

?

?

?

?

?

?

1abcdefghijklmn

2abcdef

3

4

5

6

7

8

N

Multiplying Negative Numbers

9× (−3 )=?What is the answer? Could we show it in a

similar way to how we showed ?

9+2=𝟏𝟏 9×2=𝟏𝟖???

Multiplying Negative Numbers

(−2 )× (−3 )=?What is the answer? Could we show how to get it

by starting with ?

??

!

Same applies to division.

Quickfire Examples

4× (−1 )=−𝟒??

?

?

?

?

??

?

RED ORANGE GREEN BLUE

Use your diary coloured cards to vote for the correct answer in each question.

(Use the front of your diary for blue)

4−412−12

Calculate:

−5−5050−2

Calculate:

24−10−66

Calculate:

2−210−10

Calculate:

−18−272718

Calculate:

−252512.550

Calculate:

Exercise 2Calculate the following:

Determine the missing number:

Calculate the following:

Find two numbers which have the specified sum and product.

Sum Product -3, -4Sum Product 4, -3Sum Product 2, -5Sum Product 8, -3Sum Product -5, -6Sum Product 5, -6

Calculate the following:

1abcde

gf

abcd

2

3abcde

3

abcdef

4

a

bcd

??

???

??

????

???

??

??????

?

??

??e