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Year 7 Negative Numbers
Dr J Frost ([email protected])
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?
3β7=βπClick>
β3β4=βπClick>
Bro Tip: Notice that the answer is always either the sum of the two numbers (ignoring sign) or the difference.
β6+10=πClick>
β7+5=βπClick>
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+β3=?What is the answer. How could we show it?
9+2=ππ???
Adding/subtracting negative numbers
5ββ2=?What is the answer. How could we show it?
5β2=π???
! A plus and a minus become a minus Two minuses become a plus.
Common Misunderstanding:
β4β10=14βTwo minuses make a plus!β
What did they do wrong?Two minuses only become a plus when theyβre next to each other.If we think about a number line can see the above doesnβt 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
9Γ (β3 )=?What is the answer? Could we show it in a
similar way to how we showed ?
9+2=ππ 9Γ2=ππ???
Multiplying Negative Numbers
(β2 )Γ (β3 )=?What is the answer? Could we show how to get it
by starting with ?
??
!
Same applies to division.
Quickfire Examples
4Γ (β1 )=βπ??
?
?
?
?
??
?
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)
4β412β12
Calculate:
β5β5050β2
Calculate:
24β10β66
Calculate:
2β210β10
Calculate:
β18β272718
Calculate:
β252512.550
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