Dr J Frost jfrosttiffinkingstonschuk wwwdrfrostmathscom Last modified 3 rd September 2015 Objectives Add subtract multiply and divide negative numbers as well as raise a negative number to a power ID: 649623
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Slide1
Year 7 Negative Numbers
Dr J Frost (jfrost@tiffin.kingston.sch.uk)www.drfrostmaths.com
Last modified:
3
rd September 2015
Objectives:
Add, subtract, multiply and divide negative numbers, as well as raise a negative number to a power.Slide2
For Teacher Use:
Recommended lesson structure:
Lesson 1
: Adding, subtracting negative numbers.
Lesson 2
: Multiplying, dividing and mixed questions.Slide3
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?
Click
>
Click
>
Bro Tip
: Notice that the answer is always either the sum of the two numbers (ignoring sign) or the difference.
Click
>
Click
>Slide4
Test Your Understanding
Copy and complete the following.
[JMC 2014 Q7] What is
a
b
c
d
e
f
g
h
N
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?Slide5
Adding/subtracting negative numbers
What is the answer. How could we show it?
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?Slide6
Adding/subtracting negative numbers
What is the answer. How could we show it?
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!
A plus and a minus become a minus
Two minuses become a plus.
Slide7
Common Misunderstanding:
“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:
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Check Your Understanding:
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Exercise 1
Calculate 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
A magic square has the same total in every horizont
al line, vertical, and diagonal of 3 squares. Complete:
[SMC 2009 Q3] What is the value of
Solution: 5
[Kangaroo Grey 2004 Q5] What is the value of the expression
Solution: 48
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1
a
b
c
d
e
f
g
h
i
j
k
l
m
n
2
a
b
c
d
e
f
3
4
5
6
7
8
N
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?Slide9
Multiplying Negative Numbers
What is the answer? Could we show it in a similar way to how we showed
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Multiplying Negative Numbers
What is the answer? Could we show how to get it by starting with
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!
Same applies to division.
Slide11
Quickfire
Examples
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RED
O
RANGE
GREEN
BLUE
Use your diary coloured cards to vote for the correct answer in each question.
(Use the front of your diary for blue)Slide13
Calculate:
Slide14
Calculate:
Slide15
Calculate:
Slide16
Calculate:
Slide17
Calculate:
Slide18
Calculate:
Slide19
Exercise 2
Calculate the following:
Determine the missing number:
Calculate the following:
Find two numbers which have the specified sum and product.
Sum
Product
-3, -4
Sum
Product
4
, -3
Sum
Product
2, -5
Sum
Product
8, -3
Sum
Product
-5, -6
Sum
Product
5,
-6
Calculate the following:
1
a
b
c
d
e
g
f
a
b
c
d
2
3
a
b
c
d
e
3
a
b
c
d
e
f
4
a
b
c
d
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