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Contents
6
1
What is the ninth square number?
2
Calculate.
a
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2.2 Special numbers
Exercise 2.2
Bookmarks
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2 Numbers and sequences
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52
b
102
Copy this Carroll diagram and write a number less than 100 in each section.
Odd
Not odd
Cube number
c
Not a cube number
72
3
Find two square numbers that total 45 when added together.
4
Here are three cubes of increasing size.
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Find two cube numbers that total 152 when added together.
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Classify these expressions into two groups. Explain how you chose the groups.
2
3
3
2
2 +1
3
half of 4
2
3 –1
2
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2 ×2
2
Discuss your answer with your partner.
My Activity
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Think like a mathematician
Adding two consecutive square numbers
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1 and 4 are two consecutive square numbers. 1 + 4 = 5
4 and 9 are two consecutive square numbers. 4 + 9 = 13
Glossary
Investigate the sums of two consecutive square numbers.
If you are systematic you should find an interesting pattern.
Adding odd numbers
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The first two odd numbers are 1 and 3. Their sum is 4.
A
B
The first five odd numbers are 1, 3, 5, 7 and 9. What is their sum?
C
Investigate the sums of consecutive odd numbers starting at 1.
What do you notice?
How many small cubes are in each of the large cubes?
You will show you are conjecturing if you set yourself questions to
answer as you investigate the numbers.
Tip
You will show you are convincing when you explain your results.
In cube A: There are 2 small cubes along each edge
There are 4 or 2 2 small cubes in each layer
There are 8 or 2 2 × 2 or 23 small cubes in cube A
5
Look what I can do!
a
53
b
13
c
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I can work out the square number in any position, for example,
the ninth square number is 9 × 9 = 81.
Calculate.
33
I can use the notation 2 to represent squared.
Check your answers to questions 4 and 5 with your partner.
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I can work out the cube of numbers up to 5, for example, 5 3 = 5 × 5 × 5 or 5 2 × 5
which is 125.
28
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28-29/264
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