Page 28 - 新思维数学学生用书6 样章

2.2 Special numbers

6 Copy this Carroll diagram and write a number less than 100 in each section.

Odd Not odd

Cube number
Not a cube number

7 Find two cube numbers that total 152 when added together.

8 Classify these expressions into two groups. Explain how you chose the groups.
2 3 2 + 1 half of 4 3 – 1 2 × 2
2
3
3
2
2
2
Discuss your answer with your partner.
Think like a mathematician

Adding two consecutive square numbers
1 and 4 are two consecutive square numbers. 1 + 4 = 5

4 and 9 are two consecutive square numbers. 4 + 9 = 13
Investigate the sums of two consecutive square numbers.

If you are systematic you should find an interesting pattern.

Adding odd numbers
The first two odd numbers are 1 and 3. Their sum is 4.

The first five odd numbers are 1, 3, 5, 7 and 9. What is their sum?
Investigate the sums of consecutive odd numbers starting at 1. What do you notice?

You will show you are conjecturing if you set yourself questions to answer as you

investigate the numbers.
You will show you are convincing when you explain your results.

Look what I can do!

I can work out the square number in any position, for example, the ninth

square number is 9 × 9 = 81.
I can use the notation to represent squared.
2
I can work out the cube of numbers up to 5, for example, 5 = 5 × 5 × 5 or
3
5 × 5 which is 125.
2

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