The document focuses on an investigation of square and cube numbers using multilink, instructing students to continue patterns and record findings in tables. It details the first 15 square numbers and the first 5 cube numbers, explaining their definitions and properties. The document concludes with a section on roots and how to calculate them, alongside an interactive component for engagement.

1. Square and Cube Numbers

2. Investigation
In the pairs where you are sat you are going to have a
challenge.
Using the multilink you need to carry on the pattern on the
next slide using multilink.
Record your findings in a table like this one…
Square Numbers
Let’s recall the first 15 square numbers using multiplication facts.

3. Pattern Number Amount of Multilink Used
1
2
3
4
5
6
7
8
9
10
11
12
Square Numbers
2ba2 recall the first 15 square numbers using multiplication facts.

4. Square Numbers
2ba2 recall the first 15 square numbers using multiplication facts.
Carry on this pattern!
Pattern 1 Pattern 2 Pattern 3

5. Does your table look like this?
Pattern Number Amount of Multilink Used
1
2
3
4
5
6
7
8
9
10
11
12
Square Numbers
2ba2 recall the first 15 square numbers using multiplication facts.
1
4
9
16
25
36
49
64
81
100
121
144

6. What are square numbers?
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196 and 225.
These are known as square numbers!
But why are they square numbers?
Square Numbers
2ba2 recall the first 15 square numbers using multiplication facts.

7. What are square numbers?
Square Numbers
2ba2 recall the first 15 square numbers using multiplication facts.

8. Extension: I am a two digit multiple of 11. The product
of my two digits is both a cube and a square. Who am I?
9
10
8
7
6
4
5
3
2
1
Square Numbers
2ba2 recall the first 15 square numbers using multiplication facts.

9. Extension: I am a two digit multiple of 11. The product
of my two digits is both a cube and a square. Who am I?
25 13 29
83 77 140
26 101 326
90 68 91
476
98 12
88!
Square Numbers
2ba2 recall the first 15 square numbers using multiplication facts.

10. Cube Numbers
Discover the first 5 cube numbers using an investigation.
Starter: Today’s number is 18.
a) Is it a square number? Why?
b) Find its HCF with 9.
c) Multiply it by 7.

11. Time for another investigation!
Cube Numbers
Discover the first 5 cube numbers using an investigation.
In the groups of 3 or 4 where you are sat you are going to have
a challenge.
Using the multilink you need to carry on the pattern on the
next slide using multilink.
Record your findings in a table like this one…

12. Pattern Number Amount of Multilink Used
1
2
3
4
5
Cube Numbers
2ba2 to discover the first 5 cube numbers using an investigation.

13. Carry on this pattern!
Pattern 1 Pattern 2 Pattern 3
Cube Numbers
2ba2 to discover the first 5 cube numbers using an investigation.

14. Pattern Number Amount of Multilink Used
1
2
3
4
5
Cube Numbers
2ba2 to discover the first 5 cube numbers using an investigation.
1
8
27
64
125

15. What do you notice?
1, 8, 27, 64 and 125.
These numbers are known as cube numbers.
But why?
Cube Numbers
2ba2 to discover the first 5 cube numbers using an investigation.

16. Cube Numbers
2ba2 to discover the first 5 cube numbers using an investigation.

17. Putting it all together!
The square numbers are…
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 186 and 225.
1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 4 x 4= = 16
The cube numbers are…
1, 8, 27, 64 and 125.
1 x 1 x 1 = 1 2 x 2 x 2 = 8 3 x 3 x 3 = 27
Cube Numbers
2ba2 to discover the first 5 cube numbers using an investigation.

18. Kahoot time!
https://play.kahoot.it/#/?quizId=dca5d8c4-bf04-405e-9
2ca-0f0f72a8bc66
Cube Numbers
2ba2 to discover the first 5 cube numbers using an investigation.

19. Roots
2ba2 complete calculations
using both cube and square
roots.
Starter: Find the hidden star!

21. What do we know so far?
Roots
2ba2 complete calculations using both cube and square roots.

22. What are roots?
Roots
2ba2 complete calculations using both cube and square roots.
A square root is the opposite to squaring a number.
A cube root is the opposite to squaring a cube number.

23. Examples
This is because .
This is because .
Roots
2ba2 complete calculations using both cube and square roots.

24. Because .
Because .
Examples
Roots
2ba2 complete calculations using both cube and square roots.

25. √
√
√
√ √ 4
√
√ x √
= 10
= 2
= 5
= 5
= 9
= 24
√ 64
√ + √
√ x √
√ √ 25
√ x √
√ x √
= 18
= 6
= 10
= 14
= 6
= 56
√ 64 x √16
√ x √144
√ x √ 36 x √16
√36 x √49
√ x √
= 32
= 64
= 120
= 216
= 42
= 156
√ 64 x √64
Roots
2ba2 complete calculations using both cube and square roots.
I don’t really
understand…
I think I
understand…
I completely
understand!

26. Treasure Hunt Time!
Work in pairs.
Sensible behaviour at all times.
Make a note of what order you visit the cards.