# Teaching Notes

Patterns, Sequences and Relationships

Welcome to week 2, this week we are focusing on the area of Number Patterns, Relationships and Sequences. Understanding the relationships between numbers and identifying patterns and sequences is one of the key principles of number sense. Gaining a secure understanding of number patterns, sequences and relationships lays the foundations for topics like algebra.

The main learning intention this week, is developing our understanding of how numbers are interconnected and how numbers can be used in meaningful ways.

Monday - Factors and Multiples

Factors

Factors are numbers that divide exactly into another number. For example, the factors of 15 are 1, 3, 5 and 15.

Try and work out the factors of 16, 24, 30, 56 and 80? Did you get them all?

Factors can be shown in pairs. Each pair multiplies to make 15. The factor pairs of 15 are:

1 x 15 = 15

3 x 5 = 15

Now try and work out the factor pairs for 20, 28, 36, 48 and 60!

Multiples

A multiple is a number that can be divided by another number a certain number of times without a remainder. They are an extension of your times tables.

For example the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 etc.

Can you think of all the multiples of 4? What about 6? Try a challenge of listing the multiples of 12! Tuesday - Prime and Composite Numbers

Prime numbers are numbers that can only be divided by themselves and 1.

For example, 13 is a prime number, it can only be divided by 1 and 13. Where as 12 is not a prime number. It can be divided by 2, 3, 4, 6 and 12 as well as 1. Remember 1 is not a prime number, the first and only even prime number is 2!

Composite numbers are all other numbers, this just means they can be divided by more than just themselves and 1. For example, 20 is a composite number, it can be divided by 1,2,4,5,10 and 20.

Click on the link below to play Prime and Composite Fruit Splat.

Step 1 play numbers to 20.

Step 2 play numbers to 50.

Step 3 play numbers to 99.

http://www.sheppardsoftware.com/mathgames/numbers/fruit_shoot_prime.htm Wednesday - Square and Cube Numbers

Square Numbers

When you multiply a number by itself, the result is a square number:

1 x 1 = 1                           7 x 7 = 49
2 x 2 = 4                           8 x 8 = 64
3 x 3 = 9                           9 x 9 = 81
4 x 4 = 16                        10 x 10 = 100
5 x 5 = 25                        11 x 11 = 121
6 x 6 = 36                        12 x 12 = 144

To write the mathematical formula for square numbers we add a small 2 next to and above the number, for example: 42 =16.

Cube Numbers

A cube number is a number that is the product of three numbers which are the same. In other words, if you multiply a number by itself and then by itself again, the result is a cube number. To write the mathematical formula for cube numbers we add a small 3 next to and above the number, for example: 23 = 8.

Check out the link below for more on square and cube numbers.

https://www.bbc.co.uk/bitesize/topics/zyhs7p3/articles/z2ndsrd

Thursday - Triangular Numbers

A triangular number sequence is made by the number of dots in a triangular pattern. Look at the picture below, to make the next number in the sequence, you add another row of dots. By adding another row of dots and counting all the dots we can find the next number of the sequence.

• The first triangle has just one dot.
• The second triangle has another row with 2 extra dots, making 1 + 2 = 3
• The third triangle has another row with 3 extra dots, making 1 + 2 + 3 = 6
• The fourth has 1 + 2 + 3 + 4 = 10

Triangular numbers form a pattern and, as such, are a useful way of getting P7 to think about algebraic functions and about the importance of number formulas. This forms part of a crucial knowledge base for maths students going forward!

To explore triangular numbers further, click on the link below and then scroll down to the section labelled 'Rule'.

https://www.mathsisfun.com/algebra/triangular-numbers.html

Friday - Consolidation of Learning & Friday Test

The children have all been working so hard this week, that today we are going to have an artistic activity which will allows them to consolidate their learning from this week and show their understanding of multiples, factors, prime, composite, square, cube and triangular numbers. Their job is to design a poster, however they choose (paper or computer) to show what they have learnt this week. They could complete a spider diagram or split their page into sections for each area. Be creative, if possible please send a picture of the completed task into our Facebook page via the messenger button.

Friday Test

This week's times table focus was x3. Ask your child their x3 tables in a random order ensuring you cover all times tables from 0 x 3 to 12 x 3. Due to the number work we have been covering, we have put together an additional 10 questions relating to this weeks topic.

1. What is the next prime number after 13?  17

2. What is 8 squared? 64

3. What is the next triangular number after 21? 28

4. What is 3 cubed? 27

5. List the factor pairs for 36 - 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6

6. What are the first 5 multiples of 9? 9, 18, 27, 36, 45

7. Write down 5 composite numbers between 2 and 20 - 4, 6, 8, 9 and 10

8. List the prime numbers between 40 and 50 - 41, 43, 47 and 49

9. Write down the first 5 square numbers - 1, 4, 9, 16 and 25

10. List the factor pairs for 60 - 1 and 60, 2 and 30, 3 and 20, 4 and 15, 5 and 12, 6 and 10

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