1. Supporting children’s understanding of number
Workshop for Parents
Created by Mwright (CVF)

2. How do you feel about maths?

3. How many mathematical statements can you make about you age?

4. Procedural Vs Conceptual understanding
Procedural understand gives the children a ridged method to follow without the understanding underpinning the mathematics. Often making children appear to be successful at mathematics as they calculate with massive numbers but they lack the ability to problem solve when they make a mistake or have to apply their knowledge in a unfamiliar context:
An extreme example: The Spanish navy have had to scrap a brand new 1.25Bn Euro submarine after an engineer put the decimal point in the wrong place and the submarine was 70 tonnes over weight and would never float.
Conceptual understanding immerses children in the rich language of mathematics allowing them to articulate what number is doing, building links between different areas of mathematics and being successful when following a method.

5. How does the number system work?
Base-10 system
• our everyday number system is a Base-10 system. • the Base-10 number system is known as the decimal system and has 10 digits to show all numbers 0,1,2,3,4,5,6,7,8,9 using place value and a decimal point to separate whole numbers from decimal fractions.
EXAMPLE:

6. Why do we separate every third number with a comma?
1,327,849

7. Why do we separate every third number with a comma?
1,HT1,HT1
1,327,849

8. Early challenges:
The first challenge for children is understanding how the numbers 0-9 function. Zero is easily explained as the symbol for nothing (although care needs to taken as zero has an important function as a place holder).
Consider our understanding of ‘1ness’. Young children often appear to be fluent counters, we teach them number names through song and play for example the song 10 green bottles. It is important to promote an understanding of the increasing value of the next number.

9. The number one is tricky….
As we count 1-9 the numbers increase by one.
Why is this difficult?
What does this look like?
Difficulty of one:
Early counting experience are often gained through a range of contexts ‘how many lambs are their?’ or ‘how many cars are there?’
Two great contexts both answers could be 1 but both ones look very different. Even more confusing when we say ‘there is a cow, a lamb and a chicken in the farmers field, how many animals are there?’
Clearly it is three 1+1+1=3 but each one could appear to have a different value based on relative size.

10. Numbers 0-9: what must we know
Each next number has a greater value than the one before it, a value of one more.
0,1,2,3,4,5,6,7,8,9.
The importance of 10.
The numbers 1 and 0 combine to form 10.
1 0
This is 1 lot of ten and no 1’s.

11. How would you calculate:=

12. = 45
This relies on secure number bonds to 10.
We want children to be fluent with the language of number and not rely on counting in ones from the starting number all the way to the equals sign.

13. Being able to make 10 is massively important:
If we understand that = 10 also begin to understand that:
= 100
= 1000
7,000+ 3,000= 10,000
= 1
= 0.1
When going further and faced with more challenge calculations such as bridging through 10 or 100 knowledge of numberbonds to 10 is vital.
= ( ) = 95 +8
Some children are reliant on counting in 1’s or need to use apparatus or a formal method to calculate this, this is not efficient.

14. Supporting place value:
Playing nasty or nice

15. When teaching a number operation the inverse needs to be taught at the same time. Addition and subtraction, multiplication and division.
Subtraction:
95 – 8 = 87. Children need to understand how one undoes the other. Can be employed as a check to a calculation.
There are two forms of subtraction.
Subtraction: Minus and difference.
I have £95 pounds and I spend £87 on a food shop, that leaves me with £8.
My friend spent £95 on a pair of football boots and I spent £87 on the same model, the difference in what we paid is £8.

16. Secure numberbonds are as important with subtraction.
= ( – 3) = 87 -8 95 87
Subtraction as minus
Subtraction as difference

17. Multiplication and division can be challenging.
Earliest experience of both comes through grouping, lots of and sharing.
Barriers to understanding is that we talk in terms of x smaller, children assume x gives bigger results and gives smaller results.
For example: 5.6 is 10 x smaller than 56.

18. Knowing our tables:
In the same way as knowing our numberbonds to 10, knowing times tables, with their related division facts is important. Traditionally learnt by rote ability to recall them help children make mathematical statements:
7x8=56
Therefore we know that:
0.7x8=5.6
So why is 0.7x0.8=0.56?
“0.7 is 10x smaller than 7 and 0.8 is 10x smaller than 8, 10x10 is 100 therefore the answer of 0.7x0.8 has to be 100x smaller than 7x8.” (A year six child )

19. Supporting all four standard number operations:

20. Images that promote Addition and Subtraction:
Pictorial
Numberlines
Formal methods =
2007
1999=
Counting up

21. Images that promote multiplication and division:
Repeated addition
Numberlines
Arrays
Grouping

22. Useful websites to support mathematics
- loads of games, puzzles, problems on all mathematical concepts from early years to secondary school (please only use the student site).
-Maths arithmagons – number patterns and problems
Countdown game (does not offer solutions)
- all KPS children have a log in for the content you would otherwise need to pay for. Interactive challenges, play against the programme or other children internationally.
Lots of things, I like their puzzles!
-Good for explaining concepts, when unsure, however the site is undergoing changes!

23. Bibliography: http://www. amathsdictionaryforkids
Bibliography: KPS Year 6 children.