Mastering Maths the Singapore Way Jo Cronin

Reflect By age fifteen, pupils in Singapore, Japan, South Korea and China are three years ahead of pupils in England with their mathematical achievement. In these countries there is a relatively small gap in achievement between pupils from different backgrounds, genders and overall. What’s stopping our pupils from achieving just as much?

A mastery approach: a set of principles and beliefs. This includes a belief that all pupils are capable of understanding and doing mathematics, given sufficient time. Pupils are neither ‘born with the maths gene’ nor ‘just no good at maths’. With good teaching, appropriate resources, effort and a ‘can do’ attitude all children can achieve in and enjoy mathematics.

What do we mean by mastery? The pupils that have ‘mastered’ the year group expectations will be those that the evidence: fluency; reasoning; and problem solving in relation to their learning. These children will be able to take their mathematics learning and apply it, independently, in a wider range of contexts.

What does Mastery mean? In mathematics, you know you’ve mastered something when you can apply it to a totally new problem in an unfamiliar situation.

Assessing for Depth

Concrete – Pictorial - Abstract

Representations in Calculations

Ben spent 2 ⁄ 5 of his money on a CD. The CD cost £10. How much money did he have at first?’

Word Problems

? £10 ?

Number Sense

=?

hundredsonestens

What is a ten frame and how could you use it?

These are ten-frame cards:

Magic ‘10’

What if we wanted to ADD these two numbers together? 9 4 +

One way to think about this might be: Ten And 3 more... 13

Bridging tens

Abstract =

Try 7+5=

Make models and/or drawings to find these sums

What did you do? Are there other ways?

Subtraction 13 – 6 =

13 – 6 = ?

Abstract 13 – 6 = 7

+=?

-=?

+ = ?

-=?

41 Part-Part-Whole Relationships In order to develop a flexible sense of number, students need many opportunities to compose and decompose numbers. Think about the number 8 Show how 8 things can be shown in two parts. Invent a story to go along with your display or picture.

Number Bonds

There are 8 children, three of them are boys, how many girls? 8 – 3 = 5

part whole part

whole What will your drawing look like? Do you know the value of the whole? Value of parts? part

What can you do to make solving a word problem easier? Mrs. Dawson has 8 blue marbles and 4 green marbles in a bag. She puts in 2 more marbles. How many marbles are in the bag now?

Mrs. Dawson has 8 blue marbles and 4 green marbles in a bag. She puts in 2 more marbles. How many marbles are in the bag now? Mrs. Dawson has marbles in her bag now. Understand the problem

Who and What

Who and What Chunk and Draw

Mrs. Dawson has 8 blue marbles and 4 green marbles in a bag. She puts in 2 more marbles. How many marbles are in the bag now? Chunking

Mrs. Dawson’s marbles Mrs. Dawson has 8 blue marbles and 4 green marbles in a bag. She puts in 2 more marbles. How many marbles are in the bag now? ?

Understand the problem Who and What Chunk and Draw Compute

= ? = ? Mrs. Dawson’s marbles ?

Understand the problem Who and What Chunk and Draw Compute Check

Mrs. Dawson has 8 blue marbles and 4 green marbles in a bag. She puts in 2 more marbles. How many marbles are in the bag now? Mrs. Dawson has marbles in her bag now. 14 Mrs. Dawson’s marbles

Addition – Aggregation (Combining) There are 3 footballs in the red basket 2 footballs in the blue basket. How many footballs are there altogether?

Given 2 parts, find the whole. Ben has 6 toy cars. Stacey has 8 toy cars. How many toy cars do they have altogether ? = 14 They have 14 toy cars altogether.

14 ? Helen has 14 breadsticks. Her friend has 17. How may do they have altogether? Do you know the value of the whole? Value of parts? Consider: Should the whole always be on top? Do the parts need to be proportional? 17

13 22 What will your drawing look like? Do you know the value of the whole? Value of parts? ?

Problems to Solve Tom has a bag of 64 marbles, his friend gives him 28 more, how many does he have now? Kelsey was running a 26 mile marathon, after 18 miles she felt very tired. How many more miles did she have to run? Carly bought an apple for 17p and a banana for 26p, how much has she spent?

Sally has 145 stickers. She has 27 fewer stickers than John. How many stickers do they have altogether?

5 children shared the cost of a present equally. Each of them paid £6. What was the cost of the present? Cost of the present £6 ? £6 x 5 = £30 one part number of parts whole ?

There were 27 desks to clean. 3 boys shared the work equally. How many desks did each boy clean? Desks 27 ? Each boy cleaned 9 desks. 3 units = 27 1 units = 9 27

Peter has four books. Harry has five times as many books as Peter. How many more books does Harry have?

Peter has 4 books Harry has five times as many books as Peter. How many books has Harry?

Arithmetic KS1 Sample Questions NC Tests 2016

? 4/5 of the children in the choir are girls. If there are 8 boys, how many children are there altogether? GirlsBoys x 5 = 40 There are 40 children altogether. Children in the choir