The Importance of Bar Models and part whole model Parent Workshop 31/1/18

CPA approach 4 3 1 Concrete: Resources such as cubes, counters and shapes Pictorial: Pictures, drawings Abstract: Numbers and symbols

Session Contents What is the Part Whole Model? What are ‘bar models’? How can bar models be used in Early Years and KS1? How can bar models be introduced? What do bar models look like across key stages?

The part, whole model Here is the part, part, whole model used in the mastery approach. It works on the principle that if you know two values out of three, you can calculate the missing value using addition or subtraction.

6 ? 4 The part, whole model 6 and 4 more makes ? The two parts (6 and 4) combine to make 10. 6 4 ?

The part, whole model The part whole model can be orientated differently and is used for addition and subtraction problems

? 10 4 The part, whole model Something and 4 makes 10 This leads to a missing box calculation. + 4 = 10 In other words algebra. The new national curriculum insists children know their number families for all the operations, for example: 6 + 4 = 10 3 x 7 = 21 4 + 6 = 10 7 x 3 = 21 10 – 6 = 4 21÷ 7 = 3 10 – 4 = 6 21÷ 3 = 7 10 4 ?

There are 7 cubes under the cups. You can only lift one cup up There are 7 cubes under the cups. You can only lift one cup up. Can you work out how many cubes are under the second cup?

There are 5 cubes under this cup. There are 7 cubes altogether There are 5 cubes under this cup. There are 7 cubes altogether. 7 – 5 = 2. I know that there are 2 cubes under the other cup.

Cups activity 1 Now try this activity again taking turns to hide the cubes. Use different totals.

Discussion What do bar models look like? Why are bar models used?

What Are Bar Models? 16 9 7 9 16 7 1 2 3 4 5 6 7 8

5 x 4 = ? 20 : A Consistent Picture 2 of 20 = ? 4 + 11 = ? 5 Share 20 in the ratio 2:3 20 : 4 4 + 11 = ? 4 ? 11 5 x 4 = ?

A Consistent Picture 4 11 ? 4 15 ? 4 ? ? 20 20 ? 20 ? 4 + 11 = ? 15 - 4 = ? 4 15 ? 5 x 4 = ? 4 ? 20 ÷ 5 = ? ? 20 2 of 20 = ? 5 20 ? Share 20 in the ratio 2:3 20 ?

The importance of bar modelling “Instead of relying on superficial and unreliable clues like key words, the simple visual diagrams help children understand why the appropriate operations make sense.” Beckmann 2014 “Although bar models will not always help children carry out required calculations, they are clearly designed to help children decide which operations to use.” Beckmann 2014 “When children have experience and exposure to many concrete materials, they are able to develop the ability to visualise” Ban Har 2016 “Model drawing trains children to think analytically, providing an important transition between the concrete and the abstract.” Forsten 2014 “Bar models are a tool to help children visualise stories” Ban Har 2016

Introducing Bar Models

Introducing Bar Models in EYFS It is important that children start with the concrete object, in this case apples, and transition to iconic representations (counters or cubes). The final stage would be to draw boxes to show a bar.

KS1 bar modelling

KS1 Bar Modelling Tim has 4 sweets and Ben has 2 sweets. How many sweets do they have altogether? 6 6 6 6 6 Tim Tim Ben Ben Tim 4 Tim Ben Tim 4 Ben Ben 2

Small steps 4 + 2 = 6

They bake altogether 22 biscuits altogether. Omar bakes 10 biscuits. Ruby bakes 12 biscuits. How many biscuits to they bake altogether? 10 12 ? They bake altogether 22 biscuits altogether.

Hardeep buys large eggs and small eggs Hardeep buys large eggs and small eggs. Altogether he buys 20 eggs There are 7 small eggs. How many large eggs are there? 7 ? 20 There are 13 large eggs.

There are 20 bread rolls altogether. Peter puts 5 bread rolls into each packet. He has 4 packets. How many bread rolls does he put into the 4 packets altogether? 5 5 5 5 ? There are 20 bread rolls altogether.

There are 4 pears in each box. Hardeep buys 12 pears. He puts and equal number of pears into 3 boxes. How many pears are there in each box? ? ? ? 12 There are 4 pears in each box.

How can I help my child? Help by… Knowledge of number, help them explain what comes before or after a given number, how the number is made, e.g. tens and ones. Encourage them to draw pictures and models such as part, whole and bar models. Support them with their homework, encourage them to answer questions in full sentences. If you are unsure, please ask your child’s teacher to explain