Maths Mastery Workshop for Year 2: Concrete-Pictorial-Abstract Approach at Manor Way School

1. Year 2 Inspire Workshop

2. Aims of the session • National Curriculum • Background to CPA approach • How we teach mathematics in Year 2 at Manor Way • Same-day intervention • How we group children • How you can support at home

3. National Curriculum • The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace... Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding through additional practice, before moving on (NC 2014:3). • Children are stretched in a number of ways: • Have I found all of the solutions? • Is that always true? • True and False questions

4. Background to Concrete-Pictorial-Abstract Approach • Children and adults find maths difficult because it is abstract. • The CPA approach helps children learn new ideas and build on their existing knowledge by introducing abstract concepts in a more familiar and tangible way.

5. Concrete • Concrete is the “doing” stage, using concrete objects to model problems. Instead of the traditional method of maths teaching, where a teacher demonstrates how to solve a problem, the CPA approach brings concepts to life by allowing children to experience and handle physical objects themselves. Every new abstract concept is learned first with a “concrete” or physical experience. • For example, if a problem is about adding up four baskets of fruit , the children might first handle actual fruit before progressing to handling counters or cubes which are used to represent the fruit.

6. Pictorial • Pictorial is the “seeing” stage, using representations of the objects to model problems. This stage encourages children to make a mental connection between the physical object and abstract levels of understanding by drawing or looking at pictures, circles, diagrams or models which represent the objects in the problem. • Building or drawing a model makes it easier for children to grasp concepts they traditionally find more difficult, such as fractions, as it helps them visualise the problem and make it more accessible.

7. Abstract • Only once a child has demonstrated that they have a solid understanding of the “concrete” and “pictorial” representations of the problem, can the teacher introduce the more “abstract” concept, such as mathematical symbols. Children are introduced to the concept at a symbolic level, using only numbers, notation, and mathematical symbols, for example +, –, x, ÷ to indicate addition, multiplication, or division. • Concrete Pictorial Abstract 3 x 5 = 15 5 x 3 = 15 15 ÷ 3 = 5 3 + 3 + 3 + 3 + 3 = 15

8. Ability groups • Children work in mixed-ability groupings as each child is working on the same concept and mixing up the groupings widens children’s opportunities for exploring, discussing and sharing their understanding with others.

9. Structure of a maths lesson • Anchor Task – Children are posed with a problem. • They work together to find solutions to the problem. • Children share their ideas with the class and teacher. • Class teacher will teach the method making links from CPA. • Children are given the opportunity to practise whilst being guided. • Children work on the independent activity. Children who have not fully grasped the concept will work with the teacher in a small group. TA will circulate across the classroom to provide further challenge. • Children who still need further support will have a maths intervention at the end of the day with the teacher. • Sentence stems – There are 5 equal groups with 4 in each group.

10. Same-day intervention • It is important that no gaps in understanding are ever left unfilled (maths competence depends on mastering concepts one by one in a logical progression). • Same-day interventions –either within or after a lesson – are a crucial safety net for any child who has not fully made the small step covered that day. Intervention is always about keeping up, not catching up so that every child is able to tackle the next lesson. • We have within-lesson intervention (teacher works with a focus group) and after-lesson intervention.

11. How can you support at home? • You can help your child in a number of ways: • Help the children to learn and understand their 2x table, 5x table and 10x table and related division facts. • Encourage them to draw pictures and models such as part-whole and bar models to answer questions. • Encourage them to apply their knowledge of maths in real life situations, such as telling the time or using money to pay for shopping. • Support them with home activities, and encourage them to answer questions in full sentences.

12. Y1 facts Adding 1 and 2 Bonds to 10 Adding 10 Bridging/ compensating Y2 facts Doubles Near doubles Adding 0

13. Warm Up Chant 5x table facts.

14. Anchor Task There are 4 bowls and 12 oranges. How many oranges are there in each bowl? Find the missing number. 4 x ______ = 12 12 What does the 4 represent? What does the 12 represent? Depth: Can you represent the problem using an array? Can you write all the related facts from the array?

15. 12 ÷ 4 = ____ Stem Sentence The inverse of multiplication is division 12 12 oranges shared between 4 bowls gives 3 oranges each bowl. There are 4 equal groups with 3 oranges in each group. The missing number is 3.

16. Stem Sentence: The inverse of multiplication is division. 25 5 x ____ = 25 There are 25 paper clips sorted into 5 equal groups. How many are in each group? We use the inverse operation to solve the problem. 5 x _____ = 25 becomes 25 ÷ 5 = _____ What does the 5 represent? What does the 25 represent? Depth What if there were 2 boxes of paperclips sorted into groups of 5. Can you find the missing number?

17. We use the inverse operation to solve the problem. 5 x _____ = 25 becomes 25 ÷ 5 = _____ 25 There are 25 paperclips divided into 5 equal groups. There are 5 equal groups with 5 paper clips in each group.

18. Here is a row from an array. There are 6 counters in each row. _____ x 6 = 30 Find the missing number. Stem Sentence: The inverse of multiplication is division. Depth: Create your own missing number problem and show one row of the array.

19. ____ x 6 = 30 becomes 30 ÷ 6 = ____ There are 6 equal groups. There are 5 counters in each group. The missing number is 5.

20. Solve these missing number problems with your partner. • Remember! • ____ x 2 = 16 • 5 x ____ = 35 Stem Sentence: The inverse of multiplication is division. Represent your solution using an array.

21. Intelligent Practice Stem Sentence: Division is the inverse of multiplication. • Solve these missing number equations. • 2 x ____ = 24 • 5 x ____ = 20 • ____ x 5 = 35 • ____ x 10 = 40 • ____ x 2 = 16

22. Depth: Lucy says that the missing number is 10. Is she correct? Explain how you know. x 2 = 22

23. Depth Tubes of bubbles come in packs of 2 and 5. Lily has 22 tubes of bubbles. How many of each pack could she have? How many ways can you do it?

24. Depth There are 5 floors in a car park. Each floor has the same amount of cars on it. There are 45 cars altogether. Write a missing number sentence for this problem then use the inverse operation to solve it. Prove your answer using an array.

25. Depth: Some of the array is hidden. What could the array show?