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A CPD day from

Concrete, Pictorial, Abstract, Language. A CPD day from. Mark McCourt @ EmathsUK La Salle Education @ LaSalleEd. Six interconnected, though not dependent, days … Mastery in Mathematics Concrete, Pictorial, Abstract, Language Bar Modelling Deeper Understanding in Mathematics

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A CPD day from

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  1. Concrete, Pictorial, Abstract, Language A CPD day from

  2. Mark McCourt @EmathsUK La Salle Education @LaSalleEd

  3. Six interconnected, though not dependent, days… • Mastery in Mathematics • Concrete, Pictorial, Abstract, Language • Bar Modelling • Deeper Understanding in Mathematics • Embedding Problem Solving in Mathematics • Making Maths Memorable - Lessons for Cognitive Science

  4. 0930 - 1030   Welcome, Introduction and Cuisenaire Rods 1030 - 1115   Bar modelling 1115 - 1130   Coffee break 1130 - 1230   Algebra tiles 1230 - 1315   Lunch 1315 - 1415   Approaches to equations 1415 - 1515   Using paper 1515 - 1530   Any questions and farewells

  5. Connecting the learning

  6. Jerome BrunerAmerican (1915 –2016) Concrete – Pictorial – Abstract (E-S-I) Zoltan Dienes Variation Theory Hungarian (1916– 2014) Richard Skemp Conceptual and procedural understanding British (1919 – 1995)

  7. Application Conceptual Understanding Procedural Fluency

  8. Kilpatrick, Swafford, Findell - 2001 - Adding It Up Helping Children Learn Mathematics

  9. Cuisenaire Rods 22 12 10 6 4

  10. Cuisenaire Rods

  11. Cuisenaire Rods b = g + y o = 5r

  12. Cuisenaire Rods 7 + 3 + 4 10 + 4

  13. Cuisenaire Rods 4 + 8 + 3 4 + 8 + 3 = 4 + 6 + 2 + 3 = 10 + 5 = 15

  14. Cuisenaire Rods 9 – 4 = 5 or What is the difference?

  15. Cuisenaire Rods 6 × 4 = 4 × 6

  16. Cuisenaire Rods 12 × 4 = 48

  17. Cuisenaire Rods 12 × 13 = 156

  18. Cuisenaire Rods

  19. Cuisenaire Rods

  20. Cuisenaire Rods

  21. Cuisenaire Rods 1/3 ×1/4 =

  22. Cuisenaire Rods 2/3 ×1/4 =

  23. Cuisenaire Rods 2/3 ×1/4 =

  24. Cuisenaire Rods 3/4 ÷1/2 =

  25. Cuisenaire Rods Using each number once, place the numbers 11, 12, 13, 14, 15 and 16 in the circles, such that the sum of the three numbers on each side of the triangle is 40.

  26. Cuisenaire Rods

  27. Cuisenaire Rods

  28. Bar modelling Nick has 3 apples and Becky has 5 apples. How many apples do they have altogether? ? Nick Becky ? Nick Becky ? 3 Nick Becky Nick Becky 8 3 + 5 = 8 5 3 Nick Becky

  29. Bar modelling Solve… Matthew has a 300g block of cheese. He eats of the cheese and puts the rest back in the fridge. How much cheese did Matthew put back in the fridge? Model Calculations 300g 60 300 ÷ 5 = 60 60 60 60 60 3 x 60 = 180 Eats Put back ? 180

  30. Bar modelling 3a + 4 = a + 8 Model Calculations = a + 8 3a + 4 a a a 4 -a -a 2a + 4 = 8 -4 -4 8 a 4 2a = 4 ÷2 ÷2 a = 2

  31. Bar modelling Solve 2a + 3 = a + 7 2a + 3 = a + 7 a a 3 -a -a a + 3 = 7 -3 -3 a 7 4 a = 4

  32. Word Problems Raju had 3 times as much money as Gopal. After Raju spent $60 and Gopal spent $10, they each had equal amount of money. How much money did Raju have at first? Model Calculations $10 $50 50 ÷ 2 = 25 $75 ? Raju $25 $25 $25 3 x 25 = 75 $60 Gopal $10 Primary Mathematics volume 6B

  33. Naomi has 85p She has 20p less than her sister How much money do Naomi and her sister have altogether? Show using different manipulatives

  34. Bar modelling Sarah was given a gift of £240. She spent 3/8 of the money and put the rest in savings. How much did Sarah save? £240 £30 £30 £30 £30 £30 £30 £30 £30 spends saves £150 £90

  35. Tom has half as much money as Amit. Amit has £30 less than Nihal but £40 more than Ben. If the mean amount of money the four people have is £120, how much money does Ben have? Ben has £_____. IM Assessment Book 5 P.70

  36. There are 1250 marbles in a box. There are 150 more red marbles than blue marbles. There are twice as many green marbles as red marbles. There are only three different colours of marbles. How many blue marbles are there in the box? There are _____ blue marbles in the box. IM Assessment Book 4 P. 74

  37. The difference between two numbers is 285. If the larger number is 4 times the smaller number, find the sum of the two numbers. Comparison multiplicative models

  38. Algebra Tiles

  39. Which question is hardest? 168 ÷ 12 Factorisex2 + 5x + 6 Factorise2x2 + 5x + 2 Write x2 + 4x + 3 in completed square form Divide (2x2 + 5x + 3) by (x + 1) Connecting the learning

  40. 168 ÷12 Connecting the learning 168 12

  41. 168 ÷12 Connecting the learning 168 12 120 48

  42. 168 ÷12 14 Connecting the learning 168 12 120 48 48 0

  43. Factorisex2 + 5x + 6 (x + 2) (x + 3) Connecting the learning

  44. Factorise 2x2 + 5x + 2 Connecting the learning

  45. Factorise 2x2 + 5x + 2 (2x + 1) (x + 2) Connecting the learning

  46. Write x2 + 4x + 3 in completed square form Connecting the learning

  47. Write x2 + 4x + 3 in completed square form Connecting the learning (x + 2)2 – 1

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