1. What Is the Concrete- Representational-Abstract (CRA) Instructional Approach? “CRA is an intervention for mathematics instruction that research suggests can enhance the mathematics performance of students with learning disabilities. It is a three-part instructional strategy, with each part building on the previous instruction to promote student learning and retention and to address conceptual knowledge.” http://www.k8accesscenter.org/training_resources/documents/CRAApplicationFinal_000.pdf

2. The CRA instructional sequence consists of three stages: concrete, representation, and abstract: Concrete. “In the concrete stage, the teacher begins instruction by modeling each mathematical concept with concrete materials (e.g., red and yellow chips, cubes, base ten blocks, pattern blocks, fraction bars, and geometric figures).” http://www.k8accesscenter.org/training_resources/documents/CRAApplicati onFinal_000.pdf — +

3. The CRA instructional sequence consists of three stages: concrete, representation, and abstract: Representational. “In this stage, the teacher transforms the concrete model into a representational (semi- concrete) level, which may involve drawing pictures; using circles, dots, and tallies; or using stamps to imprint pictures for counting.” http://www.k8accesscenter.org/training_resources/documents/CRAApplicati onFinal_000.pdf

4. The CRA instructional sequence consists of three stages: concrete, representation, and abstract: Abstract “At this stage, the teacher models the mathematics concept at a symbolic level, using only numbers, notation, and mathematical symbols to represent the number of circles or groups of circles. The teacher uses operation symbols (+, –,×, ÷ ) to indicate addition, multiplication, or division.” http://www.k8accesscenter.org/training_resources/documents/CRAApplicati onFinal_000.pdf

5. Vocabulary You Should Know Addends, Sum, menuend, subtrahend, difference, mixed/multiple signs, factors, products, divisor, dividend, quotients, absolute value, opposites CRA Sequence of Instruction, manipulatives, pedagogy, concrete, representational, and abstract

6. — — + +

7. What is 4 + 3 ? + + + ++ + ++ + + + + + + + + The Answer is 7.

8. What is -2 + -4? — — — — — — ———— ——— The Answer is -6.

9. What is -3 + 1? — — — ———— The Answer is -2. + + ———— +

10. What is 2 + (-5)? — — — The Answer is -3. + ———— + — + — —— + ———— + —— +

11. What is 5 + 2? The Answer is 7.

12. What is -3 + -3? The Answer is -6.

13. What is -3 + 5? The Answer is 2.

14. What is -5 + 2? The Answer is -3.

15. What is 15 + 14? The Answer is 29. What is -12 + (-4)? What is 5 + (-4)? The Answer is -16. The Answer is 1. What do you think?

16. — — + +

17. What is 5 – 3? + + + + + The Answer is 2.

18. What is -5 - -2 ? — — — — — The Answer is -3.

19. What is 5 – (-6) ? + + + + + + — — — — — — ++ ++++ ++++ ++ ———— ——— + + + + + + The Answer is 11.

20. What is 3 - 6 ? + + + — — — ++ +++ +++ —— — — + + + The Answer is -3.

21. What is -6 - 3 ? — — — ++ +++ — — — — + + + The Answer is -9. — — — ——— — —— — — —

22. What is 4 - 2? The Answer is 2.

23. What is -3 - -2? The Answer is -1.

24. What is 7 - 8? The Answer is -1.

25. What is 6 - -3? The Answer is 9.

26. What is -7 – (-9)? The Answer is 2. What is 13 -15? What is 12 – (-2)? The Answer is -2. The Answer is 14. What do you think?

28. What is 3 x 5? +++++ The Answer is 15. +++++ +++++

29. What is 3 x -5 ? ————— The Answer is -15. ————— —————

30. What is -3 x 2 ? — ++ + ———— ——— + The Answer is -6. —+ —+ —+ —+ —+ ++ +++ Empty

31. What is -3 x (-2) ? — ++ + ———— ——— + The Answer is 6. —+ —+ —+ —+ —+ ++ +++ Empty

32. What is 3 x -4? The Answer is -12.

33. What is -3 x -4? The Answer is 12.

34. What is -7 x (-3)? The Answer is 21. What is 13 x (-2)? What is -12 (2)? The Answer is -26. The Answer is -24. What do you think?

36. What is 8 ÷ 2? ++++ The Answer is 4. ++++ ++++ ++++

37. What is -16 ÷ 4 ? ———— The Answer is -4. ———— ———— ———— ———— ———— ———— ————

38. What is -9 ÷ (-3)? The Answer is 3. What is ? What is -12 /2? The Answer is -7. The Answer is -6. What do you think?

39. In Groups of 2-4, create your own Power Point Lesson. You can choose any topic, but you must use the concrete or the representational method of instruction. You will have 30 minutes to prepare a 5 minute lesson. You will be timed so make sure you restrict your lesson to 5 minutes.

40. Here are some suggested topics with corresponding links From the Promethean Planet website. Absolute Value Additive Inverses (Opposites) Ordering Numbers on the Number Line Rational or Irrational Numbers Rounding