1. Using Concrete and Pictorial Tools to Help Students Understand Fractions

2. srpowell@austin.utexas.edu @sarahpowellphd
119

3. Instructional Platform
INSTRUCTIONAL DELIVERY
Explicit instruction
Precise language
Multiple representations
INSTRUCTIONAL STRATEGIES
Fluency building
Problem solving instruction
Motivation component

4. Explicit Instruction Modeling Practice Clear Explanation Guided
Independent Practice
Planned
Examples
Supporting Practices
Asking the right questions
Eliciting frequent responses
Providing immediate specific feedback
Maintaining a brisk pace

5. Use formal math language
Precise Language
Use formal math language
concise
Use terms precisely

6. Multiple Representations
Abstract
Pictorial
Concrete

8. Length/Measurement Fractions are appropriated by length
Fraction tiles/bars

9. Length/Measurement Fractions are appropriated by length
Cuisenaire rods

10. Length/Measurement
Fractions are appropriated by length
Number line

11. Select a fraction and teach using the length model.
Explicit instruction
Precise language
Multiple representations

12. Area/Region
Shapes divided into equal sections
Fraction circles

13. Area/Region
Shapes divided into equal sections
Geoboards

14. Area/Region
Shapes divided into equal sections
Pattern blocks

15. Area/Region
Shapes divided into equal sections
Legos

16. Area/Region
Shapes divided into equal sections
Anglegs

17. Select a fraction and teach using the area model.
Explicit instruction
Precise language
Multiple representations

18. Set/Discrete
Individual shapes match the fraction
Two-color counters

19. Set/Discrete
Individual shapes match the fraction

20. Select a fraction and teach using the set model.
Explicit instruction
Precise language
Multiple representations

22. Improper Fractions Mixed Numbers
Fractions equal to or greater than 1 Numerator is equal to or greater than denominator
Select a fraction and teach using two models of fractions.
Explicit instruction
Multiple representations
Precise language
Mixed Numbers
A mix of a whole number and a fraction

23. Equivalent Fractions Determine equivalent fractions.
Explicit instruction
Precise language
Multiple representations

24. Multiple representations
Comparing Fractions
Compare two fractions.
Explicit instruction
Precise language
Multiple representations

25. Multiple representations
Ordering Fractions
Compare to benchmark fractions
Order three fractions.
Explicit instruction
Precise language
Multiple representations

27. Addition

28. Addition

29. Multiple representations
Explicit instruction
Precise language
Multiple representations

30. Addition

31. Addition
2: 2, 4, 6, 8, 10
4: 4, 8, 12, 16, 20

32. Addition

33. Multiple representations
Explicit instruction
Precise language
Multiple representations

34. Subtraction

35. Multiple representations
Explicit instruction
Precise language
Multiple representations

36. Subtraction
Take away from this set
This is for reference

37. Multiple representations
Explicit instruction
Precise language
Multiple representations

39. Multiplication Multiplication Interpret multiplication sign as “of”

40. One-half of four-fourths
Multiplication
Show
One-half of four-fourths

41. One-half of two-fourths
Multiplication
Show
One-half of two-fourths

42. One-half of one-fourth One-half of one-fourth
Multiplication
Show
One-half of one-fourth
One-half of one-fourth

43. One-half of three-fourths
Multiplication
Show
One-half of three-fourths

44. One-half of one-fourth One-half of one-fourth One-half of one-fourth
Multiplication
Show
One-half of one-fourth
One-half of one-fourth
One-half of one-fourth

45. Multiplication
Show

46. Multiplication

47. Division
Division
“How many sets of the second fraction fit into the first fraction?”

48. Division Show 1 set of one-third 2 sets of one-third

49. Division
Show
1 set of one-third
2 sets of one-third

50. Two-thirds set of one-half
Division
Show
1 set of one-half
Two-thirds set of one-half

51. Division
Show

52. Division

53. Instructional Platform
INSTRUCTIONAL DELIVERY
Explicit instruction
Concise language
Multiple representations
INSTRUCTIONAL STRATEGIES
Fluency building
Problem solving instruction
Motivation component

54. srpowell@austin.utexas.edu @sarahpowellphd
119