This document discusses using Cuisenaire rods to develop conceptual understanding of mathematical concepts. It provides examples of spatial puzzles and activities with the rods to help children decompose and recompose shapes. These activities build the foundation for understanding geometry. Examples also show using the rods to represent numbers in different ways, compare quantities, explore properties like commutative and distributive, build patterns, use measurement conversion and develop fraction concepts. The document emphasizes that experiences with the manipulatives are important for building number sense and geometry understanding in children.

1. Conceptual Understanding
Through Cuisenaire Rods
Surrey Focus Day • February 2020

2. Chris Hunter
K-12 Numeracy Helping Teacher
reflectionsinthewhy.wordpress.com
@ChrisHunter36
hunter_c@surreyschools.ca

3. Spatial Puzzles

4. Spatial Puzzles

5. Spatial Puzzles

6. 171789171790

7. “Just as experiences composing and
decomposing numbers are important
for the development of children’s number
sense […], it is important for children’s
understanding in geometry that they
experience decomposing a shape into
small parts and recomposing those parts
into a whole.
Spatial Thinking
174344

8. The ability to predict what shape is made
when geometric shapes are put together to
form a new and composite shape is the
beginning of a strong foundation for
future success in geometry.”
Spatial Thinking
174344

9. Number/Colour Match

10. Number/Colour Match

11. Jumping Frogs

15. Concept Circle

16. 12
424
27
36
6
9
183

17. 12
424
27
36
6
9
183 You choose:
or

18. 424
27
36
6
9
183 You choose:
or
121

19. 1
3
2
21
4
3
1
2
3
4
3
2
1
4 You choose:
or
1

20. You choose:
or

21. Why or ?

22. “You can represent a number in a variety of ways.
Each representation of a number can focus on a
different aspect of a number.”
–Marian Small

24. “How many ways can you make 1?”

25. constraints

26. Find a rod that is half the length of the orange rod.
Find as many rod pairs as you can that show .
Find as many rod pairs as you can that show .
1
2
1
3
Fraction Pairs

27. 1
2
1
3
Fraction Pairs

28. 1
3
1
3
Fraction Pairs

29. Rod Ratios
What is the ratio of this
pair of Cuisenaire rods?
How do you know?
How many pairs can you
find with the same ratio?

30. Naming Rods

31. 1
Naming Rods

32. 1
?
?
?
Naming Rods

33. ?
?
?
?
? ?
1
?
?
?
Naming Rods

34. ?
1
?
?
?
?
?
?
?
?
Naming Rods

35. “What’s the difference?”
Subtraction
comparison
?

36. “What’s missing?”
part-part-whole
?
Subtraction

37. What Is The Same? What’s Different?

38. What Is The Same? What’s Different?

39. 3 × 5 = 5 × 3
commutative property
What Is The Same? What’s Different?

40. How Many?

41. How Many?
6(5 + 2)
= 6 × 5 + 6 × 2
= 30 + 12
= 42
6(5 + 2)
= 6(7)
= 42
distributive property

42. How Many?
6(5 + 2)
= 6 × 5 + 6 × 2
= 30 + 12
= 42
6(5 + 2)
= 6(7)
= 42

43. Patterns
…

44. Patterns
What comes next?
What else might come next?
How are these patterns the same?
How are they different?
What makes a pattern a pattern?
Do all patterns repeat? …

45. Can they…
build a simple repeating
pattern?
describe their pattern using
attributes?
predict what comes next?
before?
create more complex
patterns?
What to L k For

46. Measurement
If you know a length is 10 light
green rods long, will it be more
or fewer than 10 dark green
rods long?
Will it be more or fewer than 10
red rods long?
How do you know?
1 dark green = 2 light green
1 dark green = 2 light green
2 dark green = 3 light green

47. Measurement
Big Ideas for Measurement
• Familiarity with known
benchmark measurements can
help you estimate and calculate
other measurements.
• The unit chosen for
measurement affects the
numerical value of the
measurement; if you use a bigger
unit, fewer units are required.
K-3: 150663; 4-8: 150668

48. Chris Hunter
K-12 Numeracy Helping Teacher
reflectionsinthewhy.wordpress.com
@ChrisHunter36
hunter_c@surreyschools.ca