RME Talk Sept 2013

Transcript

1. Developing  Algebraic   Reasoning  Using   Progressive   Formalization   Kim Bunning, Instructor, CU Boulder bunning@colorado.edu cuteach.colorado.edu
2. Colored  Tiles   16 62 55 64 ? ? 51 40
3. 81 66 52 60 ? 65 88 ?
4. CCMS  -­‐  Algebra   CCSS.Math.Content.6.EE.C.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity … in terms of the other quantity. Analyze the relationship between the two variables using graphs and tables, and relate these to the equation.
5. Equality  &  Relationships   What are all of the possible answers children might give for the question, “What goes in the box?” 6 + 2 = +3 Explain each possible answer. Include different explanations for the same answer if necessary. Carpenter, Franke, & Levi, 2003
6. Two  Views  of  Equality   Computational Output (or ‘the answer is’) 6 + 2 =8 8 - 3= 5 Relational 6 + 2 = 5 + 3 Carpenter, Franke, & Levi, 2003
7. How many bananas do you need to balance the third scale? Math in Context, Comparing Quantities, 2006
8. Who will win the tug of war and why? Math in Context, Comparing Quantities, 2006
9. ?
10. School Store Info: What combinations make the total $1.05 Erasers Price 0 $0.00 1 $0.25 2 $0.50 3 $0.75 4 $1.00 Pencils Price 0 $0.00 1 $0.15 2 $0.30 3 $0.45 4 $0.60 Math in Context, Comparing Quantities, 2006
11. Looking at Combinations: Chart 15 40 0 25 0 1 2 3 4 Number of Erasers 4 3 2 1 0 Number of Pencils Math in Context, Comparing Quantities, 2006
12. Looking at Combinations: Patterns 60 85 110 135 160 45 70 95 120 145 30 55 80 105 130 15 40 65 90 115 0 25 50 75 100 Number of Pencils 4 3 2 1 0 0 1 2 3 4 Number of Erasers Math in Context, Comparing Quantities, 2006
13. $50.00 $50.00 Hats & Sunglasses Math in Context, Comparing Quantities, 2006
14. Math in Context, Comparing Quantities, 2006
15. S M L Weight (in kg) 0 1 1 10.6 1 0 1 8.5 1 1 0 6.1 How can you find the total weight of the three chickens by using notebook notation? Make new combinations until you find the weight of each chicken. Math in Context, Comparing Quantities, 2006
16. Relational  Thinking  -­‐   Revisited   Larson