Test 2 study topics (sample problems coming soon)
Derived fact strategies questions:
1. Describe two ways to use derived fact strategies to solve 7+9
2. Tell a basic addition fact for which using doubles would be a more efficient strategy than counting on.
3. Tell a basic addition fact for which making 10/using 10 would be a more efficient strategy that counting on.
4. Tell a basic addition fact that you can't use the make 10 strategy to solve.
5. Describe how to solve 14 - 8 by a. building up through 10 and b. backing down through 10.
6. Tell a basic subtraction fact that you can't solve by backing down through 10.
7. Show how so use doubles to solve 7+9 using ten frames.
8. Show how you would write a use doubles strategy solution of 7+9 using equations.
9. Show how to use the make 10 strategy to solve 7+9 on ten frames
10. Show how to use the make 10 strategy to solve 7+9 on a number line (in the more efficient way)
11. Show how you would write a make 10 strategy solutions of 7+9 using equations
12. Show how you would show a build up through 10 strategy for solving 14-8 on a number line
13. Show how you would wite a build up through 10 strategy for solving 14-8 using equations.
14. Show how you would show a back down through 10 solution for 14-8 on a number line
15. Show how you would write a back down through 10 solution for 14-8 using equations.
Equals signs and fixing running equations
16. If we say we want children to understand the correct meaning of the equals sign, what is it that we want children to understand?
17. What is the most common misunderstanding children have about the equals sign?
18. Write a tricky equals sign problem (that children would get wrong if they don't understand the correct/balance meaning of the equals sign):
19. Fix these equations so that they show the same steps, but there is no incorrect use of the equals sign:
a. 6 × 4 = 24 ÷ 2 = 12 × 4 = 48 + 36 = 84
b. (1/3) × 36 × 5 = (1/3) × 180 = 120 + 36 = 156
20. In a way that uses equals signs properly, write down this strategy for subtracting 73-29:
"First I took away 30 from 70, because 30 is close to 29, and that gave me 40, and then I had to add 1 back on because it was 29 and not 30, so I got 41, and then I added the 3 and got 44." (Note that you don't have to write down all of the reasons, just the calculations that were actually done.)
Base 10 manipulatives
21. Explain the difference between a proportional and a non-proportional manipulative and give an example of each.
22. Explain the difference between a decomposable/groupable manipulative and a non-decomposable manipulative, and give an example of each.
23. If I use lima beans to show 1's, and glue 10 lima beans each to a bunch of popsicle sticks to show 10's, is that decomposable or not decomposable? Is it proportional or non-proportional?
24. When choosing a base 10 manipulative for first grade students, what properties would you want that manipulative to have?
Childrens understanding of base 10 numbers
25. Describe two different ways that base 10 understanding was assessed in the video interviews you watched (Marilyn Burns talking to Cena and Jonathan). Why might children seem to understand base 10 numbers in one assessment and not in the other?