Test 1 things to study: Measurement and equality.

Equality:

1. When it says in CCSS" "understand the meaning of the equals sign", what are children supposed to understand that it means? (Your explanation should use different vocabulary than "it means that both sides are equal").

2. What is the most common misunderstanding about the equals sign?

3. Write a tricky missing number problem that would tell you whether children misunderstood the equal sign or not. Explain what makes the problem tricky.

4. Explain and give examples of what true-false equations are and how they are relevant for discussing the meaning of the equals sign.

5. Fix these equations so that they mean the same thing, but there are equals signs that don't work:

a. 6 × 7 = 6 × 5 = 30 + 6 = 36 + 6 = 42

b. 4 × 4 = 16 ÷ 2 = 8

Measurement:

6. What is the difference between standard and non standard units? Give examples.

7. What important concepts do children learn from working with non-standard units?

8. Why are standard units important?

9. Explain what in indirect comparison of lengths is. Give an example.

10. What would be a good non-standard unit for measuring the length of the whiteboard? Estimate how long the white board is in terms of your non-standard unit.

11. What would be a good standard measurement tool for finding the circumference of your head?

12. What is conservation of number? What is conservation of length? Conservation of volume?

13. What is a common error children use when using a ruler?

14. Give a benchmark for length in inches, feet, cm and meters.

15. A book is 20 cm across. Is that significantly shorter than the width of your paper (less than 2/3 of the width of your paper) ? About the same as the width of your paper? About the same as the length of your paper? Significantly longer than the length of your paper? Explain how you estimated the answer without measuring (I'm looking for a sensible explanation and a reasonable estimate)

16. Write and solve Join or PPW (addition) Separate (take away) a nd Comparison word problems using length measurements.

17. Find horizontal and vertical lengths and perimeters on a grid

18. Find areas consisting of whole squares and half-squares on a grid.

19. Estimate areas of irregular shapes on a grid

20. Explain how to find a perimeter of an irregular shape (what tools would you use? What would you do with them?)

21. Explain how a diagonal length on a grid is different from a horizontal or vertical length.

22. Explain what the most common errors are when measuring on a grid.

23. Given a fixed area, tell what would be the rectangle with the smallest perimeter

24. Given a fixed perimeter, tell what would be the rectangle with the largest area.

25. Given a fixed perimeter, tell how to make a rectangle with a very small area

26. Illustrate the distributive law using rectangle area as a way of thinking about multiplication

27. Explain what makes estimating and comparing weights and volumes tricky.

28. Write addition, subtraction and multiplication word problems using volume or weight.

Answers to selected problems