All questions
Question 1
Sara makes this pattern with blocks: First she puts 5 blocks in one way: 5=1+4. Then she moves exactly 1 block to make a different way. What is her new equation?
- Sara's new equation could be 5=0+5
- Sara's new equation could be 5=2+3 (correct answer)
- Sara's new equation could be 5=3+2
- Sara's new equation must be 5=4+1
Explanation: Starting with 5 = 1 + 4, moving exactly 1 block from the group of 4 to the group of 1 gives 5 = 2 + 3. Distractor A requires moving 1 block out entirely. Distractor C is the same as B just reordered. Distractor D assumes moving from the smaller group to larger group, but this would require moving 3 blocks, not 1.
Question 2
Review the number line. If you move from 0 to show 6=2+4, what is the correct sequence of moves?
- Move right 2 spaces, then move right 4 more spaces to reach 6 (correct answer)
- Move right 4 spaces, then move left 2 spaces to reach 6
- Move right 6 spaces, then move left 2 spaces to reach 4
- Move left 2 spaces, then move right 4 spaces to reach 6
Explanation: To show 6 = 2 + 4 on a number line starting from 0, you move right 2 spaces (to position 2), then right 4 more spaces (to position 6), demonstrating the addition of the two parts. Distractor B would end at position 2, not 6. Distractor C starts with the total instead of the parts. Distractor D would end at position 2, not 6.
Question 3
Using the diagram, which statement about decomposing 7 is correct?
- The diagram shows exactly 2 ways to decompose 7
- The diagram shows exactly 3 ways to decompose 7 (correct answer)
- The diagram shows exactly 4 ways to decompose 7
- The diagram shows exactly 5 ways to decompose 7
Explanation: The diagram shows three valid decompositions: 7 = 1 + 6, 7 = 2 + 5, and 7 = 3 + 4. Students choosing A might miss one decomposition or miscount. Students choosing C might count 4 + 3 as different from 3 + 4. Students choosing D might include invalid combinations or double-count.
Question 4
Anna writes: 4=1+3 and 4=2+2. She wants to write one more equation to show all the ways to make 4. What should her third equation be?
- Anna's third equation should be 4=3+1 to complete all ways
- Anna's third equation should be 4=0+4 to complete all ways (correct answer)
- Anna's third equation should be 4=4+0 to complete all ways
- Anna already has all the ways to make 4 written down
Explanation: The ways to make 4 with different number pairs are: 4 = 0 + 4, 4 = 1 + 3, and 4 = 2 + 2. Anna has 1 + 3 and 2 + 2, so she needs 0 + 4. Choice A (3 + 1) is the same as 1 + 3, just switched around. Choice C (4 + 0) means the same as 0 + 4. Choice D is wrong because Anna is missing one way.
Question 5
Ben wants to show 8=3+5 using red and blue crayons. He colors some circles red and some blue. How many circles should he color red?
- Ben should color exactly 3 circles red and 8 circles blue
- Ben should color exactly 5 circles red and 3 circles blue
- Ben should color exactly 3 circles red and 5 circles blue (correct answer)
- Ben should color exactly 8 circles red and no circles blue
Explanation: To show 8 = 3 + 5, Ben needs 8 total circles with 3 red and 5 blue, representing the addends 3 and 5. Distractor A uses 11 total circles (3+8). Distractor B reverses the colors (5 red, 3 blue). Distractor D ignores the decomposition entirely.