1. 16 Misconceptions

2. 1 2 < 3 4 3 > 1 7 2 > 2 Can you identify the misconception? What might this student believe to be true about all fractions?

3. 6 961 - 537 Can you identify the misconception? 43 What is the misconception?

4. How many circles? Can you identify the misconception? 10 Can you tell what this student likely did when counting?

5. Round to the nearest ten. Can you identify the misconception? 23 20 86 90 184 200 4,369 4,000 What does this tell you about the student’s understanding of rounding?

6. 1 3 < Can you identify the misconception? 1 4 1 10 > 1 7 What likely happened here?

7. 387.265 Can you identify the misconception? What digit is in the tenths place? 6 What digit is in the hundredths place? 2 The “2” reveals something very useful, and then we realize that the student’s reason for answering “6” is incorrect. What was it?

8. Can you identify the misconception? Is the number of circles odd or even? od d Why might this student have decided to respond with “odd?”

9. Can you identify the misconception? Identify the digit in each place. 4.261 hundredths _____ thousandths _____ 6 2 What does “2” thousandths reveal about the student’s understanding?

10. Can you identify the misconception? Divide each shape into thirds. Why were the lines drawn like this?

11. Can you identify the misconception? What is ten more? 56 Does this look familiar? Do you know why a student may write 46 in the box?

12. Can you identify the misconception? Is each number prime or composite? 72 __________57 __________ pr im e Why? This student had a specific reason for writing “prime.” What do you think it was?

13. Can you identify the misconception? Evaluate. 5 ×2³ Can you see specifically where this number came from? What misconception does this reveal?

14. Can you identify the misconception? What is the volume? 4 cm 3 cm 10 ½ cm Why 60? Look carefully.

15. Can you identify the misconception? Each box has 9 mints. There are 6 boxes. Chuck ate 2 mints. How many are left? Do you see how the student interpreted the language?

16. Can you identify the misconception? 95, 96, 97, _____, _____, _____, _____ 98 991001001 Why 1001?

17. Can you identify the misconception? 012345678910 3 + 4 =2 + 8 =5 + 3 = Can you tell specifically what the student did in each case? Is this a misconception?