Download Low Floor, High Ceiling Math Questions Grades 6

Low Floor, High Ceiling Math Questions
Grades 6-8
Number and Operations
1. Which number does not belong and why? Use words like factor,
multiple, odd, even, prime and composite to support your thinking.
24, 12, 2, 11
2. Explain how each number below is different
81 √81 36 14
3. You can find the difference between two integers by doubling the
first integer. What might the computation be?
4. If you add three integers and get a sum of zero, what could the
integers be?
5. The product of three integers is (-48). What could the integers be?
6. Place one square root, one integer and one fraction on the number
line below. How did you decide where to place your numbers?
2√2
7. The hypotenuse of a right-angled triangle is between 8 and 9. What
might have been the measurements of the other 2 sides?
8. My number is between 3 and 4 million. All digits are odd. The digits
in the thousands period are the same and the digits in the ones
period are the same. All my digits add up to make 31. What could my
number be?
9. I am thinking of a two-digit number. It is odd and has only three
factors. What number(s) might I be thinking of?
10. For a given pair of numbers, how can you tell whether the least
common multiple will be less than or equal to their product?
11. You add two irrational numbers and the answer is around 20. What
numbers might you have added?
12. A multiple of π is estimated to be 5000. What might it be?
13. Can a square number be a prime number? Why or why not?
14. Using the numbers 1,2,3 and 4, create the largest possible product
by filling in the blanks and then the smallest possible product:
__x__
___x_
15. Create a division problem with a remainder of 18. How does the
remainder affect your solution?
16. What four-digit number can be divisible by two, three, five and six.
Explain your thinking.
17. Last year the ratio of boys to girls at camp was three to one. How
would enrollment have to change in order for the ratio to be one to
two?
18. That ratio of cats to dogs in a neighbourhood is exactly 2.4 to 1. How
many cats and how many dogs might be in this neighbourhood?
19. 4 is a factor of two different numbers. What else might be true
about both of the numbers?
20. Choose two fractions with different denominators. Tell how to
compare them.
21. How are numbers 6.001 and 1.006 alike? How are they different?
22. You add a 3-digit number to 348. You do not find it difficult to do it
in your head. What might you be adding? Why is it easy?
23. You add two different 2-digit numbers. Then you multiply them.
About how much do you think the difference between those answers
would be? Explain.
24. About how many days have you been in school? Tell how you
estimated and what mathematical operations you used.
25. Create a sentence that use these number and words:
5, 3995, share, almost
26. You know 5 x 6 = 30. What decimal multiplication could you work
out using this fact?
27. Create a question involving multiplication and division of decimals
where the digits 4,9, and 2 appear somewhere.
28. You multiply two fractions. The result is 24/60. What numbers might
you have been multiplying?
29. You divide two fractions and the numerator of the quotient is a 4.
What could the fractions be?
30. You know 60% of the students in a school are participating in a
special fundraiser. If between 200 and 400 students are participating,
exactly how many students might be in the school? How do you
know?