The National Council of Mathematics has great problems on their website. Here are some questions that have been put together for the elementary, middle and high school level.

Good Questions: These are good questions that can be used from kindergarten to grade 10. There are multiple entry points for students to answer questions.

Brandon and Vanessa went to their grandfather’s barn. When they got back to the house, their mom asked what they had seen. Brandon said they saw some chickens and pigs. Vanessa agreed and said that she had counted 18 animals. Brandon hadn’t noticed that, but he had counted 52 legs. If Brandon and Vanessa are correct, how many chickens and pigs were there?

The Assessment for Learning Tool helps teachers to make anecdotal notes while working with the class to determine student understanding and to plan for the next lesson. The Assessment Tool is organized to help teachers set a clear Learning Goal, Pre-think of possible strategies the students will use to solve the problem; Misconceptions the students may have about the math and Guiding Question to ask the students to deepen their understanding of the math.

This Assessment for Learning Tool for the chicken and pig question was created by Math Coach, Alana Hardy.

This document has good problem solving questions for the primary grades. This document also has great information on using questions to simulate mathematical thinking. It relates the level of questions we ask to Bloom's Taxonomy.

Figure This! has great word problems for the intermediate grades. Figure This uses the questions as homework but they are great for classroom use. There are 80 word problems on the site.

Figure This! Challenge Questions The Locker Problem Grade(s): 2-8 Strand(s): Patterning & Algebra, Number Sense, Data Management Problem:
In a school of 1000 students, every student has a locker. Imaging that one student opens all the doors of all 1000 lockers.
Then, a second student starts at the second locker and closes every second door.
Then, a third student starts at the third locker and changes the state of every third door (closes it if it was open or opens it if it was closed.)
Then a fourth student starts at the fourth locker and changes the state of every fourth door and a fifth student starts at the fifth locker and changes the state of every fifth door.
After 1000 students have followed the same pattern, which doors will be open and which doors will be closed? What to look for: By the 25th student a recognizable pattern should emerge. While working on this problem (ideally in groups), students may explore factors, multiples, prime numbers and particularly perfect squares. This problem can be done physically in class with paper used as locker doors, taped to the blackboard and students in the class participating in the problem. For older students this provides an opportunity to demonstrate data management skills while solving the problem on chart paper.

Source: Intermediate Math ABQ Package - Summer 2009 (Compiled by Trevor Brown) Posted by: Mark Ross, Norseman JMS Frogs

Grade(s): 4-8 Strand(s): Patterning & Algebra Problem:
Begin the problem by creating a single row of seven connected squares. Start with three "frogs" in a line on the left side and three "toads" on the right side, with a space in between them. Your goal is to move all of the frogs and toads to the opposite side while making as few moves as possible. The amphibians can slide to an adjacent empty space or hopover one other frog or toad to an empty space on the other side.

1) Can you move all of the frogs from the left side to the right and all toads from the right side to the left without moving any backwards?
2) With 3 frogs, 3 toads, and one space between how many moves does it take? How many hops? How many slides?
3) Can you find a formula?
4) What happens when you begin with 9 spaces, 4 frogs and 4 toads? What to look for: This provides a great opportunity for students to work in groups. Students can solve this problem by actively participating in the problem with hula hoops on the ground. They can model it on paper using double-sided counters, or they can use pencil and paper.

Good Questions: These are good questions that can be used from kindergarten to grade 10. There are multiple entry points for students to answer questions.

Brandon and Vanessa went to their grandfather’s barn. When they got back to the house, their mom asked what they had seen. Brandon said they saw some chickens and pigs. Vanessa agreed and said that she had counted 18 animals. Brandon hadn’t noticed that, but he had counted 52 legs. If Brandon and Vanessa are correct, how many chickens and pigs were there?

The Assessment for Learning Tool helps teachers to make anecdotal notes while working with the class to determine student understanding and to plan for the next lesson. The Assessment Tool is organized to help teachers set a clear Learning Goal, Pre-think of possible strategies the students will use to solve the problem; Misconceptions the students may have about the math and Guiding Question to ask the students to deepen their understanding of the math.

This Assessment for Learning Tool for the chicken and pig question was created by Math Coach, Alana Hardy.

Black Line Master of Assessment For Learning.

This document has good problem solving questions for the primary grades. This document also has great information on using questions to simulate mathematical thinking. It relates the level of questions we ask to Bloom's Taxonomy.

Figure This! has great word problems for the intermediate grades. Figure This uses the questions as homework but they are great for classroom use. There are 80 word problems on the site.

Figure This! Challenge Questions

The Locker Problem

Grade(s):2-8Strand(s):Patterning & Algebra, Number Sense, Data ManagementProblem:In a school of 1000 students, every student has a locker. Imaging that one student opens all the doors of all 1000 lockers.

Then, a second student starts at the second locker and closes every second door.

Then, a third student starts at the third locker and changes the state of every third door (closes it if it was open or opens it if it was closed.)

Then a fourth student starts at the fourth locker and changes the state of every fourth door and a fifth student starts at the fifth locker and changes the state of every fifth door.

After 1000 students have followed the same pattern, which doors will be open and which doors will be closed?

What to look for:By the 25th student a recognizable pattern should emerge. While working on this problem (ideally in groups), students may explore factors, multiples, prime numbers and particularlyperfect squares. This problem can be done physically in class with paper used as locker doors, taped to the blackboard and students in the class participating in the problem. For older students this provides an opportunity to demonstrate data management skills while solving the problem on chart paper.Source:Intermediate Math ABQ Package - Summer 2009 (Compiled by Trevor Brown)Posted by:Mark Ross, Norseman JMSFrogs

Grade(s):4-8Strand(s):Patterning & AlgebraProblem:Begin the problem by creating a single row of seven connected squares. Start with three "frogs" in a line on the left side and three "toads" on the right side, with a space in between them. Your goal is to move all of the frogs and toads to the opposite side while

making as few movesas possible. The amphibians canslideto an adjacent empty space orhopover oneother frog or toad to an empty space on the other side.1) Can you move all of the frogs from the left side to the right and all toads from the right side to the left

without moving any backwards?2) With 3 frogs, 3 toads, and one space between how many moves does it take? How many hops? How many slides?

3) Can you find a formula?

4) What happens when you begin with 9 spaces, 4 frogs and 4 toads?

What to look for:This provides a great opportunity for students to work in groups. Students can solve this problem by actively participating in the problem with hula hoops on the ground. They can model it on paper using double-sided counters, or they can use pencil and paper.Source:Intermediate Math ABQ Package - Summer 2009 (Compiled by Trevor Brown)Posted by:Mark Ross, Norseman JMS