One of the most common questions I receive when I am working with a group of elementary math teachers is, “what does homework look like with this new way of teaching math?” To elaborate a bit more, when during class time, students are working on number talks and problem solving done with a group of students, how do we take that collaborative learning home?

Here are a few suggestions that are influenced by Lydia Song who put on a great workshop on extending and connecting number talks and problem solving.

Number Talk – Have the students do a number talk for homework with the directions, “solve the problem in two different ways. Show your thinking.” Below the two columns, have students explain one of their strategies and why it is an efficient way to solve the problem.
One of These Things – Students are given 4 numbers, pictures, or equations and need to explain why one of them is not like the others. The ultimate objective is for students to be able to provide mathematical reasoning for why each one of the 4 is different than the others.
Same, Same, Different – Copy 2 samples of student work from a number talk or problem solving side by side. Students then write about how the strategies are the same and how they are different.
Make it Easy- What number would you put in this equation to make it easier to solve? 39 + _____ + 46 = You can put any number in the blank. The key is to explain why did you select that number and why did that number make the problem easier to solve. “I would add a 1 to this problem because 39 and 1 makes 40 and 40 plus 46 is an easy problem to solve. 86” You can have the students answer each one of these in two different ways. “Another way is to add 5. I would add 5 because 4 goes to 46 to make 50 and 1 goes to 39 to make 40. 40+50= 90.” Or “I added 61 because 61 and 39 is 100 so 100+46=146.”
Which Strategy is More Efficient – This is set up the same as Same, Same, Different above with two student strategies put sided by side. The prompt is for students to analyze the work to determine which strategy is more efficient and why.

KEY CONSIDERATIONS
Homework gives parents a glimpse of what math looks like in the classroom. What message do you want to send parents? What message does a page of similar math problems on a worksheet send parents? Parents want to know what is happening at school so regular homework is important.

If students can’t do it at school, they can’t do it at home. If you have students solve 432 ÷ 12 = in at least two different ways for homework, be sure they have a variety of different strategies for solving similar problems in class first.

This is new to teachers, new to parents, and new to students. Be sure students have done similar assignments in class before they become homework. If a child goes home and says, “ I don’t understand what to do”, it often leaves parents with a negative perception of shifts in math education. With this in mind, I like the above homework ideas because they can become routine and problems and strategies can easily be swapped out to match the weekly content.

All of the above incorporate the standards of mathematical practice while building conceptual understanding and fluency.