Number Routine, Number Talk or Problem String?

Posted on by

smith
Nina Smith

Math Teacher grades 3-5 and Math Specialist grade K-8

Marcy Open School, Minneapolis Public Schools

MCTM Region 5 Director

The terms number routine, number talk, and problem string, are often used interchangeably. Recently I have been wondering is there a difference? And if so, how would I describe it and when should I use one over the other?

Routines in any classroom, especially math, are important for many reasons. There are routines that we establish for organization and structure of our class and there are routines that we use to develop students mathematical understanding, reasoning and flexibility. Routines are the universe that number talks and problem strings live in. McCoy, Barnett and Combs (High-Yield Routines: Grades K-8) describe a high-yield routine as having the following characteristics:

  • A structured activity that helps students gain proficiency with a range of concepts and practices
  • Offer access to the big ideas of mathematics and allow deep understanding of concepts
  • Give students opportunities to develop expertise with the eight Standards for Mathematical Practice (Common Core Standards)
  • Offer opportunities for students to demonstrate their thinking and for teachers to gain insight into the thinking of their students

Both number talks and problem strings are routines that accomplish these goals.

Kara Imm and Rachel Lambert posted on numberstrings.com a comparison between the two powerful routines. Both routines represent student’s strategies and the teacher’s role is to facilitate discussion. They differ in that a number talk uses a single problem that generates multiple solution strategies and a problem string uses a purposeful sequence of problems to funnel students to use a chosen strategy.

This winter I used Marilyn Burns’ Math Reasoning Inventory to assess whole number thinking of a group of twenty-two sixth grade students who were in a 30-minute daily intervention class. The inventory (https://mathreasoninginventory.com/Home/Index) is an online formative assessment tool designed to reveal the strategies students use to reason with whole numbers, decimals and fractions. This assessment was an individual interview. I asked the students 10 questions that they were expected to answer using mental math strategies. 64% of the students could not answer or answered incorrectly 60 x 40. The students who could answer this question mentally used some version of the associative property (6 x 4 x 100). The students who could not answer this question attempted the standard algorithm in their head or some version of 6 x 4 plus a zero. The most common wrong answer was 240 but one student answered 1024. His thinking was 6 x 4 is 24 and you have to add a zero for the 10 so he put it in front. I needed to nix the times ten is the same as adding a zero trick.

I wasn’t sure whether to create a number talk or a problem string so I crafted both. My number talk would be a problem like 60 x 40. I could start with problems like these below to get students to see the pattern when multiplying by 10.

6 x 4

6 x 10

6 x 40

60 x 4

60 x 40

I was worried that if I started here I might not get a variety of strategies from my students. Since most of my students relied on the standard algorithm and/or added a zero for multiplying by 10, I assumed this might reinforce their misconceptions. I decided my goal was to highlight how the associative property could help us to break apart our numbers to make multiplication easier. So I crafted this problem string:

4 x 10 = 10 + 10 + 10 + 10                                            T/F

4 x 10 = (4 x 1) + 0                                                         T/F

6 x 40 = (6 x 10) + (6 x 10) + (6 x 10) + (6 x 10)     T/F

6 x 40 = 2 (6 x 10) + 2 (6 x 10)                                    T/F

6 x 40 = 4 x 6 x 10                                                          T/F

60 x 40 = (6 x 4) x (   ?   x    ?   )

60 x 40 = ?

This allowed all of my students an opportunity to have a rich discussion connecting the concept of equal grouping in multiplication to use the associative property for multiplication. With the structure of having to prove each statement true or false students had to think about their reasoning and build a justification for each number sentence. My students needed a more direct experience to build the idea that we can change the grouping of factors and it does not change the product. In fact it can make the problem easier to solve. Once my students had enough experience with this idea then moving to a number talk about multiplying by a power of 10 with one problem was more successful. More of my students had a strategy other than adding a zero.

In conclusion, number talks and problem strings are both high-yield routines that can be used to develop mathematical understanding in students who reason efficiently, flexibly and accurately. One is not better than the other, but it is important to consider where your student’s level of understanding is when choosing the appropriate routine in the moment. It is essential to build opportunities in the classroom where students understand numerical relationships are not based on memorization of rules or tricks.