Using Number Choice to Differentiate Whole Group Math Instruction

I’m not sure what the official name is for this strategy, but one of my favorite ways to differentiate a problem in a whole group setting is to give students options for the numbers in the problems. It is quick, easy, and you can do this with any problem from any curriculum. I believe the first time I came across this strategy was in the CGI (Cognitively Guided Instruction) book Extending Children’s Mathematics by Susan B. Empson (another fantastic book that I have recommended before and will continue to always recommend!).

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Here’s how it’s done…

• Take out the numbers in a problem and replace them with blanks.

• Choose sets of numbers that would be appropriate for students at different stages in the learning process.

• Offer all sets of numbers as options for students to choose from at the end of the problem, and let them choose which numbers to insert into the problem.

The beauty in this strategy is that it offers students a problem that is appropriate for where they are currently at in their learning. It also gives them choice, which immediately increases engagement and gives them ownership in their learning.

Another great thing about this strategy is that all of your students can be at an equal level of struggle with JUST ONE PROBLEM. The best way to achieve this is to be strategic in the numbers that you select. Think about what strategies students might need to use to solve a specific set numbers and create multiple sets accordingly. Take a look at the example below.

A’moni made ____ pitchers of fruit punch to share with friends at her birthday party. If she plans to give each friend ____ of a pitcher of punch, how many friends will she be able to serve? (2, 1/2) (3, 1/5) (2 1/2, 1/4) (6, 2/3) (1/2, 1/8)

This problem can be given to students at all different levels of understanding. I chose 2 and 1/2 for the first set of numbers because 1/2 is a pretty easy number for students who aren’t as comfortable with fractions to wrap their brains around. Most students have some understanding of half. A student who has little to no understanding of division with fractions could model this problem either with manipulatives or drawings and come to a correct solution.

The second and third sets of numbers could be modeled exactly like you would model the first set of numbers, only these sets can be a bit more challenging because of the fractions I have selected. These two sets would actually be the level at which I would want all students in my 5th grade class to get to because these meet the expectations of our standards (i.e. students should be able to divide a whole number by a unit fraction and a unit fraction by a whole number).

We usually have students in our class who are ready for content beyond our grade level expectations, so the fourth and fifth sets of numbers provide an appropriate challenge for these students because really they could use the same strategies other students in the class are using for the earlier sets with numbers that are far more challenging and likely beyond what we’ve worked with together in this type of situation.

You may be thinking, “But what if a student who you know should choose the more challenging set of numbers chooses an easier set?” That’s okay! They will finish sooner than you would like and you can then encourage them to move on to a more challenging set of numbers. They can then continue working on more and more challenging sets while you circulate the room and work with students who may be struggling on a lower level set of numbers. Students working on less challenging sets of numbers can apply what they learned on their first set to work on a more challenging set.

When you bring everyone back together, as a class you can discuss the same problem and many of the same strategies, just with different numbers. Ultimately many of the strategies students used will be similar even though they used different numbers. This will lead to great discussion where students can learn from each other and continue to deepen their understanding of the topic!

In thinking about the problem above, the student who you might think of as “advanced” will likely need to use some visual representation to solve the most challenging set of numbers because they are faced with numbers they haven’t worked with before (a fraction divided by a fraction). That’s what we want! This is the same strategy the students who are struggling with the concept will use to solve the first set of numbers.

Giving students a choice in the numbers they use is effective whether students use the same strategies or different strategies. We want students to have the freedom to use whatever strategy they are most comfortable with because there is a lot of learning that comes from comparing the different strategies students use regardless if the numbers are the same or not!

What are your thoughts on number choice as a way to differentiate? Is this a strategy you might use in your own classroom?

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