The move
Mix a few older problems into today’s practice, in random order, so students have to figure out which strategy each problem needs before they solve it.
See how it works
A Today’s skill B Older skill 1 C Older skill 2
At a glance
- Time in class
- 10–15 minutes. It replaces practice time you already use, so it adds no time.
- Prep
- 5 minutes: pull 2–3 problems from earlier units.
- Materials
- The practice set you were already going to use.
- Grouping
- Individual, then pairs to check.
- Use it when
- Students have had some focused practice on today’s skill and are ready to apply it.
Why it works
When every problem on a page is the same type, students know the method before they read the problem, so they never practice choosing it. Mixing problem types (researchers call this interleaving) makes students identify the right strategy each time, which is what tests and real life ask of them. It feels harder in the moment, and that extra effort is what makes the learning last.
Step by step
In class: about 10–14 min
- 4Launch30 seconds
- 5Solve8–10 minutes
- 6Check strategies first2–3 minutes
Before class: Add 2–3 older problems
- Start with today’s setNo extra timeTake the 6–8 practice problems you already planned.
- Add 2–3 older problems5 minutes, before classPick problems from earlier units that look similar to today’s but need a different strategy.
- Shuffle the orderMix the older problems in among the new ones, not all at the end.
- Launch30 seconds“Heads up: these problems are mixed. Before you solve each one, write the strategy you’ll use in the margin.”
- Solve8–10 minutesStudents work on their own.
- Check strategies first2–3 minutes“Compare with a partner. Did you pick the same strategy for each problem? Where you disagree, convince each other before you check answers.”
See it in action
Mix addition and subtraction word problems so students must decide which operation each story needs.
Mix area, perimeter and volume problems in one set.
In algebra, mix factoring, completing the square and the quadratic formula. In history, mix source-analysis questions from three different units.
In world languages, mix verb tenses in one translation set. In science, mix questions on three cell processes.
Watch out for
- Mixing too early: students need a little focused practice on a new skill first. Shuffle once they can do it with help.
- Too many old problems: keep it to 2–3 so today’s skill still gets most of the practice.
- “This is harder!”: tell students that’s the point. Struggling to choose a strategy is exactly the practice they need.
Level up
- Students write a trap problem for classmates: one that looks like one type but needs another strategy.
- Remove the margin step: students solve without naming the strategy first, then explain their choice afterward.
Make it work for everyone
- Multilingual learners: post a strategy word bank with a small example next to each strategy.
- IEP and 504 supports: give a short menu of the 2–3 strategies to choose from, and reduce the number of problems rather than the mixing.
- Early finishers: write a trap problem and trade it with another early finisher.
Tech option
Google Forms and most quiz platforms can shuffle question order automatically. Build one bank with old and new questions and turn on shuffle.
Resources
Pairs well with
Reflect
Which strategies did students confuse most often? That pair is your next mini-lesson.
Evidence
StrongRohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35(6), 481–498. Students who practiced with mixed problem types did better on a later test than students who practiced one type at a time.
Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013). Improving students’ learning with effective learning techniques. Psychological Science in the Public Interest, 14(1), 4–58. A review of ten study techniques that includes interleaved practice.
Find the research: Rohrer (2007) · Dunlosky (2013)
