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Math classroom activities, ready to run

In math you see the answer, but not whether a student understands why it is right. In these structures students explain their reasoning to each other, take a position on a claim and check each other's steps.

They are already filled with questions on fractions, percents, area and math in everyday life, for grades 6 to 8. Not this week's topic? Put in your own problems.

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  • Open it without an account. On the start screen you adapt the questions to your own class.
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29 ready-made structures

Cooperative learning structures for math

Math can look like solitary work: solve the problem, check the answer. But a student only finds out whether they really understand a solution when they have to explain it. That is why active learning in math is about reasoning and explaining, not about computing faster, and it is the same math talk the standards ask for when they say students should construct arguments and critique the reasoning of others.

Cooperative learning structures make explaining a fixed step. In Numbered Minds, any group member can be called on, so the group makes sure everyone understands the solution. In Pair Coach, one student solves a problem while the other coaches, and then they switch.

Which structure for which part of the lesson?

At the start of class, activate prior knowledge with Taking Turns: name a fraction equal to one half, name a place where you see percentages. Stand Up & Sit Down is good at surfacing misconceptions: is one half always bigger than one fourth?

During practice, Pair Coach and Numbered Minds are the strongest, because students check each other's steps. Four Corners asks students to pick one of four answers and defend their choice, which works well for estimation and multiple-choice questions.

At the end of the lesson, a team Knowledge Quiz quickly shows you what the class has mastered, without any student being wrong alone in front of everyone.

What to watch for

Choose problems where the path matters, not just the answer: why does this work, how do you know, is there another way? And give enough time for the explanation. An explanation in thirty seconds is often just the answer said out loud.

Learning to learn in this subject

Three ways of learning studied in this very subject, each with the structure that makes it happen in class. The board tells the class what it is training.

  • Interleaved practice

    Which approach?

    Mixed problems, no solving: first say which type this is and what tells you.

  • Solve aloud with feedback

    Pair Coach

    One solves aloud, the other asks within half a minute «what are you doing now?»; swap after every problem.

  • Retrieve from memory

    One by one

    One problem at a time for the whole class, book closed; then look back together at where it stuck.

Spaced practice works here too, but it needs a series of lessons, not one.

Sources: Rohrer & Taylor (2007), interleaving in maths · Chi et al. (1989), self-explanation while solving · Dunlosky et al. (2013), practice testing

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