The lesson: Math students learn that a factor is a number that is multiplied to get a product and to "make mistakes and ask questions."

The lesson: Math students learn that a factor is a number that is multiplied to get a product and to "make mistakes and ask questions."

In an hour, third- and fourth-grade students at John Muir School practiced factoring numbers, found that 1, 2, 4, 5, 10, 20, 25, 50 and 100 are divisors of 100, and eagerly shared their results. Then they started factoring 200.

Throughout the lesson, teacher Camille Siders checked that they understood the concept by saying, "Tell me in other words." or "Defend your answer." Mathematical thinking followed the students' yes or no answers, leading to lively discussions.

Next, students split into small groups around the classroom to continue to practice factoring and record their results while the teacher checked in with each group. She could be heard saying, "In math, make mistakes and ask questions."

Some students built arrays using multicolored, 1-inch squares to check a possible factor. After creating the systematic arrangements, Nathan Desmond said, "It is clearly impossible to get to 100 with 15 as a factor." The proof was in the array. Other students used calculators.

The session ended with the last question of the day: Can factors of 100 also be factors of 300? Students enthusiastically called out their answers.

— Heidi Monjure