From the beginning of their work with division, children are asked to make sense out of remainders in problem situations. Students explore division by reading The Doorbell Rang by Pat Hutchins. In this story, Victoria and Sam must share 12 cookies with increasing numbers of friends. Students can use counters to show how many cookies each person gets. Students use streets and alleys as both a mental model of multiplication and a useful way to recover facts when needed.
Students use a double maker on a calculator for practice with doubles.
Any number pressed then, followed by the equal sign, will show the number's double. Students work together to try to say the double for each number before the calculator shows it. They also recover facts by knowledge of the role of zero and one in multiplication, of commutativity, and of the regular patterned behavior of multiples of nines. Practice sets of problems are structured so that use of all these strategies is encouraged and the students are regularly asked to explain the procedures they are using. Each student rolls a die and draws as many circles as the number shown, then rolls again and puts that number of stars in every circle, and then writes a multiplication number sentence and records how many stars there are all together.