My kids can : making math accessible to all learners, K–5

in thinking about how what they already know or learned can help them solve a
new problem.
I knew that the students in my small group had a difficult time remembering
some of the multiplication facts. Because they had just explored the distributive
property of multiplication, they should have been able to use that knowledge to find
the products for facts they did not know. I was aware that they might not be able to
make that connection by themselves, so I planned to bring it up for consideration.
I explained that we were going to work on facts that were hard for them to
remember. I wanted the students to be invested in the activity, so I asked them
to choose the facts we would focus on. They suggested 9 8 and 9 7. Before
they tried to find the products, I reminded them of the conversation we had the
week before about why (3 8)(48) 7 8. They shared their ideas about
the equivalency of those expressions, making reference to the cookie trays and
how we had the same amount of cookies if we counted the cookies on 1 tray at a
time or on both trays together. Then I asked, “Could that idea help you solve
problems involving multiplication facts you don’t know? Could you use facts you
know as a starting point?”
To solve 9 8, Fleurette used multiplying by 5s, a relatively easy times table
to remember, and then continued with the additional groups:

9  5  45

9  3  27

45  27  72

9  8  72

Julio solved the problem very differently. He used the idea of doubling: if 8  3 
24, 8 6 has to be the double of 8 3 because 8 6 is 2 groups of 8 3:

8  3  24

8  6  48

24  48  72

Both students identified prior knowledge that helped them solve this number
problem. I had not told them in advance which ideas would be helpful. In previ-
ous lessons, they had to explain why the distributive property of multiplication
worked (even though they did not name it), so they knew that their procedures
made sense. I was pleased to see that they did not turn to their usual procedure of
skip counting or even counting by ones until they got to the answer, but rather
they accessed their knowledge of factor pairs.
Reasoning to solve problems by using what they knew continued very spon-
taneously when they worked on the second problem: 9 7.

MAKINGMATHEMATICSEXPLICIT