Division

I have heard it through the grapevine that some of you are having some problems with division. I looked at the problems for division and most of them are accessible by using multiplication to solve them. Some, however, have smaller starting points. If you look at page 66, the problem is 64 divided by 4. If a child knows that ten groups of six make forty, he or she has gotten more than halfway through the problem. You will need to model notation that looks something like this:
10 x 4 = 40
Teacher questions: Do you think that there are more than ten fours in 64? How many more?
Some student will give you a number. If they say something like two groups of four, you write:
2 x 4 = 8.
Teacher: how many groups of four have we found? (12) How much do we have? (48)
Are there more fours hiding in this number?
Kids may choose to go by twos or give you larger numbers. If they give a number that is too large, take it and work through it, asking the students if they are satisfied with the total. Kids need to try things that don't work, and make decisions about the results.
Kids need to use starting points that they know. Sometimes tens will be too large. If they suggest ten and it is too big, and they recognize that, ask if half of ten would work. Use doubles and halves if you can, to add up to a number or to make your strategy more efficient. Here are some possible ways students may do this for 64 divided by four.
5 x 4 = 20
5 x 4 = 20
5 x 4 = 20
1 x 4 = 4

10 x 4 = 40
5 x 4 = 20
1 x 4 = 4

10 x 4 = 20
6 x 4 = 24



Kids need to use their number sense to start to think about how many fours are hiding inside the 64.
Here is an example of a fourth grader who is still counting by ones to solve problems.

Here are some examples of students with appropriate solutions:

I photographed these from students math notebooks. Some are from morning work and some are from daily lessons.