Write and Reflect

With a partner, write a Separate (result unknown) for 23-8=?.
Write out example direct modeling, counting, and derived fact strategies.

Read

When children solve addition and subtraction word problems they begin to think of addition and subtraction in robust ways. When they discuss their strategies with each other they begin to select strategies that make sense to them. The direct modeling strategies match the content of the problems while derived fact strategies can be used flexibly and may not match the context of the given word problem. Some of the derived fact strategies that you discussed with your partner for the separate (result unknown) problem you wrote above may have matched the subtraction as take-away context you wrote about and maybe some of the strategies that you discussed did not match subtraction as take-away context. Our goal for this section is for you to learn about three ways that children use to make sense of situations involving subtraction.

Watch Videos

think Focus question: What are different ways that children can think of subtraction when using derived facts?

Each of the videos below show different ways to view subtraction and represent the action using an open number line. An open number line is different than a regular number line where the tick marks do not have to be proportional. The advantage of an open number line is that students can see and focus on chunks of numbers instead of counting the tick marks one by one.

The first video will show subtraction as take-away. To figure out 23 minus 8 using a take-away model is to start with 23 and take 8 away. The second video shows subtraction as how much more. A student using a how much more strategies for 23 - 8 would start at 8 and keep track of how much more is needed to add to get to 23. The difference is the last way to look at subtraction and the goal there is to figure out the space or distance between 8 and 23.

Watch the three videos to see three different ways that children look at subtraction.

think Keep track of how the number line is used to highlight the different ways to look at subtraction.

Subtraction as Take Away

Subtraction as How Much More

Subtraction as a difference

For additional practice and consideration...

Practice recording on an open number line

Practice recording on an open number line with a partner. Look at the verbal description of each of the strategies on the recording sheet (Microsoft Word version). Print out the sheet and practice recording what is described on an open number line as well as using symbols. In an actual number talk you might use only an open number line or just the symbols. Both representations have advantages and disadvantages. Decide together whether the verbal description represents thinking that views subtraction as take-away, how much more, or a difference. The answer key shows possible correct ways to record student thinking.

For further consideration...

Discuss the recording strategies as a whole group.

Recording Sheet

Possible Strategies Sheet