Much Much More Than Take Away

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The students will be able to use the part/part/whole model to write and solve subtraction number sentences.

Big Idea

The big idea of this lesson is the understanding that subtraction number sentences can show how to separate parts from a whole or by comparison.


10 minutes

Begin by having the students think about what they have learned about they know about the Part/Part/Whole model.  If necessary, prompt the students to think about how we can use the model to show an addition problem.  Tell the students that today they will learn about how they can solve for the missing part. 

Have the students turn and talk about how they could solve the following problem:           

I see 6 squirrels in my backyard.  4 of the squirrels climb up a tree. 

(The amount of squirrels at the beginning is the whole and the amount of squirrels that climbed up the tree is one of the parts.)

How many squirrels can I see now?

Have students share their understandings. If necessary, guide the students to think about the part/part/whole model.  Every student will need a copy of the part/part/whole mat, and some connecting cubes for the lesson.

Have students see if they can fill in the appropriate information in the part/part/whole model.  

Develop the Concept

20 minutes

I have the students create cube trains to show the number of squirrels that I saw at first.

I see 6 squirrels in my backyard.  4 of the squirrels climb up a tree. 

I remind them that to think, "How many squirrels did I see in my backyard?"

I ask the students, "How can you use your cubes to show that some squirrels climbed the tree?"  

Using a Part/Part/Whole Mat, have the students see if they can put the information they know into the mat.  They should be applying what they already have learned about the part/part/whole model in addition (see Reflection).

Finally, I have them see if they can create a number sentence to help them solve for the missing information. 

Practice the Concept

20 minutes

Rather than hearing from me whether they have correctly constructed their subtraction sentence, I have the students first turn and talk with their neighbor about how they did it. This gives students time to "hear" their own thinking, the thinking of others, and to make revisions if they think they are needed. This is a much more personal learning model than hearing from me, and it helps students to recognize what they do understand and what might be confusing.

It also gives students more confidence in sharing their thinking, which is what we do next.  Just as with the more personal partner turn and talk, our discussion is a time for students to make changes to their thinking, to use their math vocabulary in context, and it gives me information on where they are in their understanding.

Next, on their whiteboards, students practice using the information from part/part/whole models from the Subtraction Power Point to write correct subtraction sentences. To demonstrate understanding, I have students complete a practice page from their workbook, and during this time I provide support for those students who need it. You can find similar resources at the K-5MathTeachingResource site.

The part/part/whole model is a representation, or model, of how numbers are composed and decomposed (MP4). It's purpose is to guide students to think about the construction of numbers in a flexible manner. For example, if I have 7 and 3 are taken away, the part/part/whole mat provides a concrete anchor to represent the whole, and a piece of the whole that is no longer there. I can "see" that there is a piece "missing". 


10 minutes

We close by coming back together as a whole group to share what's been learned about the part/part/whole model.  I should be hearing not only the learning from today’s lesson, but also about prior learning on using the part/part/whole model to show addition as well.