Switching to Subtraction

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SWBAT use place value blocks with friendly tens / hundreds to understand regrouping when subtracting 3-digit numbers. They will use precise language to describe their thinking.

Big Idea

Place value blocks enhance understanding of regrouping in subtraction.


3 minutes

Students tend to find subtraction more difficult than addition.  Begin this lesson by asking them which they find easier/like more -- subtraction or addition.  Ask them to (silently) think about why.  Have them share with a partner.  Explain to them that the regrouping strategies that work so well for them in addition apply in the same way in subtraction, and that is what they will be reviewing and exploring today.

Direct Instruction

7 minutes

Students are already familiar with the process of using the place value blocks from the previous lessons (Take Time for Tens: Act One, Take Time for Tens: Act Two, and Happy Hundreds).  They know what the place value cubes represent ("flats" = 100, "longs" = 10, and the tiny cubes = 1).  They have already had the experience of switching out a group of tens for one and they've already used them as both a computational tool (to determine the solution) as well as a thinking model (to prove their thinking) and as a support for their oral argument. 


I demonstrate four examples before starting the guided practice because while the regrouping is, hopefully, becoming easier for my students, the change in how they manipulate the cubes can trip them up if the differences aren't emphasized.

Guided Practice

15 minutes

Together, we work through seven different examples.

I am deliberate in the equations I use in all parts of the lesson.  In this guided practice, there are four types of equations:   those that require regrouping in both the ten’s and one’s place, one that requires regrouping only in the ten’s place, two that require regrouping only in the one’s place and one that does not need to be regrouped.

113 - 87 =         146 - 27 =          128 - 99 =              134 - 85 =            

152 -71 =         191 - 28 =            197 – 145 =            196 - 49 =          


I walk the room after each step in the process to make sure students are staying with me and not confusing the steps.  

Make certain that they record each step of an exchange and move unneeded blocks off the work mat.

Independent Practice

35 minutes

I prepare bags with 3 hundreds, 30 tens, and 30 ones for students to use with this lesson.  If it were possible, I'd love to have bags with different colored tens and ones so that when students trade out they can mark the place where this occurs by using a different color.  I was able to do this with the ten cubes but not always the one cubes.  

I specifically created these problems to test different levels of the skill of subtracting and regrouping as well as to provide math fact practice.  Students in my class copy the problems off the board, working on plain lined paper but I recommend using a printed page if possible: Switching to Subtraction- Independent Practice. I ask students to work independently.


1 minutes

I let the students know that in the next lesson, they will have some choices.  They can work on 3-digit subtraction with cubes, 4-digit subtraction with cubes, or come to the carpet  to apply the Equal Change (different than equal and opposite change) algorithm to 2- and 3-digit subtraction.


It is up to you, or perhaps the child, whether or not they draw out a place value block model to help them solve the Switching to Subtraction- Homework problems.  They do need to record the changes they make to the equations and their answers.