Story Problems Involving Subtraction

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SWBAT use strategies to solve subtraction problems. SWBAT document their approach to solving subtraction problems.

Big Idea

Through discussion and cooperative learning, students will use strategies to solve and record solutions to subtraction story problems.

Warm Up

5 minutes

Advanced preparation:  You will need to print out both sets of number cards from the resource section.  Cut out the 1-30 cards and put them into one envelope and do the same with the 31-60 and put them in their own envelope.

I start this part of the lesson by asking the kids to sit in front of the classroom number line.  

"Today we are going to change up our Start At/Stop At routine.  We are going to add the numbers 31-60."  I will pull one card out of the 1-30 envelope and we will use that as our start at number.  I will then pull out a card from our 31-60 envelope and use that as our Stop At number.  We will then count as a class from our starting number to our ending number."

I will ask a student to point to each number as we count as a whole group.  I will continue this process as time allows.  I will also mix in counting backwards by starting at the higher number and counting to the lower number.  The Core Standards expect 1st graders to be able to "count to 120, starting at any number," by the end of 1st grade.  This routine is the process in which I can assure that the students are continuously working toward that standard (CCSS.Math.Content.1.NBT.A.1).   


Solving Subtraction Word Problems

15 minutes

I start this section by reminding students of the approach that we use to solve word problems.  There is a picture of the anchor poster I use in my classroom in the resources section.  I will review the strategies with them and then proceed to reading the following word problem:

"Jan found 8 acorns on the playground.  When she cam back into the classroom, she gave 1 of them to Kim.  How many acorns does she still have?"  I do repeat this story a 2nd time, this is something that I do every time I read a problem.  I want to emphasize the idea that you have to know what the problem is asking before you dive into solving it.  Slowing down and reading the problem a couple of times ensures that students will start to explain to themselves the meaning of a problem and look for entry points to its solution (CCSS.Math.Practice.MP1).  This routine for solving a word problem helps students create a process for students to understand what the problem is asking.

Once the students have gone through the routine (outlined on the poster in the resources), I ask them to share how they got the answer.

"Who can share with us how they solved this problem?"  I will model their thinking on the whiteboard as each student shares.  

After a few people have shared shared their strategies, I then read a second problem.

"There were 7 busses in the parking lot.  Then two of them drove away.  How many were still left int he parking lot?"

I repeat the same procedure as I did with the 1st problem.  

Note:  When going over I want to focus the discussion on counting backwards and using strategies such as counting in their heads, using fingers, or the class number line to solve the problems.  As students are solving and presenting, you should note if students are able to retell the problem in their own words and if students can make sense of the action in the problem.

Solving Subtraction Word Problems with Documentation

30 minutes

I tell the students that they are now going to solve one or two problems on their own.  They will use the same process that they just used with the previous problems.  I have created two problems. Everyone should solve the How Many Cats problem.  If students finish that problem early, they can then work on the How Many Dogs problem. Providing students with the opportunity to solve these problems independently supports student engagement with CCSS.Math.Content.1.OA.A.1.

"I am going to read the first problem to you.  Remember that you need to create a picture in your mind of what is going on.  I will read the problem twice.  I want you to not focus on solving the problem but rather create a picture of what is going on the problem."

I then read the problem to them and go through the established problem solving routine.  Once the students have a grasp of the problem, I let them work individually to solve the word problem.

As students are working you will want to make note of:

  • How is each student making sense of the sequence of action in the story?
  • How are the students recording their work?

Lesson Wrap Up

15 minutes

*You will want to identify three different ways that students solved the How Many Cats problem in the previous section.  You will ask these students to present their work during the discussion that occurs in this part of the lesson.

The point of this discussion is to develop an awareness of strategies that can be used to solve problems that require "removal" or "take away." Often, the concept of subtraction is a much more difficult one for first grade students to conceptualize than addition, so it's very important to engage deeply with what is going on quantitatively in the story problem.

"As you were working today, I noticed students using a variety of ways to solve the How Many Cats problem.  I am going to ask a few of you to come up and present who you solved the problem."

I will use the document camera to project each piece.  This way the student work can be seen by all.  In the resource section is a video of each presentation and a copy of each presenters work.  Each student included a subtraction equation with their solution.  I want to highlight this after each student presents, to reinforce the standard notation that was used.  

After each piece has been presented, I will then ask the class the following:

"I would like each of you to look at your solution and compare it to the three pieces of work that were just modeled.  I would like to know which one was closest to your approach?"

The student presenters used the following approaches:

  • Student 1: She drew all, then eliminated an amount, then recounted remaining items.
  • Student 2: Used a number line to count back.
  • Student 3: Same as Student 1 but had a more advanced explanation.  He actually used a known addition fact to solve the subtraction equation.  You will hear it at the end of his video clip (drawing all with advanced explanation).


Continued Practice

5 minutes

Students worked with 10 Sticks and continued their practice of counting by 10's and 1's.  See the attached video to learn how to play this activity.