Counting Backwards Works Too

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SWBAT count back on a number line or number grid to complete subtraction problems and subtraction number stories.

Big Idea

Students are more confident counting up, however, counting back is crucial to understanding subtraction. It needs to be taught and practiced more frequently.

Warm Up

10 minutes

Today we continue to share the remainder of the number stories that students wrote at the beginning of the week. I  try to pick those that require subtraction. Students solve the stories in their math journals and then the writer calls on a friend to share the solution. 

Because I will focus on subtraction today, I try to make sure that there are subtraction problems to share. We discuss that when you subtract the answer gets smaller than the amount you start with because we are taking away from the number we started with.

Once the problems have been solved I call students to the rug, asking them to do 13 hops on the way.

Teaching The Lesson

30 minutes

I hand out snap blocks to each child. They are in towers of 10. I ask them to take 3 away. How many are left? Is the new tower larger or smaller than the tower we started with. (The children may think this is easy, but it sets the stage for the discussion of what happens when you subtract.) I ask students to put the tower back together again and pose another similar problem. I continue this for 2 - 3 rounds. 

Next I ask partners to combine their towers and count to see how many they have.

How many bundles (towers) of ten did you start with? (1).

How many do you have now? (2).

What is 2 bundles of ten worth? (20).

What digit is in the tens place? (2). 

Now we will practice working with 20. I ask them to take 8 blocks away from the 20 tower.

How many are left? But before I accept any answers, I have them hold off and think about the next question first.

Can anyone could think of a number sentence for what we just did? I invite a student to write the number sentence on the interactive white board. I ask the other members of the class if this matches what our problem. We discuss why it does or does not match, and students then solve the problem. Together, we check our solution.

We repeat this several times until most students seem comfortable with what we are doing. 

Next I divide the class into 3 groups. Each group will work on subtraction problems and word problems, but the difficulty of the problems will vary.

The group that is still struggling with the concept (based on what I observed with the towers of 10 and 20) will continue to work with an adult using the snap blocks to subtract from numbers less than 20.  They work as a group to create number sentences for what they have done.

The group that seems to grasp the concept, but could benefit from more practice will take turns writing subtraction equations with numbers less than 30 for a partner. The partner will solve the problem using the blocks, while the writer will solve the problem using a number line or number grid. They will compare answers and then resolve any differences before switching roles.

The group that is already clear on the process of subtraction will solve mixed addition and subtraction word problems with numbers less than 50. They will check their own work using a number grid or blank number line.

All students are using appropriate tools strategically (snap cubes, place value (base ten) blocks, hundreds number boards, number lines) (MP5).


5 minutes

Students return to their own seats and in their math journal, read what is written on the board to find the numbers.

I have the digit 3 in the ones place and the digit 5 in the tens place.  I have the digit 2 in the tens place and the digit 7 in the ones place.  What are the two digits?

This closing is a review of a previous concept. We worked on subtraction today and also mentioned the term digit which is  a concept I do not want to be forgotten by the students. I occasionally use the closing as a review of previously learned concepts. Students need to continue to revisit the things they have been exposed to until it becomes a part of their mathematical "toolbox".

Earlier, when I asked what place the digit was in the tens place a number of students did not respond. It could be that the term digit was misunderstood. This closing gives me a way to assess this.

In 2nd grade, as we build understanding of base ten notation (critical area # 1: Extend understanding of base-ten notation) the use of the concept’s vocabulary is a valuable tool when discussing, comparing, and representing digits up to 1000.