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* *Reflection: Intervention and Extension
Counting Backwards Works Too - Section 2: Teaching The Lesson

When we started talking about subtraction, one of my students was not trying to solve the problem. When I asked her why she said, "I don't do subtraction." When I questioned her more about this she said that she only does addition. Her teacher told her that was ok in first grade.

While I doubt that is what the teacher meant, it is possible that the child was encouraged to make an addition sentence out of a subtraction sentence, but developmentally she wasn't ready for this reversal. She was unable to tell me that the answer to a subtraction problem would be smaller than the number you start with. Her concept of number was very weak as shown by this problem seeing that subtraction makes a number smaller.

As teachers we need to start where are children are in their understanding, regardless of the standards children need to meet in a given year. If they do not have the foundation necessary, we must go back and reteach those concepts before expecting them to go forward. The foundation is critical to the building of later understandings.

I will start with the basics of subtraction with this child. I hand her blocks and ask her to show me 12 blocks. Now I ask her to take away 4 of them. How many are left? She counts and says 8. I tell her she just did subtraction. We do several other problems to show her that she really can do subtraction.

*Intervention and Extension: I Don't Do Subtraction*

# Counting Backwards Works Too

Lesson 4 of 18

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

#### Warm Up

*10 min*

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.

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#### Teaching The Lesson

*30 min*

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).

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#### Closing

*5 min*

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 2^{nd} 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.

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- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work

- LESSON 1: Let Me Count The Ways to Get An Answer
- LESSON 2: Who Makes Mistakes
- LESSON 3: Counting Up to Solve Problems
- LESSON 4: Counting Backwards Works Too
- LESSON 5: Counting Bugs
- LESSON 6: Taking Apart the Problem
- LESSON 7: Getting Bigger and Smaller
- LESSON 8: Double It
- LESSON 9: Doubles Plus or Minus One
- LESSON 10: Evens and Odds
- LESSON 11: Plus Ten Minus Ten
- LESSON 12: From Tens to Nines
- LESSON 13: Equal Amounts
- LESSON 14: Understanding Subtraction
- LESSON 15: Skip Counting with 5s, 10s and 100s
- LESSON 16: Balancing Equations and Counting Backwards
- LESSON 17: Counting with Tens and Hundreds
- LESSON 18: Assessment