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* *Reflection: Diverse Entry Points
Smoothing out subtraction - Section 3: Closing

Some students can quickly transfer from addition to subtraction. They understand the fact that subtraction is a reverse process. Other students are still struggling with the concept of taking away, or making something smaller. The number line allows students to count the process, and see where they are starting, and how their answer is smaller. If students can internalize the fact that subtraction yields a smaller number and addition yields a larger number, their concept of number will be strengthened.

Do not assume that children understand what is happening in subtraction. Second grade should be a year to build a strong foundation for the skills required by Common Core in third grade. Make sure your students demonstrate a strong concept of number, before moving on. Don't trade memorization for understanding.

*Different Understandings*

*Diverse Entry Points: Different Understandings*

# Smoothing out subtraction

Lesson 9 of 14

## Objective: SWBAT develop fluency skills with subtraction.

#### Warm Up

*15 min*

Today students will do a 2 minute math facts practice page with 25 facts. Half of the page is addition and half is subtraction. The purpose of the 2 minute practice is to give students an idea of how well they handle addition and subtraction. The page includes addition facts for 1,2,3,4 and 5 and subtraction from 15. After 2 minutes students put their pencils in their desks and take out a marker. Together we correct the paper. Students look at their own work and I ask them to put a smiley face on the half of the paper that was easiest for them.

Students are discovering for themselves how well they know the facts. If I collected, corrected and returned the papers students would look at the number at the top and then put the paper away without really connecting its meaning to their own understanding. Instead I am asking them to critique their own abilities with math facts. Is addition easier than subtraction for them? Do they know more addition than subtraction facts? Each child must determine for him/herself how they feel about addition and subtraction.

I invite students to come to the rug. Here we will work more with subtraction on the Smart Board, but the lesson could be done on a white board, or easel.

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#### Teaching the Lesson

*15 min*

I post an open number line on the Smart Board. I place the number sentence 15 - 5 = __ below it. I ask for a volunteer to come up and show me how to solve the number sentence on the number line (MP5).

I repeat the process with additional subtraction sentences in traditional format, using numbers under 30. (I have chosen to go to 30 because the students who are competent with subtraction need to be challenged. I can differentiate when I call on students to solve the different problems, based on their understanding of subtraction as displayed in previous work.)

Now I present the problem 25 - ____ = 20. I ask if anyone thinks they can solve this problem on the number line. A child can show his/her work and explain how they solved the problem (MP2). We talk about why this is a bit different than the earlier problems. (We have the bigger number and the answer and need to find the mystery number.) The idea of a mystery number is one we introduced in a previous lesson to describe change unknown problems.

I present another problem 28 - _____ = 19. I ask again for a student to come and solve the problem on the number line. I ask them to explain how they knew what to do.

I tell students that today we have 3 math centers to work with mystery numbers, subtraction on number lines, and a subtraction game. Each center requires students to make sense of the subtraction problems created and then to use the tools to solve the problems (MP1 and MP5) I explain that in the subtraction game they will have a staircase that they need to go down. They will start with 50 at the top of the staircase. They roll 1 dice and write a subtraction sentence (if they roll a 6, they would write 50 - 6 = 44 on the top step). The partner starts with 50 on the top of their staircase and rolls the dice and writes their subtraction sentence on the top step. Now the first player rolls and starts with 44 and subtracts their roll and writes the new number sentence (such as 44 - 4=40). Play continues until one of the partners gets to 0 (or below 0).

I tell students that the other 2 centers will have an adult their to help them. (A parent volunteer can man a center, or it would be possible to set up directions at each center, keeping in mind the need to differentiate for the learning abilities of the group.)

Students are divided into 3 homogeneous groups and sent to 1 of the centers. They rotate through the centers after about 10 minutes of practice.

Center 2: An adult will set up a mystery number sentence with subtraction. They put down the cards for a sentence such as 18 - magnifying glass (represents mystery number) = 7. Students use the blocks to try build the sentence and find the mystery number. Students continue to practice with different sentences such as mag. glass - 6 = 12, 25 - 8 = mag. glass. (for students who are more competent, I use larger numbers, and have students try to figure out the answer before using the blocks to check their thinking (MP4).

Center 3: Students use open number lines to solve subtraction sentences posed in both traditional (A-B= mag. glass, and nontraditional format Mag. glass - B = C). See Subtracting on the Number Line. Support is given as needed to help students be successful with this process. The adult can help students work through the process step by step or let students work on their own and then review the solutions.

#### Resources

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#### Closing

*5 min*

I give each student a single subtraction sentence to solve. For students who are showing strong understanding I use a nontraditional format. Here I might write 36 - ? = 17. For students who are still struggling, I write the sentence in traditional format. 36 - 17 = ? I write them on small sentence strips. I ask students to explain how they solved the problem (MP2). I collect the strips to use as an informal assessment of student fluency with subtraction.

My goal with all of the activities today is to build comfort with subtraction that will lead to fluency in subtraction.

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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: Getting Paid for our Work
- LESSON 2: Making Change
- LESSON 3: More Dimes and Dollars
- LESSON 4: It Is About TIme
- LESSON 5: Smiley Face Number Friends
- LESSON 6: Subtracting with Partners of 100
- LESSON 7: Making Change using Partners of One Hundred
- LESSON 8: Comparing Temperatures
- LESSON 9: Smoothing out subtraction
- LESSON 10: Missing Number Equations
- LESSON 11: Time and Money
- LESSON 12: Crossing Over 100
- LESSON 13: Moving Into Thousands
- LESSON 14: Unit 3 Assessment