## 4.4 Pizza Problem Example.docx - Section 2: Pizza Problem Example

# Adding and Subtracting Fractions Day 1

Lesson 5 of 19

## Objective: SWBAT: • Make an estimate for a fraction addition or subtraction problem. • Develop strategies for adding and subtracting fractions.

## Big Idea: If Ashley ate ½ pizza, Tatyana ate 1/3 of a pizza, and Tiffany ate 5/8 of a pizza, how much pizza did they eat altogether? What’s the smallest number of pizzas they ordered? How much was left? Students work to develop strategies for adding and subtracti

*60 minutes*

#### Do Now

*10 min*

See my **Do Now** in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day. Today I want students to work on adding and subtracting fractions. This is the only example in the lesson that has fractions with common denominators. I use the do now to see that students can add fractions with the same denominator. If they can’t I will add some additional practice in before we move on with the lesson. Some students may draw pictures and combine them. Other students may use the algorithm to add and subtract the fractions.

Students participate in a **Think Pair Share**. I call on students to share out their thinking. I put a couple student’s work under the document camera to show how they approached the problem. I want students to see that they smallest number of pizzas that they could have bought was 2. To find out how much pizza is left, we need to subtract 2 – 1 2/4 (of 1 ½). I want students to see that they should be able to find that answer in their head, or by looking at a picture. It would be more complicated and time consuming to use an algorithm.

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#### Pizza Problem Example

*10 min*

Notes:

- I use the data from the
**Fractions Pretest**to**Create Homogeneous Groups.**Students will work in partners. - I have a class set of Marilyn Burns’ Fraction Kit, where each student has his/her own set of paper fraction manipulatives. Students can choose to use these to help them, but they are not required to use them.

I have students move to their partners. I have a volunteer read the problem and part a. Before students write anything, I ask them to think of an estimate for the amount of pizza Jessika and N’Yshma ate. If students can develop strong estimation skills, it will help them check their answers to see if they are reasonable. If students struggle with this I ask, “Do you think they ate more than 1 pizza or less than 1 pizza?” I have students share out their estimates. Some students may comment that they know 3/8 is less than ½ (because 4/8 is equivalent to ½) so their estimate is less than one pizza.

I give students time to solve part a on their own. I remind students that they need to show their work. Some students will draw and combine pictures. Some students may know that ½ is 4/8, so they will add 4/8 and 3/8. Some students may use an algorithm, but may not understand it. For example, a student may turn the fractions into fractions out of 16, since 16 is a common denominator. Technically, this approach will work, but it takes far longer and it tells me they are not able to see the connection between ½ and 4/8. If I see this, I quickly draw a picture of ½ and 3/8. I ask the student how many eighths make up a half. If they struggle, I ask them to split up the circle with ½ into eighths.

After a couple minutes, I have students share out their answers. Again I have a couple students who used different strategies show and explain their work. I ask the class whether they agree or not. Students are engaging in **MP3: Construct viable arguments and critique the reasoning of others.**

We go through part b and c together. I emphasize that it can sometimes be much quicker to use your fraction number sense for subtracting. If we are solving 1 – 7/8, we know that there are 8/8 in a whole, so there must be 1/8 of the pizza left.

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#### Pizza Problems

*25 min*

As students work, I walk around and monitor student progress and behavior. I make sure that partners check in with me when they have completed a page. This way I can quickly check student work and identify any glaring problems. Students are engaging in **MP4: Model with mathematics**.

If students are struggling I have them explain their models and their estimates. Do you think they ate more or less than 1 pizza? Why? How can we add halves, fourths, and eighths? How do you know? How can you find how much pizza is leftover? How could you draw a picture to represent that? If students struggle with equivalence, they need to use the fraction kit to model their thinking. This way they can make comparisons between fractions and create their own equivalent fractions.

If students successfully complete their work I give them a choice:

- Create a poster for one of the problems, showing and explaining their work.
- Work as a teacher’s assistant with a partner pair who needs help
- Play “The Smaller Answer Wins” with their partner
- This game requires dice. I start off with students replacing the 5 on the die with an 8. This makes it easier to create common denominators and compare answers.
- If students need an extra challenge, I have them use the 5 on the die, instead of replacing it.

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#### Closure and Ticket to Go

*15 min*

For **Closure **I ask students, “What is your strategy for adding and subtracting fractions?” I have them share out their answers. Then I write the question on the board and I ask, “How would you add a/3 + b/4?” Students participate in a **Think Pair Share.** They are engaging in **MP7: Look for and make use of structure**. I want students to tell me that they can change both the halves and the fifths into twelfths. Then they can add them.

My last question is, “How would you subtract 1 – d/12?” I want students to apply what they have worked on to answer the question. I want them to think, I know there are 12/12 in a whole. Then they can easily compare the two fractions, even though they don’t know the value of d.

I pass out the **Ticket to Go**. Then I pass out the **HW Adding and Subtracting Fractions Day 1.**

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Greetings,

I am a 7th grade math teacher and wanted to review fractions with my students. I love your lesson. I am going to try it out today! Thank you!

| 4 months ago | Reply

Your lessons and videos are very helpful as I go through my first year as a 6th grade math teacher. Are there answer keys to the lessons you post or is it just us going through and figuring everything out. Thanks, Jeff

| one year ago | Reply

This lesson is excellent. I will use this in my 6th grade class. Thank you Ms. Palmer for sharing.

| 2 years ago | Reply

This is great. It is so nice that we finally are having more resources for the common core.

| 3 years ago | Reply

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###### Recalling Prior Knowledge of Adding and Subtracting Fractions

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- UNIT 1: Intro to 6th Grade Math & Number Characteristics
- UNIT 2: The College Project - Working with Decimals
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Fraction Operations
- UNIT 5: Proportional Reasoning: Ratios and Rates
- UNIT 6: Expressions, Equations, & Inequalities
- UNIT 7: Geometry
- UNIT 8: Geometry
- UNIT 9: Statistics
- UNIT 10: Review Unit

- LESSON 1: Pretest
- LESSON 2: Many Names for Fractions
- LESSON 3: What Fraction of the Section Does Each Person Own?
- LESSON 4: Which Fraction is Greater?
- LESSON 5: Adding and Subtracting Fractions Day 1
- LESSON 6: Adding and Subtracting Fractions Day 2
- LESSON 7: Looking for Patterns + Show What You Know
- LESSON 8: Representing Fraction Multiplication
- LESSON 9: Representing Fraction Multiplication Day 2
- LESSON 10: Mixed Number Multiplication
- LESSON 11: The Multiplying Game
- LESSON 12: Connecting Multiplication and Division
- LESSON 13: Dividing Whole Numbers by Fractions
- LESSON 14: Dividing Fractions by Fractions
- LESSON 15: Strategies for Dividing Fractions
- LESSON 16: Strategies for Dividing Fractions Day 2 + Show What You Know
- LESSON 17: Unit Review
- LESSON 18: Unit Closure
- LESSON 19: Unit Test