## Multiplicatve invers (reciprocal).docx - Section 3: Task

*Multiplicatve invers (reciprocal).docx*

# Pizzeria Profits!

Lesson 15 of 19

## Objective: SWBAT compare two pizzerias using rational number operations and determine which is making a larger profit.

#### Do Now - Sprint + Check HW

*15 min*

Students enter silently and find another “sprint” on their desks. This assessment includes 25 questions to be completed in 1.5 minutes. The first 10 questions are fraction/decimal conversions and the remaining 15 questions are multiplication facts using positive and negative integers. Students who raise their hand to indicate they’re finished will have their paper stamped and collected for grading. Students who answer all problems correctly earn three Achievement Points.

Fluency is an important aspect to the new Common Core curriculum and it is important to practice with assignments like this to improve flexibility and efficiency with number operations. This does not mean that I expect all students to be able to perform tasks like this in the prescribed amount of time. I make sure to let students know this before reviewing the answers. *While the speed with which these problems are completed should increase over time, "fast" doesn't necessarily make you "better". Accuracy is more important than speed.*

Check HW

The HW included division problems with fractions and mixed numbers. All students are provided with an answer sheet and they are responsible for discussing the work (also shown on the paper) with a partner. I also select a few students to copy their work and answers on the board. These students are selected if they get the correct answer using a different strategy than the one I included on the answer sheet. The work I included on the answer sheet involves some reducing, but only within a single fraction. ** Some students have figured out how to reduce diagonally before multiplying by identifying common factors in the numerator and the denominator. **Other students are not yet comfortable with this concept, so they multiply straight across, and reduce their final answer. I will also ask for examples where the student did not reduce all the way and ask students if they think the answer is “wrong”. I will wrap up the discussion by asking students to always report the answer in simplest form unless the question indicates otherwise.

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#### Intro to Lesson

*10 min*

Students are asked to return the HW check papers to me by passing them up to the front and to put their binders away in their backpacks. Tasks are handed out and students are asked to read and review the top portion of the handout, including the table, independently. During this time, students are also provided vocabulary index cards with the words “net gain; profit”, “net loss”, and “multiplicative inverse (reciprocal)” to supplement their work with division from the previous lesson. This is a task which is adapted from the NY state engage website for the 7^{th} grade unit on rational numbers. Students are asked to compare two competing Pizzerias. I changed the names given to reflect our principal and assistant principal.

After 3-4 minutes of silent review of the facts within the table students are allowed to ask questions about the information provided on the table. If there aren’t any questions, I ask the following questions to check for understanding:

What supplies do you think they are spending money on?

Why would one pizzeria spend more on supplies than another?

What is different about the way Mr. Corcoran pays his employees and the ay Mr. Brenner pays his employees?

Without any calculations, who do you think makes more money in a month selling pizzas? Why?

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#### Task

*30 min*

Once information has been reviewed, students are paired up (using data from results on quiz #5 to pair by ability, mid-lo, mid-mid, mid-hi).

I work with a group of 6-8 students (mid-lo) at the front of the room, projecting our work and allowing students to write it on the SMARTboard for the entire class to check.

Students will likely struggle in figuring out how to answer each question that is posed on the task. Their use of **MP1** (persevering in solving problems) and **MP2** (reasoning abstractly and quantitatively)will ensure completion of this task. The following questions shows could be used as guides for practicing **MP1 **and** MP2**:

- What are we trying to find?
- What exactly is this problem asking me to do? (MP1)
- Can I use numbers to represents different parts of this problem? (MP1)
- What model can I draw to help me visualize this problem? (MP1)
- I know I need to multiply, but what do the numbers represent? (MP2)

After 20 minutes, all students are directed back to their seats for the closing activity.

As a final note, look out for management issues when a larger group of students is being sent to a different part of the room to complete work with partners while I work with a smaller group at the front. This can sometimes lead to incomplete work due to excessive socializing. Thus it is important to ** outline the expectations of this work time explicitly**, perhaps by

**. Also important are the routines and expectations set at the beginning of the year. At this point students know me well enough that I will only give one warning, redirecting to the expectation on the cart paper, and should there be another infraction, they will be pulled from the freedom of that space and receive a phone call home.**

*writing them on a piece of chart paper and placing it close to this part of the class**expand content*

#### Closing

*10 min*

Students are asked to take their agendas out to copy the HW (complete the Task if incomplete). Then they are asked to pack everything up except for a writing utensil. Then, journals are distributed and I project the following question on the board and students to respond in their journal for the last 6 minutes of class. Journals are collected and graded after class.

Who is running a “better” business? Use numbers and your calculations for each answer to justify your opinion.

#### Resources

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- UNIT 1: Integers
- UNIT 2: Operations with Rational Numbers
- UNIT 3: Expressions and Equations - The Basics
- UNIT 4: Multi-step Equations, Inequalities, and Factoring
- UNIT 5: Ratios and Proportional Relationships
- UNIT 6: Percent Applications
- UNIT 7: Statistics and Probability
- UNIT 8: Test Prep
- UNIT 9: Geometry

- LESSON 1: Fractions Make a Come Back
- LESSON 2: Rolling with Fractions
- LESSON 3: Musical Math
- LESSON 4: Back to The Line
- LESSON 5: Number Line Subtraction
- LESSON 6: Quiz + Unlike Denominators
- LESSON 7: Word Problem Applications A
- LESSON 8: Word Problem Applications B
- LESSON 9: Back to Basics: More Skill Drills
- LESSON 10: Word Problem Applications C
- LESSON 11: Multiplying Signed Fractions
- LESSON 12: Using the Properties of Multiplication
- LESSON 13: Express Yourself
- LESSON 14: Divide and Conquer
- LESSON 15: Pizzeria Profits!
- LESSON 16: Expressions and Word Problems
- LESSON 17: Sign Up Day
- LESSON 18: Practice on Khan Academy
- LESSON 19: Unit 2 Test