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* *Reflection: Connection to Prior Knowledge
Unit Rate - Section 3: Mini Lesson

After we completed the first example together, discussing and using a unit rate strategy, some of my advanced students discovered other strategies for solving the problem.

They realized that rather than compare the price for 1 piece, they could find a common amount of pieces to compare. (See GCF and LCM Word Problems.) They used the concept of LCM to determine that 120 pieces of Cool Mint gum would cost $8.40 and 120 pieces of Trident gum would cost $7.20. This led them to the same conclusion that the Trident gum is the better deal.

Although finding the lcm is a valid strategy, I wanted students to understand how and why the unit rate is useful. I posed the question: Which is more useful in the real world, knowing the unit rate of gum or how much 120 pieces of gum cost? (Look for *MP3*) This started an interesting, heated debate, since some students were excited to think about potentially buying 120 pieces of gum and other students felt it wasn't practical.

*Other Strategies*

*Connection to Prior Knowledge: Other Strategies*

# Unit Rate

Lesson 1 of 2

## Objective: SWBAT calculate unit rate.

*50 minutes*

#### Important Vocabulary

*10 min*

For this lesson students will need to be familiar with and differentiate between rates and unit rates. I will share the definitions of both terms with students.

*rate* – a ratio that compares two quantities with different kinds of units

Example - My rate of travel was 90 miles in 3 hours.

*Can you give an example of a rate?*

I will allow students to share their own examples.

*unit rate* – the rate for one unit of a given quantity

Example - My rate of travel was 30 miles in 1 hour.

*Can you give an example of a rate?*

I will allow students to share their own examples.

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I will read Shel Silverstein's poem, "Smart", aloud to the class. Although many students may already be familiar with the poem, we will discuss it and relate it to ratios.

*Did the boy get a good deal?*

*What was wrong with his logic?*

Ratio of money denominations will be illustrated in the discussion: 1 dollar should equal to 4 quarters (or 10 dimes/20 nickels/100 pennies), but The Smart Son swapped 1 dollar for 2 quarters (his reasoning 2 is more than 1), traded 2 quarters for 3 dimes, gave 3 dimes for 4 nickels, and took 5 pennies in the end.

*What kind of unit rate would the smartest son need to make sure he wasn't being cheated?*

This discussion generates a lot of discussion and students are quickly engaged in the lesson.

#### Resources

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#### Mini Lesson

*15 min*

To understand how to find unit rate and why it's important, I will discuss a few examples with students.

**Example 1 - Compare a Cool Mint value pack of 40 pieces of gum that costs $2.80 and a Trident pack of 12 pieces of gum that costs $0.72. Which is the better deal?**

*Is it correct to say that the Trident is the better deal because it costs less?*

Student should disagree because the quantity is different, therefore we can't compare the prices.

*How can unit rate help us?*

Students should understand that if we find how much it costs for 1 piece of gum, then it will be easier to determine the better deal.

We will work through the steps to find the unit rate of each brand.

*If a rate is really a ratio, how can we write these rates so it will be helpful for us?*

Students should remember the different ways to write ratios and conclude that writing the rates as fractions would make the most sense.

*If we want to find the cost for one piece of gum, what do we have to do with our fractions?*

Students should understand that if we want the denominator to be 1, we will have to divide both the numerator and denominator by the denominator.

They should conclude that the unit rate for the Cool Mint gum is $0.07 per piece and the unit rate for the Trident gum is $0.06; therefore the Trident is the better deal.

We will discuss and work through another example.

**Example 2 - Kiara ran 34 laps in 6 days. Tia ran 26 laps in 5 days. Who ran more laps?**

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#### Independent Practice

*10 min*

To assess students' understanding of how to find unit rates, students will complete the problems below. Students should refer to their notes for guidance on how to complete the problems. As students work, I will circulate throughout the classroom to monitor their work and answer any questions.

**Independent Practice**

1. $3.50 for 35 minutes

2. 108 points in six games

3. a rainforest can receive up to 90 cm of rain in 30 days

4. An airplane climbs to an altitude of 1,000 feet in 10 minutes

After 10 minutes, students will discuss their work and answers with their group. They should come to an agreement with their group and if their answers are different, they should compare their steps.

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#### 3-2-1 Exit Ticket

*5 min*

To conclude the lesson, students will complete a 3-2-1 Exit Ticket. The ticket is an opportunity for students to share what they understood, but more importantly, what they may still be confused about. Before collecting the exit tickets, I will ask students to share what they wrote.

**Exit Ticket**

What are 3 things you learned today?

What are 2 things you found interesting?

What is 1 question you still have?

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##### Similar Lessons

Environment: Urban

###### Review 5: Walking Trip - Using Expressions and Equations to Represent Situations

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*Resources(18)*

Environment: Urban

Environment: Urban

- UNIT 1: First Week of School
- UNIT 2: Properties of Math
- UNIT 3: Divisibility Rules
- UNIT 4: Factors and Multiples
- UNIT 5: Introduction to Fractions
- UNIT 6: Adding and Subtracting Fractions
- UNIT 7: Multiplying and Dividing Fractions
- UNIT 8: Algorithms and Decimal Operations
- UNIT 9: Multi-Unit Summative Assessments
- UNIT 10: Rational Numbers
- UNIT 11: Equivalent Ratios
- UNIT 12: Unit Rate
- UNIT 13: Fractions, Decimals, and Percents
- UNIT 14: Algebra
- UNIT 15: Geometry