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# WP: Identify the Constant of Proportionality

Lesson 8 of 10

## Objective: SWBAT identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. SWBAT represent proportional relationships by equations.

## Big Idea: Students will use MP1, 2, 3, 4, and 6 to solve real world problems identifying the constant of proportionality (unit rate) in tables, graphs, equations, diagrams.

*40 minutes*

#### Bell Ringer

*20 min*

Hand students the Bell ringer as they enter the room. For this bell ringer, students will work on problems, 2 and 4. Assign 1 and 3 for homework.

Students will sit in their **Individual Think Time** seats and begin right away using **MP1**, **MP2**, and **MP6** to grapple through two problems. Allow students 10 minutes for **I.T.T. **Students will need to write their thinking strategies in their interactive notebooks. They will use this to share during pair up time. Walk the room to check for understanding.

Once students have worked individually for 10 minutes, have students discuss their work with their pair up partners. Students should have 10 minutes to discuss their thinking and compare their responses. Students should be able to guide one another through the process of solving each of these questions. This will put into practice **MP3**.

Scale factor may be new to some students. Use the opening video for students to have a base knowledge for the I.T.T time and/or for review. This will allow an opportunity for students to have a starting point in persevering through the problems.

Student understanding of scale factor will play a part in solving these word problems. For question 2, students may be tempted to start by finding the relationship of inches to feet. Students may start by using the ratio of 12 inches = 1 foot. This is what they understand and will have at the forefront of their thinking. As students grapple through the problem, they will realize this will not work. Guiding student thinking during this time is important. Ask students:

What does the problem want us to figure out? Students will respond how many feet are in 1 inch.

This is where you can ask “What is the significance of the number 1?” Students should recognize we are finding unit rates. Several strategies should be under their belt thus far. Students should recognize dividing the numerator and denominator by the denominator will reduce the ratio to a unit rate. Students will need to understand that unit of measure attached to the 1 is the denominator. Other strategies may be used including modeling, illustrations, pictures, etc.

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#### Whole Group Discussion

*10 min*

During this time, students groups should have the opportunity to share out their pair up time discussions, and reveal each of their responses. You may not have time to have each student share. As you filter through the room during pair up time, attempt to identify a group who has understanding, some understanding and little understanding. During the whole group discussion have students debate their responses and defend their thinking. This again will practice **MP 3.** As the facilitator of the discussion, you can head the discussion with open ended questions that will evoke students to defend. One common mistake with these questions will be students wanting to convert feet to inches. This is not necessary for this standard.

#### Resources

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#### Closing

*10 min*

It is important for students to know the correct process and correct answers in order for them to correct misguided thinking. Go through the correct process in responding to each question. Students will correct mistakes. Guide students to identify what the problem is asking us to figure out first. The unit of measure associated with what the problem is asking us to figure out is our starting point. This will designate how to set up the ratio. Once we set up the ratio we can divide by the denominator to solve for the unit rate. The unit rate will determine how many feet are in each inch. Be sure student are aware of **MP6** and its importance during this process.

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- UNIT 1: Introduction to Mathematical Investigations
- UNIT 2: Integers
- UNIT 3: Proportional Reasoning with Percents
- UNIT 4: Proportional Relationships
- UNIT 5: Proportional Reasoning
- UNIT 6: Rational Numbers
- UNIT 7: Number Sense Vocabulary 5 day mini unit
- UNIT 8: Expressions and Equations
- UNIT 9: Expressions and Equations 5 Day Application of Vocabulary Mini Unit

- LESSON 1: Compute the Unit Rate Associated With a Ratio of a Fraction
- LESSON 2: Relate the Graph of a Proportional Relationship to a Table
- LESSON 3: Determine if Two Quantities are in a Proportional Relationship
- LESSON 4: Identify the Constant of Proportionality from a Table
- LESSON 5: Identify the Constant of Proportionality From a Graph
- LESSON 6: Identify the Constant of Proportionality from an Equation
- LESSON 7: Determine the Constant of Proportionality Between the Sides of Right Triangles
- LESSON 8: WP: Identify the Constant of Proportionality
- LESSON 9: Unit Assessment
- LESSON 10: Solving Multi-Step problems giving part to whole ratios