# Proportional relationship and graphs lesson 4 3

### Interpreting graphs of proportional relationships (video) | Khan Academy

Introduction: This set of lessons extends ideas developed in the September through physical experiments and interpreted using tables and graphs. The activities that follow interpret proportional relationships using a unit-rate The less familiar contexts of problems 3 and 4 can be addressed in a similar manner. and in graphs of proportional relationships as the ordered pair (1, r). representations used in daily lessons; Relationship to Essential Understandings of unit; Lesson(s) that assessment points to . Functions. 8.F.1; 8.F.2; 8.F.3; 8.F.4; 8.F Name Date Class LESSON 43 Proportional Relationships and Graphs Practice and Problem Solving: A/B Complete each table. Explain why the relationship is a .

What does the point 3, 9 indicate?

State the meaning, within the context of this example. The point 3, 9 indicates that Diagram 3 has 9 squares. What point on the graph represents the number of squares included in Diagram 4? How did you determine your answer? Diagram 5 will have 15 squares because 3 times 5 equals An x-value of 5 corresponds to a y-value of What diagram number will have a total of 21 squares? Diagram 7 will have 21 squares.

This answer may be determined by finding the x-value that corresponds to the y-value of That x-value is 7. What diagram number will have a total of 51 squares? Diagram 17 will have 51 squares. Since the rate of change is 3, the following equation may be written: What do the other points on the line indicate? The other points indicate all other combinations of diagram position numbers and number of squares in the diagram.

Name another point found on the line of the graph. State the meaning of the point. Another point is 8, This point indicates that Diagram 8 contains 24 squares.

Sample Questions Sample Responses What does the origin, or point 0, 0 indicate in the context of this example? In other words, she does not make an initial deposit prior to month 1.

You may also discern from this point that Month 1 does not include any savings, in addition to the unit rate amount.

## Common Core Grade 7 Math (Worksheets, Homework, Lesson Plans)

The unit rate is represented by the point 1, What does the point 1, 25 indicate? The point 1, 25 is the unit rate or constant of proportionality. It indicates the amount of savings per month.

This does not make sense, in the context of the example, since you cannot have a negative number of months. What point on the graph represents her cumulative savings after the third month?

How much money will she have saved after 6 months? The y-value that corresponds to the x-value of 6 is That x-value is 8. The other points indicate all other combinations of number of months and cumulative savings amounts. Mary bought 3 boxes of pencils and ended up with 15 pencils. How many pencils would she have purchased if she had bought 7 boxes of pencils? One should note that the foregoing problem actually involves two unit rates: In solving missing-value problems only one unit rate is appropriate.

Students need experience interpreting each possible unit rate so that they can determine which rate is appropriate to the problem. The unit rate expressing how many boxes for one pencil can be used in the following situation: How many boxes did she buy if she bought 30 pencils? Changing the context and numbers involved will change the difficulty level of these missing-value problems.

### Seventh Grade Team's Site / Unit 1: Ratios and Proportions

The following activities introduce the concept of unit rate in the familiar buying context but also use the less familiar money-exchange context. These activities, combined with the activities from "Interpreting Proportional Situations" referenced earlier, give students an expanded view of proportional relationships and meaningful alternatives to solving traditional missing-value problems. Activity sheets for each student, transparencies of these sheets for class discussion, and calculators optional Objectives: Students will develop an understanding of the unit rates associated with a proportional relationship.

- Unit 2: Introducing proportional relationships
- Recognizing proportional relationships in a graph
- Ogdensburg Free Academy

Students will also develop the ability to determine the appropriate rate to use in solving a problem and to use the corresponding unit rate to solve missing-value problems. Sheet 1 displays a teacher-led lesson, The pictures help students see that division is used to calculate a unit rate, as well as help students determine which of the two parts of the rate relationship should be the divisor in the division problem.

The teacher should model how to use the picture to find the unit rate. In problem 1, the teacher points out that to find the cost of one apple, the money has to be divided into three equal parts. A simple mapping, such as that in figure 1, can show the cost of one apple.

### Interpreting Points on the Graph of a Proportional Relationship - SAS

Students should find the unit rate for problem 2 in a similar manner, then write the interpretive statement. In this instance, the cost of one orange does not equal an integral amount. The less familiar contexts of problems 3 and 4 can be addressed in a similar manner. Each results in its own diagram. The following questions can be used to help students solve the problems on sheet 1: What operation was modeled in each solution? For each problem, what quantity was divided and into how many equal groups?

Can you explain why? What computation can be set up to solve each problem? How can each division problem be written using fractional notation?