### 2.1A HOMEWORK PROPORTIONAL RELATIONSHIPS

When cost is involved unit rate is often referred to as unit price. It is free to get into the park you only have to pay 2 dollars for each ride you take. Also, ask them why is the first quadrant only included for this graph. Substantial Mastery 4 I know how to find the rate of change in all the representations. Also discuss the possibility of a negative rate of change.

The y- intercept will not be as transparent in this pattern. Create a graph of these data. It will also be important to continue helping students to scale the axes of a graph you can implement warm-ups where you give students a context or table and ask them to sketch a quick graph of the situation, explaining how they would scale the graph. Substantial Mastery 4 I can identify the rate of change and initial value in all of the representatio ns of a linear model Stage 1 Stage 2 Stage 3 Rate of change: Context constant rate of 4 gallons per minute; Graph is a line; Table constant difference of 4 in the difference column; Equation: Stair-base in inches and Height in inches.

Explain how you know. As students design a set of stairs and ramps they must use decide how they can use the tools graph paper, ruler, pencil provided them most efficiently.

Partial Understanding 2 I can identify the rate of change and initial value in 3 of the representations of a linear model. Total Savings I might be able to make a graph of Jeff s savings but I do not pdoportional how it relates to the other graph.

For which person, Landon or Nate, is the relationship between time and number of hot dogs eaten proportional?? Write an equation that represents the relationship between the number of bags of popcorn that Agatha sells x and the amount of money she makes y. Answers will vary 2. On your stair drawing, draw a line from the origin 0,0 through the very tip of each stair. Write an equation that represents the relationship between the number of bags of popcorn that Propotional sells x and the amount of money he makes y.

Draw the figure at stage 5 in the space above. State the rise and propoortional for each staircase.

Agatha s relationship shows a special case where the linear relationship is also proportional.

# j Class Activity: Use Dilations and Proportionality to Derive the Equation y = mx + b – PDF

At this rate will he finish before noon? Currently, she does not have any money saved.

For example, you could have students complete each example problem and use it as relatiojships quiz. Students should come with an understanding of what a unit rate is and how to compute it.

# Identify proportional relationships (practice) | Khan Academy

They will expand their knowledge of linear functions and constant rate of change as they investigate how other functions change in future grades. At this point we are really beginning to investigate the conceptual understanding of a linear relationship by looking at how it is developed.

Complete the table below for Grace and Kelly. If students are stuck on this question, probe them to tell you how they knew how to draw stage 4.

Find and describe the unit rate for Don s smoothie. In other words, how many square feet of concrete can Doug pour in 1 hour. During this work with linear patterns and contexts, students begin to surface ideas about the two parameters of a linear relationship: The section begins by reviewing proportional relationships that were studied in 6 th and 7 th grade.

What are its different parts? Trace the triangles by color. This will set the stage for students to be able to graph and write the equation of a line given any set of conditions. Ben Bryton 6,8 1,4 Boston 4,2 a.

## 2.3j Class Activity: Use Dilations and Proportionality to Derive the Equation y = mx + b

Toby will cross the sidewalk before the cyclists reach him. How would you change the savings context so that it could be modeled by the same equation as the landscaping context? Students use their knowledge of slope and proportionality to represent and construct linear propkrtional in a variety of ways.

In the previous problem Carmen was making homemade root beer.

Some may draw out all the stages and you may want to ask if that is an efficient way of finding the total number of blocks for relationshipe 10 Measuring the Slope hhomework Stairs and Ramps b Class work: Who makes more money? How does the number of blocks in stage 0 relate to the simplified form of your rule? Monitor students while they are coming up with rules and ask a few students with different rules to present.