case 1

Exploring Proportional Situations (Slides 1-11)
Exploring Relationships Between Proportional Quantities (Slides 12-20)
Recognizing Proportional Situations (Slides 21-25)
Connecting Proportionality to Constant Speed (Slides 26-41)
Connecting Proportionality and Constant Speed to Linearity (Slides 42-47)

Exploring a Proportional Situation (Slides 1-11)

Purpose: Students will encounter situations that are proportional and begin to formlize these relationships. They will encounter various ways of representing proportional relationships (scaling, constant ratio, constant multiplier) and have to determine situations in which each is most useful.

Support comments - video * doc * pdf * html

Worksheet 1
Notes

Click for Summary/Goals
  • Students will explore what it means for two quantities to be related proportionally
  • They will have the opportunity to see different representations of proportional relationships (scaling, constant ratio, common multiplier)
  • They will begin to formalize these relationships
Click for Implementation Notes
  • This worksheet should be given prior to slide 3
  • Recommended time: 15 minutes

Creating Relationships Between Proportional Quantities (Slides 12-20)

Purpose: Students will still be working with situations that are proportional, but now the focus will be on how the changes in each quantity are proportional. This will help lay the groundwork for constant rate of change and linearity.

Support comments - video * doc * pdf * html

Worksheet 1
Notes
Click for Summary/Goals
  • Students will explore what it means for two quantities to be related proportionally
  • Students will work with changes in quantities
  • They will formalize these relationships
Click for Implementation Notes
  • This worksheet should be given prior to slide 3
  • Problems 3 and 4 on the worksheet are aligned with slides 12-21
  • These slides can assist students with the formalization of the proportional relationships
  • Recommended time: 15 minutes

Recognizing Proportional Situations (Slides 21-25)

This section should help studnets' understanding of proportionality by having them reason in new situations. They will create their own definitions of proportionality then determine whether or not situations are proportional.

Support comments - video * doc * pdf * html


Connecting Proportionality to Constant Speed (Slides 26-41)

Purpose: This section is inetended to build upon students notion of proportionality to explore when changes in a quantity are proportional. This will give meaning to the term constant rate of change and allow students to explore linearity.

Support comments - video * doc * pdf * html

Worksheet 2
Notes
Click for Summary/Goals
  • Students will continue to explore situations in which the quantities are proportional
  • They will explore situations where the changes in quantities are proportional
  • Constant speed will be used to begin discussing what it means to have a constant rate of change
Click for Implementation Notes
  • This worksheet should be given during slide 22
  • The teacher should make sure students responses are explained in terms of proportionality
  • If students set up proportions for their answers, the teacher should probe for understanding
  • Recommended time: 15 minutes
Worksheet 3
Notes
Click for Summary/Goals
  • Students will come to understand slope as representing two quantities that co-vary in a constant rate
  • They will explore the meaning of x and y-intercepts
  • They will have the opportunity to discuss constant rate of change in a variety of representations
  • They will make connections between linearity and proportionality
Click for Implementation Notes
  • This worksheet should be given at the beginning of slide 32
  • Teacher should probe student answers until they are in terms of constant rate of change
  • Teacher should ensure students are making connections to previous worksheets
  • Recommended time: 15 minutes

Connecting Proportionality and Constant Speed to Linearity (Slides 42-47)

Purpose: Students should come to see slope as the constant covariation between two quantities. They need to recognize that a situation is linear when the changes in the two quantities are proportional. They also need to understand the meaning behind the intercepts of a linear function.

Support comments - video * doc * pdf * html

 

Return to Support Home

Contact Webmaster