ALGEBRAWITH AN EMPHASIS ON DIRECT AND INVERSE VARIATIONS

Jill Keith- KCS Secondary Numeracy Coach2/11/12

ALGEBRA: Linear Equations, Linear Representations, Non-Linear Representations:6th grade-Unit 5 6th Honors-Unit 47th grade-Unit 67th Honors-Unit 6Pre-Algebra- Unit 2 & 4

Our CurriculumDivide into groups of 3: each group should contain a teacher from each grade level

Discuss the curriculum below with your group members. What are you teaching your students? What are the similarities/differences between grade levels? Are thereoverlaps in grade levels? How is the previous grade level preparing students for thenext level?

OBJECTIVETo equip teachers with strategies and resources to teach linear and nonlinear concepts.

SPI 0706.1.3Recognize whether information given a table, graph, or formula suggests a directlyproportional, linear, inversely proportional, or other non linear relationship.

Kid Friendly Learning TargetsRecognize whether information given a table, graph, or formula suggests a directly proportional, linear, inversely proportional, or other nonlinear relationship.

I can identify relationships as direct, inverse, linear, or non linear.

I can find similarities and differences between directly proportional relationships and linear relationship

4. I can find similarities and differences between inversely proportional relationships and nonlinear relationship

Directly/Inversely Proportional FoldableOn a file folder, label one side linear and one side non linear.Cut up the linear and nonlinear examples from your worksheet.Place them on the appropriate side of the folder.Do NOT glue yet!(teacher note: discuss why or why not each is linear or nonlinear before proceeding to Direct variation)

Linear: slope: 4/3Teacher note: Answers should be removed before you use this in classLinear: direct variation:constant rate of change:y/x=2Non linear: inverse variation because xy=k

6. xy=207. y=x2 4. y=2x5. y=2x+5 Linear: direct variation: no y intercept but a constant rate of change of 2linearNon linear: inverse variationCan be writte y=20/xNon linear

linear9 &10. Linear: direct variation: line passes through originInverse variationNon linear

13. The length and width of rectangles with areas of 20 square units(non linear: inverse variation: xy=20)

14. The number of hours and the distance traveled when driving in a car at a constant rate of 60 mph(linear:direct variation: y=60x

The number of touchdowns scored in a football game and the points scored (from touchdowns) (linear:direct variation: y=6x)

Direct VariationTeacher note: have students label the bottom half of the linear side of the folder direct Variation. They can record their notes on the folder. You can then have them try to divide The linear equations into just linear and direct variation. Do not glue yet!

X Marks the Spot

AnalysisDescribe the relationship between the number of seconds and the number of Xs.Explain why it may be expected that this data collection activity will produce linear-like results.5. How could the data collection process be changed so that non-linear results would be obtained?6. Explain why the activity produced a direct variation relationship.

7. How could the data collection process be changed so that the results would still be linear, but not a direct variation?8. Complete the following table of values. Explain why the table represents a direct variation.9. Describe a situation that could be represented by the table in question 8.

x0123y051020

Direct Variation SummaryTeacher Note: Have students complete their notes on direct variation and glue

Inverse VariationTeacher Note: Divide non linear side of the folder into non linear and inverse variation. DoNot glue down until the next activity is complete.

A rectangle has an area of 24 square units. Represent all possible rectangles with integral dimensions on the grid below.

2. Record the dimensions for all the rectangles in the table:3. Describe the relationship between the rectangles length andwidth values. Determine whether the table of values representsa direct variation, an inverse variation, or neither of thesetwo relationships.4. Write an equation that models the table of values. Use x for length and y for width.

LengthWidth

In your groups, discuss how this lesson and/or instructional strategies used in this lesson could be adapted to work in other grade levels.

Kagan Books

**