# Linear vs Quadratic (Day 1 of 2)

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## Objective

SWBAT compare features of linear and quadratic functions using a rectangular garden problem.

#### Big Idea

Linear and Quadratic functions can be used to model real world problems.

## Launch

15 minutes

I begin this lesson by pairing students up. A quick way of pairing is simply going down the attendance roster alphabetically and calling out two students at time. I then project GARDEN PIC AND COMPLETED TABLE on the SMART Board, being careful only to show the garden. The completed table under the garden will be shown after students complete their own table on the handout.

I then hand each pair of students a HOUSE GARDEN LAUNCH TABLE worksheet and present the following scenario:

Each pair is to make a rectangular garden for the green area in front of the house. You have exactly 16 yards of fencing to use. Complete the table showing the different combinations of dimensions that you might choose with the 16 yards of fencing.

I walk around as students are completing the table. Sometimes students may oversee that if the width is 2 yards, for example, then there will only be 12 yards of fencing left. Once students have completed the table, I scroll down on the SMART Board to show the completed table. I ask the pairs to check and correct their work.

## Activity

30 minutes

Before beginning the Activity, I ask the class to stand up and stretch a bit. Students always like this and it's good for the brain. Then, I ask them to remain with their partner and I hand each pair a copy of GRAPHS-QUESTIONS SHEET.

For this activity students are to use their table from the APK section to graph the relations width vs length and width vs area of the garden. The questions on the second page should be answered fully and discussed at the end of this section of the lesson.

As the learners are working I ask certain guiding questions to help them in their search for understanding. Some guiding questions are:

1. What happens when the width, or the length is 8 yards? Can the fence be built?
2. Is the slope of the first function positive or negative?
3. Are negative values for x and y values relevant to this situation?  Explain.
4. What do the y intercepts mean with respect to the problem?
5. What does the maximum point of the parabola mean with respect to the problem?

## Closing

10 minutes

To end the lesson, I ask each student to fill out an EXIT SLIP (Linear vs Quadratic) Venn Diagram. These I collect on their way out. They should give me some information on whether I should go right into day 2 of the lesson, or whether I should go back and review certain aspects of it, before proceding.