How long will it take? (Day 1 of 2)

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Objective

SWBAT solve equations equivalent to those of the form ax^2 = b

Big Idea

How long will it take an object to hit the ground if it falls from the top of Chicago’s John Hancock Center which is 1,127 ft. high? This lesson will help us solve equations to answer questions like this one!

Lesson Author

Mauricio Beltre

Windermere, FL

Grade Level

Ninth grade

Subjects

Math

Algebra

graphing equations

Expressions (Algebra)

Standards

8.EE.A.2

Use square root and cube root symbols to represent solutions to equations of the form x<sup>2</sup> = p and x<sup>3</sup> = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

Launch

10 minutes

As students enter the classroom I hand each an Entrance_HowLongWillItTake Card and ask that they work independently. I walk around making sure everyone is on task and correctly performing the operations. One of the things I make sure about in this initial stage of the lesson is that all learners understand that there are two solutions to each quadratic equation.

Students need to recognize an important distinction between the statements x ²= 36 and x = √36 . There are two values of x that satisfy x² = 36, which are 6 and −6. However, the symbol √36 refers to the principal square root of 36, which is nonnegative, so the only value that satisfies x in x = √36 is 6.

New Information

15 minutes

Student Thinking about Graphical Solutions using a Systems Approach

Once I'm done with the Launch entrance slips I ask a volunteer to hand out a NEW INFO HANDOUT to each student.

This lesson assumes student knowledge of the meaning of square roots presented in my Powers and Exponents unit, which means learners can solve equations of the form x^2 = b. Students will learn here that with just one additional step, they can solve an equation of the form ax^2 = b.

In Question 1, students should realize by analyzing the graph and the table that the equation has two solutions (-4, 32) and (4, 32). Have students prove this by checking each solution, showing the math.

In Question 2, students use Galileo's equation. Again, they should realize that there are two solutions, but only one that is meaningful. State that this is not always true. Sometimes both solutions in the problem are meaningful. Allow calculator use for this question.

After making sure students have finished this work, I project the NEW INFO SOLUTION PAGE on the board so students can see, discuss, and ask any question before going on to the application section.

Application

20 minutes

I like to project the Application Problems (HowLongWillitTake) on the Smartboard. They can also be printed and given to the students. I allow learners to pair up. I make sure at least one of them has a calculator. The discussions among the learners can be quite interesting. I like to walk around and listen in and check if they are considering whether the solutions obtained are both feasible or whether one of them doesn't make sense. I always ask why they are discarding an answer and what the appropriate answer means with respect to the work problem.

Students always love to go to the board, so I ask volunteers to write their work up for all their classmates to see and ask any questions if they have them.

Closure

5 minutes

Keeping the Lesson Student Centered

Today, I will close the lesson with a GQ Talk. This closing strategy is quite simple and can be effectively done in little time.

G: I call on students to verbally state what they think the General goals or ideas of the lesson were, in their own words. As they respond, I write their ideas on the board without discarding any of their responses.

Q: Once I have sufficient responses on the board, I then ask students to ask a Question about any idea in the lesson they feel uncertain about, and motivate other students in the class to answer the questions asked by their classmates. If I suspect someone may be struggling, I call on the learner and motivate him or her, to come forth with a question or indicate the area of confusion. This always sheds light on whether students have grasped what was intended to be taught in the lesson.