##
* *Reflection: Checks for Understanding
How Long Will it Take? (Day 2 of 2) - Section 4: Closure

Solving real-world problems can be difficult for some students, more-so when the problems are based on challenging content such as quadratic equations. The closure questions should be targeted at revealing content understanding, or mis-understandings for that matter. Because this is so important, closure questions must be thought of previously and carefully.

These questions that poke into student's grasp of the lesson objectives give me an idea of who actually needs more intervention on my part. I know I have to attend to these needs quickly in order to be effective in improving their learning. I try to find what students know and where they became lost. If I have to reduce the homework problems for them, or quickly write another assignment, I do. I also think about what I can provide these students with the following day that will help them get to the next step. This can be video tutoring, scaffolded material, or other internet resource. At my school, there is also after school "enrichment" where students can stay an extra 1/2 hour and receive one on one help from teachers.

*Ask questions that reveal understanding, then help where needed.*

*Checks for Understanding: Ask questions that reveal understanding, then help where needed.*

# How Long Will it Take? (Day 2 of 2)

Lesson 6 of 7

## Objective: SWBAT solve quadratic equations of higher complexity and practice solving real world problems.

## Big Idea: Students combine knowledge of solving linear equations and simple quadratics to tackle more complex equations and problems.

*50 minutes*

#### Launch

*10 min*

To begin the lesson I write the equation 4(x + 2) = 16 on the board and ask students to solve for x in their notebooks. I also ask that each step in the process be described. Students should have no problem with this. Most students will most definitely use distributive property to get 4x + 8 = 16 and go on from there.

I then proceed to ask students if there is another way of solving this equation. A student may quickly raise their hand, yet I allow some time for others to think before jumping into calling on the first to want to respond. Students will usually come up with dividing by 4 on either side first. If not, I lead them on saying, "Must we use distributive property first? Can we start by using the division property of equality first?"

Once chosen I ask the student to go up and show the work using the second route. I then write the equation 4(x + 2)^{2} = 16 and ask the students if our first method (distributive property first) works here and allow them to try it out and explain why it doesn't.

Finally I ask if our second method (dividing first) would work. I motivate the students to work it out at their desks before asking a volunteer to work it on the board.

*expand content*

#### New Info

*10 min*

After making sure students can solve the quadratic equation in the Launch, I inform the class that the "trick" is to think of (x + 2) as being one single number, say "n". In ther words the equation would be ** 4(n) ^{2 }= 16. **Making this substitution, even mentally, makes solving the equation much like the way we solved the quadratics in Day 1 of this lesson. The importance of this type of reasoning is that if a property holds for all values of a variable, then it also holds for the expressions that have those values.

After this discussion, I ask the class to solve an equation like **3(2x – 11) ^{2 }= 75. **I call on a volunteer to work on the board while his/her classmates work at their desks. I circle the room looking to see if students follow this new strategy and employ it in this case.

*expand content*

#### Application

*20 min*

For the application section of this lesson I pair students up and hand each student in the class a a copy of the Application Worksheet Day 2. I ask students to make sure they show all work.

During this time I walk around assessing students working and answering questions. Students should be able to complete the first three questions without too much trouble.

Question 4 is a slight extension of the lesson because I ask students to graph the quadratic with their graphing calculator. Students should state that the y-intercept, in this case (0, 784) represents the beginning height at 0 seconds. The positive x-intercept (7, 0) represents the moment the stone hits the ground. We assume that by now students understand that the negative x-intercept represents an answer that can be discarded based on the context.

To finalize the activity I ask students to change pairs by finding the closest elbow partner to avoid wasting time. I ask the new pairs to compare their answers and discuss possible mistakes in their work.

#### Resources

*expand content*

#### Closure

*10 min*

Open the Desmos Calculator for all to see on the Smart Board and project the graph pertaining to Problem 2 of the Application section. In other words graph:

y = 4(x – 1)^{2 }and y = 16.

I prepare this while students are working on their worksheet to save time. To end the lesson in a meaningful manner, I have a student volunteer go up to the board, and write the algebraic work done to solve this equation. I ask the student to discuss the process, including the key points of the graph in relation to the equation and its solutions. If the key points of the lesson are missed by the student, I pose questions about the process to help the student address these points.

Example questions that can be asked:

- What do the intersections of both graphs represent?
- Where in your work did you use reason by chunking (or substituting) as a means of solving?
- Are both equations meaningful here?

*expand content*

##### Similar Lessons

###### Racing Molecules

*Favorites(8)*

*Resources(14)*

Environment: Rural

Environment: Urban

Environment: Suburban

- UNIT 1: Number Sense
- UNIT 2: Solving Linear Equations
- UNIT 3: Relationships between Quantities/Reasoning with Equations
- UNIT 4: Powers and Exponents
- UNIT 5: Congruence and Similarity
- UNIT 6: Systems of Linear Equations
- UNIT 7: Functions
- UNIT 8: Advanced Equations and Functions
- UNIT 9: The Pythagorean Theorem
- UNIT 10: Volumes of Cylinders, Cones, and Spheres
- UNIT 11: Bivariate Data

- LESSON 1: Linear vs Quadratic (Day 1 of 2)
- LESSON 2: Linear vs Quadratic (Day 2 of 2)
- LESSON 3: The Biggest Possible Area
- LESSON 4: Playing with Parabolas - Hands on
- LESSON 5: How long will it take? (Day 1 of 2)
- LESSON 6: How Long Will it Take? (Day 2 of 2)
- LESSON 7: Are Absolute Value Functions Linear?