Learning Opportunities to Refresh, Review, and Reinforce

1

Concept/Skill: Systems of Equations, Inequalities, Quadratics, Functions, and Exponents & Radicals

Activity: Khan Academy

Supplies needed: Device with Internet access, pencil, scrap paper, basic calculator

2

Concept/Skill: Exponential Growth

Activity: How much did Peterson Lose By Note Cashing His Check

Supplies needed: Pencil, basic calculator, graph paper (optional)

3

Concept/Skill: Multiplying Polynomials

Activity: Multiplying Polynomials notes and activity

Supplies needed: pencil

4

Concept/Skill: Analyzing Quadratic Graphs

Activity: Angry Birds

Supplies needed: Internet access, pencil, basic calculator

5

Concept/Skill: Completing the Square

Activity: Quadratic Equations By Completing the Square

Supplies needed: Pencil

6

Concept/Skill: Quadratic Formula

Activity: Quadratic Formula –Kuta Practice

Supplies needed:

7

Concept/Skill:

Activity:

Supplies needed:

8

Concept/Skill:

Activity:

Supplies needed:

Khan Academy Instructions

8th grade math and Boost

To create your account, go to the Khan Academy homepage. If you click Parents, start here, you will be guided through the process of adding children. No matter what you select, your account will still allow you the option to learn, coach, or parent.

If you’re looking to parent or coach a student, once you've created your account, you can access Khan Academy's coaching tools by clicking your name at the top right of your screen and then selecting either Your students or Your children.

Once you've created an account for yourself, you can create accounts for your students or children. If your child is under 13, their account will have special privacy considerations.

For instructions, choose the appropriate guide below.

If you're a parent and you already have a Khan Academy account, you can visit this page and click the Add your child button. (If you don't have an account for yourself yet, go to this link to create one.)

Once you click Add your child, you will be asked to enter your child's birthday:

Your child's birthday is needed to determine permissions. Accounts for students younger than 13 are managed by a parent to protect the child's privacy. You can find more information about accounts for students younger than 13 here.

If Your Child is Younger Than Age 13

You will get a form to fill in for your child (note that the account is a restricted child account):

Fill in the form and click Next to create the account.

If Your Child is Age 13 or Older

You will be asked if your child has an email address. If your child has an email address you may either send your child an invitation to join Khan Academy, or you could create the account for your child:

If your child does not have an email address (or you choose to create the account yourself) you will get a form similar to the form if your child were younger than 13:

Fill in the form and click Next.

Multiple Children

If you have more children you can continue creating accounts now by clicking Add another child.

In addition, you can click Add your child from your parent homepage at any time.

After Account Creation

After you have created your child account(s) you can return to your homepage and log out and your child can log into his/her account.

Note: Always remember to log out of your account when you are done using it and teach your child to do the same! We frequently get reports of progress being made on the wrong account because parents or children forgot to log out.

After you have your accounts set up you can then begin working in your courses. Please follow the list below

depending on your math class. We will be assigning additional topics in a few weeks. We are encouraging

students that took Boost to continue to review Boost material. Students should aim to work on math for 40

minutes per day. The goal of our learning opportunities will be to review, reinforce and refresh!

8th Grade Math Boost

1. From the courses tab choose 8th grade math

1. From the courses tab choose Algebra 1

2. Under the courses summary choose systems of equations.

2. Under the course summary choose systems of equations.

3. Begin working through Systems of Equations subtopics.

3. Begin working through Systems of Equations subtopics.

4. Once completed, you can then proceed to Geometry Transformations.

4. Once completed, you can then proceed to Inequalities (systems & Graphs)

5. Proceed to Solving Equatioins with One Unknown

5. Students may then proceed to Quadratics (Multiplying and Factoring)

6. Once completed, students can move to Linear Equations and Functions

6. Proceed to Quadratic Functions and Equations

7. Last Unit: Geometry 7. Last Unit: Exponents and Radicals

Exponential Task

How Much Did Peterson Lose By Not Cashing His Check?

The Situation

NFL cornerback Patrick Peterson received a $15,361,000 signing bonus as part of a five-year, $70

million contract extension. However, he didn’t immediately cash the check. When asked why, he

said, “I just haven’t gotten around to it.”

The Challenge(s)

How much interest money did Peterson lose by not immediately cashing his check?

Question(s) To Ask

These questions may be useful in helping you down the problem solving path:

What is a guess that is too low?

What is a guess that is too high?

What is a guess that you know is wrong?

What is your best guess?

What information do we need to figure this out?

How much money would he have lost if he took 3 months to deposit the check?

How much money would he have lost if he took n months to deposit the check?

Consider This

This context makes for an interesting application of calculating interest. Normally we don’t think much about the

interest we lose out on from not immediately cashing a check, but when the check is for over $15,000,000, it

becomes noteworthy. To determine the amount of interest money Peterson lost, you will need to know:

the original amount of money

the amount of time that passed between the date the check was issued and the date the check was

deposited.

the interest rate for the money could have earned had it been deposited.

The image below is a screen shot from Bleacher Report that provides some of the necessary information.

In terms of actually finding the amount of money Patrick Peterson lost by not depositing his check, I am using

the formula of: A = p(1 + r/n) ^ (n * t) where p is the amount of principal, r is the rate, n is the # of times per year

the amount is compounded, and t is the # of years.

What is the problem you are trying to solve?

What do you already know about

the problem?

What do you need to know to solve

the problem?

Your conclusion and work to back it up. (Table, graph, equation and

detailed explanation.

Answer: The check was written for $15,361,000 so that is the original amount of money. Assuming that Peterson

received the check on the date the contract was signed, he got it on July 29, 2014. While we don’t know the

exact date he cashed it, I believe that it was not cashed as of the day the story was written which was August

25, 2014. There are 27 days from the date he received it to the date of the article.

As for the interest rate, these were the rates available for certificates of deposit (CDs) in August 2014. In general,

CD interest rates are slightly higher than the rates earned from a savings or money market account. They are

usually lower than the rates you could earn through other means, such as stocks, but have little risk unless the

bank goes out of business. The best interest rates available were 1.1% compounded daily.

p = 15361000

r = 1.1% or 0.011

n = 365 for daily compounding

t = 27/365 (fraction of the year it was compounded which is the # of days he waited to cash the check

divided by 365 days per year)

This gives us a total of $15,373,504.12 which results in $12,504.12 in lost interest over the 27 days. Now this

amount does not include deductions for income tax but is still a staggering amount of money for 27 days of

conservative interest. If he had earned a more aggressive interest rate like 6%, the interest would have been over

$68,000 for the same period of time! I believe that if Patrick Peterson knew he could have earned enough money

to buy a small car or go on a trip to anywhere in the world, he would have deposited the check sooner.

I have also made an interactive graphical version of this problem using Desmos with a slider for the rate. It is fun

to play around with the rate to see how things change. The image below shows you a sneak preview with the

amounts of money at day 0 and day 27.

MULTIPLYING POLYNOMIALS Look at the two photos and review how to use the area model to multiply binomials and

polynomials. Then use the worksheet to practice. Solve the problem using the area model and

look for the answer in the answer bank below.

(x – 5)(x + 2)

(3x + 5)(x2 + 6x +11)

answer answer

(x - 1)(x2 + x + 1) (x + 8)(x + 5)

answer answer

(x - 2)(x2 – 10x +2) (3x – 1)2

answer answer

(x – 4)(x – 1) (7x + 3)(x – 9)

answer answer

(3x + 5)(x2 – 10x + 2) (4x + 1)(3x – 7)

answer answer

(x + 7)2 (2x – 3)(3x2 – 7x + 8)

answer answer

A x2 + 13x + 40 B 3x3 + 23x2 +63x +55

C 3x3 – 25x2 – 44x + 10 D 9x2 – 6x + 1

E x2 – 3x – 10 F 6x3 – 23x2 + 37x – 24

G x2 + 14x + 49 H 12x2 – 25x – 7

I x2 – 5x + 4 J x3 – 1

K x3 – 12x2 + 22x – 4 L 7x2 – 60x – 27

Quadratic Equation Work:

Where Would The Angry Birds Have Landed?

The Situation

Watch Video At:

https://youtu.be/H8YBiJF62Us

The Challenge(s)

Where would the Angry Birds have hit the ground if they hadn’t crashed into anything on the way?

Question(s) To Ask

These questions may be useful in helping you with the problem solving path:

What is a guess that is too close?

What is a guess that is too far? What is

your best guess?

What would be a way to help us have locations that are easier to communicate to each other?

What are the coordinates for your best guesses?

What information would do you need to figure this out? What factors may

affect your answer’s accuracy?

Consider This

Make guesses as to where each of the birds will land.

Angry Bird #1 (without grid)

Angry Bird #2 (without grid)

Angry Bird #3 (without grid)

Without a coordinate plane, it is hard to have uniform answers.

“What would be a way to help us have answers that are easier to communicate to each other?”

“What are the coordinates for your best guesses?”.

Angry Bird #1 (with grid)

Angry Bird #2 (with grid)

Angry Bird #3 (with grid)

How will you label or number the graph? Where should the origin be?

What are you looking for? What data points will you need to solve for?

Which of the graphs is easiest to start with? Why? What information does it provide that the others don’t?

Can you write equations for the parabolas?

What is the problem you are trying to solve?

What do you already know about the problem?

What do you need to know to solve the problem?

Your conclusion and work to back it up. (Table, graph, equation and detailed explanation.

measurements. I then plugged my information to into y = a(x – h)^2 + k to get 0 = a(0 – 9.44)^2 + 10.56. Ultimately I

found that a ≈ -0.1185004 giving me an equation of y = - 0.1185004(x – 9.44)^2 + 10.56.

Angry Bird #3 (with grid and graph)

Students need to be reminded at this point that we are still looking for the coordinates of where the Angry Bird would

have landed. There are at least two methods for figuring out the location. One would be to graph the parabola for the

equation and superimpose that upon the Angry Birds screenshot. I used the Desmos Graphing Calculator website. If

students choose that path, I have included what that will look like assuming students picked the origin I picked (refer to the

image “Angry Bird #3 (with grid and graph)”). I also included the graph by itself so that students can adjust it to their

origin as needed. Using the graphing method, the third bird would land on the ground (note that it is below the x-axis) at

about (20.2, -2.2).

Graph of y = -0.1185004(x – 9.44)^2 + 10.56

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Name

Alternatively students could try to find the location by solving the equation we came up with for when y = -2.2 which is

about where it it would hit the ground. Using the solving equation method the third bird would land on the ground at

about (19.82, -2.2). The graphing and solving equation answers are not the same and it is worth revisiting the

question “What factors may affect your answer’s accuracy?”

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1) p p

2) v v 2) v v

Kuta Software - Infinite Algebra 2

Solving Quadratic Equations By Completing the Square

Solve each equation by completing the square.

3) a a 4) x x

5) x x 6) n n

7) x x 8) k k

9) r r 10) x x

11) k k 12) b b

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15) k k 16) x x

17) x x 18) n n

19) a a 20) x x

21) n n 22) k k

23) p p 24) x x

Kuta Software - Infinite Algebra 1 Name

Date Period

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Using the Quadratic Formula

Solve each equation with the quadratic formula.

1) m m 2) b b

3) m m 4) x x

5) x x 6) x x

7) b b 8) m m

Kuta Software - Infinite Algebra 1 Name

Date Period

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11) k k 12) r

13) x x 14) x x

15) k k k k 16) n n

17) n n n 18) n n

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