Warm Up - PowerPoint Presentation

Slide1

Warm Up

Write down objective and homework in agenda

Lay out homework (

Kuta

Multi-Step Fractions, pick any 15)

Homework (Multi Step Word Problems

wkst

)Slide2

Unit 1 Common Core Standards

8.EE.7 Solve linear equations in one variable.

a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given

equation into simpler forms, until an equivalent equation of the form

x = a

,

a = a

, or

a = b

results (where

a

and

b

are different numbers).

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

8.G.6 Explain a proof of the Pythagorean Theorem and its converse.

8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include

equations arising from linear and quadratic functions, and simple rational and exponential functions.

Note:

At this level, focus on linear and exponential functions.

A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

For example, rearrange Ohm's law V = IR to highlight resistance R.

Note:

At this level, limit to formulas that are linear in the variable of interest, or to formulas involving squared or cubed variables.Slide3

Unit 1 Common Core Standards

A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A-REI.11 Explain why the

x

-coordinates of the points where the graphs of the equations

y = f(x)

and

y = g(x)

intersect are the solutions of the equation

f(x) = g(x);

find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where

f(x)

and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Note:

At this level, focus on linear and exponential functions.

A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A-SSE.1 Interpret expressions that represent a quantity in terms of its context.

a. Interpret parts of an expression, such as terms, factors, and coefficients.

b. Interpret complicated expressions by viewing one or more of their parts as a single entity.

For

example, interpret P(1+r)n as the product of P and a factor not depending on P.

Note:

At this level, limit to linear expressions, exponential expressions with integer exponents and

quadratic expressions.

G-GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a

circle, volume of a cylinder, pyramid, and cone. Use dissection arguments,

Cavalieri's

principle, and

informal limit arguments.

Note:

Informal limit arguments are not the intent at this level.

G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

Note:

At this level, formulas for pyramids, cones and spheres will be given.

G-GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles,

e.g., using the distance formula.Slide4

Unit 1 Common Core Standards

N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (5 1/3)3 must equal 5.

N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Note:

At this level, focus on fractional exponents with a numerator of 1.

MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP.4 Model with mathematics.

MP.7 Look for and make use of structure.Slide5

Warm UpSlide6

Writing Algebraic Equations

Juan’s

salary plus $125 is $600.  

Six

times as many visitors is 120 visitors.

Twenty

-seven is seven fewer students than last

year.

Two

and one-half times the amount of interest is $2500

s + 125 = 600

6v = 120

27 = x – 7

2.5x = 2500Slide7

You Try!

The number of cats decreased by 17 is 19.

Four

times the number of feet is 12 feet.

The

price decreased by $4 is $29

.

After

dividing the money 5 ways, each person got $67

.

Three

more than 8 times as many trees is 75 trees.

X – 17 = 19

4x = 12

X – 4 = 29

x/5 = 67

8x + 3 = 75Slide8

Multi – Step Equations

Word Problems

1. Define the variable!

What is it you are looking for?

2. Write the equation

3. Solve

4. LABEL your answerSlide9

Equation Word Problems

Example 1

A public beach in Florida charges nonresidents $8 per day for a fishing license and $2.50 per day for live bait. Florida residents pay an annual fee of $114 plus $1 per day for live bait. How many days must both a resident and a nonresident use the beach in one year so that both pay the same amount? Show all work.Slide10

Answer

Let

d

represent the number of days

.

12 daysSlide11

Example

Jane is buying

Apps

for her iPhone. She can buy 5

apps

and have $3 left on her iTunes

Giftcard

or she can by 2

apps

and have $9 left on her

giftcard

. Write and solve an equation to find the cost of one app.X = cost of 1 appSlide12

Answer

5x + 3 = 2x + 9

x =

2

$2 for 1 appSlide13

Example 3

Sean has a stomach ache! He ate some cupcakes at breakfast, three times that number of cupcakes at lunch and 6 cupcakes at dinner. If he ate 18 cupcakes total, write and solve an equation to determine how many cupcakes he ate at lunch

.

x = number of cupcakes

x + 3x + 6 = 18

x = 3

9 cupcakes Slide14

Example 4

Consecutive Integers

Find three consecutive even integers such that the sum of the smallest and the largest is 36

.

x, x +2, x + 4

X + (x + 4) = 36

X = 16Slide15

Example 5

Find four

consecutive integers whose

sum is 56.

x, x + 1, x + 2, x + 3

x + (x + 1) + (x + 2) + (x + 3) = 56

X = 15Slide16

I ordered four new CDs by mail. Each costs the same amount and there was an additional $5.00 shipping/handling charge that brought the total to $33.00. Write and solve an equation to find the cost of one CD

.

$7

YOU TRY!!!Slide17

You Try!

Trevor is a salesperson who is paid a salary of $500 plus 2% commission. Write and solve an equation to determine how much Trevor must sell to earn $2,000 this month

.

$75, 000Slide18

You Try!

Four year old Anna Jane has been working hard all day making sandcastles. She was able to make twice as many sandcastles before lunch as she made after lunch (nap time got in the way!). If the total number of sandcastles Anna Jane made that day was three times her age, write and solve an equation to determine how many sandcastles she made after lunch

?

4 sandcastlesSlide19

You Try!

Hayden is on her school’s Battle of the Books team. She still has 40 pages to read in her final book before the competition. If she reads 5 times the number of pages tonight as she read last night, and then the last 10 pages tomorrow night, she will be finished with her book. Write and solve an equation to determine how many pages Hayden has to read tonight

.

P = 5

25 pages tonightSlide20

You Try!

Daniel Davis Dillard is proud of the lawn care business he runs after school. He charges a flat rate of $10 plus $5 per quarter acre of lawn. After mowing Mr. Stafford’s lawn 5 times, he made a total of $125. Write and solve an equation to determine how many acres of lawn Mr. Stafford has.

3 quarter acresSlide21

You Try!

Maggie is selling Girl Scout cookies. This week Ms. Coleman bought 3 boxes, Mr.

Papile

bought 4 boxes, and her friend Carroll bought 1box. Mr.

Somma

cannot eat cookies so he gave a $7 donation to Maggie’s troop. If Maggie sold 10 boxes last week and the amount of money she collected last week equals the amount of money she collected this week, write and solve an equation to determine how much each box of cookies costs.

$3.50Slide22

More Examples!

The Smiths are planning their daughter’s wedding. They will pay $225 to rent a reception hall for the evening. The cost to the reception hall per plate for dinner is $6.50, and the reception hall is charging the Smith’s $15.00 per plate. If the reception hall will earn a profit of $1,287.50 for the wedding, how many attendees will be present? Assume that the cost to rent the hall is entirely profit.Slide23

Answer

number of attendees = 125

Let

x

be the number of attendees and

p

be the profit.

hall rental + 15

x

– 6.5

x

= pSlide24

More Examples!

The total bill for new dirt and fencing at

Clovernook

baseball field is $378.00. The cost of new fencing is $270.00. If the cost of new dirt is $4.50 for a cubic foot, how many cubic feet of dirt were used for the field? Show all work.Slide25

Answer

Let

x

represent the number of cubic feet used.Slide26

Extra Practice

http://www.quia.com/cb/77775.htmlSlide27