Unit 1 Lesson 1: Numbers & EstimationLesson Opener: https://youtu.be/vFv5bwPjMto

10 Easy Math RiddlesVocabularyEstimation A rough calculation of a value, number, quantity, or

the extent of somethingNumerical Expression

A mathematical sentence involving only numbers and one or more operations

Algebraic Expression

A mathematical sentence involving numbers, variables, and one or more operations

Simplify Putting a mathematical sentence in a reduced formed by using properties of mathematics

Example: Estimate to find the answer.1) The river ferry makes 5 trips a day. There are between 40

and 60 people each trip. About how many people ride the ferry each day?

2) Peter has 25 plants in his garden. Each plant produces 3 to 5 quarts of beans. How many quarts of beans will Peter have?

FYI…SUB TOTAL – AMOUNT BEFORE TAXES

SALES TAX – ADD TO SUB TOTAL

TIP/GRATUITY – ADD TO SUB TOTALDISCOUNT – SUBTRACT FROM SUB TOTAL

Examples: Write a numerical expression and solve.1) Marty bought 2 gallons of milk at $2.39 each, 5-2L of Pepsi

at $1.39 each. The sales tax is 6%. a) What was the total BEFORE taxes?

b) What was the total amount of his grocery bill?

2) Marsha’s sub total at Bahama Breeze was $16.78. She wants to leave a 15% tip.a) What is the amount of her tip?

b) If sales tax is 8.5%, what is her total?

3) New York & Company has a 40% off discount on dress shirts. Teresa bought 3 shirts costing $35 each. a) What was her subtotal BEFORE the discount?

b) What is the amount of her discount?

c) If sales tax is 6%, what is the total cost of her shirts?

You Try…1) Dara bought 4 bouquet of roses from Flower’s R Us for

$22.99 each. a) She discovered a coupon which said she can get 25% off

her price. What is her subtotal?

b) If sales tax is 6%, what was the total she paid for her roses?

Challenge….

Unit 1 Lesson 2: Writing Algebraic Expressions

Lesson Opener: Guess the Magic Number!Description Numerical

Expression Simplify

Choose a number between 1 and 20Double your original numberAdd 6Divide by 2Subtract your original number from the new number

Final Answer

Example #1

Description Numerical Simplify

Expression Write the number of the month of your birthdayMultiply by 7Subtract 1 from the resultMultiply the result by 13Add the number that represents the day of your birthAdd 3 Multiply by 11Subtract the month of birthSubtract the day of birthDivide by 10Add 11Divide by 100 Final Answer

Examples: Write the expression.1. Triple a number subtracted from ten.

2. The difference of twice times a number and thirteen.

3. Eight times a number plus five.

Examples: Write AND simplify the expression.1. A fourth of the difference of twelve and eight times a number.

2. Nine times a number subtracted from the same number

Let’s redo the opener using Algebra…

Description Algebraic Expression

Simplify

Let x represent a number between 1 and 20Double your original numberAdd 6Divide by 2Subtract your original number from the new number

Final Answer:

You Try….Description Algebraic

Expression Simplify

Let x represent your cousin’s ageTriple your numberSubtract 6Divide by 3Subtract your original number from the new number

Final Answer:

Unit 1 Lesson 3: Distributive Property

Example #1: 1) -6(a + 8) 3) 4(1 + 9x)

2) 6(-5n + 7) 4) 2(x – 4) – 6x + 1

Example #2: Are these expressions equivalent? Justify your answer.1) x(x + 4) and x2 + 4

2) y(x + 2) and xy + 2y

3) (x + 5)2 and x2 + 25

Example #3:Marcus bought 3 pair of jeans and a shirt. Write an expression that represents the total cost.

You Try… Which expressions are the same? Justify your answer.#1

#2Shawn spent $20 at Walmart. He then went to Publix and spent $8.97 for 2 gallons of milk. Write and expression that represents the total cost.

Unit 1 Lesson 5: Recognizing PatternsDo you remember?Writing an equation using 2 coordinates…1st: Find the slope 2nd: Solve for b

Example: (2, 4) (4, 6)

You try… (5, 2) (10, 1)

Unit 1 Lesson 3: Reading & Evaluating Algebraic ExpressionsThings to remember…..Examples: Simplify the algebraic expressions

1) 5a + 3a

2) g – g

3) 3a – c + 4a + 6c

Examples: Evaluate the expression

1) Let x = 1 and y = 2, y2 + x

2) Let m = 1 and p = 5, m2 – p

Examples: Write and evaluate each word problem.1) Craig washes car. He charges $8 per car. How much will he make if

he washes 23 cars?a) Expression: _____________________________

b) Answer: _________________________________

2) You have $60. You buy a pair of jeans and a shirt. You spent $27 on a pair of jeans and you had $15 left. How much did the shirt cost?a) Expression: _________________________

b) Answer: _____________________________You try…..

1) Simplify: -6x + .3x – 16

2) Evaluate: let a = 5 and b = -1, 2b + 5a

3) Write and evaluate: RJ has $15 in his account. He bought a 5 bags of chips for $2.39 each and a 2-liter bottle of Sprite for $1.49. Expression: ________________________________________

Answer: ____________________________________________Challenge…

a) Abby’s expression___________________________________

b) Renato’s expression___________________________________

c) Do the 2 methods give the same answer? Justify your answer.

Example #1:

a) Write the expression to generate the algebraic expression needed to generate the numbers of blocks needed.

b) How many blocks are needed for the 8th pattern?

Example #2:Below is a visual of a toothpick pattern. Complete the table.

a) Write the expression to generate the algebraic expression needed to generate the numbers of blocks needed.

b) How many blocks are needed for the 23rd pattern?

Design Number

Number of Toothpicks

1 42 73 1046