Copy and then find the number Warm-up Copy and then find the number I am thinking of a number. I divide it by 2, then subtract 9 and finally divide by 3 to get answer of -1. What number did I begin with? I have 2. I subtract 8, divide by 3, add 2. What is my answer? What is the answer to 3 – 3 • 4 ÷ 6 + 3? USE ELSEWERE

Clear your desk except for paper/pencil Copy the DATE and TOPIC DATE: August 52 – 2 TOPIC: Modeling expressions ESSENTIAL QUESTION: How do you interpret algebraic expressions in terms of their context? AGENDA: Warm-up Understanding vocabulary Interpret expressions Worked examples with independent practice

Warm-up Copy and Solve the following equations mentally. 3x + 2 = 10 2 min

-3 is the coefficient of the variable x2 Terms There are 2 types of terms: Constant terms which are number only terms. - All constants are like terms Variable terms which are a product of a number called a coefficient and a letter called a variable -Variable terms are only like terms if they have the same letter and the same exponent. 3. Terms are separated by + or – Variable term The factors are -3 and x2. -3 is the coefficient of the variable x2 -3xx woud be 3 factors Constant 5 - 3x2 copy

Expressions An expression is made up of constants and/or variable terms. (no = sign) Example 1: 5x + 3 – 7x + x + 1 Example 2: 2 – 3x + 7 + 2x + 5 – x Example 3: 2y – 3x + 7y3 + 2x2 + 5y3 – x3 Clarify that an expression may be a number, a variable or combination of both. Refer to the circled ones as variable terms and the non-variables as constants Circle the variable terms and underline the constant terms How many terms does the expression have? Tell the coefficient of the variable terms In ex. 3 are there any like terms? copy

REVIEW An expression in simplest form has No parenthesis B) No like terms To simplify an expression (do in order) Use the distributive property to remove parenthesis (by multiplying) 2. Combine [coefficients of] like terms (by using the commutative and associative properties) copy

Simplifying expressions Example 1: 4(2x – 7) + x 1 8x – 28 + 1x 9x – 28 2: 3x + 5 – x + 4x + 6x – 9 12x – 4 3: 2 7 (4x + 7) – 4(- 8) 8 7 𝑥 + 2 + 32 8 7 𝑥 + 34 copy

EXAMPLE In the expression, 3x – 7y + 3 – x2 + 4, there are _____ terms. There are ____ variable terms and ____ constant(s). The coefficient of the y term is _____ and the coefficient of the x2 term is ______. The 3 in the first term is called a _________________ and the 3 in the third term is called a __________. The factors of the fourth term are ______ and ______. 5 3 2 –7 –1 coefficient constant –1 x and x Do not copy

YOUR TURN In the expression, 5(x) – 2(x) – x5 + 10, there are _____ terms. There are ____ variable terms and ____ constant(s). The coefficients of the (x) terms are _____ and ______. The coefficient of the x5 term is ______. The 5 in the first term is called a _________________ and the 5 in the third term is called a __________. The factors of the second term are ______ and ________. 4 3 1 5 –2 –1 coefficient Power or exponent –2 x

Class Discussion 2x + 4y = 16 Start by asking students what x means (We do not know, so x can be anything, like what? A bicycle? What about the bike? Price? Maybe just the number of bikes of x type) Then, if x is a bike what would 2x be? What happens if I add 4y? Can y be the same thing as x? What if I told you y was number of cars car? What do bikes have two of and cars have 4 of? Tires! Now, what happens if I add a total? What could that mean?

Therefore 1.49p represents _______________________________. EXAMPLE Curtis is buying supplies for his school. He buys p packages of crayons at $1.49 per package and q packages of markers at $3.49 per package. What does the expression 1.49p + 3.49q represent? the price of a pack In the term 1.49p the coefficient 1.49 represents _____________ ____________ and the variable p __________________________. Therefore 1.49p represents _______________________________. In the term 3.49q _______________________________________ ______________________________________________________ Therefore________________________________________________  the expression 1.49p + 3.49q represents __________________ ________________________________________________________ of crayons the number of packages of crayons the total price for p packages of crayons 3.49 is the price per pack of markers and q represents the number of packages bought. Page 46 3.49q represents the total price for q packages of markers The total price for p packages of crayons and q packages of markers.

a) amount of Laser jet paper bought: ______________ YOUR TURN Jill is buying ink jet paper and laser jet paper for her business. She buys 8 more packages of ink jet paper than m packages of laser jet paper. Ink jet paper costs $6.95 per package and laser jet paper costs $8. Write an expression for each of the following a) amount of Laser jet paper bought: ______________ b) price for each package of Laser J. paper:_______________ c) amount of Ink jet paper bought: ______________ d) price for each package of Ink J. paper:_______________ e) Total cost of paper bought for the business: _______________ m packages $8 per package (m + 8) packages $6.95 per package Page 46/47 8m + 6.95(m + 8)

Discussion Chris buys p pairs of pants and a lesser amount of shirts than pairs of pants. This is represented by 25p + 18(p – 4). What does the term 18(p – 4) in the expression represent? What does the entire expression represent? 
 
 Chris buys p pairs of pants and 4 more shirts than pairs of pants. Shirts cost $18 each and pair of pants cost $25 each. What does each term in the expression 25p + 18(p + 4) represent? What does the entire expression represent? 


The price of an item plus 6% sales tax Write an algebraic expression to model the given context, in simplest form. The price of an item plus 6% sales tax Price of an item + 6% of price of the item ______ + ______ OR _____________________________ The number of cookies in a jar that had 40 cookies, after Gabriel ate 3 cookies per day for d days. # of cookies in a jar – cookies eaten ______ – ______ Or ______________________________________ p 0.06p 1p + o.06 p = (1 + 0.06)p = 1.06p Page 48 40 3d 40 – 3d (cannot be simplified)

Your turn Write an algebraic expression to model the given context, in simplest form. The number of gallons of water in a tank, that already has 300 gallons in it, after being filled at 35 gallons per minute for m minutes. The original price p of an item less a discount of 15%. 300 + 35m p – 0.15p 0.85p

Higher Order Thinking Question

EXAMPLE Suppose x and y are the populations of two different cities where x > y. Compare the expressions below: a) x + y and 2x b) 𝑥 𝑦 𝑎𝑛𝑑 𝑦 𝑥 Hint: What type of numbers are x and y? negatives? Positives? fractions? Decimals? Whole numbers? < > Your turn Suppose x and y are the populations of two different cities where x > y. Compare the expressions below: a) 𝑥 𝑥+𝑦 𝑎𝑛𝑑 𝑥+𝑦 𝑥 b) 2(x + y) and (x + y)2 Page 47

INDEPENDENT PRACTICE

In the expression: 6x – 21, there are ______ terms. ___ is considered a coefficient and _______ a constant. The term _______ has factors of _______ and ______. During 60-minute period, a traffic engineer counted 66 trucks and cars that crossed a bridge. The ratio of trucks and cars that travel across the bridge is usually 3:8. In the expression 𝑡 66 −𝑡 , which term represents the number of cars, t or 66 – t?

The expression 1650 + 0.15s is used to calculate Marta’s monthly earnings, which is based on a fixed salary plus a percent of her sales. What percent of her sales does she earn? The expression 2c + f + 3d + 4t represents the cost in dollars, to buy c bags of Cheetos, f bags of Fritos, d bags of Doritos and t bags of Tostitos. What does the term 3d represent? What does the coefficient of the term 2c represent? What is the cost of a bag of Fritos? Can you tell which is the most expensive chip?

Name_________________________ Date _________ Per __ In the expression: 6x – 2, there are ______ terms. ___ is considered a coefficient and _______ a constant. The term _______ has factors of _______ and ______. In the expression: 6 – 2x, there are ______ terms. ___ is considered a coefficient and _______ a constant. The term _______ has factors of _______ and ______. During a 60-minute period, a traffic engineer counted 66 trucks and cars that crossed a bridge. The ratio of trucks and cars that travel across the bridge is usually 3:8. In the expression 𝑡 66 −𝑡 , which term represents the number of cars, t or 66- t? During a 60-minute period, a traffic engineer counted 66 trucks and cars that crossed a bridge. The ratio of trucks and cars that travel across the bridge is usually 3:8. In the expression 𝑡 66 −𝑡 , what term represents the number of cars, t or 66- t? The expression 1650 + 0.15s is used to calculate Marta’s monthly earnings, which is based on a fixed salary plus a percent of her sales. What percent of her sales does she get? The expression 1650 + 0.15s is used to calculate on Marta’s monthly earnings, which is based on a fixed salary plus a percent of her sales. What is her fixed salary? The expression 2c + f + 3d + 4t represents the cost in dollars, to buy c bags of Cheetos, f bags of Fritos, d bags of Doritos and t bags of Tostitos. What does the term 3d represent? What does the coefficient of the term 2c represent? The expression 2c + f + 3d + 4t represents the cost in dollars, to buy c bags of Cheetos, f bags of Fritos, d bags of Doritos and t bags of Tostitos. What is the cost of a bag of Fritos? Can you tell which is the most expensive chip? Why?

Name_________________________ Date _________ Per __ In the expression: 6x – 21, there are ______ terms. ___ is considered a coefficient and _______ a constant. The term _______ has factors of _______ and ______. In the expression: 6x – 21, there are ______ terms. ___ is considered a coefficient and _______ a constant. The term _______ has factors of _______ and ______. During a 60-minute period, a traffic engineer counted 66 trucks and cars that crossed a bridge. The ratio of trucks and cars that travel across the bridge is usually 3:8. In the expression 𝑡 66 −𝑡 , which term represents the number of cars, t or 66- t? During a 60-minute period, a traffic engineer counted 66 trucks and cars that crossed a bridge. The ratio of trucks and cars that travel across the bridge is usually 3:8. In the expression 𝑡 66 −𝑡 , what term represents the number of cars, t or 66- t? The expression 1650 + 0.15s is used to calculate Marta’s monthly earnings, which is based on a fixed salary plus a percent of her sales. What percent of her sales does she get? The expression 1650 + 0.15s is used to calculate on Marta’s monthly earnings, which is based on a fixed salary plus a percent of her sales. What percent of her sales does she get? The expression 2c + f + 3d + 4t represents the cost in dollars, to buy c bags of Cheetos, f bags of Fritos, d bags of Doritos and t bags of Tostitos. What does the term 3d represent? What does the coefficient of the term 2c represent? What is the cost of a bag of Fritos? Can you tell which is the most expensive chip? Why? The expression 2c + f + 3d + 4t represents the cost in dollars, to buy c bags of Cheetos, f bags of Fritos, d bags of Doritos and t bags of Tostitos. What does the term 3d represent? What does the coefficient of the term 2c represent? What is the cost of a bag of Fritos? Can you tell which is the most expensive chip? Why?