do now:. unit 3.5 swbat: combine like terms use the distributive property
TRANSCRIPT
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Do Now:
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Unit 3.5SWBAT:•Combine like terms•Use the distributive property
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AgendaDo now
Homework Pass-in
Agenda
Notes
Reward!
Practice
Reward!
Exit Ticket
Clean-up
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Reward you say?!
Yes, a reward!
Vote for your top 2 choices, and if you are on task (as a class), have 100% participation, we can earn these great rewards as a brain break!
Listen to music as you work
Watch a funny YouTube video
5 minute chat break
Play a math game as your independent practice
3 rounds of “heads up 7up”
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Remember past vocab: Term
Term: a number, variable, or the product (multiplication) of a number and a variable.
4 + 3y + 2 – 7
TERMS are separated by operation symbols
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New Vocabulary: Like Terms
Terms that have exactly the same variable factors
(Exactly the same variables multiplied by a number)
Like Terms: Not Like Terms:
-5 and 8 -5x and 8
2x and -3x 2x2 and -3x
2xy and -3xy 2x and -3xy
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Identify the like terms
Which ones are like terms with 4xy?
1) -5xy 2) 3x
3) (3/5)xy 4) 7020234xy2
5) 52 6) 809xyz
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Identify the like terms
Which ones are like terms with 4xy?
1) -5xy 2) 3x
THIS ONE
3) (3/5)xy 4) 7020234xy2
THIS ONE
5) 52 6) 809xyz
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Quick Answer!
First table team to have everyone raise their hands gets a sticker!
Which letter(s) are similar terms with 16xy?
A) 14x
B) 5y
C) 16xy2
D) 4xy
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Quick Answer!
First table team to have everyone raise their hands gets a sticker!
Which letter(s) are similar terms with 16xy?
A) 14x
B) 5y
C) 16xy2
D) 4xy
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Like terms can be simplified
Simplifying happens only on ONE SIDE of an equation or expression.
Only like terms can be simplified.
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Side Note: Variables w/out numbers
Remember: variables without numbers in front of them are the same as a variable being multiplied by 1.
X = 1x
-Y = -1Y
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Combining like terms
Combining like terms: On the SAME side of an equation you will add/subtract them together, based on what their signs say. You’re just re-organizing.
Ex. 5y + 4y – 2y = 2 (5 + 4 – 2)y = 2
7y = 2
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Combining like terms: Example 1
Combine like terms in 5m + 9m + m
= (5 + 9 + 1)m
= 15m
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Combining like terms: Example 2
Simplify 6p + 4y + 8 – 4p + 3
(6 – 4)p + 4y + (8 + 3)
2p + 4y + 11
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You Try
Simplify 6x + 7y + 3x
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You Try: ANSWERS
= 6x + 7y + 3x
= (6 + 3)x + 7y
= 9x + 7y
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Now Try:
1) 7x + 5y + 6y + 3
2) 4x + 10p – 15 + 6
3) 8y – 3p + 12 - 1
4) 7y – 3p + 17x – 1
5) 28p – 12p + 11 – 15
6) 3p + 12r + 6p - 10
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Now Try:
1) 7x + 5y + 6y + 3
7x + 11y + 3
2) 4x + 10p – 15 + 6
4x + 10p - 9
3) 8y – 3p + 12 – 1
8y – 3p + 11
4) 7y – 3p + 17x – 1
7y – 3p + 17x - 1
5) 28p – 12p + 11 – 15
16p - 4
6) 3p + 12r + 6p – 10
9p + 12r - 10
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Word Problems!!!! YAAAAAYYYYYYY!!!!!
Robert buys 5 loaves of bread and 8 cans of tuna for a picnic. Melissa buys a loaf of bread and 2 cans of tuna. Define and use variables to represent the total cost.
B = cost of a loaf of bread
T = cost of a can of tuna
Robert: 5b + 8t
Melissa: 2t + 1b
5b + 8t + 2t + 1b
= 6b + 10t
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You try:
In one trip to a hardware store, you buy 16 boards, 2 boxes of nails, and a hammer. On a second trip, you buy 10 more boards and a box of nails. Define and use variables to represent the total cost.
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You try:In one trip to a hardware store, you buy 16 boards, 2 boxes of nails, and a hammer. On a second trip, you buy 10 more boards and a box of nails. Define and use variables to represent the total cost.
b = cost of board
n = cost of nails
h = cost of a hammer
16b + 2n + h + 10b + n
=26b + 3n + h
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Now Try: Write the expression for the following situations
1) Alexis buys a beach house, 2 dogs and a pet cat one day, and a second beach house, 4 more dogs, and another pet cat the next day.
2) Tyreek runs for 12 miles, then hikes for 19 upwards, continues to run 4 miles, then hikes upwards 6 miles.
3) Bryena eats 14 candy bars, then 3 bags of chips, then another 8 candy bars before eating a whole cake.
4) Cye-Enn colors for 8 minutes, then dances for 15 minutes, colors for another 12 minutes, then eats for 12.
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Now Try: Write the expression for the following situations
1) 2b + 6d + 2c
2) 16r + 25h
3) 22b + 3h + c
(where b = candy bars, h=chips, c = cake)
4) 20c + 15d + 12e
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Distributive Property
Distributive property: a (b + c) = ab + ac
You’re multiplying the number outside the parenthesis by both of the numbers inside the parenthesis, but keeping the same sign.
Ex) 5 (4t – 3)
= 5(4t) – 5(3)
= 20t - 15
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Distributive property slow-mo
Simplify:
3 ( x - 2 )
3x - 3(2)
3x - 6
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Distributive Property Simplifying: Example
Simplify 5(t + 3) + 8t
5t + 15 + 8t
(5 + 8)t + 15
13t + 15
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You Try
• Simplify 6t – 14 + 3(t – 2)
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You Try: ANSWERS
• Simplify 6t – 14 + 3(t – 2)
6t – 14 + 3t – 6
(6 + 3)t + (-14 – 6)
9t + -20
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Now Try
• 1) 8c – 3(c + 5)
• 2) 8d + 6(4 – d)
• 3) 4x – 12 + 5(d + 2)
• 4) 3x – 11 + 3(4-x)
• 5) 2x + 2(-3x – 11)
• 6) -5(c + 3) - 13
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Now Try
• 1) 8c – 3(c + 5)
5c - 15
• 2) 8d + 6(4 – d)
2d + 24
• 3) 4x – 12 + 5(d + 2)
4x + 5d - 2
• 4) 3x – 11 + 3(4 - x)
15x - 11
• 5) 2x + 2(-3x – 11)
-4x - 22
• 6) -5(c + 3) – 13
-5c -28