Download Notes and Homework - Unit 2 Packet 2 of 6

6th Grade
Unit 2 – Expressions
and Equations:
Packet 2 of 6
Mr. Rothdiener
Name: _______________________________________________
Packet Outline, Page 1
 2.7: Distributive Property (6.EE.A.3, 6.EE.A.4), Pages 2-4
o I can apply the distributive property to move from a factored form to
an expanded form of an expression.
 2.8: Factor Expressions Using GCF (6.EE.A.3, 6.EE.A.4), Pages 5-7
o I can apply the distributive property to move from an expanded form
to a factored form of an expression.
 2.9: Combine Like Terms (6.EE.A.3, 6.EE.A.4), Pages 8-10
o I can simplify expressions by combining like terms.
o I can evaluate expressions using given values for variables.
 2.10: Distributive Property and Combining Like Terms (6.EE.A.3, 6.EE.A.4),
Pages 11-13
o I can simplify expressions by applying the distributive property and
combining like terms.
 2.11: Translate Expressions (6.EE.A.2a), Pages 14-16
o I can write algebraic expressions that record all operations with
numbers and letters standing for numbers.
 2.12: Translate Expressions (6.EE.A.2a), Pages 17-20
o I can write algebraic expressions that record all operations with
numbers and letters standing for numbers.
 2.13: Translate Complex Expressions (6.EE.A.2a), Pages 21-23
o I can write algebraic expressions that record all operations with
numbers and letters standing for numbers.
 Quiz 2.2 Review (6.EE.A.2a, 6.EE.A.3, 6.EE.A.4) Pages 24-25
o I can apply the properties of operations to generate equivalent
expressions.
o I can identify when two expressions are equivalent.
o I can write expressions that record operations with numbers and
with letters standing for numbers.
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2.7: Distributive Property (6.EE.A.3, 6.EE.A.4)
Bell Work:
1.) Evaluate 2(a + b) when a = 3 and b = 4
2.) Evaluate 2a + 2b when a = 3 and b = 4
Whole-Class:
Apply the distributive property to generate equivalent expressions.
1.) 3(x + y)
2.) 4(2h + g)
3.) a(9b + 13)
4.) j(7k + 12m)
5.) 5(7h + 3m)
6.) y(4x + 5)
2
Guided Practice:
Apply the distributive property to generate equivalent expressions.
7.) e(f + g)
8.) 8(h + 3)
9.) 5(3x + 9y)
10.) 4(x + y)
11.) 3(2x + 11y)
12.) c(3a + b)
Independent Practice:
Apply the distributive property to generate equivalent expressions.
13.) k(m + n)
14.) 3(2h + 7)
15.) 4(11h + 3g)
16.) 8(a + 3b)
17.) 9(7a + 6b)
18.) y(2x + 11z)
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HOMEWORK 2.7
Apply the distributive property to generate equivalent expressions.
1.) 7(i + 2)
2.) 2(5m + 9)
3.) 5(2a + 7b)
4.) 6(10c + 4d)
5.) 23(s + t)
6.) 11(e + 6f)
7.) 7(3g + 5h)
8.) 11(7j + 9k)
9.) z(4x + y)
10.) b(3a + 15c)
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2.8: Factor Expressions Using GCF (6.EE.A.3, 6.EE.A.4)
Bell Work:
Distribute: 7(x + y)
Whole-Class:
Apply the distributive property to generate equivalent expressions.
1.) 7x + 7y
2.) 15g + 20h
3.) 18m +42n
4.) 30a + 30b
5.) 11f + 15f
6.) 7 + 56y
5
Guided Practice:
Apply the distributive property to generate equivalent expressions.
7.) 18h + 13h
8.) 55m + 11
9.) 6x + 21y
10.) 5g + 7g
11.) 14x + 2
12.) 100x + 700y
Independent Practice:
Apply the distributive property to generate equivalent expressions.
13.) 4x + 12y
14.) 35x + 50y
15.) 18x + 9y
16.) 32x + 8y
17.) 2q + 10r
18.) 4b + 7b
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HOMEWORK 2.8
Apply the distributive property to generate equivalent expressions.
1.) 6𝑥 + 6𝑦
2.) 25𝑔 + 35ℎ
3.) 9𝑚 + 45𝑛
4.) 6𝑎 + 15𝑏
5.) 13𝑓 + 17𝑓
6.) 8𝑒 + 9𝑒
7.) 60𝑚 + 10
8.) 5 + 45𝑦
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2.9: Combine Like Terms (6.EE.A.3, 6.EE.A.4)
Bell Work:
Evaluate:
5x + 2 + 3x
if x = 5
Whole-Class:
Simplify each expression by collecting like terms.
1.) 5x + 2 + 3x
2.) 9x + 3 + 7x + 4
3.) 3z + 6u + 8z + 9 + u
Simplify the expression, then evaluate for the given values.
4.) 5x + 5y + 9y + 2x + y
if x = 8, y = 3
Guided Practice:
Simplify each expression by collecting like terms.
5.) 7t + 6 + 3v + 6v
6.) 4y + 3x + 2y + 9x + 4
8
7.) 5u + 7z + 6u + u + 4z
Simplify the expression, then evaluate for the given values.
8.) 3x + 2y + 4 + 9y
if x = 8, y = 4
Independent Practice:
Simplify each expression by collecting like terms.
9.) 3 + 7x + 8
10.) 3t + 4v + 5t
11.) t + 5v + 6 + 7t
12.) x + 7y + 9 + 3y + 6y
Simplify the expression, then evaluate for the given value.
13.) 3x + 7x + 2
if x = 6
14.) 9y + 5 + y + 8
9
if y = 7
HOMEWORK 2.9
Simplify each expression by collecting like terms.
1.) 4x + 7 + 4
2.) x + 3x + 6
3.) 3t + 9v + 4t + 9v
4.) 3t + v + t + 7v
5.) 1 + 8x + 3y + x + 9y
6.) 2u + 4 + 3z + 6 + 9
Simplify the expression, then evaluate for the given value(s).
7.) 9 + x + 4x
if x = 8
8.) 9x + 6y + 5x + 4y
10
if x = 1, y = 9
2.10: Distributive Property and Combine Like Terms (6.EE.A.3, 6.EE.A.4)
Bell Work:
Simplify:
3(2x + 5) + 7x
Whole-Class:
Simplify each expression.
1.) 5(x + 2) + 3x
2.) 3(9x + 3) + 7(x + 4)
3.) 9(4a + 3b) + 8(4a + 9b)
4.) 4(5d + 4) + 8(4k + 6)
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Guided Practice:
Simplify each expression.
5.) 6(m + 6) + 15m
6.) 5(6g + 5h) + 9(5g + 6j)
Independent Practice:
Simplify each expression.
7.) 3(8y + 7) + 7y
8.) 6(7w + 1) + 9(4w + 2)
9.) 11(5p + 8q) + 10(3p + q)
10.) 5(2e + 1) + 7(5f + 9)
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HOMEWORK 2.10
Simplify each expression.
1.) 2(x + 7) + 9x
2.) 6(8x + 4) + 4(x + 11)
3.) 7(2a + 3b) + 3(3a + b)
4.) 5(3m + 7) + 10(6n + 9)
5.) 8(2x + y) + 9(2x + 5y)
6.) 11(6q + 5r) + 1(5q + 6u)
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2.11: Translate Expressions (6.EE.A.2a)
Bell Work:
Fill in the chart below with terms that relate to each operation.
Addition
Subtraction
Multiplication
Division
Whole-Class:
Write a variable expression for each word phrase.
1.) t decreased by 3
2.) the product of 5 and w
3.) the sum of 18 and r
4.) 36 divided by g
5.) x less than 9
6.) m times n
7.) the quotient of 88 and v
8.) p fewer than 13
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Guided Practice:
Write a variable expression for each word phrase.
9.) 6 increased by y
10.) the quotient of 8 and e
11.) the difference of h and 3
12.) 4 times w
13.) 5 more than n
14.) r divided by 2
Independent Practice:
Write a variable expression for each word phrase.
15.) the difference of s and 8
16.) the product of six and m
17.) x less than 24
18.) 6 more than a number b
19.) 8 decreased by a number m
20.) the quotient of z and 14
21.) 21 fewer than k
22.) the sum of 19 and b
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HOMEWORK 2.11
Write an algebraic expression for each word phrase.
1.) 12 more than a number x
2.) 32 less than a number m
3.) The sum of a number b and 6
4.) The product of a number p and 3
5.) The quotient of d and 9
6.) 12 times a number v
7.) The difference of a number z and 3
8.) 21 divided by g
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2.12: Translate Expressions (6.EE.A.2a)
Bell Work:
Complete the graphic organizer with mathematical words that indicate each
operation. Some words may not indicate only one operation. Use the word bank
below:
Difference
Product
Cubed
More
than
Triple
Fewer
than
Decreased
by
In all
Sum
How
many
fewer
Subtract
Multiply
Quotient
All
together
As much
Left
Every
Divide
Double
Split
Total
Times
Less than
Increased
by
Each
Add
Plus
Minus
Squared
Of
Per
power
ADDITION
SUBTRACTION
MULTIPLICATION
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DIVISION
EXPONENTS
Whole-Class:
Write a variable expression for each word phrase.
1.) 5 times m
2.) 9 less than t
3.) three times a number w decreased by 4
4.) 5 more than the sum of twice a number h and 6
5.) the sum of 10 and a number y divided by 5
6.) the quotient of a number and f decreased by 11
Guided Practice:
Write a variable expression for each word phrase.
7.) the sum of 8 and b
8.) eleven more than a number
9.) 100 less than the product of 9 and y
10.) six times the difference of 8 and g
18
11.) the difference of s and twice a number h
12.) nine plus twice x
Independent Practice:
Write a variable expression for each word phrase.
13.) 10 less than c
14.) 700 divided by a number q
15.) the quotient of 18 and a
16.) 2 times a number w
17.) 10 more than twice a number k
18.) the sum of twice a number j and 5
19.) 9 fewer than the product of a and b
20.) the sum of quadruple a number q and 50
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HOMEWORK 2.12
Write an algebraic expression for each word phrase.
1.) 13 more than three times a number x
2.) 23 minus the product of 5 and a number m
3.) The quotient if 6 plus a number b and 11
4.) 4 times a number p minus 7
5.) Twice m plus 10
6.) The quotient when a number z minus 5 is divided by 14
7.) 5 times b minus 18
8.) a plus the difference of d and 6
20
2.13: Translate Complex Expressions (6.EE.A.2a)
Bell Work:
Translate: The difference of three times a number x and 4
Whole-Class:
Write a variable expression for each word phrase.
1.) The sum of twice b and 5
2.) 5 times d increased by 8
3.) b decreased by c squared
4.) 150 decreased by the quantity of 6 plus b
5.) Marlo had $35 but then spent $m
6.) a raised to the fifth power, increased by the product of 5 and c
Guided Practice:
Write a variable expression for each word phrase.
7.) The quotient of c and d
8.) 10 less than the product of 15 and c
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9.) Veronica increased her grade, g, by 4 points, and then doubled it
10.) To find out how much paint is needed, Mr. Jones must square the side length
of the gate, s, and then subtract 15
11.) 24 divided by the product of 2 and a
12.) Samantha saved her money and was able to quadruple the original amount, m
Independent Practice:
Write a variable expression for each word phrase.
13.) the sum of twice c and 10
14.) the quantity of a plus b divided by 4
15.) 15 less than the quotient of e and d
16.) a number h is tripled and then
decreased by 8
17.) Adam had m pieces of candy and ate 5 of them. Then he split the remaining
candy equally among 4 friends.
18.) Luis bought x cans of cola to the party, Faith brought d cans of cola, and De’Shawn
brought h cans of cola. How many cans of cola did they bring all together?
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HOMEWORK 2.13
Write an algebraic expression for each word phrase.
1.) Justin can type 𝑤 words per minute. Melvin can type 4 times as many words
as Justin. Write an expression that represents the rate at which Melvin can
type.
2.) Joanna swam 𝑦 yards yesterday. Shae swam 5 yards less than half the amount
of yards as Joanna. Write an expression that represents the number of yards
Shae swam yesterday.
3.) A number 𝑑 is decreased by 5 and then doubled.
4.) Nick had 𝑛 baseball cards and Shaun had 𝑠 baseball cards. They combined
their baseball cards and then sold 10 of them.
5.) The sum of 25 and ℎ is divided by 𝑓 cubed.
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Quiz 2.2 Review
(6.EE.A.2a, 6.EE.A.3, 6.EE.A.4)
Use your knowledge of math to complete each of the following questions. Show
your work!
1-6: Apply the distributive property to generate equivalent expressions.
1.) 5(x + y)
2.) 7(3h + g)
3.) a(7b + 4)
4.) 5x + 15y
5.) 30x + 70y
6.) 20x + 4y
7-11: Simplify each expression.
7.) 8x + 5 + 3x
8.) 4x + 7 + 3x + 8
10.) 9(4a + 3b) + 8(4a + 9b)
9.) 6z + 5u + z + 7
11.) 4(5d + 4) + 8(4k + 6)
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12-20: Write an algebraic expression for each word phrase.
12.) 6 more than a number b
13.) 8 decreased by a number m
14.) The product of 4 and a number x
15.) The quotient when a number z is divided by 14
16.) 6 more than a twice a number b
17.) The quotient when a number z minus 5 is divided by 14
18.) a divided by the sum of b and 2
19.) Jazmin has increased her $45 by 𝑚 dollars and then spends a third of the
entire amount.
20.) Bill has 𝑑 more than 3 times the number of baseball cards as Frank. Frank
has 𝑓 baseball cards.
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