6th Grade Math - Unit 7 - Bar Models + Algebraic Expressions
2d = 2x3 = 6 = 2 9 9 9 3
2d when d = 3 9
3m + 2 = 3x5 + 2 = 15 + 2 = 17
3m + 2 when m = 5
40 - 5p = 40 - 5x6 = 40 - 30 = 10
40 - 5p when p = 6
4k/3 = 4x2/3 = 8/3 = 2 2/3
4k/3
6 + 3x2/6 = 6 + 6/6 = 6 + 1 = 7
6 + 3k/6 when k = 2
7 - r/2 = 7 - 4/2 = 7 - 2 = 5
7 - r/2 when r = 4
8k - 2 = 8x2 - 2 = 16 - 2 = 14
8k - 2 when k=2
9k/5 = 9x2/5 - 2 = 18/5 - 2 = 3 3/5 - 2 = 13/5
9k/5 - 2
8h cm
A piece of wire is bent in the shape of an octagon. Each side is h centimeters long. what is the total length of the wire in terms of h?
m + 2 + m + 2 = 2 * m + 4 = 2m + 4 feet
A rectangle has a width of 2 feet and a length of m feet. Find the perimeter of the rectangle in terms of m.
g + g + g + g = 4 *g = 4g yards
A square has a length of g yards. Find the perimeter of the square in terms of g.
d + d + d = 3 * d = 3d inches
An equilateral triangle has sides measuring d inches long. Find the perimeter in terms of d.
term
a number, a variable, or a product or quotient of numbers and variables (4x + 12 + x)
like term
a term that contains the same variables raised to the same power (5x and 6x) (4b² and 5b²)
constant
a term that does not contain a variable (ex - the 12 in 4x + 12)
sum
addition answer
part + part = whole
addition bar model
5, 5d + 3
d + d + d + d + d + 5 - 2 = _____ * d + 5-2 = _____ + _____
quotient
division answer
whole ÷ number of parts = unknown part
division bar model
e/3 - 6 = 24/3 - 6 = 8 - 6 = 2
e/3 - 6 when e = 24
product
multiplication answer
part x number of parts = whole
multiplication bar model
coefficient
numerical factor of a term that contains a variable (ex - the 6 in 6x)
addition bar model
part + part = whole
multiplication bar model
part x number of parts = whole
difference
subtraction answer
whole - known part = unknown part
subtraction bar model
subtraction bar model
whole - known part = unknown part
division bar model
whole ÷ number of parts = unknown part
z - 13 = 20 - 13 = 7
z - 13 when z=20
4x - x + 5x + 4 - 2 = 8x + 2
Simplify. 4x + 4 - x - 2 + 5x
3x - 2x + 8x + 8 - 5 = 9x + 3
Simplify. 8 + 3x - 5 - 2x + 8x
3x - 3x + 14 - 10 = 0 + 4 = 4
Simplify. x + x + x + 14 - 3x - 10
a) equivalent b) equivalent c) not equivalent d) not equivalent
State whether each pair of expressions is equivalent: a) 6(x + 5) and 6x + 30 b) 7(x + 3) and 21 + 7x c) 4(y - 4) and 4y - 4 d) 3(y - 6) and 18 - 3y
a) equivalent b) equivalent c) not equivalent d) not equivalent e) equivalent f) not equivalent
State whether each pair of expressions is equivalent: a) 8x + 6 and 2(4x + 3) b) 3(y + 6) and 18 + 3y c) 5x - 10 and 5(x - 5) d) 4(y - 4) and 16 - 4y e) 3(x + 5) and 15 + 3x f) 12 - 8y and 4(2y - 3)
x - 7
Write an algebraic expression for: the difference of 7 less than x
6z or 6 x z
Write an algebraic expression for: the product of z and 6
8 ÷ w
Write an algebraic expression for: the quotient of w and 8
15a, - 10a 3n, -9n
Write one positive term and one negative term from the expression: -10a - 9n + 16 - 30 + 3n + 15a + 50 + 1a
1.55 more than b
Write the algebraic expression in words: 1.55 + b
the quotient of 4 and m
Write the algebraic expression in words: 4 m
-10, -9 3, 15, 1
Write the coefficients from the expression: -10a - 9n + 16 - 30 + 3n + 15a + 50 + 1a
16j
Simplify 5j + 2j + 9j
3t
Simplify 5t - 2t
6v
Simplify 7v - 3v + 2v
3x
Simplify 7x - 4x
5y
Simplify 8y - 5y + 2y
10k
Simplify 9k + 3k - 2k
3, 3p, 3
Simplify the expression and write the coefficient of the variable. p + p + p = _____ * p = _____
5t + 2t + 4 = 7t + 4
Simplify the expression. 5t + 4 + 2t
6m - 2m - m - 10 = 3m - 10
Simplify the expression. 6m - 10 - 2m - m
12r - 12
Simplify the expression. 7r + 5r - 12
8 - 5 + 3j - 2j + 8j = 3 + 9j
Simplify the expression. 8 + 3j - 5 - 2j + 8j
5g + 6g + 8 - 2 = 11g + 6
Simplify the expression. 8 + 5g - 2 + 6g
8*y + 8*3 + 6 - 3y 8y + 24 + 6 - 3y 8y - 3y + 24 + 6 5y + 30 GCF: 5 5(y + 6)
Simplify then factor the expression: 8(y + 3) + 6 - 3y
a) = b) > c) < d) =
Compare each expression with >, < or = a) 7p + 2p and 3p + 6p b) 9r + 3r and 5r + 3r c) 6m + m and 8m d) 8y + 4y and 12y
a) < b) = c) = d) <
Compare whether each is expression is equivalent. a) 5n - n and 6n b) 4e - 4e and 10w - 10w c) 7a - 2a and 9a - 4a d) 9u and 12u - 2u
x = 18 - 7 x = 11
Draw a Bar Model for 18 - 7
x = 20 - 8 x = 12
Draw a Bar Model for 20 - 8
x = 25 ÷ 5 x = 5
Draw a Bar Model for 25 ÷ 5
x = 3 + 8 x = 11
Draw a Bar Model for 3 + 8
7 - 4/2 = 7 - 2 = 5
Evaluate the expression 7 - x/2 when x = 4
(-10a + 15a + 1a) + (-9n + 3n) + (16 - 30 + 50) 6a - 6n + 36
Simplify this expression by combining like terms: -10a - 9n + 16 - 30 + 3n + 15a + 50 + 1a
(r+8) + (r +8) = r + r + 8 + 8 = 2r + 16 or 2*r + 2*8 = 2r + 16
Expand 2(r + 8)
3*k + 3*6 = 3k + 18
Expand 3(k + 6)
5*y - 5*3 = 5y - 15
Expand 5(y - 3)
3*m + 3*2 + 4*6 + 4*m 3m + 6 + 24 + 4m 3m + 4m + 6 + 24 7m + 30
Expand and simplify the expression: 3(m + 2) + 4(6 + m)
14x - 21
Expand the expression: 7(2x - 3)
Factors of 12: 1,2,3,4,6,12 Factors of 8: 1,2,4,8 GCF: 4 4(3 - 2x)
Factor 12 - 8x
Factors of 2: 1,2 Factors of 10: 1,2,5,10 GCF: 2 2(y + 5)
Factor 2y + 10
Factors of 6: 1,2,3,6 Factors of 9: 1,3,9 GCF: 3 3(2z - 3)
Factor 6z - 9
e) 6r - 7r
Find the like terms in the expression 6r - 2 + 3b - 7r a) -7r b) + 6r c) + 3b d) -2 e) 6r - 7r
5w + 1 + 5w +1 + 4w = 5w + 5w + 4w + 1 + 1 = 14w + 2 yards
Find the perimeter of the isosceles triangle.
5y + 2y + 2 + 5y + 2y + 2 = 5y + 2y + 5y + 2y + 2 + 2 = 14y + 4
Find the perimeter of the rectangle.
17 - d + 5d + 11 + d + 8 = 17 + 11 + 8 - d + 5d + d = 36 + 5d inches
Find the perimeter of the trapezoid.
15a and 1a -9n and 3n
Give an example of two "like terms" in the expression: -10a - 9n + 16 - 30 + 3n + 15a + 50 + 1a
8
How many terms are in the expression: -10a - 9n + 16 - 30 + 3n + 15a + 50 + 1a
5
In the term 5b, the coefficient of b is _____?
6x - 4x + 3b + 12 - 5 = 2x + 3b + 7
Simplify. 12 + 6x - 5 - 4x + 3b
6c
Simplify 12c - 3c - 3c
5c
Simplify 2c + 3c
7g
Simplify 3g + 4g
43d
Simplify 42d + d
29z
Simplify 44z - 15z
16, -30, 50
What are the constants in the expression: -10a - 9n + 16 - 30 + 3n + 15a + 50 + 1a
a, n
What are the variables in the expression: -10a - 9n + 16 - 30 + 3n + 15a + 50 + 1a
5
What is the coefficient of d in the term 5d?
12 - y
Write an algebraic expression for the difference "y less than 12"
9h
Write an algebraic expression for the product of h and 9
x ÷ 4
Write an algebraic expression for the quotient of x and 4
12 + m
Write an algebraic expression for the sum of 12 and m
24 + n
Write an algebraic expression for: 24 more than a number