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