Core Connections 1 (6th Grade Mathematics)
Chapter 6: Dividing and Building Expressions
Learning Targets
We are learning to
determine portions
resulting from
dividing a quantity
among a specified
number of groups.
Example Problems:
6-5, 6-10, 6-34, 6-52, 6-59 and 6-99
6-5. If you had 2 pieces of licorice to share equally among 3 people, how much licorice
would each person get? Show your thinking clearly.


6-5. See below:
Each person should get a quantity equivalent to
of a piece.
6-52. At the school’s fall bake sale, all of the pies were cut into 6 pieces, so each person who
bought a piece bought
of a pie. Each slice of pie sold for $1.00. How much money did
the school make if all eleven pies were sold? (In other words, find 11 divided by


6-52. See below:
$66
.)
We are learning to use
diagrams to divide by
portions.
6-21, 6-34, 6-38, 6-99and CL 6-124
6-34. Draw a diagram that shows how to divide 9 pieces of licorice into packages that hold 5
pieces each. Then find 9 ÷ 5.

6-34. See below:

See sample diagram below. 1

So, when you divide 9 into groups of 5, you have one whole group and 4/5
of a second group

CL 6-124. Draw diagrams to calculate each of the following quotients.
a.
You can make 7 groups of 2/3
b.
You can make 4 groups of 2 1/2
Learning Targets
Example Problems:
We are learning to
simplify algebraic
expressions, including
writing and
simplifying
expressions to
describe the area and
perimeter of shapes
formed by algebra
tiles.
6-106, 6-107, 6-115, CL 6-121 (a) & (b) and CL 126.

6-107. Sketch the collection of algebra tiles that is described by the following
expression. Rewrite the area of the collection by combining like terms.
7x + 2x2 + 3x2 + 3 + x
CL 6-126. Copy the following expressions on your paper and simplify them
by combining like terms. Using algebra tiles may be helpful.

a.
4x + 2 + 2x + x2 + x
b.
10x + 4 −3 + 8x + 2
c.
4 + x2 + 3x + 2x2 + 4
d.
x + 4 + (x − 1) + 3 + 2x
a. x2 + 7x + 2
b. 18x + 3
c. 3x2 + 3x + 8
d. 4x + 6
We are learning to
calculate the
perimeter of shapes
composed of
rectangles and of
algebra tiles.
6-91, 6-96, 6-106, and CL 6-121 ©

6-96. Copy the diagrams of algebra tiles below on your paper. Then find the
perimeter of each shape.
A.
B.

6-96. See below:
a.
4x + 4 units
b.
4x + 4 units

CL 6-121. On your paper, sketch the algebra-tile shape at right. Then answer
parts (a) through (c) below.
a.
Find the perimeter of the figure.
b.
Find the area of the figure.
c.
If the algebra tiles were rearranged how would the area
change?
CL 6-121.
a. P = 4x + 6 units
b. A = x2 + 2x + 2 square units
c. The area would not change.
Learning Targets
Example Problems:
We are learning to
evaluate simple
algebraic expressions.
6-75, 6-110, 6-115, and CL 6-122

6-75. Evaluate the expressions below using r = 3 and h = 5.

a.
a. 6h − 4
b. 8r + h
c. r2

6-75. See below:
a.
26
b.
29
c.
9
6-110. Evaluate the expressions below for the given values of the variables
a.
6j − 3 for j = 4
b.
b2 + 5
c.
8 + 4k for k = 3.5


6-110. See below:
a.
21
b.
14
c.
22
for b = 3
We are learning to
locate points on a
number line and on a
coordinate graph.
6-13, 6-25, 6-37, 6-40, 6-51, 6-56, 6-73, 6-88, and 6-119.

6-13. Copy the number line and label the following numbers at their
approximate place on the number line
a.
b.
0.75
c.
d.


6-13. See below:
See diagram below.
Write the points on the graph below as ordered pairs.


6-25. See below:
A (2, 3), B (3.5, 8), C (4, 1.5), D (5.5, 4.5), E(8, 8)