


In today’s lesson, you will continue to simplify expressions using the correct order of
operations. You will also learn how to identify terms in expressions that are more
complicated.
3-12. For each of the following expressions:

Draw a diagram that could represent the expression.

Simplify the expression.
c. −3 + 4(−2)3 + 5
d. −32 + 4(−2 + 5)

3-13. Katrina and Madeline were working on problem 3-12 when
Madeline noticed, “These two expressions look almost the same, except that one has
two terms, while the other has three!”

Discuss Madeline’s observation with your team. Explain which expression has two
terms and which has three. Terms in expressions are separated by addition (+) and
subtraction (–) signs unless the sum or difference is inside parentheses.

3-14. Consider the expression 3(5 + 2 · 4) + 2(−3).
. Work with your team to draw a diagram representing this expression. Your
diagram could show Cecil’s movements, for example, or it could
show + and – tiles that could be represented by this expression.
a. Simplify the expression.
b. Discuss with your team how you might circle terms in this expression. Be
ready to explain your ideas to the class.

3-15. For each of the following expressions, visualize them as Cecil’s movements on
a tightrope or as groups of + and – tiles. Then:

Describe to your team members how you see each expression.

Circle the terms and simplify each expression.
b. 3(8.63) + 1
c. 1 + 3(8.63)
d. 4
+ 2(3 ) + 5
e. 4
+ 2(3
+ 5)
f. 4 +(−2) + 3(5)
g. 2(−4 + 3 + 5)
h. 2.68(20) + 4 + 3(−5)
i. 4(−7.6) + 3 (100 + 5)

3-16. AIM FOR 16

In this game, you and the other players will create expressions that contain the same
four numbers. Then you will compare the numbers that your expressions represent to
see whose number is closest to 16.

Your teacher will roll four number cubes or use 3-16 Number Cubes (CPM) to
virtually roll four number cubes to determine the four numbers you can use in your
expression. You may use each number as either a positive or negative integer, and
each number must appear exactly once in your expression. For example, if a number
cube lands on 5, you can use either 5 or −5 in your expression. Try to make an
expression that represents a number that is as close to 16 as possible.

Your score is how far your expression’s value is from 16. For example, for an
expression that represents 20, the score would be 4, and for an expression that
represents 13, the score would be 3. Compare your expression with your
opponent’s. Whoever has the lowest score wins that round. As you continue playing
more rounds, keep track of your total score and try to keep it as low as you can.

3-17. Additional Challenge: Simplify each of the expressions below. For each one,
be sure to show your work or explain your reasoning.
. (4 + 2(−5) + 3(2 + (−3)) + 2) 6 + (−2)
a. (9 + 3(−2 + 4)) + (6 + 2(5 + (−7)) + 1)

3-18. LEARNING LOG

In your Learning Log, summarize what you have learned in this section about
simplifying expressions with multiplication and addition. Be sure to include examples
to demonstrate your thinking. Title this entry “Simplifying Expressions with
Multiplication and Addition” and label it with today’s date.

Expressions, Terms, and Order of Operations

A mathematical expression is a combination of numbers, variables, and operation
symbols. Addition and subtraction separate expressions into parts called terms. For
example, 4x2 −3x + 6 is an expression. It has three terms: 4x2, 3x, and 6.

A more complex expression is 2x + 3(5 − 2x) + 8, which also has three terms: 2x, 3(5
− 2x), and 8. But the term 3(5 − 2x) has another expression, 5 − 2x, inside the
parentheses. The terms of this expression are 5 and 2x.

Mathematicians have agreed on an order of operations for simplifying expressions.
Original expression:
Circle expressions that are grouped within
parentheses or by a fraction bar:
Simplify within circled terms using the order of
operations:

Evaluate exponents

Multiply and divide from left to right.

Combine terms by adding and subtracting
from left to right.
Circle the remaining terms:
Simplify within circled terms using the order of
operations as described above:

3-19. Show the numbers of + and – tiles represented by each expression
below. Sketch each model and state the number that it represents. Homework Help
✎
a. (−2) + (−6)
b. (−2) + 4 + (−2)
c. 5 + (−8)

3-20. Copy each expression below and circle each term. Then simplify
each expression. Homework Help ✎
. −8 + 2(−5)
a. 3(7.5 + 2) + 4.6
b. 4 (−2 + 1 + 7)
c. 5(6 + 2) + 4 + 2 (−5 + 8)

3-21. Justin is working with the integer tiles shown in the diagram at
right. Homework Help ✎
. What is the value of Justin’s diagram?
a. If Justin removes three positive tiles, what will the value be?
b. If Justin starts with the original diagram and removes three negative tiles, what
will the value be?
c.

Justin has a new arrangement of tiles shown at right. If he removes
four positive tiles, what will the value be?
3-22. Linh has a bag of beads that contains 10 glass beads, 7 metal beads, 15 plastic
beads, and 3 clay beads. For each part below, if the bead selected is replaced before
the next draw, what is the probability that Linh will pull out a. 3-22 HW
eTool (CPM). Homework Help ✎
. Metal bead?
a. Bead that is not plastic?
b. Glass or plastic bead?

3-23. Copy each portions web below and fill in the missing parts. Homework Help ✎
.
a.