SESSION 2.4A
Order of Operations
Math Focus Points
Solving problems using the order of operations
Vocabulary
Writing and interpreting expressions involving
grouping symbols
grouping symbols
Today’s Plan
Materials
t Student Activity Book, pp. 35A–35B or
ACTIVITY
ACTI
AC
TIVVIT
ITYY
Following the Order of
Operations
50 MIN CLASS
PAIRS INDIVIDUALS
t Student Activity Book p. 35B or C3 (completed)
DISCUSSION
Using Grouping Symbols
t
C2-C3, Order of Operations Make copies.
(as needed)
Chart paper (Prepare a chart showing the Order
of Operations stated on page CC5.)
10 MIN CLASS
t Student Activity Book, p. 35C or
SESSION FOLLOW-UP
Daily Practice
C4, Using the Order of Operations Make
copies. (as needed)
Ten-Minute Math
Number Puzzles Draw one card from each set (A, B, C) of Number Puzzle Clue Cards
(M35–M43) and read them aloud. Students work with a partner and find the
number(s) that fit the set of three clues. If the solution is inconclusive, students
modify the clues. Have students share their strategies for solving the number puzzle.
CC4
INVESTIGATION 2
Multiplication Strategies
1 Activity
AC TIVIT Y
Following the Order of
Operations
50 MIN CLASS
2 Discussion
3 Session Follow-Up
PAIRS INDIVIDUALS
This activity introduces order of operations, which will continue in
Unit 2 as a Ten-Minute Math activity.
Write 4 + 3 × 6 = on the board.
Explain how you would solve this equation.
Students might say:
“I think the answer is 42, since 4 plus 3 is
7, and 7 times 6 is 42.”
“The answer is 22. I multiplied 3 times 6
and got 18. Then I added 4 to get 22.”
To avoid having more than one possible answer for equations like
these, mathematicians have agreed on the following order of
operations.
Display the chart you prepared showing the order of operations.
Order of Operations
1. Perform operations within grouping
symbols first.
2. Multiply and divide in order from left
to right.
3. Add and subtract in order from left
to right.
Grouping symbols are symbols such as parentheses. They tell
you which numbers get grouped together. Since this equation
has no grouping symbols, we then need to figure out which
operation to do first. We are supposed to multiply and divide
first. 3 × 6 = 18. That’s the only multiplication or division
in the equation, so now we do the addition and subtraction.
4 + 18 = 22, so 22 is the correct answer.
Write 22 after the equal sign in the equation you wrote on
the board.
Session 2.4A
Order of Operations
CC5
1 Activity
2 Discussion
3 Session Follow-Up
What if we wanted to write the equation in such a way that it
tells someone to add first? Let me give you a context.
Tamira baked cookies for a bake sale. She put 6 cookies on each
plate. She made 4 plates of oatmeal cookies and 3 plates of peanut
butter cookies. How many cookies did she make in all?
You could solve this problem by first adding 4 + 3 to find how
many plates of cookies Tamira made. Then you would multiply
by 6 to find the total number of cookies. How could you write
the equation to show that you should add first?
Students might say:
“Put the 4 + 3 in parentheses. That would
tell you to add first. If there were no
parentheses you would multiply first.”
Write (4 + 3) × 6 = 42 under the first equation on the board.
Some equations include other grouping symbols, such as brackets
or braces. Here’s one with both parentheses and brackets.
On the board, write the following equation:
2 × [(3 + 7) – (2 + 4)] =
This equation has parentheses inside brackets. If there are
brackets they are always outside parentheses, and if there are
braces they are always outside brackets. You always do the
operations inside the parentheses first. Then if there are brackets,
you do the operations in the brackets, and then do the operations
in the braces if there are braces. Then do the operations outside
the grouping symbols. Another way to think about it is that you
go from the inside to the outside. Unless the grouping symbols
tell you otherwise, you always do multiplication and division
before addition and subtraction. Work with a partner to solve
this problem.
After several minutes, ask students to share their answers and
provide explanations. As students offer correct responses, record the
work on the board.
2 × [(3 + 7) − (2 + 4)] =
2 × [10 − 6] =
2×4=
8
CC6
INVESTIGATION 2
Multiplication Strategies
1 Activity
Write the following on the board:
2 Discussion
Name
3 Session Follow-Up
Date
Number Puzzles and Multiple Towers
4 × {8 – [(3 + 9) ÷ 2]} + 3 =
Order of Operations (page 1 of 2)
Here’s an equation that also has braces. Work with a partner to
solve the equation. Write out each step as I just did for the
problem that had parentheses and brackets. Remember, you do
the operations in the parentheses first, then the brackets, then the
braces, going from inside to the outside. Also, unless there are
some grouping symbols that tell you to do something different,
you do multiplication and division first and then addition and
subtraction, always moving from left to right.
1. 8 + 12 ÷ 2 =
2. 10 × (12 – 3) =
3. 7 × 2 – (3 + 8) =
4. 16 ÷ (16 – 4 × 2) =
5. (9 + 9) ÷ (7 – 4) =
6. 15 – [(4 – 2 ) × 3] =
© Pearson Education 5
Give students a few minutes to solve the problem. Then ask for the
solution and write it on the board. Carefully discuss each step of
the solution.
In Problems 1–6, solve the equation using the order of operations.
Show your work.
Session 2.4A
Unit 1
35A
▲ Student Activity Book, Unit 1, p. 35A;
Resource Masters, C2
4 × {8 − [(3 + 9) ÷ 2]} + 3 =
4 × {8 − [12 ÷ 2]} + 3 =
4 × {8 − 6} + 3 =
4×2+3=
Name
Date
Number Puzzles and Multiple Towers
Order of Operations (page 2 of 2)
In Problems 7–10, insert parentheses, brackets, and/or braces to make each
equation true.
7. 17 – 6 + 1 = 10
8. 8 – 8 × 2 + 3 = 0
8+3=
9. 5 × 6 – 1 + 3 = 28
10. 5 + 4 – 5 + 3 × 8 ÷ 2 = 4
11
11. For the following problem, use grouping symbols to write an equation
that represents the situation. Then solve the problem.
Samantha made a photo book. She put 8 pictures on each page.
She filled 7 pages with pictures of her trip to Washington, D.C., and
5 pages with pictures of her trip to the Grand Canyon. How many
pictures are in her photo book?
© Pearson Education 5
Write on the board:
14 – 3 + 2 ÷ 3 = 3
How would you insert parentheses, brackets, and maybe even
braces to make this equation true? Work with your partner.
Remember, put the operations you want done first in parentheses,
the ones you want done next in brackets, then in braces, and
finally the ones you want done last outside of the grouping
symbols. Multiplication and division will be done first if you do
not indicate otherwise with grouping symbols. When you’re done,
check to make sure that your placement of grouping symbols
makes the equation correct.
35B
Unit 1
Session 2.4A
▲ Student Activity Book, Unit 1, p. 35B;
Resource Masters, C3
Have a student share the correct equation: [14 – (3 + 2)] ÷ 3 = 3.
Tell students that they will work on some more problems like these
on Student Activity Book pages 35A and 35B or C2 and C3. Have
them be prepared to share their solutions to Problem 11 during
the discussion.
Session 2.4A
Order of Operations
CC7
1 Activity
2 Discussion
3 Session Follow-Up
ONGOING ASSESSMENT: Observing Students at Work
Students follow the order of operations to evaluate and
write expressions.
• Can students determine the order in which they should
perform the operations? Do they understand that when there
are grouping symbols, they need to work “from the inside to
the outside”? Do they know they should do multiplication and
division first unless otherwise indicated?
• Can students place grouping symbols in an equation to
make the equation true?
DIFFERENTIATION: Supporting the Range of Learners
Some students may be overwhelmed by equations
with many operations and grouping symbols. Give these students
simpler equations with no more than three operations and one
pair of parentheses.
Have students write problems like Problems 7–10
on Student Activity Book page 35B or C3, and ask partners to
solve them.
DISCUSSION
Using Grouping Symbols
10 MIN
CLASS
Math Focus Points for Discussion
Solving problems using the order of operations
Writing and interpreting expressions involving
grouping symbols
Ask students to share their solutions to Problem 11 on Student
Activity Book page 35B or C3.
CC8
INVESTIGATION 2
Multiplication Strategies
1 Activity
Students might say:
“I knew that first I needed to add 7 and 5
to find how many pages in all. So I put that
in parentheses. Then I multiplied by 8 to
get the total number of pictures. My
equation is 8 × (7 + 5), and that’s equal
to 96. Samantha had 96 pictures.”
Name
3 Session Follow-Up
Date
Number Puzzles and Multiple Towers
Daily Practice
Using the Order of Operations
In Problems 1–5, solve the equation using the order
of operations. Show your work.
NOTE Students use the order
of operations to solve problems.
1. 20 – 16 ÷ 4 =
2. (19 – 1) ÷ (3 × 2) =
3. 3 × 7 – (2 + 5) =
4. [(3 + 4) × 2] – (1 + 9) =
5. [6 + (3 + 4) × (3 – 1)] ÷ 5 =
In Problems 6–9, insert parentheses, brackets, and/or braces to make each
equation true.
6. 1 + 8 × 4 = 36
7. 10 + 2 – 6 + 3 = 3
8. 2 + 3 × 10 – 3 = 35
9. 4 × 8 – 4 + 1 = 12
10. Write an equation that means “Multiply 8 by the sum of 4 and 2.”
© Pearson Education 5
If any students offer an alternate solution, such as
(8 × 7) + (8 × 5) = 96, take the opportunity to discuss whether
parentheses are needed in this equation. Students should use the
order of operations to reason that since multiplication is done
before addition, (8 × 7) + (8 × 5) has the same value as
8 × 7 + 8 × 5.
2 Discussion
Session 2.4A
Unit 1
35C
▲ Student Activity Book, Unit 1, p. 35C;
Resource Masters, C4
SESSION FOLLOW-UP
Daily Practice
Daily Practice: For reinforcement of this unit’s content,
have students complete Student Activity Book page 35C
or C4.
Session 2.4A
Order of Operations
CC9
Name
Date
Number Puzzles and Multiple Towers
Order of Operations (page 1 of 2)
In Problems 1–6, solve the equation using the order of operations.
Show your work.
1. 8 + 12 ÷ 2 =
2. 10 × (12 – 3) =
3. 7 × 2 – (3 + 8) =
4. 16 ÷ (16 – 4 × 2) =
5. (9 + 9) ÷ (7 – 4) =
6. 15 – [(4 – 2 ) × 3] =
Unit 1 Session 2.4A
C2
© Pearson Education, Inc., or its affiliates. All Rights Reserved. 5
Name
Date
Number Puzzles and Multiple Towers
Order of Operations (page 2 of 2)
In Problems 7–10, insert parentheses, brackets, and/or braces to make
each equation true.
7. 17 – 6 + 1 = 10
9. 5 × 6 – 1 + 3 = 28
8. 8 – 8 × 2 + 3 = 0
10. 5 + 4 – 5 + 3 × 8 ÷ 2 = 4
11. For the following problem, use grouping symbols to write an
equation that represents the situation. Then solve the problem.
Samantha made a photo book. She put 8 pictures on each page.
She filled 7 pages with pictures of her trip to Washington, D.C., and
5 pages with pictures of her trip to the Grand Canyon. How many
pictures are in her photo book?
Unit 1 Session2.4A
C3
© Pearson Education, Inc., or its affiliates. All Rights Reserved. 5
Name
Date
Number Puzzles and Multiple Towers
Daily Practice
Using the Order of
Operations
NOTE Students use the order
of operations to solve problems.
In Problems 1–5, solve the equation using the order
of operations. Show your work.
1. 20 – 16 ÷ 4 =
2. (19 – 1) ÷ (3 × 2) =
3. 3 × 7 – (2 + 5) =
4. [(3 + 4) × 2] – (1 + 9) =
5. [6 + (3 + 4) × (3 – 1)] ÷ 5 =
In Problems 6–9, insert parentheses, brackets, and/or braces to make each
equation true.
6. 1 + 8 × 4 = 36
7. 10 + 2 – 6 + 3 = 3
8. 2 + 3 × 10 – 3 = 35
9. 4 × 8 – 4 + 1 = 12
10. Write an equation that means “Multiply 8 by the sum of 4 and 2.”
Unit 1 Session 2.4A
C4
© Pearson Education, Inc., or its affiliates. All Rights Reserved. 5
Name
Date
Number Puzzles and Multiple Towers
Daily Practice
Understanding the Order
of Operations
NOTE Students use the order
of operations to solve problems.
In Problems 1–4, solve the equation using the order of
operations.
1. 12 + 4 × 6 ÷ 3 =
2. 15 – [(10 + 26) ÷ 4] =
3. (19 – 1) × (7 – 6) =
4. 2 × (8 – 4) × 10 ÷ 8 =
In Problems 5–8, insert parentheses, brackets, and/or braces to make each
equation true.
5. 8 + 28 ÷ 4 = 15
6. 5 × 9 – 6 + 2 = 17
7. 20 – 3 + 1 × 3 = 8
8. 9 – 2 × 4 + 6 = 70
9. For the following problem, use grouping symbols to write an equation
that represents the situation. Then solve the problem.
A florist planted pots of tulip bulbs, with 5 bulbs in each pot. He planted
6 pots with white tulip bulbs and 4 pots with red tulip bulbs. How many
bulbs did he plant in all?
Unit 1 Session 3.6
C5
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