Central Valley School District 5th Grade Math Module Two Part One – Writing/Solving Expressions Topic One – Order of Operations Warm Up Time....please solve the following problem on scratch paper.
12 + 8 x 2 - 4 2 + (8-6) x 2
What are some answers you got? Let's share
Why would we as a class get so many different answers? We all did the same
problem, right? Any ideas....
Since math has four different operations (________________, __________________,
__________________, and __________________), a smart mathematician a LONG
time ago figured out that there better be certain rules that everyone follows for
doing problems with more than one operation. We call this the ORDER OF OPERATIONS.
Here is a list of letter that should help you remember them. Let's go through
them.
P -
E -
M -
D -
A -
S -
Page 1
Central Valley School District 5th Grade Math Module Two Part One – Writing/Solving Expressions Topic One – Order of Operations So lets go through that first problem together again since we now know what we
SHOULD have done. Let's try another one or two together. These won't be as long.
Page 2
Central Valley School District 5th Grade Math Module Two Part One – Writing/Solving Expressions Topic One – Order of Operations Now I want you to try some on your own. These are taken from a math book.
Let's break up into groups for a bit and practice some leveled problems. We'll
come back together in about ten minutes for a class challenge. Page 3
Central Valley School District Module Two Part One – Writing/Solving Expressions
Solve.
1) 5 + 99 ÷ 11
Easy
2) 7 × 6 – 4
Ans =
Ans =
3) 30 ÷ 5 – 2
4) 10 + 3 × 6
Ans =
Ans =
5) 9 × 3 + 8
6) 31 – 10 ÷ 5
Ans =
Ans =
7) 72 ÷ 9 + 1
8) 58 × 2 – 85
Ans =
Ans =
9) 16 + 7 × 4
10) 82 – 15 ÷ 5
Ans =
Ans =
Page 4
5th Grade Math Topic One – Order of Operations Central Valley School District Module Two Part One – Writing/Solving Expressions
5th Grade Math Topic One – Order of Operations Medium
A) Fill in the box with an appropriate symbol ( = or ! ).
1) 2 × 3 + 5
6÷2+5
2) 12 – 2 × 8 + 7
4+5–3×2
3) 7 – 3 × 4 ÷ 6
10 ÷ 2 + 3
4) 6 + 4 ÷ 2
7 + 12 ÷ 3
5) 8 + 2 × 3 ÷ 6 – 4
5 × 4 –15
6) 3 × 2 + 8
11 + 2 × 3 – 3
B)) Fill in the box with an appropriate symbol ( <, > or = ).
7) 8 × 4 + 2 – 8
9÷3+1
9) 5 + 2 – 4 × 7 ÷ 2
12 – 6 ÷ 2 × 5
10) 7 + 5 × 2 – 4
18 ÷ 9 + 7 – 3
7×3+9–2
12) 6 – 51 ÷ 3
24 ÷ 6 + 2 – 8 × 5
11) 12 + 8 × 2
8) 15 × 2 – 9 ÷ 3
C) Match the equal quantities.
13)
12 + 3 × 2 – 8
14 ÷ 7 + 21 – 4
14)
9 – 12 ÷ 3 + 2 × 7
6 + 2 × 3 – 23
15)
24 ÷ 6 – 8
3×3+1
16)
10 + 7 – 14 × 2
2 × 3 – 10
Page 5
30 – 15 ÷ 5
Central Valley School District Module Two Part One – Writing/Solving Expressions
Solve.
1) 28 ÷ 4 + 2 × 8 + 2 – 37
5th Grade Math Topic One – Order of Operations Harder
2) 15 + 7 × 2 – 11 + 35
Ans =
Ans =
3) 75 ÷ 5 × 9 – 9
4) 81 ÷ 3 – 12 × 3 + 36 ÷ 4
Ans =
Ans =
5) 26 ÷ 2 + 15 × 4
6) 42 + 8 – 6 × 11 + 2
Ans =
Ans =
7) 9 + 4 × 30 ÷ 6 + 5 × 8
8) 18 × 2 ÷ 4 + 52
Ans =
Ans =
9) 56 ÷ 7 × 12 + 3 – 4
10) 13 × 5 + 7 – 16
Ans =
Ans =
Page 6
Central Valley School District Module Two Part One – Writing/Solving Expressions
5th Grade Math Topic One – Order of Operations Class challenge - Put signs or parentheses into these problems to get the
correct answer. You may work together with the person next to you to get a
correct.
1)
2)
3)
Page 7
Central Valley School District Module Two Part One – Writing/Solving Expressions
5th Grade Math Topic One – Order of Operations ALGEBRA
Name
Lesson 1.11
Evaluate Numerical Expressions
COMMON CORE STANDARD MACC.5.OA.1.1
Write and interpret numerical expressions.
Evaluate the numerical expression.
1.
24 3 5 2 41
120 2 41
2. (32 2 20) 4 4
79
___
5.
43827
___
3.
___
6.
16 4 (2 1 6)
4.
___
27 1 5 3 6
7.
___
3433416
___
8.
___
15 3 (8 2 3)
14 1 4 3 4 2 9
___
Rewrite the expression with parentheses to equal the given value.
9.
3342112
value: 11
10.
2364211
value: 4
12. Sandy has several pitchers to hold lemonade
11.
5133226
value: 10
13. At the bake sale, Jonah sold 4 cakes for
for the school bake sale. Two pitchers can
hold 64 ounces each, and four pitchers can
hold 48 ounces each. How many total ounces
can Sandy’s pitchers hold?
$8 each and 36 muffins for $2 each. What
was the total amount, in dollars, that Jonah
received from these sales?
_______
_______
Page 8
Central Valley School District 5th Grade Math Module Two Part One – Writing/Solving Expressions Topic Two – Solving Expressions Essential Question:
How do grouping
symbols affect the
values of numerical
expressions?
Guided Instruction
In this lesson you will write and evaluate expressions that have
parentheses and other grouping symbols.
5.OA.1, 5.OA.2
Words to Know:
Understand: Order of Operations and parentheses
numerical expression
parentheses
grouping symbols
evaluate
brackets
braces
Mr. Jay’s class wins 10 books for its library. 3 books are
nonfiction, 5 books are fiction, and the remaining books
are reference books. Write and evaluate an expression to
find the number of reference books.
To find the number of reference books, you add to find
the total number of nonfiction and fiction books, and then
subtract the sum from the total number of books. Write a
numerical expression to model this.
A numerical expression
is a mathematical phrase
containing only numbers
and one or more
operation symbols.
Use parentheses, ( ), to show that the addition is done before the
subtraction. Parentheses are grouping symbols. They group part of
an expression together to show that it should be evaluated first.
number of
nonfiction books
total number of books
the class wins
10
(3
number of
fiction books
5)
Now, evaluate, or find the value of, the expression to find the number
of reference books. Do the calculations inside parentheses first.
( )
10 2
Numerical expression.
Add inside parentheses.
Subtract.
Two of the books the class wins are reference books.
Zak wrote the expression 10 3 5 to represent the
problem. Explain why the expression Zak wrote is not correct.
Page 9
Remember!
Order of Operations:
• Evaluate inside
grouping symbols.
• Multiply or divide
from left to right.
• Add or subtract
from left to right.
Central Valley School District Module Two Part One – Writing/Solving Expressions 5th Grade Math Topic Two – Solving Expressions Understand: Using more than one set of grouping symbols
A baking company makes 634 loaves of bread each day. They sell 350
loaves to supermarkets and 275 loaves to restaurants. They donate the
rest to a local shelter. Write and evaluate an expression to find the
number of loaves the company donates over a 5-day workweek.
Step 1
Write an expression for the number of loaves the company sells each day.
350
loaves sold to supermarkets
275
loaves sold to restaurants
Step 2
Subtract that sum from 634 to represent the number
of loaves the company donates each day.
634
loaves made each day
(35 275) loaves sold
Use parentheses to
show that the addition
is done first.
each day
Step 3
Multiply the expression from Step 2 by 5 to represent the number of
loaves the company donates in 5 days. You need to use another set of
grouping symbols to show that the expression in Step 2 is evaluated
before the multiplication. When you need to put one set of grouping
symbols inside another, use brackets, [ ], for the outside set.
[634 (350 275)]
loaves donated each day
5
Number of days
Step 4
Evaluate the expression. When there is more than one set of grouping
symbols in an expression, work from the inside out.
[634 (350 275)] 5
[634 625] 5
9 5
45
Numerical expression.
Add inside the parentheses.
Subtract inside the brackets.
Multiply.
The baking company donates 45 loaves of bread during a 5-day
workweek.
Page 10
Central Valley School District 5th Grade Math Module Two Part One – Writing/Solving Expressions Topic Two – Solving Expressions Connect: What you know about grouping symbols and
evaluating expressions
2
5
2
- Evaluate: {6 [4 ( 6 6 )]} 5
2
5
2
- The expression {6 [4 ( 6 6 )]} 5 contains three sets of grouping
symbols: parentheses, brackets, and braces { }.
To evaluate an expression with more than one set of grouping symbols,
work from the inside set of grouping symbols (the parentheses) out.
2
5
2
- {6 [4 ( 6 6 )]} 5
2
7
Numerical expression.
{6 [4 6 ]} 5
Add inside the parentheses.
2
—28
—
{6 6 } 5
Multiply inside the brackets.
—30
—
6 5
Add inside the braces.
5 5 1
Divide.
2
5
2
- The value of {6 [4 × ( 6 6 )]} 5 is 1.
Sam and Raj wrote expressions for the following problem:
Olivia’s grandfather gave her $10 for mowing his lawn. She spent $6 of her
earnings on a movie and added the rest to $32 she already had saved. How
much in total has she saved?
Sam wrote (10 6) 32, and Raj wrote 10 6 32. Explain why both
expressions are correct.
Page 11
Central Valley School District Module Two Part One – Writing/Solving Expressions 5th Grade Math Topic Two – Solving Expressions Complete the operations within the grouping symbols first
to evaluate each expression.
1. [1,225 (568 203)] 10
[1,225 2
4
2. 5 (4 5 3)
2
5 ] 10
10
Solve the problem.
3. Amy has twenty $1 bills and twelve $10 bills. Kevin has forty-two
$1 bills and eighteen $5 bills. How much more money than
Kevin does Amy have?
a. Insert grouping symbols to write a numerical expression that models
this problem.
Amy:
Kevin:
20 1 12 10 42 1 18 5
b. Evaluate the expression and answer the question.
Think • Pair • Share
MP7
4. Compare expressions a–d. Then evaluate each and tell which two
expressions are equivalent. Explain your reasoning.
a. 36 {[15 (3 10)] 5}
b. 36 [15 (3 10 5)]
c. 36 [(15 3) (10 5)]
d. 36 15 3 10 5
Page 12
Central Valley School District 5th Grade Math Module Two Part One – Writing/Solving Expressions Topic Two – Solving Expressions Evaluate each expression.
1. 15 (7 6)
2. (24 10) (2 5)
15 3. [100 (58 16)] 91
[100 ] 91
91
3
1
7
4. 8 [(1 1 8 ) 8 2]
3
8 [
3
8 [
3
8 7
8 2]
]
0
List the operations in the order they should be performed.
5. 160 [9 (12 4) 6]
6. {[(18 3) 3] 2} 7
multiplication
division
7. Which expression is equivalent to [8 (2 7) 12] 2?
MP2
a. 8 2 7 12 2
b. [8 (2 7 12) 2]
c. (8 2 7 12) 2
d. (8 2) 7 12 2
8. Interpret the two expressions below without evaluating them.
19 (6 6) and 19 6 6
Page 13
Central Valley School District Module Two Part One – Writing/Solving Expressions 5th Grade Math Topic Two – Solving Expressions Evaluate each expression. Show your work.
1
1
9. (4 11) 9
10. 52 (2 3 2 )
11. (9 7) 10 145
12. [(5 8 5 8 ) (19 11)] 16
13. 205 [14 (2 1) 37]
14. 2 [5 6 (3 6 1 6 )
4
3
1
1
5
For exercises 15–17, circle the correct answer.
15. A bouquet of flowers contains 4 carnations, 3 roses, and 5 tulips.
Which expression represents how many flowers are in 10 bouquets?
a. 10 (4 3 5)
b. 10 4 3 5
c. (10 4) 3 5
d. 4 3 5 10
3
16. Don has 45 yards of fabric. He uses 5 4 yards to make a blanket and
1
14 yards to make a pillow. If Don makes 4 blankets and pillows, which
expression represents how many yards of fabric will he have left?
3
1
3
a. 45 5 4 1 4 4
3
1
b. 4 (5 4 1 4 ) 45
1
3
c. 45 [(5 4 1 4 ) 4]
1
d. (45 4) (5 4 1 4 )
17. Lucia and Matteo want to buy a basketball that costs $17 and a
backboard that costs $85. Lucia babysat for 5 hours last week and
earned $6 per hour. Matteo babysat for 7 hours and earned $5 per
hour. If they combine their babysitting money, which expression
represents how much more money will they need to buy the basketball
and backboard?
a. (5 6 7 5) (17 85)
b. [(17 85) 5 6 7]
c. 5 [6 (7 5)] (17 85)
d. (17 85) (5 6 7 5)
Page 14
Central Valley School District 5th Grade Math Module Two Part One – Writing/Solving Expressions Topic Two – Solving Expressions MP2
18. Look at the expression below. Without evaluating, tell whether the
value of the expression would be the same or different without
parentheses. Explain.
(5 1) (3 5) (2 10)
MP3
19. Ari has 4 boxes of pencils. Each box has 6 red pencils and 8 blue pencils.
He wants to divide all the pencils equally between his 2 sisters. Ari wrote
the expression (4 6 8) 2 and plans to give each sister 16 pencils.
Is he correct? Explain.
MP1
20. Which expression below has the greater value?
a. {1340 [15 (4 16)]} 18
b. 1340 {[(15 4) 16] 18}
Show your work.
Answer
MP2
21. Rewrite the expression below inserting parentheses so that the value of
the expression is 144.
12 9 45 3
Show your work.
Answer
Page 15
Central Valley School District Module Two Part One – Writing/Solving Expressions MP3
5th Grade Math Topic Two – Solving Expressions 22. Joseph says that [(5 12) 2] (9 7) is the same as
5 12 2 9 7. What is his error?
Show your work.
Answer
Write and evaluate an expression to solve the problem.
MP2
1
3
23. Leila uses 14 cups of orange juice, 2 4 cups of cranberry juice, and
3 cups of seltzer to make punch. If Leila wants to serve the punch to
7 people, how many cups of punch will each person get?
Show your work.
Answer
MP2
24. Ralf is packing 180 books. He has 3 large boxes, and each box holds
25 books. He has 2 medium boxes, and each box holds 18 books.
He has 5 small boxes, and each box holds 12 books. Can Ralf pack
all 180 books with the boxes he has? Explain.
Show your work.
Answer
Page 16
Order of Operation Bowling
Directions:
Roll 4 dice, and write down each number in the frame box. Using all four numbers, try
to find an equation with an answer that is one of the numbers on the bowling pins.
Example: if you roll a 3,4,2,2, you could make the equation (4+3)+2-2 = 7. You would
then color in pin #7
Do this as many times as you can and try to knock over all the pins.
Once you run out of possibilities or the time has run out, move on to the next frame.
Or
Try for a SPARE, students roll a second time. The first numbers are void, and students
may only use the numbers generated from the second roll.
Adaptations:
Make a list that has 4 numbers in a set. Everyone needs a different set of 4 numbers (at
first these numbers may need to be chosen by the teacher).
Then they can use any order of operations to make it come out to a number that is set
up in bowling pins. So the possible answers are 1-10.
Example: if you choose the numbers 52, 16, 45, 15 you could make the equation (5245)x(16-15) = 7. You would then color in pin #7
They use the same set of 4 numbers until all the answers have been found. Then
choose another 4 numbers
First person to get all ten pins down. Wins!
Page 17
Frame 1 The four numbers I rolled are _______________________________.
Show your work here:
Cross off your pins:
Frame 2 The four numbers I rolled are _______________________________.
Show your work here:
Cross off your pins:
Frame 3 The four numbers I rolled are _______________________________.
Show your work here:
Cross off your pins:
Page 18
Frame 4 The four numbers I rolled are _______________________________.
Show your work here:
Cross off your pins:
Frame 5 The four numbers I rolled are _______________________________.
Show your work here:
Cross off your pins:
Frame 6 The four numbers I rolled are _______________________________.
Show your work here:
Cross off your pins:
Page 19
Frame 7 The four numbers I rolled are _______________________________.
Show your work here:
Cross off your pins:
Frame 8 The four numbers I rolled are _______________________________.
Show your work here:
Cross off your pins:
Frame 9 The four numbers I rolled are _______________________________.
Show your work here:
Cross off your pins:
Page 20
Frame 10 The four numbers I rolled are _______________________________.
Show your work here:
Cross off your pins:
Page 21
Central Valley School District 5th Grade Math Module Two Part One – Writing/Solving Expressions Topic Three – Writing Expressions In this lesson you will write expressions to represent calculations
with numbers. You will also interpret numerical expressions
without evaluating them.
Essential Question:
How do you write and
interpret numerical
expressions?
Understand: How to write numerical expressions
5.OA.2
Write a numerical expression to represent each of the following phrases.
“twice the sum of five and seven”
“three times the result of subtracting four from nine”
“two less than the result of dividing fifteen by three”
“one more than five groups of two-fifths”
To write a numerical expression for each phrase, think about what the
words mean. Identify the operations, and use numbers, symbols, and
parentheses.
Remember!
• “twice the sum of five and seven”
(5 7) 2
• “three times the result of subtracting four from nine”
3 (9 4)
• “two less than the result of dividing fifteen by three”
15 3 2
When necessary,
use parentheses to
group the operation
that needs to be
performed first.
• “one more than five groups of two-fifths”
2
5 5 1
The numerical expressions for the phrases:
(5 7) 2
3 (9 4)
15 3 2
2
5 5 1
Parentheses are not needed in the last two expressions because
multiplication and division are done before addition and subtraction.
What is another way to write “one more than five groups of
two-fifths” in words?
Page 22
Central Valley School District Module Two Part One – Writing/Solving Expressions 5th Grade Math Topic Three – Writing Expressions Understand: How to interpret numerical expressions
Andrea writes the expression 3 (235 62) to represent the inventory
in her store. Jacob writes the expression 235 62 to represent the
inventory at his store. How does Andrea’s inventory compare to
Jacob’s inventory.
To compare the values of Andrea and Jacob’s expressions without
evaluating them, interpret the numbers, operations, and the placement
of the parentheses.
Both expressions contain 235 62, or the sum of 235 and 62.
Andrea’s expression 3 (235 62), multiplies 235 62 by 3, or triples
that sum.
The value of Andrea’s expression 3 (235 62) is 3 times as much as the
value of Jacob’s expression 235 62.
Andrea has 3 times as many items in inventory at her store as Jacob has
at his store.
There are many ways to compare expressions using words.
Less
Equal
less than
fewer than
smaller than
More
the same as
equal to
equivalent to
more than
greater than
larger than
times as many
Interpret the expressions below. Then compare their
values without evaluating them.
a. (30 100) 15 and (100 30) 15
5
7
5
7
b. 4 (2 6 1 6 ) and 5 (2 6 1 6 )
Page 23
Equivalent numerical
expressions are
numerical expressions
with the same value.
Central Valley School District 5th Grade Math Module Two Part One – Writing/Solving Expressions Topic Three – Writing Expressions Connect: What you know about writing and interpreting
numerical expressions
Jamal and Katie bring water bottles to the soccer tournament for the
team. Jamie brings three cases of twenty-four bottles, plus four extra
bottles. Katie brings three cases of twenty-four bottles, but she and her
brother drink two of the bottles on the way to the tournament.
Write numerical expressions to represent how many water bottles Jamal
and Katie each bring to the soccer tournament. How does the number of
water bottles that Jamal brings compare to the number that Katie brings?
Step 1
Write word phrases and numerical expressions to represent how many
water bottles Jamal and Katie bring.
Jamal: three groups of twenty-four plus four more.
3 24 4
Katie: three groups of twenty-four less two.
3 24 2
Step 2
Interpret the expressions.
Both expressions contain 3 24, or 3 groups of 24.
Jamal’s expression is 4 more than 3 24.
Katie’s expression is 2 less than 3 24.
Step 3
Compare the values of the expressions.
The value of 3 24 4 is greater than the value of 3 24 2.
Both expressions contain 3 24, but the value of Jamal’s expression is
greater than the value of Katie’s expression because it adds 4 to 3 24
instead of subtracting 2.
Jamal brings 6 more water bottles to the soccer tournament.
Page 24
Central Valley School District Module Two Part One – Writing/Solving Expressions 5th Grade Math Topic Three – Writing Expressions Guided Practice
Write a numerical expression for each phrase. The first two are
started for you.
1. eleven plus three and seven-eighths
11
7
38
2. ten less than one hundred twenty
120
3. five more than eight groups
of seven-tenths
4. eight more than the result of dividing
three hundred fifty by two
Interpret and explain the two expressions without evaluating them.
The first one is started for you.
3
5. 7 (4 8) and 4 8
7 (4 8) is 7 times as much as
4 8 because
6. (19 2 4 ) 5
3
and (19 2 4 ) 5
Think • Pair • Share
MP7
7. Two students compared the expressions below.
2
2
12 3 3 and (12 3 3 ) 2
2
2
Tricia says (12 3 3 ) is half as much as (12 3 3 ) 2.
2
2
Ava says (12 3 3 ) 2 is twice as much as (12 3 3 ).
Explain why both students are correct.
Page 25
Central Valley School District 5th Grade Math Module Two Part One – Writing/Solving Expressions Topic Three – Writing Expressions Independent Practice
Complete the numerical expression for each phrase.
1. thirteen multiplied by eight and
one half
2. twenty-one less than
two hundred thirty
1
13
82
230
3. seventeen added to two groups
of five
17
2
21
4. nine less than the result of
dividing twelve by four
5
12
4
9
Complete the phrase for each numerical expression.
5. 18 (9 1)
eighteen
the number that is one
nine
6. 7 (10 4)
than ten
seven
four
3
7. (6 4 4 ) 2
of six and four and three-fourths
the
by two
3
8. (4 4 ) 5
five
than the
of four and three-fourths
Without evaluating, compare the two expressions. Tell whether the
value of the first expression is less than, greater than, or equal to the
value of the second expression.
11
11
-9. 7 13 and 3 (7 13)
1
1
11. 15 4 2 and (15 4 2) 3
10. (8 2) (5 1) and
(5 1) (8 2)
12. (15 6) 7 2 and
(15 6) 4 2
Page 26
Central Valley School District Module Two Part One – Writing/Solving Expressions 5th Grade Math Topic Three – Writing Expressions Write a numerical expression for each phrase.
13. twenty minus four and
two-thirds plus two
14. seven less than the product
of five and sixty
15. eighteen and five-sixths
divided by three
16. twice the sum of three and
nineteen
Write a word phrase for each numerical expression.
17. 5 10 2
18. 903 (1 7)
2
20. 17 (12 6)
19. (13 3 3) 8
Interpret and explain the two expressions without evaluating them.
21. 3 (16 2) and 16 2
3
22. (10 4 4 ) 9
3
and 9 (10 4 4)
Page 27
Central Valley School District 5th Grade Math Module Two Part One – Writing/Solving Expressions Topic Three – Writing Expressions Solve the problems.
MP3
23. Luke said that “three divided by twenty-one” is the same as “twenty-one
divided by three”. Is Luke correct? Explain why or why not.
MP3
24. Is “seven and one seventh less than the product of two times five” the
same as “two multiplied by five and then decreased by seven and one
seventh”? Explain why or why not.
MP2
25. Tyrone has (17 2) 100 baseball cards. Evelyn has 17 2 baseball
cards. Without evaluating, explain how the number of Tyrone’s baseball
cards compares to the number of Evelyn’s baseball cards.
MP7
26. Jaime has 14 2 3 3 feet of string. Charlotte has 14 2 feet of
string. Without evaluating, compare the expressions to tell who has
more string. Explain.
1
Page 28
Central Valley School District Module Two Part One – Writing/Solving Expressions MP2
5th Grade Math Topic Three – Writing Expressions 27. Petra and Billy have stamp collections. Petra has three groups of one
hundred stamps, plus nine more. Billy has three groups of one
hundred stamps.
Write numerical expressions to show how many stamps Petra and
Billy have. How do the expressions compare? Who has more stamps?
Answer
Justify your answer using words, drawings, or numbers.
MP2
28. Rajit and Samantha are playing a game. Rajit scored seven hundred
plus the result of subtracting eleven from two hundred nineteen points.
Samantha scored the result of subtracting eleven from two hundred
nineteen, increased by seven hundred points.
Write numerical expressions to represent each player’s score.
How do the expressions compare? Who scored more points?
Answer
Justify your answer using words, drawings, or numbers.
MP3
29. Janelle says that “two groups of nine, plus four and two-thirds” is the
same as “nine plus four and two-thirds, multiplied by two.” What is
her error?
Page 29
Lesson 3 Problem Set 5
A STORY OF UNITS
Name
Date
1. Draw a model. Then, write the numerical expressions.
a. The sum of 8 and 7, doubled
b. 4 times the sum of 14 and 26
c. 3 times the difference between 37.5 and 24.5
d. The sum of 3 sixteens and 2 nines
e. The difference between 4 twenty-fives and 3
twenty-fives
f.
Lesson 3:
Triple the sum of 33 and 27
Write and interpret numerical expressions and compare expressions
using a visual model.
Date:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Page 30
2.B.10
Lesson 3 Problem Set 5
A STORY OF UNITS
2. Write the numerical expressions in words. Then, solve.
Expression
Words
The Value of the
Expression
a. 12 × (5 + 25)
b. (62 – 12) × 11
c. (45 + 55) × 23
d. (30 × 2) + (8 × 2)
3. Compare the two expressions using > , < , or = . In the space beneath each pair of expressions, explain
how you can compare without calculating. Draw a model if it helps you.
a. 24 × (20 + 5)
(20 + 5) × 12
b. 18 × 27
20 twenty-sevens minus 1 twenty-seven
c. 19 × 9
3 nineteens, tripled
Lesson 3:
Write and interpret numerical expressions and compare expressions
using a visual model.
Date:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Page 31
2.B.11
Lesson 3 Problem Set 5
A STORY OF UNITS
4. Mr. Huynh wrote the sum of 7 fifteens and 38 fifteens on the board.
Draw a model, and write the correct expression.
5. Two students wrote the following numerical expressions.
Angeline: (7 + 15) × (38 + 15)
MeiLing: 15 × (7 + 38)
Are the students’ expressions equivalent to your answer in Problem 4? Explain your answer.
6. A box contains 24 oranges. Mr. Lee ordered 8 boxes for his store and 12 boxes for his restaurant.
a. Write an expression to show how to find the total number of oranges ordered.
b. Next week, Mr. Lee will double the number of boxes he orders. Write a new expression to represent
the number of oranges in next week’s order.
c. Evaluate your expression from Part (b) to find the total number of oranges ordered in both weeks.
Lesson 3:
Write and interpret numerical expressions and compare expressions
using a visual model.
Date:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Page 32
2.B.12
Lesson 3 Exit Ticket 5
A STORY OF UNITS
Name
Date
1. Draw a model. Then, write the numerical expressions.
a. The difference between 8 forty-sevens and
7 forty-sevens
b. 6 times the sum of 12 and 8
2. Compare the two expressions using >, <, or =.
62 × (70 + 8)
Lesson 3:
(70 + 8) × 26
Write and interpret numerical expressions and compare expressions
using a visual model.
Date:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Page 33
2.B.13
Lesson 3 Homework 5
A STORY OF UNITS
Name
Date
1. Draw a model. Then, write the numerical expressions.
a. The sum of 21 and 4, doubled
b. 5 times the sum of 7 and 23
c. 2 times the difference between 49.5 and 37.5
d. The sum of 3 fifteens and 4 twos
e. The difference between 9 thirty-sevens and 8
thirty-sevens
f.
Lesson 3:
Triple the sum of 45 and 55
Write and interpret numerical expressions and compare expressions
using a visual model.
Date:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Page 34
2.B.14
Lesson 3 Homework 5
A STORY OF UNITS
2. Write the numerical expressions in words. Then, solve.
Expression
Words
The Value of the
Expression
a. 10 × (2.5 + 13.5)
b. (98 – 78) × 11
(71 + 29) × 26
c. (50 × 2) + (15 × 2)
3. Compare the two expressions using > , < , or = . In the space beneath each pair of expressions, explain
how you can compare without calculating. Draw a model if it helps you.
a. 93 × (40 + 2)
(40 + 2) × 39
b. 61 × 25
60 twenty-fives minus 1 twenty-five
Lesson 3:
Write and interpret numerical expressions and compare expressions
using a visual model.
Date:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Page 35
2.B.15
Lesson 3 Homework 5
A STORY OF UNITS
4. Larry claims that (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are equivalent because they have the same
digits and the same operations.
a. Is Larry correct? Explain your thinking.
b. Which expression is greater? How much greater?
Lesson 3:
Write and interpret numerical expressions and compare expressions
using a visual model.
Date:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Page 36
2.B.16