5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
5th Grade
Overview
This document contains two full lessons and some tasks to support Grade 5 students’ work with 5.OA.1, 5.OA.2, 5.NBT.1,
and 5.NBT.2.
The lessons in this unit address the following Standards.
Operations and Algebraic Thinking
5.OA
5.OA.1. Write simple expressions that record calculations with numbers, and interpret numerical expressions without
evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 ×
(18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
5.OA.2. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Number and Operations in Base Ten
5.NBT
5.NBT.1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the
place to its right and 1/10 of what it represents in the place to its left.
5.NBT.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain
patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number
exponents to denote powers of 10.
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5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
Lesson #1: Hair Bow Packaging
Cluster: Measure and estimate lengths in standard units.
Standards:
5.OA.2. Use parentheses, brackets, or braces in numerical expressions,
and evaluate expressions with these symbols.
Standards for Mathematical Practice
MP 3: Reason abstractly and quantitatively
MP 6: Attend to Precision
5.NBT.1. Recognize that in a multi-digit number, a digit in one place
represents 10 times as much as it represents in the place to its right and
1/10 of what it represents in the place to its left.
5.NBT.2. Explain patterns in the number of zeros of the product when
multiplying a number by powers of 10, and explain patterns in the
placement of the decimal point when a decimal is multiplied or divided by a
power of 10. Use whole-number exponents to denote powers of 10.
Mathematical Goal:
Students will explore the values of digits in a number, and complete tasks
involving powers of ten and exponents.
Materials:
Activity sheet (included). Calculator (optional).
Words you should hear students use in mathematical conversations:
Multiply, divide, add, subtract, group, parentheses
Ten Minute Math: Practicing Place Value (5.OA.1)
Solve the following two tasks:
63 x 10 + 85 and 63 x (10 + 85).
What are the two solutions (answers)?
What does the parentheses tell you to do?
If time permits solve the following two tasks:
63 x 25 + 68 and 63 x (25 + 68)
Pose the same questions above.
Before:
The Harrisburg Hair bow Company puts hairbows in various sized containers. A box will hold 10 hairbows. A case will hold 10 boxes. A
carton will hold 10 cases. A palate holds 10 cartons.
If this square (display a small square or hold up a base-ten one piece) represents one hair bow, what would the size be of a box? A
case> A carton? A palate? Draw in your notebook (or paper) what you think they would look like.
During:
Pass out the activity sheet or display the task for students to see. Give them time to work on Part 1. If students struggle to get started
talk to them about the relative sizes of 1 hair bow, a box, and possibly a case. The use of base-ten blocks or graph paper may support
this work.
The Harrisburg Hair bow Company puts hairbows in various sized containers. A box will hold 10 hairbows. A case will hold 10 boxes. A
carton will hold 10 cases. A palate holds 10 cartons.
Part 1) The company’s Board of Directors wants you to write multiplication equations to compare the number of hair bows that each
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5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
container will hold. They only want you to use the number 10 in your equation.
What would the multiplication equation be for:
A box? (1 x 10)
A case? (1 x 10 x 10)
A carton? (1 x 10 x 10 x 10)
A palate? (1 x 10 x 10 x 10 x 10)
Bring students back together to discuss Part 1. If you have access to Base Ten Blocks use them or display them using this website
(http://www-k6.thinkcentral.com/content/hsp/math/hspmath/na/gr3-5/itools_intermediate_9780547274058_/basetenblocks.html)
Questions to ask:
How did you know the multiplication equation for the case? How did the information in the task help you?
How did you know the multiplication equation for the carton? How did the information in the task help you?
During the discussion ask students questions to fill in the table below. Encourage them to also create the table in their notebook so
they can reference it. Leave the last column for Part 2.
Container
Multiplication Equation
Box
Case
Carton
Palate
1 x 10
1 x 10 x 10
1 x 10 x 10 x 10
1 x 10 x 10 x 10 x 10
Number of Hair
Bows
Expression with
Exponents
10
100
1,000
10,000
Move onto Part 2. Either refer to the activity sheet or display it for students.
Part 2) Mathematicians sometimes write expressions with numbers called exponents to help them with place value.
How many hair bows did a box hold?
What was the multiplication equation for a box?
Mathematicians would write those numbers down or write that number as 1 x 101 . The exponent is the small number at the top. What
is the exponent in this expression? If we had 2 boxes the expression would be 2 x 101 . The exponent 1 tells us how many times we
multiply the base, which is 10. Since the exponent is 101 , we would multiply 10 one time so we would multiply 2 x 10.
How many hair bows did a case hold?
What was the multiplication equation for a case?
Mathematicians would write those numbers down or write that number as 1 x 102 . If we had 2 cases the expression would be 2 x 102
, which is equal to 2 x 10 x 10. Remember the exponent tells us how many times to multiply the base. If we have the exponent 102 we
would multiply 10 twice (10 x 10).
In your table what do you think the expressions will be for cartons? What do you think the expression will be for palates? Go ahead and
complete the table.
Container
Multiplication Equation
Number of Hair
Expression with
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5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
Bows
Box
Case
Carton
Palate
1 x 10
1 x 10 x 10
1 x 10 x 10 x 10
1 x 10 x 10 x 10 x 10
Exponents
10
100
1,000
10,000
1 x 101
1 x 102
1 x 103
1 x 104
Close this phase of the lesson by asking students: Look at the multiplication equation and the expressions with exponents. What
relationship do you see? (The number of times that we multiply by 10 is the same as the exponent).
After:
The following tasks can be explored by students individually or in partners. If needed you may pull a small group and complete these
tasks with them while the other students explore other tasks or math games from Units 1 or 3.
Part 1:
Find the multiplication equation, the number of hair bows and the expression with exponents for:
5 boxes
7 cases
4 cartons
3 palates
Part 2:
You have the following combined containers in different orders. For each write the addition sentence as expressions with exponents
then solve to find the total number of hair bows.
5 boxes and 3 cases: (5 x 101) + (3 x 102) = 50 + 300 = 350
3 palates and 8 cartons: (3 x 104) + (8 x 103) = 30,000 + 8,000 = 38,000.
6 palates and 5 cases: (6 x 104) + (5 x 102) = 60,000 + 500 = 60,500
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5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
Hair Bow Collections
The Harrisburg Hair bow Company puts hairbows in various sized containers. A box will hold 10 hairbows. A case
will hold 10 boxes. A carton will hold 10 cases. A palate holds 10 cartons.
Part 1) The company’s Board of Directors wants you to write multiplication equations to compare the number of
hair bows that each container will hold. They only want you to use the number 10 in your equation.
What would the multiplication equation be for:
A box?
A case?
A carton?
A palate?
Container
Multiplication Equation
Number of Hair
Bows
Expression with
Exponents
Box
Case
Carton
Palate
Reflection:
Look at the multiplication equation and the expressions with exponents. What relationship do you see? (The number of
times that we multiply by 10 is the same as the exponent).
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5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
More Tasks about Hair Bow Collections
Part 1:
Find the multiplication equation, the number of hair bows and the expression with exponents for:
5 boxes
7 cases
4 cartons
3 palates
Part 2:
You have the following combined containers in different orders. For each write the addition sentence as expressions with
exponents then solve to find the total number of hair bows.
5 boxes and 3 cases:
3 palates and 8 cartons:
6 palates and 5 cases:
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5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
Lesson #2 Hair Bows and Bouncy Balls
Cluster: Measure and estimate lengths in standard units.
Standards:
5.OA.2. Use parentheses, brackets, or braces in numerical expressions,
and evaluate expressions with these symbols.
Standards for Mathematical Practice
MP 3: Reason abstractly and quantitatively
MP 6: Attend to Precision
5.NBT.1. Recognize that in a multi-digit number, a digit in one place
represents 10 times as much as it represents in the place to its right and
1/10 of what it represents in the place to its left.
5.NBT.2. Explain patterns in the number of zeros of the product when
multiplying a number by powers of 10, and explain patterns in the
placement of the decimal point when a decimal is multiplied or divided by a
power of 10. Use whole-number exponents to denote powers of 10.
Mathematical Goal:
Students will explore the values of digits in a number, and complete tasks
involving powers of ten and exponents.
Materials:
Activity sheet (included). Calculator (optional).
Words you should hear students use in mathematical conversations:
Multiply, divide, add, subtract, group, parentheses
Ten Minute Math: Practicing Place Value (5.OA.1)
Solve the following two tasks:
78 x 71 - 49 and 78 x (71 - 49).
What are the two solutions (answers)?
What do the parentheses tell you to do?
If time permits solve the following two tasks:
68 x 35 – 19 and 68 x (35 – 19)
Pose the same questions above.
Before:
Yesterday we looked at a Hair Bow Company. Does anyone remember the types of containers that hair bows were packaged in?
If needed display the activity sheet from the prior lesson with this information:
The Harrisburg Hair bow Company puts hair bows in various sized containers. A box will hold 10 hair bows. A case will hold 10 boxes.
A carton will hold 10 cases. A palate holds 10 cartons.
Does anyone recall how many hair bows we can hold in 1 case? How many in 3 cases?
How could we show the number of hair bows that we can hold in 3 cases in an expression with exponents?
Does anyone recall how many hair bows we can hold in 1 palate? 4 palates?
How could we show the number of hair bows that we can hold in 4 palates in an expression with exponents?
The same company decides that in addition to packaging hair bows they are also going to package bouncy balls in the same size
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5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
containers. A box will hold 10 bouncy balls. Today we are going to look at how bouncy balls can be packaged to meet the needs of the
company’s customers.
During:
Pass out or display the activity sheet so that students can see the task.
Part 1:
We have 4,321 bouncy balls. Remember, a box will hold 10 bouncy balls. A case will hold 10 boxes. A carton will hold 10 cases. A
palate holds 10 cartons. Using the smallest number of containers possible, how can we package the 4,321 bouncy balls?
Feel free to make this chart with your students to help remind them about the sizes of the containers from the previous lesson.
Container
Box
Multiplication
Equation
1x 10
Case
1 x 10 x 10
Carton
1 x 10 x 10 x 10
Palate
1 x 10 x 10 x 10 x 10
Expression with
Exponents
Number of bouncy
balls
1 x 101
1 x 102
1 x 103
1 x 104
10
100
1,000
10,000
What is the number of bouncy balls that are in a carton?
What is the number of bouncy balls that are in a case?
What is the number of bouncy balls that are in a box?
What is the number of bouncy balls that are not in a container?
If the company needed to package an order of 12,345 bouncy balls and wanted to use the smallest number of containers?
how could they package the order?
What is the number of bouncy balls that are in a palate?
What is the number of bouncy balls that are in a carton?
What is the number of bouncy balls that are in a case?
What is the number of bouncy balls that are in a box?
What is the number of bouncy balls that are not in a container?
Take time to discuss students’ strategies and approaches to the tasks in Part 1.
QuestionsWhat strategy did you use to determine the smallest number of containers?
What strategy did you use to determine the number of bouncy balls in each container?
Part 2:
Allow students to work on Part 2 of this task. Provide questions to help them get started if needed.
In Part 1, we determined that the 4,321 bouncy balls would be packaged best if we used 4 cartons, 3 cases, 2 boxes, and we had 1 left
over bouncy ball. The company now wants to determine the sizes of the containers related to each other.
How many boxes will fit inside of a case?
How many boxes will fit inside of a carton?
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5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
How many boxes will fit inside of a palate?
How many cases will fit inside of a carton?
What is the size of the box compared to the size of the case?
What is the size of the carton compared to the size of the case?
What is the size of the carton compared to the size of the palate?
Teacher note: If students struggle with these questions, have them reference their drawings from lesson 1 or guide them through
creating an accurate pictorial representation.
Part 3:
Based on what we determined in Part 2 we want to think about the values of digits in a number. If we had 5,555 bouncy balls, we have
the digit 5 in each place.
How does the value of the 5 in the hundreds place compare to the 5 in the tens place?
How does the value of the 5 in the ones place compare to the value of the 5 in the tens place?
How does the value of the 5 in the hundreds place compare to the value of the 5 in the ones place?
After:
Bring students together to discuss Part 3.
QuestionsWhat do you know about the value of the digit in the ___ place? How do you know that you are correct?
Ask this question about the various digits in the number.
What strategies did you use to help you solve the task?
If time permits give students the following writing prompt:
In a number, how does the value of the tens place compare to the value of the one thousands place? How do you know?
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5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
More Practice
The following tasks can be given to students in order to give them more practice with these Standards. Remember that
these tasks are intended to be first used at the end of Unit 3 and revisited during the year as needed.
5.OA.1. Write simple expressions that record calculations with numbers, and interpret numerical expressions without
evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 ×
(18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
Comparing Areas
How does the area of a rectangle that is 12” x 6” compare to the area of a rectangle that is 12” x 3”?
Comparing Areas II
How does the area of a rectangle that is 8” x 6” compare to the area of a rectangle that is 16” x 6”?
Comparing Classes
Sedgewick Elementary has 6 fourth grade classes with 23 students in each class and 2 fifth grade classes with 24 students
in each class. Manteoak has 12 fourth grade classes with 23 students in each class and 6 fifth grade classes with 24
students. Write an equation to show the number of students in each school.
Part 2: Write equations to just show the number of fourth grade students in each school. How does the number of fourth
grade students compare between schools? Explain your reasoning.
Part 3: Write equations to just show the number of fifth grade students in each school. How does the number of fifth grade
students compare between schools? Explain your reasoning.
Comparing Basketball Statistics
Marquel scores 18 points in each of the first five games of the season and 16 points in each of the last five games of the
season. Travis scores half as many points as Marquel in every game. Write an equation for each player to show the
number of points that each scored during the season. How does Marquel’s number of points compare to Travis’ number of
points?
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5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
5.OA.2. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Drink Selections
In the cafeteria there are 36 fifth grade girls drink juice and 29 fifth grade girls drink milk. Also, 48 fifth grade boys drink juice and 14
fifth grade boys drink milk. Write an equation to show the number of juices that fifth grade students drank in one day. Write an equation
to show the number of milks that fifth grade students drank in one day.
Part 2: If the fifth grade students ordered the same drink every day during the school week, write an equation to show the number of
juices that fifth grade students drank. Also write an equation to show the number of milks that fifth grade students drank.
Part 3: Solve both of you equations from Part 2 to determine how many juices and milks that fifth grade students drank.
Make This True
Use 2 sets of parentheses to make the following statements true
8+6÷2+5x4=8
(8 + 6) ÷ (2 + 5) x 4 = 8
9 x 3 x 5 + 5 ÷ 10 x 3 = 9
9 x 3 x (5 + 5) ÷ (10 x 3) = 9
7 x 3 + 8 + 6 x 4 + 7 x 2 = 154
7 x 3 + (8 + 6) x 4 + (7 x 2) = 154
Mowing Lawns
In order to save $222 for a new video game system Steve decides to mow lawns during the summer. Each week Steve mows 4 lawns
and earns $12 per lawn. Each week he also spends $9 on supplies. Write an equation to show how much money Steve earns in a
week.
Write an equation using a variable to represent the number of weeks that Steve needs to work in order to have enough money to buy a
video game system.
After writing an equation, solve the equation to find out how many weeks Steve needs to work in order to buy a video game system.
Solve each of the expressions below. How do the parentheses influence how you solve each task.
(12 + 6) x 10 = _______
12 + 6 x 10 = _______
10 x (6 + 12) = _____
Solve each of the expressions below. How do the parentheses influence how you solve each task.
(27 + 23) x 25 = _______
27 + 23 x 25 = _______
25 x (23 + 27) = _____
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5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
5.NBT.1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the
place to its right and 1/10 of what it represents in the place to its left.
Instagram Followers
I have 4,215 people following me on Instagram.
How does the value of the place where the 2 is compare to the value of the place where the 1 is?
How does the value of the place where the 5 is compare to the value of the place where the 1 is?
How does the value of the place where the 4 is compare to the value of the place where the 1 is?
When I multiply 36 x 10 what is the product? Describe how the values of the 3, the 6, and the 2 change in the product
compared to the number 36.
1
When I multiply 120 x 10 what is the product? Describe how the values of the 1 and the 2 change in the product compared
the number 120.
When I multiply 789 x 10 what is the product? Describe how the values of the 7, the 8, and the 9 change in the product
compared to the number 789.
1
When I multiply 540 x 10 what is the product? Describe how the values of the 5 and the 4 change in the product compared
the number 54.
Football Fans
There are 94,528 fans at the University of Georgia football game.
How does the value of the place where the 4 is compare to the value of the place where the 5 is?
How does the value of the place where the 2 is compare to the value of the place where the 5 is?
How does the value of the place where the 9 is compare to the value of the place where the 5 is?
How does the value of the place where the 9 is compare to the value of the place where the 8 is?
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5th Grade Unit- Exploring Quantities Charlotte Mecklenburg Schools
5.NBT.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain
patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number
exponents to denote powers of 10.
Solve the following:
6 x 103 + 4 x 102 =
8 x 104 + 9 x 103 =
5 x 104 + 7 x 103 + 1 x 102 =
7 x 103 – 8 x 102 =
4 x 103 – 11 =
Write the following multiplication equations using an exponent with 10 as the base. Then solve each expression.
3 x 10 x 10 x 10 =
6 x 10 x 10 =
10 x 10 x 4 x 10 =
10 x 10 x 10 x 10 x 5 =
10 x 10 x 2 x 3 x 10 =
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