Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Targeted Content Standard(s):
Student Friendly Learning Targets
4.OA.1 Interpret a multiplication equation as a comparison, e.g. interpret
35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as
many as 5. Represent verbal statements of multiplicative comparisons as
multiplication equations.
I can…
 Solve word problems that involve
comparing multiplicative situations.
 Solve multiplication equations.
 Explain why a model accurately
represents a multiplicative situation.
4.OA.2 Multiply or divide to solve word problems involving multiplicative
comparison, e.g. by using drawings and equations with a symbol for the
unknown number to represent the problem, distinguishing multiplicative
comparison from additive comparison.
Targeted Mathematical Practice(s):
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively
3 Construct viable arguments and critique the reasoning of others
4 Model with mathematics
5 Use appropriate tools strategically
6 Attend to precision
7 Look for and make use of structure.
8 Look for an express regularity in repeated reasoning
Supporting Content Standard(s): (optional)
3.OA.3
Explanation of Rigor: (Fill in those that are appropriate.)
Conceptual:
Students develop the concept of
multiplicative comparison.
Procedural:
Students represent multiplicative
comparison using diagrams and
equations.
Application:
Students solve multi-step word
problems, including those that involve
multiplicative comparison.
Vocabulary:
Multiplicative
comparison
prime
array
Standard form
composite
area model
Written form
divisor
equation
Expanded form
dividend
product
Factor
remainder
quotient
Multiple
bar model
Evidence of Learning (Assessment):
Pre-Assessment: Additive Comparison Exit Slip
Formative Assessment(s): Multiplication Situation Card Sort Activity
Multiplicative Comparison Card Activity
Summative Assessment: Grade 4 Unit 1 Multiplicative Comparison Assessment
Self-Assessment: Journal Prompt: What have I learned about Multiplicative Comparisons?
1
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Lesson Segments:
1. Addition and Subtraction Problem Solving
2. Mental Multiplication and Division using Reasoning
3. Multiplication and Division Problem Solving
4. Multiplicative Comparison
2
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Lesson Procedures:
Segment 1
Approximate Time Frame:
90 – 120 mins
Lesson Format:
Whole Group
Small Group
Independent
Modeled
Guided
Collaborative
Assessment
Focus:
Students will review the common
addition and subtraction situations
found on pg. 88 of the Common Core
Glossary, Table 1
Math Practice Look For(s):
Make sense of problems and persevere: watch that students fill in the
bar model correctly and can explain their thinking
Model with Mathematics: students transfer information found on the
bar model into equations
Use Tools Strategically: students use the bar model graphic as a way to
organize the information
Resources:
Problem Solving Structures (Common Core
Glossary pg 88 table 1: Common addition
and subtraction situations)
Handout 1: Addition and subtraction bar
model blank sheet
Handout 2: Exit Slip
Modalities Represented:
Concrete/Manipulative
Picture/Graph
Table/Chart
Symbolic
Oral/Written Language
Real-Life Situation
Differentiation for Remediation:
Have manipulatives available to solve the
problems as needed
Differentiation for English Language
Learners:
Ensure students know the difference
between hole and whole
Differentiation for Enrichment:
Potential Pitfall(s):
Independent Practice (Homework):
Set up their bar model incorrectly.
Handout 2: Exit Slip
Addition errors.
Steps:
Teacher Notes/Reflections:
Students will work in pairs as they engage in this review of addition and
subtraction. They should have handout 1 with the bar model graphic or
white boards and markers. Explain that this is an opportunity for them
to re-engage with content from the past few years to get ready to
extend that thinking into multiplication situations this year.
Put a bar model graphic up on display. Share the word problem
examples below one at a time. Have the students work in pairs to come
to agreement on how to fill in their bar model. After working in pairs,
have the students share where to put the numbers into the graphic.
3
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Note that you will add the labels as you add them to the graphic. Have
the students justify their thinking. Record the equation after the
graphic is filled in – discuss the use of a letter (n) for the unknown.
Make sure the students understand different situations require
different parts of the graphic to be filled in.
Repeat this procedure for each example. This is an opportunity to
support an environment rich in hearing one another’s thinking and
justification, so be sure to prompt students to ask clarifying questions
and re-state students’ explanations. Agreement should come from the
students rather than the teacher telling them their solutions are
correct.
Examples
Result Unknown (Putting Together)
124 cars and 84 trucks are in a parking lot. How many vehicles are there
altogether? 208 vehicles
124 + 84 = n
124 cars
84 trucks
124 + 84 = ?
n total vehicles
Discussion: Encourage the students to create their bar models with
precision. The parts must match the total.
Change Unknown (Taking Apart)
208 vehicles are in a parking lot. 124 are cars and the rest are trucks.
How many vehicles are trucks? 84 trucks
124 + n = 208
124 cars
124 + ?
n trucks
208 total vehicles
=208
Start Unknown
Some cars were in a parking lot in the morning. 84 trucks drove into the
lot in the afternoon. Now there are 208 total vehicles parked. How
many cars were in the parking lot to start with? 124 cars
n + 84 = 208
4
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
n Cars
84 Trucks
208 Total Vehicles
? +84 = 208
Continue the lesson with the remaining structures.
Adding To
Result Unknown
48 horses were in the pasture. 27 more horses came to join them. How
many horses are in the pasture now? 75 horses
48 + 27 = n
Change Unknown
48 horses were in the pasture. Some more horses came to join them.
There are now 75 horses. How many horses joined them? 27 horses
48 + n = 75
Start Unknown
Some horses were in the pasture. 27 more horses came to join them.
Now there are 75 horses in the pasture. How many horses were there
before? 48 horses
n + 27 = 75
5
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Taking From
Result Unknown
48 horses were in the pasture. 27 of the horses left. How many horses
are in the pasture now? 21 horses
48 – 27 = n
Change Unknown
48 horses were in the pasture. Some horses left. There are now 21
horses. How many horses left the pasture? 27 horses
48 - n = 21
Start Unknown
Some horses were in the pasture. 27 horses galloped away. Now there
are 21 left. How many horses were in the pasture before? 48 horses
n – 27 = 21
Compare
Difference Unknown
(“How many more?” version)
Manny has 63 baseball cards. Jeff has 47 baseball cards. How many
more baseball cards does Manny have than Jeff? 16 cards
6
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
63 – 47 = n 47 + n = 63 63 – n = 47
(any of these equations are acceptable)
Manny’s Cards
Jeff’s Cards
63
47
n
(“How many fewer?” version)
Manny has 63 baseball cards. Jeff has 47 baseball cards. How many
fewer baseball cards does Jeff have than Manny? 16 cards
47 + n = 63 63 – n = 47 63 – 47 = n
(any of these equations are acceptable)
Bigger Unknown
(Version with “more”)
Manny has 16 more baseball cards than Jeff. Jeff has 47 baseball cards.
How many baseball cards does Manny have? 63 cards
47 + 16 = n n – 16 = 47 (any of these equations are acceptable)
Manny’s Cards
Jeff’s Cards
n
47
16
(Version with “fewer”)
Jeff has 16 fewer baseball cards than Manny. Jeff has 47 baseball cards.
How many baseball cards does Manny have? 63 cards
47 + 16 = n n – 16 = 47 (any of these equations are acceptable)
Smaller Unknown
(Version with “more”)
Manny has 16 more baseball cards than Jeff. Manny has 63 baseball
cards. How many baseball cards does Jeff have? 47 cards
n + 16 = 63 63 – n = 16 63 – 16 = n
(any of these equations are acceptable)
Manny’s Cards
Jeff’s Cards
63
n
16
(Version with “fewer”)
Jeff has 16 fewer baseball cards than Manny. Manny has 63 baseball
cards. How many baseball cards does Jeff have? 47 cards
n + 16 = 63 63 – n = 16 63 – 16 = n
7
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
(any of these equations are acceptable)
Exit Slip: Solve two different additive comparison problems. Fill in a bar
model and write an equation for each problem.
8
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Segment 2
Approximate Time Frame:
Lesson Format:
10 minute opener (this should be an
on-going opener for this unit to
provide quick mental fluency
opportunities)
Resources:
Whole Group
Small Group
Independent
Handout 3: Multiplication Reasoning
Number grid
Number line
Counters
Modeled
Guided
Collaborative
Assessment
Resources for teachers on math talk
www.mathsolutions.com
Eyes on Math: a visual approach to
teaching math concepts by Marian
Small
Focus:
Modalities Represented:
Concrete/Manipulative
Picture/Graph
Table/Chart
Symbolic
Oral/Written Language
Real-Life Situation
Students select and accurately apply
strategies to mentally calculate
products. This develops fluency with
efficient procedures.
Math Practice Look For(s):
Differentiation for Remediation:
Differentiation for English Language Learners:
Differentiation for Enrichment:
Potential Pitfall(s):
Independent Practice (Homework):
Re-adjusting or compensating incorrectly.
Steps:
Teacher Notes/Reflections:
Visual Math:
Another opportunity for teachers to support students’ fluency with
computation strategies is to provide short visual math number talks.
Show a pictorial array of a multiplication fact (Handout 3: Multiplication
Reasoning)
XXXXXX XX
XXXXXX XX
XXXXXX XX
9
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
XXXXXX XX
Ask the following Questions:
 What multiplication does the picture show? We want students
to notice that the array can be seen as both 4 x 8 but also 8 x 4.
This will support the understanding of commutative property of
multiplication introduced in grade 3 (3.0A.5).
 How can you rearrange the rows or columns to show the other
ways to figure out 4 x 8? (We want students to know that any
combination of rows or columns could be used such as (2 x 8) +
(2 x 8) is the same as 4 x 8. Try to find students who have
divided the array in different vertical or horizontal ways. This
will support their understanding of the distributive property.
XXXXXX XX
XXXXXX XX
XXXXXX XX
XXXXXX XX

What does the picture tell you about how you can figure out
multiplication facts you don’t already know? (We want students
to come to realize that knowing smaller facts can help them
with bigger facts.) Have them justify their thinking.
Teachers should use this time to do some informal observation of how
comfortably students can use the strategy of breaking multiplication
arrays into easier chunks. Students struggling with this should receive
some explicit instruction in small group at a later time.
This activity will carry forward to later when they work with two-digit by
two-digit multiplication. (This is a great connection to subsequent
learning.)
10
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Segment 3
Approximate Time Frame:
60 min
Lesson Format:
Whole Group
Small Group
Independent
Modeled
Guided
Collaborative
Assessment
Resources:
Problem Solving Structures (Common
Core Glossary pg 89 table 2:
Common Multiplication and Division
Situations)
Color chips (1 bag for 2 students)
Overhead (optional, but will be
helpful)
Overhead color chips (optional)
Centimeter grid paper, to be used for
arrays (several sheets per student,
plus a transparency for the teacher)
Spiral notebooks (for students to
write/draw examples)
Handout 4: Multiplication Models
Formative Assessment: Handout 5:
Multiplication Story Situation Sorting
Cards
Focus:
Students will review the common
multiplication and division situations found
on pg. 89 of the Common Core Glossary,
Table 2
Math Practice Look For(s):
Make sense of problems and persevere: watch that students fill in the bar
model and area model correctly and can explain their thinking
Model with Mathematics: students transfer information found on the models
into equations
Use Tools Strategically: students use the bar models, counters, and area
models as ways to organize the information
Modalities Represented:
Concrete/Manipulative
Picture/Graph
Table/Chart
Symbolic
Oral/Written Language
Real-Life Situation
Differentiation for Remediation:
Give students a copy of the Problem
Solving Structures handout to help
them sort the Problem Solving Cards.
Differentiation for English Language
Learners: Make Vocabulary Cards
showing the different models for
multiplication and division problem
situations.
Differentiation for Enrichment: Have
students create their own Problem
Solving Cards using the different
types of multiplication and division
structures.
11
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Potential Pitfall(s):
Set up their models incorrectly.
Independent Practice (Homework):
Handout 4: Multiplication Models
Multiplication fact errors.
Steps:
Teacher Notes/Reflections:
Students will work in pairs as they engage in this activity. Explain that they are
going to build on what they learned about addition and subtraction situations
to model multiplication situations.
Using the examples below, build/draw the graphic support (bar model or array
model) with the group for each problem. It will help to have the students write
out the problems in their spiral notebooks (or notes) as you work through the
examples.
For the EQUAL GROUPS examples, the students will draw a bar model. Share
the word problem examples below one at a time. Have the students work in
pairs to come to agreement on how to fill in their bar model. After working in
pairs, have the students share where to put the numbers into the graphic. Note
that you will add the labels as you add them to the graphic. Have the students
justify their thinking. Record the equation after the graphic is filled in. Make
sure the students understand different situations require different parts of the
graphic to be filled in.
Repeat this procedure for the EQUAL GROUPS examples. This is an opportunity
to support an environment rich in hearing one another’s thinking and
justification, so be sure to prompt students to ask clarifying questions and restate students’ explanations. Agreement should come from the students rather
than the teacher telling them their solutions are correct.
For the ARRAYS, AREA examples, the students will use an array model to
support their thinking about the multiplication situations. For each word
problem, have the students write the problem, model the problem with color
chips, use centimeter grid paper to draw the arrays, write the equation using a
variable (e.g., 3×6=p) and figure out the answer. Again, ensure they know how
to label their model. Pairs will again fill in the diagrams together and be
prepared to explain their reasoning.
EQUAL GROUPS: EXAMPLES
Unknown Product (Equal Groups)
There are 6 boxes with 8 muffins in each box. How many muffins are there in
all? 48 muffins
6×8=n
12
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Group Size Unknown (Equal Groups)
If 48 muffins are shared equally into 6 boxes, then how many muffins will be in
each box? 8 muffins
6 × n = 48 and 48 ÷ 6 = n
Number of Groups Unknown (Equal Groups)
If 48 muffins are to be packed 8 to a box, then how many boxes are needed? 6
boxes
n × 8 = 48 and 48 ÷ 8 = n
ARRAYS, AREA: EXAMPLES
Unknown Product (Arrays, Area)
There are 5 rows of chairs with 7 chairs in each row. How many chairs are there
in all? 35 chairs
5×7=n
13
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Group Size Unknown (Arrays, Area)
If 35 chairs are arranged into 5 equal rows, how many chairs will be in each
row? 7 chairs
5 × n = 35 and 35 ÷ 5 = n
Number of Groups Unknown (Arrays, Area)
If 35 chairs are arranged into equal rows of 7 chairs, how many rows will there
be? 5 rows
n × 7 = 35 and 35 ÷ 7 = n
Observation Assessment: Students work in small groups. Each group gets a
deck of the Multiplication Situation Sorting Cards. (Cut apart handout) As a
group, they sort the cards under the shaded situation type cards. The teacher
can informally observe and assess the students on their ability to recognize the
various multiplication situations.
Note: There are examples of the three types of Multiplicative Comparison
Problems in the Sorting Cards. You may wish to take those out and repeat this
activity at the end of the lesson using all of the cards, or you may wish to keep
the cards in and have a whole class discussion as an introduction to Segment 4.
14
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Segment 4
Approximate Time Frame:
120 - 180 mins
Lesson Format:
Whole Group
Small Group
Independent
Modeled
Guided
Collaborative
Assessment
Resources:
Problem Solving Structures (Common
Core Glossary pg 89 table 2: Common
Multiplication and Division Situations)
Handout 6: Multiplicative Comparison
Cards (1 set for 2 students)
Handout 7: Multiplicative Comparison
Workspace worksheets (1 per
student)
Handout 8: Multiplicative
Comparisons Worksheet
Summative Assessment: Grade 4 Unit
1 Multiplicative Comparison
Focus:
Students will identify, solve and
explain how to solve multiplicative
comparison problems by using
drawings and equations with a letter
for the unknown number.
Math Practice Look For(s):
Make sense of problems and persevere: watch that students
fill in the bar model correctly and can explain their thinking
Model with Mathematics: students transfer information found
on the bar model into equations
Use Tools Strategically: students use the bar model graphic as
a way to organize the information
Modalities Represented:
Concrete/Manipulative
Picture/Graph
Table/Chart
Symbolic
Oral/Written Language
Real-Life Situation
Differentiation for Remediation: Make posters
showing the models for multiplicative comparison
situations for students to refer to when solving
problems.
Differentiation for English Language Learners: Draw
simple illustrations to show what “times as much”
means. For example: If you have 3 apples, 4 times as
much would be 12 apples. An illustration can help
visualize that 4 times as much would be 12, and would
not look like 4 more (7).
Differentiation for Enrichment: Give students
multiplication equations and have them create
multiplicative comparison word problems for each
equation.
Potential Pitfall(s):
Set up their models incorrectly.
Independent Practice (Homework):
Handout 8: Multiplicative Comparisons Worksheet
Multiplication fact errors.
15
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Steps:
Teacher Notes/Reflections:
1) Number Talk Openers
At the start of lessons during this unit students will be engaged in
mental math activities to support fluency in multiplication strategies.
Day 1: Have students gather for a Math Talk. Show the multiplication
fact below and ask them to solve it mentally. Students should share
their strategies to deepen their understanding about why the
procedures work based on place value and properties of operations.
They will later use this skill to solve problems.
3 × 2 × ___ = 30
Day 2: Have students gather for a Math Talk. Show the multiplication
facts below and ask them to express the equations as multiplicative
comparisons. Discuss.
5 × 8 = 40
(40 is 5 times as much as 8)
18 = 6 × 3
(18 is 6 times as much as 3)
Show the multiplication statements below and ask them to write (on
the board) the multiplicative comparisons as equations. Discuss.
12 is 3 times as much as 4
(3 × 4 = 12)
28 is 4 times as much as 7
(28 = 4 × 7)
2) Multiplicative Comparison – Bar Model and Equations
Technology Resource: http://www.thinkingblocks.com/index.html
(online models for multiplicative comparisons)
A multiplicative comparison is a situation in which one quantity is
multiplied by a specified number to get another quantity (e.g., “a times
as much as b”). Students should be able to identify and verbalize which
quantity is being multiplied and which number tells how many times.
16
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Students should be given opportunities to practice the concept. The
Problem Solving Structures table can be used to provide students with
more examples of the different types of multiplicative comparisons.
Explain that “unknowns” in math problems can come in different forms.
It can be the product (answer), group size, or the number of groups that
need to be solved for in a multiplicative comparison. Variables should
be used to hold the place of the “unknown” in any type of multiplicative
comparison problem.
Using the examples below, draw the bar model with the group for each
problem. (Following each example are more problems that can be used
for guided practice/independent practice during instruction.) It will
help to have the students write out the problems in their spiral
notebooks (or notes) as you work through the examples. Share the
word problem examples below one at a time. Have the students work
in pairs to come to agreement on how to fill in their bar model. After
working in pairs, have the students share where to put the numbers
into the graphic. Note that you will add the labels as you add them to
the graphic. Have the students justify their thinking. Record the
equation after the graphic is filled in.
Unknown Product (Compare)
A tennis ball costs $2. A soccer ball costs 6 times as much as the tennis
ball. How much does the soccer ball cost? $12
6×2=n
6
SOCCER BALL
TENNIS BALL
n
$2
A. Raygen is 5 years old. Her mother is 8 times as old as she is. How
old is Raygen’s mother? 40 years old
B. Garrett’s stack of coins is 4 times as high as Cade’s stack of coins. If
Cade’s stack is 3 inches tall, how high is Garrett’s stack? 12 inches
C. Jaden has 7 baseball cards. Juan has 6 times as many baseball cards
as Jaden. How many baseball cards does Juan have? 42 baseball cards
D. During the summer reading program at the library, children who
read 10 books won a new book. To win the Grand Prize of a book bag,
children had to read 5 times that amount. How many books did a
participant need to read to win the Grand Prize? 50 books
17
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
Group Size Unknown (Compare)
A soccer ball costs $12 and that is 6 times as much as a tennis ball costs.
How much does a tennis ball cost? $2
6 × n = 12 and 12 ÷ 6 = n
6
SOCCER BALL
TENNIS BALL
$12
n
A. Manny has lived in Illinois for 21 years and that is 7 times as many
years as Lucas. How many years has Lucas lived in Illinois? 3 years
B. Jackie has saved 4 times as much money as Heather. If Jackie has
saved $32, how much money has Heather saved? $8
C. Amy has 35 marbles. She has 7 times as many marbles as Scott.
How many marbles does Scott have? 5 marbles
D. Jake’s grandmother lives 48 miles away from him. She lives 8 times
as far away from him as his aunt. How many miles away from Jake does
his aunt live? 6 miles
Number of Groups Unknown (Compare)
A soccer ball costs $12 and a tennis ball costs $2. How many times as
much does the soccer ball cost as the tennis ball? 6 times as much
n × 2 = 12 and 12 ÷ 2 = n
n
SOCCER BALL
$2
TENNIS BALL
$2
$12
A. A tree in Ashton’s yard is 15 feet tall. Ashton is 3 feet tall. The tree
is how many times as tall as Ashton? 5 times as tall
B. A marshmallow was 4 cm long to start. Now it has been stretched to
be 16 cm long. How many times as long is the marshmallow now than
it was at first? 4 times as long
C. The fourth grade class has two class pets, a turtle and a hamster.
The turtle weighs 12 ounces and the hamster weighs 4 ounces. The
turtle weighs how many times as much as the hamster? 3 times as
much
D. 40 is __________ times as much as 4. 10
Note: Provide more examples of each type of problem if the students
seem to be having trouble understanding the concepts taught in this
lesson. Use the examples as the guide to making up new problems.
18
Grade _4_ Lesson Title: Problem Solving and Multiplicative Comparison
Unit 1: Multiplication and Division Concepts
Time Frame: 5-7 Days
Essential Question: What real-life situations require the use of multiplication or division and how are they modeled?
3) Multiplicative Comparison Cards
Distribute the Multiplicative Comparison Cards and Multiplicative
Comparison Workspace worksheets when students are ready for
additional practice. Students work in groups of 2 to answer the
questions. Students should draw a bar model for each problem and
write an equation using a variable for the unknown number in the
problem (see answer key). The teacher may want to check student
answers before allowing students to go on to the next card OR the
teacher can give each group of students an answer key, so students
can check their own work when they have completed each problem.
It would not be beneficial to have students do all of the problems
without checking.
Note: There are many ways that problem-solving cards can be used.
Listed are a few resources/strategies:
*Partner work - http://www.kaganonline.com/index.php
*Math Scavenger Hunt http://www.mathnspire.net/2012/01/scavenger-hunt-revisited-reviewgame.html
*Group Work – Assign a problem for each group to work on. Each
group member completes a step to solve the problem and then passes
the work to the next member, repeat until the problem is complete.
Formative Assessment: Assign one problem from the Multiplication
Comparison Cards for students to complete independently. Evaluate
their ability to draw and label a bar model, write an equation, and solve
the problem.
Self-Assessment: Journal Prompt - What have I learned about
Multiplicative Comparisons?
Summative Assessment: Grade 4 Unit 1 Multiplicative Comparison
Assessment
19