Multiplication and Division:
What's the Connection?
Fourth Grade
Math, ESL
Numbers are connected in many ways! Take students on a journey to uncover multiplication and division fact
families and inverse relationships. Teach this lesson on its own or prior to the lesson Division and Multiplication
Relationship.
Objectives
Objectives
Academic
Students will be able to show understanding of the inverse relationship between multiplication and division.
Language
Students will be able to identify the number that does not belong in the fact family and explain their reasoning
using sentence starters and peer support.
Materials and preparation
Vocabulary
Class set of Multiplication and Division: How Do
the Numbers Relate?
Teacher copy of Vocabulary Cards
Class set of Glossary
Half a class set of whiteboards and markers
Document camera
Teacher copy of Teach Background Knowledge
Template
Teacher copy of Write Student-Facing Language
Objectives Reference
TIER 2
divide: to separate into equal groups
multiply: to add a number to itself a certain number
of times
TIER 3
factor: a number that is multiplied to get another
number
inverse operation: the opposite operation (addition,
subtraction, multiplication, division)
product: the answer when two or more numbers are
multiplied
quotient: the answer to a division problem
Attachments
Multiplication and Division: How Do the Numbers Relate? (PDF)
Vocabulary Cards: Multiplication and Division: What's the Connection? (PDF)
Glossary: Multiplication and Division: What's the Connection? (PDF)
Teach Background Knowledge Template (PDF)
Write Student-Facing Language Objectives Reference (PDF)
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Math language routine
Compare and Connect
Introduction (4 minutes)
Gather information on students' background knowledge by asking them to define the term "fact family"
to a partner. Tell them to talk about what "fact family" means to them and how they have encountered
the term before.
Ask students to share their conversations with the whole class and record students' responses on the
board. Some students may mention addition and subtraction fact families while others may relate
multiplication and division fact families. Acknowledge all students' background information and make a
point of restating their ideas using correct terminology.
Tell students that today they will delve deeper into the concept of inverse relationships in math as they
relate specifically to multiplication and division.
Explicit Instruction/Teacher modeling (8 minutes)
Tell students that they will first review some key vocabulary that will help them discuss the math
concepts in this lesson.
Have students conduct a brief self-assessment on their depth of knowledge of each vocabulary term.
Read each vocabulary word aloud, one at a time. Have students show you a thumbs-up if they know the
word and can explain its meaning to a friend, a thumb to the side if they have heard the term before but
cannot explain it to a friend, or a thumbs-down if they have not heard the term before. Based on
students' self-assessments, determine how much time to spend on vocabulary development.
Distribute a copy of the Glossary worksheet to each student. Have them write "Example" in the far right
empty column on the Glossary. Model how to come up with an example for each term to add in this
column. Have students continue adding examples, either in their home language (L1) or in English (L2)
for the rest of the vocabulary terms. Invite a few students to share their examples with the class. Have
students paste the Glossary into their math journals, if applicable, for future reference.
Introduce the concept of number relationships by showing an example of a simple multiplication equation
on the board or document camera such as 7 x 2 = 14. Ask students to think of other number sentences
or equations related to it. Remind students of the commutative property of multiplication which states
that the order of factors in a multiplication sentence does not matter, therefore we can also write 2 x 7 =
14.
Show students how you can write two division equations with these three numbers too. Have students
work with a partner to orally state the division problems we could write with these numbers (14 divided
by 2 = 7 and 14 divided by 7 = 2). Write out the four number sentences one on top of another to show
the pattern and relationship. Explain that multiplication and division are inverse operations which means
that they are opposite operations.
Ask a student volunteer to come up and draw a visual representation of one of the multiplication and
division sentences from this fact family (e.g., a 7 x 2 array, 7 circles with 2 items in each circle, etc.).
Guided Practice (8 minutes)
Explain to students that it is useful to know the multiplication facts to be able to accurately and quickly
discover multiplication and division fact families. However, tell students that if they need the support of a
multiplication chart, they are welcome to use one as a resource.
Place students into partnerships and hand out a whiteboard and marker to each pair of students.
State another multiplication fact such as 6 x 7 = 42. Tell kids to work together with their partner to write
the other three multiplication and division sentences that go with the fact family.
Instruct students to compare their whiteboards with another pair of students and notice if there are any
differences.
Repeat this process with 9 x 8 = 72.
Have students share their strategies of writing out the complete fact family and provide the following
sentence starters as a guide:
"First, I... Then, I... Finally, I..."
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"I know my fact family is complete and correct because..."
Ask students to share their feedback on ways of knowing the entire fact family. Lead them to the
realization that if you know just one multiplication or division fact, you can easily figure out the other
three.
Group work time (12 minutes)
Distribute the Multiplication and Division: How Do the Numbers Relate? worksheet and read aloud the
directions.
Go over the sample problem. Ensure that students have access to their Glossary from earlier in case they
need help with word definitions or images.
Tell students to complete all but the last problem on the worksheet independently. Students are to circle
the number that does not belong in the fact family, complete the sentence frames that explain the
relationship of the numbers, and draw a visual representation of the fact family.
Gather students together once they have completed the four problems. Have students share their work
and read their answers aloud to a partner. Tell students to also describe the visual representation they
drew and how it accurately demonstrates the fact family. Listen in on students' conversations as they
share.
Ask students to share if there were any discrepancies or differences in their work and that of their
partner's. Ask them to share how they worked through the differences.
Review any challenging problems as a whole group.
Additional EL adaptations
Beginning
Allow students to do acitivities with a partner.
Translate key terms into students' home language (L1).
Have students work in a small, teacher-led group during group work time.
Create and display a word/phrase bank with helpful terms from the lesson for students to refer to, with
images if applicable.
Advanced
Tell students to create a story situation or word problem based on a multiplication and division fact
family.
Ask students to rephrase instructions and paraphrase important learning points throughout the lesson.
Assessment (5 minutes)
Instruct students to solve the last problem on the worksheet using their own words to explain the
relationship between the numbers. Students are also to draw a visual representation and explain how the
drawing matches the fact family.
Review and closing (3 minutes)
Invite a few students to share their explanations and drawings on the document camera.
Reiterate that it is helpful for us to know the relationship between division and multiplication so that we
are able to have a strong number sense to manipulate numbers when solving more difficult math
problems.
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Name
Date
Multiplication and Division: How Do the Numbers Relate?
Directions: Circle the number that does not belong in the multiplication and division fact family. Then, write an explanation and draw a picture to
show how the three other numbers relate to each other. The first problem has been done as an example.
16
6
18
3
Explanation: The number _______________
does not belong in this fact
16
Drawing:
six times three does not equal 16
family because ________________________________________________
_______________________________________________________. One
6 x 3 = 18
multiplication fact that can be built from these numbers is ____________
_________________________________. The inverse operation of this fact
18 divided by 6 is 3
is ________________________________.
Another multiplication/division
3 x 6 = 18
fact from these numbers is _____________________________________.
28
4
7
Explanation: The number _______________ does not belong in this fact
9
Drawing:
family because ________________________________________________
_______________________________________________________. One
multiplication fact that can be built from these numbers is ____________
_________________________________. The inverse operation of this fact
is ________________________________. Another multiplication/division
fact from these numbers is _____________________________________.
4
20
5
10
Explanation: The number _______________ does not belong in this fact
Drawing:
family because ________________________________________________
_______________________________________________________. One
multiplication fact that can be built from these numbers is ____________
_________________________________. The inverse operation of this fact
is ________________________________. Another multiplication/division
fact from these numbers is _____________________________________.
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Name
Date
Multiplication and Division: How Do the Numbers Relate?
56
8
6
Explanation: The number _______________ does not belong in this fact
7
Drawing:
family because ________________________________________________
_______________________________________________________. One
multiplication fact that can be built from these numbers is ____________
_________________________________. The inverse operation of this fact
is ________________________________. Another multiplication/division
fact from these numbers is _____________________________________.
12
14
132
Explanation: The number _______________ does not belong in this fact
11
Drawing:
family because ________________________________________________
_______________________________________________________. One
multiplication fact that can be built from these numbers is ____________
_________________________________. The inverse operation of this fact
is ________________________________. Another multiplication/division
fact from these numbers is _____________________________________.
48
Explanation: (use your own words)
52
6
8
Drawing:
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Vocabulary Cards
EL Support Lesson Plan: Multiplication and Division: What's the Connection?
divide
factor
to separate into
equal groups
a number that is multiplied
to get another number
inverse operation
multiply
the opposite operation
(addition, subtraction,
multiplication, division)
to add a number to itself
a certain number of times
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Vocabulary Cards
EL Support Lesson Plan: Multiplication and Division: What's the Connection?
product
quotient
the answer when two or
more numbers are multiplied
the answer to a
division problem
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Glossary for EL Support Lesson PLAN:
Multiplication and Division: What's the Connection ?
Word
Definition
divide
to separate into
equal groups
factor
a number that is multiplied
to get another number
inverse operation
Visual
the opposite operation
(addition, subtraction,
multiplication, division)
multiply
to add a number to
itself a certain
number of times
product
the answer when two
or more numbers
are multiplied
quotient
the answer to a
division problem
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Teach Background Knowledge
Lesson Topic:
Choose a topic from the main content
lesson that will help ELs understand the
main content lesson. Your non-ELs will
already have knowledge about this topic.
Total Lesson Time:
(20 - 30 minutes)
Student-Facing Language
Objective:
Example: I can learn new vocabulary
using pictures and sentence frames.
Student ELP Level(s):
Consider each student’s ELP level and
their academic strengths when choosing
scaffolds for the lesson.
Potential Scaffolds:
Choose some of these material supports
and instructional scaffolds based on each
EL’s individual strengths and needs.
Groupings (pairs, small-groups, a teacher-led group)
Word banks, word wall, and bilingual glossaries
Sentence frames, sentence stems, and paragraph frames
Home language materials
Reduced linguistic load, repetition, rephrasing and modeling
Practice new academic skills with familiar topics
Materials & Resources List
List the materials you’ll use in the lesson.
Key Vocabulary Words (5-8 words)
List the words with student-friendly
definitions in English. Provide
definitions in student’s home language
when appropriate.
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Introduction
Access EL’s prior knowledge about the
lesson topic with a brief comprehension
check.
Potential activities:
Creating captions for images
Opinionnaires
Carousel brainstorming
Conversations with sentence starters
Time estimate for Introduction
(3 - 5 minutes)
Explicit Instruction of
Background Knowledge
Model a learning activity that embeds
the teaching of academic language and
background knowledge.
Potential activities:
Lunch brunch discussion
Teacher-created, adjusted text and
questions
Brief videos or visuals
Text-based instruction
Home-language connections
Pre-teach a small number of
vocabulary words
Show real-world objects
Complete word family or bilingual
glossaries
Word walls or word bank creation
Time Estimate for Explicit Instruction
(4 - 6 minutes)
Guided Practice
Provide an opportunity for students (in
pairs or small groups) to practice the skill
or information taught during Explicit
Instruction, offering appropriate
scaffolds as needed.
Time Estimate for Guided Practice
(5 - 7 minutes)
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Formative Assessment
Ask students to show comprehension of
new background knowledge and
associated skills through an oral or
written task. Provide appropriate
scaffolds dependent on their ELP level.
Potential assessments:
Act out concepts
Hands on tasks
Drawings, models, or graphs
Graphic organizer completion
Captions of images
Reading response or content
area logs
Retellings
Role plays
Audio or video recordings
Oral interviews
Time estimate for Assessment
(5 - 7 minutes)
Review and Closing
Refer to the student objective and relate
information to future lessons. Allow
students to share thoughts about
whether they reached their objective
and/or mention lingering questions.
Provide sentence stems or frames for their
discussion.
Time estimate for Review and Closing
(3 - 5 minutes)
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Write Student-Facing Language Objectives
A teacher-facing language objective:
A student-facing language objective:
begins with “Students will be able to...”
is designed to raise students' self-awareness of and
promote their language development.
incorporates a language function, grammar structure, and
supports or scaffolds.
is intended to guide the teacher’s lesson planning
and instruction.
begins with “I can...”
is designed to raise students' self-awareness of and
promote their language development.
incorporates a language function, grammar structure, and
supports or scaffolds.
is easy to understand for students at all levels of
English proficiency.
Steps to convert a teacher-facing objective to a student-facing objective:
1.
2.
Replace “Students will be able to” with “I can.”
Simplify challenging words but maintain key vocabulary words you’ll address in the lesson.
Students will be able to describe a character with adjectives using graphic organizers.
Language
Function
Grammar
Structure
Support/
Scaffold
I can talk about a character with adjectives using graphic organizers.
Language
Function
Language Functions
locate
show
sort
tell
contrast
create
describe
ask questions
brainstorm
classify
identify
infer
interpret
collect
compare
Grammar
Structure
Support/
Scaffold
Supports/Scaffolds
Grammar Structures
nouns
modals
verb forms
conjunctions
sentence structure
pronouns
comparatives
adverbs
academic vocabulary
adjectives
phrases
prepositions
complex sentences
graphic organizers
teacher modeling
word banks/walls
sentence starters
strategic grouping
home language supports
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Reserved
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