Decomposing Numbers
Third Grade
Math, ESL
Why make things harder on ourselves? Teach your students to decompose numbers to make math easier! Use
this as a stand alone lesson or a pre-lesson for Decompose to Multiply: 6, 7, 8, and 9.
Objectives
Objectives
Academic
Students will be able to decompose factors to find multiples of six, seven, eight, and nine.
Language
Students will be able to explain how to decompose numbers using peer supports.
Materials and preparation
Teacher copy of the Teach Background
Knowledge Template
Teacher copy of the Write Student-Facing
Language Objectives Reference
Class set of whiteboards and whiteboard
markers
Class set of manipulatives
Document camera
Vocabulary
TIER 2
decompose: to break apart
TIER 3
factor: any one of two or more numbers that
are multiplied together to give a product
Attachments
Teach Background Knowledge Template (PDF)
Write Student-Facing Language Objectives Reference (PDF)
Math language routine
Number Talks
Introduction (4 minutes)
Invite students to do a quick number talk by looking at a set of dots displayed on the document camera.
Explain that they will only briefly see a set of dots because you don't want them to count the dots
individually. Tell them that they will then be asked to share how many dots they saw. Then they will
explain how they saw the pattern of dots and figured out the total number. Emphasize that they need to
group the dots in their minds to find the total number rather than counting each individual dot.
Display a set of dots (such as three rows of four dots) for about two or three seconds.
Engage the students in a class discussion about how many dots they saw and the patterns in which they
saw them. As students share their explanations, create visuals on the board and ask them to verify if you
are capturing their visual correctly.
Explain that you did the number talk about the dots because you want to point out how we all see
numbers and patterns in different ways. We can all see a collection of dots, but we may see the patterns,
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or how the set is broken up, differently.
Share the Language Objective for the lesson and explain that today students will learn how to explain
how to decompose numbers.
Explicit Instruction/Teacher modeling (8 minutes)
Introduce the key term decompose and explain that it means to break apart. Provide an example of
things that decompose in different contexts. (e.g., In our every day lives, food will decompose, or break
apart, over time and it is no longer good to eat. In science, a tree's leaves will decompose into dirt.) Ask
students to think of any additional things they know that decompose.
Explain that in math, we decompose numbers to break them apart and make them smaller and easier to
work with. Tell students you have a certain number of cookies, and you'd like to break them up into
different amounts. Write the number 10 on the board, and underneath it write two equations: ____ + ____
= 10 and ____ + ____ + ____ = 10.
Model thinking aloud about how you could break apart the number 10 and create different equations.
(e.g., Say, "I could decompose 10 by adding five and five. Or I could decompose 10 by adding two and
three and five.") Point out that 10 is a friendly number to work with, so decomposing 10 would not always
be necessary. The reason for decomposing is to make a problem simpler with friendlier numbers.
Provide an additional example of a number that you'd like to decompose. For example, share that you
have a multiplication problem (e.g., You need to figure out how many seats there are in the theater if
there are 13 rows of five seats. You know the expression is 13 x 5) and you'd like to break one factor,
which is any one of two or more numbers that are multiplied together to give a product. Tell students that
you'd like to break 13 into easier numbers since math facts with 13 aren't as easy as others. Use
manipulatives while you think aloud by sorting 13 blocks or counters to model decomposing the number.
Guided Practice (12 minutes)
Instruct students to take out their whiteboard and whiteboard marker. Distribute enough manipulatives to
each student so they can visually decompose the numbers in the following practice problems.
Put students into groups of 3-4 students and ask them to decompose the number 9. Challenge them to
show at least two different ways to decompose the number. Discuss as a class by calling on
nonvolunteers to share one way to decompose the number. Then, follow the same process with the
number 17.
Write a multiplication expression on the board (e.g., 8 x 4) and provide a real-world example to give
students context for the numbers. Then, model decomposing one of the numbers. Think aloud about how
you'd like to decompose the number eight, which is the larger factor, because it will make the problem
easier for you. Explain that when you decompose one of the factors, you multiply each of the parts by the
other factor in the expression, and then you add them together. For example, the new expression will be
(2 x 4) + (6 x 4). Share that you will not be fully solving the multiplication expressions, but instead focus
on how to decompose and set up the new problem.
Have small groups use their whiteboards, markers, and manipulatives to decompose one of the factors in
the following problems without solving it:
The tray has six rows of five donuts each. How many donuts are on the tray? The expression is 6 x
5.
The farm has nine baskets of three apples each. How many apples are in the baskets? The
expression is 9 x 3.
Discuss each of the problems as a class and ask questions such as, "How are the two strategies or
methods the same? How are they different?" and "Why did you choose to decompose this factor?"
Provide sentence frames for students to use as they participate in discussions.
Group work time (10 minutes)
Introduce the Number Talk activity that students will do by explaining the following steps:
1 - Independent Think Time: Tell students that they will see a multiplication expression displayed
on the board and they will be given 1-2 minutes to decompose one of the factors and create a new
multiplication expression without paper or talking.
2 - Whole Class Share Time: Explain that this portion of the activity will be when students share
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their method or strategy they used to decompose one factor and create the new multiplication
expression.
3 - Display Ideas: Share that you will create a visual display for each of their methods while they
share their strategies, but that they also have the option to create their own visual displays to
show.
4 - Questions: Explain that you will ask questions to get students thinking and talking about the
different methods, so this will be a time for discussion.
Begin the Number Talk by sharing a real-life scenario, such as "My kitchen was really messy, so I
organized the cabinets with my dishes. I made seven stacks of four plates. How many plates did I
organize?"
Display the following multiplication expression: 7 x 4. Follow the steps that you shared with the students.
Ask questions such as "How are the two strategies or methods the same? How are they different?" and
"Why did you choose to decompose this factor?" and "How can you represent that factor in a different
way?" and "Do you agree/disagree with their answer? Why?" Support learners by displaying sentence
stems that they can use while answering the discussion questions.
Additional EL adaptations
Beginning
Distribute manipulatives as needed.
Have learners repeat instructions and key vocabulary to the teacher.
Group students intentionally based on academic and language needs.
Give students the option to share their answers in their home language (L1).
Provide a word bank of key terms and phrases for students to use in group and class discussions.
Advanced
Choose advanced ELs to share their ideas first in group and class discussions.
Instruct learners to support beginning ELs in partner and small group discussions.
Have learners repeat instructions and key vocabulary, summarizing important information for the class.
Assessment (4 minutes)
Distribute a half sheet of blank paper to each student and have them write 6 x 7 on the top.
Instruct them to:
Circle the factor they would decompose if they were asked to solve this problem using that
strategy.
Write a sentence that explains why they chose that number to decompose. Provide a sentence
frame for students who may need it, such as "I chose to decompose the number ____ because
____."
Decompose the number and create a new multiplication expression.
Review and closing (2 minutes)
Engage the class in a conversation about which number would be best to decompose in 6 x 7. Make the
connection between the different opinions about which number to decompose and how the original
number talk with the collection of dots showed different viewpoints as well.
Reiterate that decomposing one of the factors in a multiplication problem is a helpful strategy when
problem solving. It is also a strategy that we can use to help us memorize our multiplication facts
because we are making connections between numbers.
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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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