Grade Five Lesson Plan: What Makes a Number Odd or Even?
Note: Defining odd and even is not a grade five standard. The example lesson is meant to focus on the reasoning and
explaining practices, not the standard itself.
Mathematical goals
This lesson is intended to:

Assess how well students understand the concepts of odd and even. It will help to identify and support students
who have difficulty in identifying whether a number is odd or even.

Introduce students to making a viable argument about a number being odd or even.
Common Core State Standards
This lesson involves mathematical content in the standards from Operations and Algebraic Thinking:

2.OA.3. Determine whether a group of objects (up to 20) has an odd or even number or members (e.g., by
pairing objects or counting them by 2s). Write an equation to express an even number as a sum of two equal
addends.

4.OA.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern
that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate
terms in the resulting sequence and observe that the terms appear to alternate between odd an even numbers.
Explain informally why the numbers will continue to alternate in this way.
This lesson involves a range of mathematical practices, with emphasis on:
1. Reason abstractly and quantitatively
2. Construct viable arguments and critique the reasoning of others
3. Attend to precision
Language goals
This lesson is intended to help assess whether students have the academic language to communicate their ideas
about odd and even.
Vocabulary: Words in bold is essential vocabulary; non-bold is useful vocabulary.
skeptic, represent, representation, representative, diagram, group, members, pair, paired, pairing, sum,
addends, odd, even
Phrases





odd (even) number of members in a group
number sentence
by pairing objects
making twos
making pairs
Structure of the Lesson
Students are introduced to the main question to work on: “Is 50 odd or even? How do you know?”
Students think about the question independently for a minute and then work with a partner to make an argument for
50 being an odd or even number.
During the lesson, students work in pairs or threes to justify their thinking to each other and to create a
representation showing that 50 is either odd or even.
In a whole-class discussion, students show their different representations of the number 50 and explain their
answers.
Time needed (approximate and will vary depending on needs of class)
5 minutes to introduce the task
1 minute to work independently
10 minutes to work with partner
5 minutes to create representation
15 minutes to discuss with whole class
Lesson
Structure
The Rules of
the Game
(sociomathematical
norms that
promote
learning)
Whole class:
5 minutes
Instructions / Questions to Students
Errors are gifts because they promote discussion.
The answer is important, but it is not the whole
math!
Ask questions until it makes sense.
Think with language and use language to think.
INTRO
Multiple strategies … multiple representations.
The purpose of today’s lesson is for me to learn
what you know about odd and even.
Purpose
I am a skeptic [do you know what a skeptic is?].
Your job is to convince me and convince the class
[with words, diagrams, pictures, examples, nonexamples, different representations] that you
know the answer to this question.
Instructions / Questions for Teacher

Clarify language

No hints at solutions

Avoid answer-getting game

Show students the situation and ask them to
formulate possible questions

Write the questions on a poster. This is
motivating particularly if you assign
authorship. Jose’s question…

Focus on the language of the mathematics
problem.
This is your time to think and to make sense of the
problem.

This time is essential for making sense of
the problem.
Think about…
What am I asking you to do?
What is 50?
What are ways to represent 50?

Solo time honors thinking.

The sound of individual thinking is silence.

Circulate enforcing silence and making
happy faces when pencils hit paper.
Is 50 odd or even? How do you know?
The Problem
[5 min]
We are going to watch a movie of a student
working on this question. Then, you will have time
to think about whether you agree or disagree with
the student in the movie and explain (with a
partner) why.
Remember you have to be convincing — you have
to convince me and your classmates.
Do you understand what I am asking you to do?
Intro
Solo Thinking
[Individual – 1
min.]
You won’t have time to finish solving the problem,
but you will need to explain your way of thinking
about the problem to your partner and possibly the
class later.
Now we need silence with pencil in hand, paper on
the table.
Solving
Answering the
question
[Pairs, table
10 min.]
Work in pairs to answer the question. Show your
thinking.
Remember, Alice can’t see what you are pointing
to when you point to something inside your head.
Write something down; draw something that will
help Alice see what you are thinking.
Use words, diagrams, pictures, examples, nonexamples, different representations.
Think-pair-share: Prompt social norms of listening to
each other by asking Alice what Alyssa thinks.
Model curiosity about and respect for the thinking of
others. Try to identify the different ways of thinking
in the class. Preserve the differences. Start thinking
about who can present each way of thinking. You
will have time for 3.
Insist on replacing hand waving with drawing
diagrams, writing things down, using labels, using
the language of mathematics to express yourself.
This is extremely valuable for developing fluency
with expressions, diagrams and other
representations.
Lesson
Structure
Instructions / Questions to Students
Discussing
With your partner make a poster to help others in
the class understand your thinking.
Decide with your partner who is going to say what.
Prepare a
presentation
[Pairs
5 min.]
Discuss
The preparation should be a focused team effort by
partners. Once the culture of partner work has been
established, partners can present to other partners
at tables, and then tables can prepare for the whole
class. Preparation means making a poster or
equivalent that can help make the thinking clear to
the class during the student presentation.
Someone listening to you and wanting to know what
you think is almost irresistible motivation to talk.
This is especially important for students who shy
away from mathematics.
Orchestrating discourse:
Presentations
[3 – 5 Pairs
15 min.]
Instructions / Questions for Teacher



Please listen carefully to ___ and ___.
Do they have a clear answer?
Do they convince you?
Whole class listens to and interacts with selected
presenters.
You model what someone does who wants to
understand the other person’s thinking. This is
important when that person is going through
something that might be confusing.
Lesson
Structure
Instructions / Questions to Students
What did we learn today?
Closure
[Whole class
10 min.]
Praise good habits: “That was easy for me to
understand.”
Who can summarize?
What do we need to learn next?
Closure
Instructions / Questions for Teacher
Highlight high value content: “Why did she just do
that?” or “Distributive property. 5 bonus points.
Thank you.”
Slow presenters down to make thinking explicit.
Thank each presenter by name.
Engage the whole class in questions.
Objective and focus is for all to understand the
thinking of each, including approaches that didn’t
work.
Make thinking explicit by drawing, with a marker,
correspondences across approaches.
Converge on mathematical target of lesson.