Grade Five Lesson Plan: What Makes a Number Odd or Even?


 Geoffrey Preston
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1 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
2 Language goals 3. Attend to precision 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; nonbold 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 wholeclass discussion, students show their different representations of the number 50 and explain their answers.
3 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
4 INTRO 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. Multiple strategies multiple representations. Instructions / Questions for Teacher 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.
5 Intro The Problem [5 min] Is 50 odd or even? How do you know? 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. Clarify language No hints at solutions Avoid answergetting game Show students the situation and ask them to formulate possible questions Remember you have to be convincing you have to convince me and your classmates. Do you understand what I am asking you to do? 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. Solo Thinking [Individual 1 min.] Think about What am I asking you to do? What is 50? What are ways to represent 50? 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. Solo time honors thinking. The sound of individual thinking is silence. Circulate enforcing silence and making happy faces when pencils hit paper. Now we need silence with pencil in hand, paper on the table.
6 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. Thinkpairshare: 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. Use words, diagrams, pictures, examples, nonexamples, different representations. 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.
7 Discuss Discussing Lesson Structure Instructions / Questions to Students Instructions / Questions for Teacher Prepare a presentation [Pairs 5 min.] 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. 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: Whole class listens to and interacts with selected presenters. Presentations [3 5 Pairs 15 min.] Please listen carefully to and. Do they have a clear answer? Do they convince you? 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.
8 Closure Lesson Structure Closure [Whole class 10 min.] Instructions / Questions to Students What did we learn today? Who can summarize? What do we need to learn next? Instructions / Questions for Teacher Praise good habits: That was easy for me to understand. 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.
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