# Explaining odd and even

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## Objective

SWBAT use words to explain why a number is even or odd.

#### Big Idea

In this lesson students use their place value knowledge and their conceptual understanding of even and odd numbers to use words to explain why a number is even or odd.

## Introduction/Hook

10 minutes

I post a problem of the day on the board:

Anthony has 12 rocks in his rock collection.  Does he have an even or odd number of rocks in his collection?

How do you know?

Hand out white boards to students and allow them to figure out if 18 is even or odd AND to write how they know.

## Introduction to New Material

10 minutes

Today we are going to work on explaining WHY a number is odd or even.  When we write about whether a number is even or odd, we can use the following criteria for success to help us (you can post the criteria for success on an anchor chart or write it on the board).

My Excellent Mathematical Explanations Need:

__Mathematical vocabulary (even, odd, multiple, partner, pair, equal groups)

__How do you know?  (Key word: because)

__A capital letter at the beginning of the sentence and a period at the end of the sentence.

Let's read some responses and decide whether they are excellent mathematical explanations.

(You can use your student's explanations from the hook or you can use explanations below )

Explanation 1:

I know that 18 is even.

﻿Turn and Talk: Is this an excellent mathematical explanation?  How can you make it more excellent?

Students should be able to indicate that this explanation is not good enough because it does not use mathematical vocabulary nor does it explain WHY 18 is even.

Explanation 2:

I know 18 is even because I can make equal groups of 2 with 18.﻿

﻿﻿Turn and Talk: Is this an excellent mathematical explanation?  How can you make it more excellent?

This response uses mathematical vocabulary, explains why, and has a capital letter and a period.  It meets all expectations.  However, push students to ask themselves what they could do to make this response better or clearer.

## Guided Practice

10 minutes

Now I am going to give you a chance to use this criteria for success to write your own explanations. Make sure that you are checking the criteria for success to determine whether your response is an excellent mathematical explanation.

I hand out the worksheet. As students work, circulate to determine any common trends and to remind students to use the checklist.

When finished, I bring students back together and hand each student a blank checklist. Have students sit with partners on the rug.  Have the students read their writing to each other and grade each others work.  (If your students are not used to grading each others' work or using a checklist, have one partner model before you begin this activity!)

Finally, I instruct each partner to give the following feedback (in writing at the bottom of the checklist, or verbally)

I liked the way that you....

Next time, remember to....

## Independent Practice

10 minutes

Now you are going to work independently on another explanation.  As you work, remember the feedback that  your teammate gave you.

During independent practice, I pull the students who have struggled the most with their explanations to the rug and work with them to craft clearer explanations.  This small group instruction might include (1) modeling how to make equal groups (2) Drawing ten frames to demonstrate odd/even, or (3) modeling how to write an "ideal" explanation, (4) going through the check list with students as they write their own responses.

## Closing

5 minutes

Today we have worked on crafting excellent mathematical explanations using our criteria for success. Before we end our math block, I would like for two students to read their explanations aloud so that every one can hear what you have been working on.

I pick two students, have them read aloud and give feedback as necessary or ask other students to give feedback.