##
* *Reflection: Developing a Conceptual Understanding
Two Digit Numbers: Even or Odd? - Section 2: Introduction to New Material

In years past, I might have simply told students "when you are trying to find out whether a two-digit number is even or odd, just look at the ones place." However, now as I am working to help my students gain a deeper conceptual understanding (MP7), I push students to determine this rule on their own (MP1). I also encourage students to be able to explain WHY this rule exists instead of just memorizing a new "trick". Additionally, for students who are struggling to understand, they will walk away with a greater conceptual understanding regardless because they will be able to hear their classmates struggle to identify this rule. It is okay for students to think hard and struggle and it's okay for some of them to walk away still working to grasp the conversation during the independent practice. These deep, meaningful conversations help students to deeply internalize the concepts and to gain new strategies for solving problems and thinking about numbers.

*Allowing Students to Struggle*

*Developing a Conceptual Understanding: Allowing Students to Struggle*

# Two Digit Numbers: Even or Odd?

Lesson 2 of 4

## Objective: SWBAT explain whether two-digit numbers are even or odd.

*40 minutes*

#### Introduction/Hook

*5 min*

*Yesterday we talked about what makes numbers either even or odd. We discussed u sing a ten frame to decide whether a number is even or odd. However, we only looked at single-digit numbers. Right now, I want you to help me decide whether 12 is an EVEN or an ODD number. You may use the cubes at your desk, your white board, and/ or a ten frame.*

As students work, I circulate to discover what strategies they are using (using cubes to make equal groups of two, drawing two ten frames, looking only at the ones place,etc.) and to catch any common misconceptions.

#### Resources

*expand content*

#### Introduction to New Material

*15 min*

*Now that you have worked on your own, I want you to share with the group whether 12 is even or odd AND how you know. *

I Invite students to come forward and share what they think. Some students may share that they know 12 is even because they created equal groups of 2 and found that there was no "odd one out". Others might indicate that they drew ten frames. Others might say that they counted by twos. There is no right answer for how students figured out the problem and allow ever student ample time to share their strategy.

Depending on overall student mastery, I either have students work on another problem independently or do another problem as a class.

I ask students: **is 15 odd or even? **

When they have finished working, I have one or two students share their answer and their strategy.

Then I ask students: ** is 5 an even or an odd number? **

Students should be able to identify that 5 is an odd number.

*So both 15 and 5 are odd numbers. *

This would also be a good time to use the same ten frames we used yesterday--students will see that 15 is made up of 10 and 5. Since ten is even they only need to look at the "leftovers" (5).

*Let's look at 12. We know that 12 is an even number. Is 2 an even or odd number? *

Students should be able to identify that 2 is an even number.

**Turn and Talk: What pattern do we notice when we look at these numbers?**

Some students might struggle to notice that they need to look at the ones place in order to identify whether a number is even or odd--allow them to think carefully about what pattern is present and struggle with not knowing.

I allow any student who has identified a pattern to share out.

I push students to consider the pattern more deeply by asking them: *Do you think 22 is an even or odd number? How about 32? How do you know? *

*So, I know that both 15 and 5 are odd and both 12 and 2 are even. I think this might mean that I only need to look at the ones place to determine whether a number is even or odd. Why do you think that might be? *

If students are struggling to determine why this rule holds, encourage them to think about whether ten is an even or odd number. Students should be able to identify that since 10 is always even, they only need to look at the ones place.

#### Resources

*expand content*

#### Guided Practice

*5 min*

*Now, we are going to do a few practice problems on our white boards. I am going to write a number on the board and I want you to use your white board to determine whether that number is EVEN or ODD. *

I show between 2 and 6 two-digit numbers. After each number, have one student share their work. For students who are struggling, I support them by circulating and reminding them of what we discussed during the independent practice.

*expand content*

#### Independent Practice

*10 min*

Independent Practice differentiated base on proficiency with this subject (I use yesterday's independent work or mastery during guided practice to determine groupings).

**Group A: In need of intervention**

Students in group A will determine whether numbers 8-20 are even or odd using cubes, white boards, and/or counters. Having a concrete representation of the numbers will allow them to more deeply understand whether numbers are even or odd. NOTE: Do not have students in group A only look at the ones place if they cannot explain why they are only looking at the ones place.

**Group B: Right on track! **

Students in group B will determine whether numbers 10-30 are even or odd. They can use a ten frame and/or a white board to help explain their thinking.

**Group C: Extension**

Students in group C will determine whether numbers 10-50 are even or odd. Since these students will likely have a more abstract understanding of the concepts, they will not use manipulatives. During my time with this group, I will also work with them to discuss counting by 2s as a way to determine whether a number is even or odd.

#### Resources

*expand content*

#### Closing

*5 min*

*In order to show what we know, we are going to work on an exit ticket. Work silently on your exit ticket so I can tell exactly what you know. *

As students work, circulate to determine student mastery. I will use these exit tickets to determine my A/B/C groupings for independent work tomorrow.

#### Resources

*expand content*

I like this lesson and will use it for my students, with few variations. However, I believe the resources you posted here are not for this lesson.

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