T4T Odds & Evens
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Lesson excerpt:
NC Mathematics Standard:
Work with equal groups of objects to gain foundations for multiplication.
NC.2.OA.3 Determine whether a group of objects, within 20, has an odd or even number of members by:
· Pairing objects, then counting them by 2s.
· Determining whether objects can be placed into two equal groups.
· Writing an equation to express an even number as a sum of two equal addends.
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others..
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Student Outcomes:
- I can write an equation to show that a number that is doubled has an even sum.
- I can explain why two even numbers have an even sum and why two odd numbers have an even sum and why an odd and even have an odd sum.
Materials:
- Odds and Evens gameboard (one for partners)
- Paperclip and pencil to use as spinner or a clear spinner to use on top of the gameboard
- Pencil to record on gameboard
- Color tiles or grid paper for students needing additional instruction
- Two of Everything by Lily Toy Hong
- Chart paper or a way to display the chart, marker
- Index cards with 1+1=, 2+2=, 3+3=, etc. to 10+10, one card for each set of partners
- Color tiles or grid paper to model
Advance Preparation:
Thinking:
Students will need to have an understanding of odd and even numbers and know addition “doubles”.
Materials:
Gameboards would need to be copied, index cards created, and materials listed above collected prior to this lesson.
Directions:
- Read Two of Everything to the class. Chart what happens when something is put in the pot. For example, if 3 of something goes in the pot, then how many come out? 3+3=6. Continue this with at least five examples.
- Give partners an index card with 1+1= or 2+2= or 3+3=, etc. Ask partners to find something or think of something in the real world that represents their equation. For example, 1+1= a pair of shoes, 4+4= the legs on an octopus (4 on each side), 5+5= the number of cents in a dime (nickel plus nickel)
- Bring the cards back to the group and share the “doubles” found. Ask students about the sums. Do you notice what happens when you add two equal addends? Why do you think this happens? Brainstorm with the class and model with color tiles by creating rectangles to “prove” this concept.
- Introduce the game Odds and Evens to the class by the teacher playing the game against the class. One player is Even Steven and one player is Odd Rod, each player spins one spinner and the two addends are added together. If the sum is even Steven records it by writing the equation on a blank sheet of paper or in their math journal, and then writing the sum in the box under Even Steven. If the sum is odd Rod records it by writing the equation on a blank sheet of paper or in their math journal, and then writing the sum in the box under Odd Rod and the number goes to Rod. The first player to fill all the blanks is the winner.
- While the students are playing, the teacher should rotate around the room and see if students are starting to notice what is happening when an even and an even are added together, odd and odd, even and odd? Ask students if they played again if they would like to be Even Steven or Odd Rod and why.
- After playing discuss the game and the generalizations students were able to construct about even and odd numbers and what happens when you have two equal addends. As students share what they learned, the teacher could chart their ideas such as “odd + odd = even, odd+ even= odd, even + even = even.”
Questions to Pose:
Before:
What do you know about “doubles” facts?
How do we know if a number is odd or even?
During:
What have you noticed about the sums you are getting while playing the game?
What happens when you add two equal addends? Why do you think this happens?
Are you starting to notice what is happening when an even and an even are added together, odd and odd, even and odd?
If you played again would you like to be Even Steven or Odd Rod? Why?
After:
As a whole group discuss the questions listed above and focus on what student learned about odd and even addends.
Possible Misconceptions/Suggestions:
Possible Misconceptions |
Suggestions |
Students may think an odd and an odd will equal an odd. |
Show students a rectangle made with color tiles of an odd number and make another rectangle of an odd number then match the two odd tiles together so that it becomes even. |
Students may think an even and odd will equal an even. |
Repeat the task above using an odd and even number so students can see that you still have an odd tile left over. |
Special Notes:
This task addresses the second part of the standard. This task would need to come in a progression of lessons where an understanding of grouping to create an odd or even number has already been taught.
This standard asks that students understand that two equal addends have an even sum, therefore, an extension of this lesson would be for students to understand why an even number and an odd number have an odd sum but this is not addressed in the standard.
Solutions: N/A