### Timothy Mark DillehayLee County School District

#### Description

Students complete a roll playing activity to build understanding of number concepts. Students use 'Algebraic Closure' throughout six operations to better comprehend and review basic number theory.

#### Objectives

Selects and justifies alternative strategies, such as using properties of numbers.

#### Materials

- Chalk and chalk board.
- "Closure Math" one for each student
- Tape for taping off small area on floor.
- One "Definitions" sheet.
- Optional overhead from step #13 in procedures.

#### Preparations

1. Tape of an area on the floor for approximately 10 students to stand in.
2. Photocopy a "Closure Math" worksheet for each student.
3. Chalk board area for students to write definitions.
4. One copy of the word document "Definitions".
5. Optional: prepare overhead that is mentioned in the procedure (step 13).

#### Procedures

1. Teacher sections off a circle on the floor using tape. (Can hold up to 10 standing students)

2. Teacher chooses one student is wearing glasses to come stand in the circle. “____ you have on glasses, could you come stand in my circle?”

3. Teacher then chooses a second student wearing glasses to join the first student in the circle.

4. Teacher says, “I would like my circle to have closure under the operation of wearing glasses.

5. Teacher ask, ” Could someone in the class tell me the name of a student I should have join the circle?” Teacher calls on all students.

6. Teacher continues to accept only those people wearing glasses into the circle.

7. Teacher “Thank you, you may be seated, Now we are going to do another. Would ______ please come stand in the circle? (The teacher has selected a student who has a particular characteristic about him; i.e. earring, no socks, wearing red.)

8. Teacher now asks for a second student to join him. The student has the same characteristic.

9. Teacher ask the two students in the taped circle, ‘ Give me a name of a student who should join you.’

10. The teacher allows only students who have that particular characteristic to join the circle.

11. Teacher ,”Could someone please repeat this next sentence, while replacing the blanks ? “I would like my circle to have closure under the operation of blank.”

12. Teacher, ”This exercise can help us understand closure for numbers under certain operations.”

13. Have students begin to take notes. Reveal the overhead one question at a time, or write on the board steps 14-16.

14. Does addition have closure within the even numbers?
This means when you add one even number with another even number, do you always get an even number? If you said no, what example shows you that it doesn’t?

15. Does addition have closure within the odd numbers ? This means when you add one odd number with another odd number, do you always get an odd number? If you said no, what example shows you that it doesn’t?

16. Does division have closure within the integer numbers? This means when you divide one integer with another integer do you always get an integer? If no, what is the example that shows you it doesn’t?

17. Teacher distributes the 'Closure Math' Worksheet.

18. While the students are completing the worksheet, have an area on the board for students to write definitions of sets. When a student ask what a set is, have them use the Number Set reference sheet to write on the board what that sets definition is. Students may question what other sets of numbers are called; i.e. real, decimals.

19. Collect the worksheets for final assessment.

#### Assessments

Use completed "Closure Math Worksheet" to assess the student's ability to determine if a particular set of numbers maintains closure under a given operation. Acceptable work is no more than 5 incorrect answers from the worksheet.

#### Attached Files

The following document includes 'Closure Math, Answers, and Definitions'     File Extension: pdf