## Least Common Multiples (Word Problems)

### Timothy Mark DillehayLee County School District

#### Description

Students cooperatively complete several real world problems using Least Common Multiples and sequencing. Creativity and understanding are used to finalize the packet with a student made real world problem.

#### Objectives

Applies special number relationships such as sequences and series to real-world problems.

#### Materials

-LCM Teacher (1 copy needed)
-LCM Student (1 copy per student)

#### Preparations

1. Have the LCM Student packets photocopied and stapled together. (1 for each student)
2. Have one copy of the LCM Teacher printed out.
3. Pre-Read the LCM Teacher printout.

#### Procedures

1. Teacher says, “ Have you ever wondered how some of the word problems could be answered using a set pattern? Have you ever wondered when LCM’s (Least Common Multiples) will be used in every day life? Today we are going o investigate the answer to both of these questions.”

2. Teacher says, “ Let me ask you this question. Do not blurt out an answer, but write you answer on a scrap paper, and be ready to explain how you got your answer.
If the work whistle blew every 10 minutes (allowing you to punch your time clock and quit working for the day), but the exit gate only opens every 12 minutes, when would be the first time the workers could leave the job?

3. Wait until it appears that most students have answered the question. Take volunteer answers. Accept all answers, probing to find out how the student came to that answer. Even after you have heard the correct answer, ask for others students to give their answer, and have them explain how they got to that point. (even if they say,’the same way she did’)

4. Teacher says, "Let me ask you a more difficult question. Do not blurt out an answer, but write you answer on a scrap paper, and be ready to explain how you got your answer."

If the work whistle blew every 9 minutes (allowing you to punch your time clock and quit working for the day), but the exit gate only opens every 13 minutes, when would be the first time the workers could leave the job?

5. Teacher says, “Since the numbers meet at a more complex number, it may be easier to get the answer using a particular method.”

6. Wait until it appears that most students have answered the question. Take volunteer answers. Accept all answers, probing to find out how the student came to that answer. Even after you have heard the correct answer, ask for others students to give their answer, and have them explain how they got to that point. (even ,’the same way she did’)

8. Have students give answers to Cookies. Make statements of explanation and demonstrating when needed.

10. Have students give answers to Ride. Make statements of explanation and demonstrating when needed.

11. Continue by instructing students to read alone Father of the Bride.

12. Have students give answers to Father of the Bride. Make statements of explanation and demonstrating when needed.

13. Have students break in to groups of two to read and answer Cabins in the Woods.

14. Have students give answers to Cabin in the Woods. Make statements of explanation and demonstrating when needed.

15. Ask students to work alone to answer Cabin in the Woods if each guys cabin could now hold nine campers each.

16. Have students break in to different groups of three to read and answer the next two questions. The one about pizza and testing .

17. Have students give answers to these two questions. Make statements of explanation and demonstrating when needed.

18. Collect all LCM Student packets.

#### Assessments

Note: This lesson assesses focuses on the skill of LCM.

Use completed “LCM Student” packet (associated file) to formatively assess the student’s ability to use Least Common Multiplies to answer word problems.
Acceptable work is both:
(1) at least 80% correct work packet.
(2) class participation in cooperative groups.

#### Attached Files

LCM Teacher.     File Extension: pdf

LCM Student.     File Extension: pdf