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Clap Counting with Multiples
Students will be able to identify the least common multiple of two numbers.
- Ask students if they know what a multiple is.
- Explain that a multiple is a number that can be divided evenly by another number, with no remainder. "For example, 15 is a multiple of 5, because 15 divided by 5 is 3. 49 is a multiple of 7, because 49 divided by 7 is 7."
- Write the number 5 on the board. Say several numbers and ask students to give you a thumbs up or a thumbs down if the number is a multiple of 5.
- Tell students that today they will be finding the least common multiple of two numbers. Explain that this will be an important skill for working with more difficult fraction problems in the future.
Explicit Instruction/Teacher modeling(10 minutes)
- Ask students what "least" means. Explain that least means the item with the smallest value.
- Ask students what "common" means. Explain that common means when something belongs to two or more values. Give some examples of the concept of "common."
- Tell students that when we find the least common multiple, we find the smallest multiple that two numbers have in common. In order to do this, we must first list several multiples of each number.
- Write the number 3 on the board. Have students help you list the multiples. Remind them that in order to come up with the multiples, they can either count by 3s or use multiplication.
- After listing several multiples of 3, write the number 9 on the board. Have students help you list the multiples of 9.
- Show students how to underline the multiples that are common, and then circle the one that is the smallest.
- Students should see that 9 is the least common multiple.
- Repeat this exercise at least one more time with different numbers, such as 4 and 6.
Guided Practice(15 minutes)
- Have students stand up and create a circle around the classroom.
- Explain that they will be doing something called "clap counting."
- The teacher will give a number. Students will take turns counting up by one.
- If a student's number is a multiple of the given number, they will clap instead of saying the number. The next person will continue counting up. For example, if the number three were given, the sequence would be as follows: one, two, clap, four, five, clap, seven, eight, clap, etc. The sequence will continue until all students have said a number or clapped.
- Complete this exercise several times with various numbers.
- Have students sit back down and work with a partner and distribute scratch paper to them. Give them two sets of numbers of which to find the least common multiple. Instruct students to write down the multiples of the two numbers assigned to them. Students should do "clap counting" with each number as they list the multiples. Remind students to underline all common multiples and circle the least common multiple.
- Review partner work as a class.
Independent working time(15 minutes)
- Hand out the Least Common Multiple: Easy worksheet.
- Circulate the room as students are working.
- Review the answers to the worksheet when students are finished.
- Encourage these students to use repeated addition if they are having difficulty coming up with some of the multiples. You could also have these students write out each multiplication problem to show the multiples.
- Students who finish the worksheet quickly can work on the Least Common Multiples: Hard worksheet (see optional materials).
- Distribute index cards to students and instruct them to list the multiples of 3 and 5. Then have them circle the least common multiple.
- Collect the index cards to check for students' understanding.
Review and closing(5 minutes)
- Complete one more round of "clap counting."
- Remind students that the skill of finding the least common multiple will come in handy as they begin solving more complex fraction problems!