SINGING

Keep a steady beat in patterns of strong and weak beats

Keep a steady beat in patterns of strong and weak beats

MATH: OPERATIONS & ALGEBRAIC THINKING

Factors and Multiples

Factors and Multiples

Students will recognize Least Common Multiples and Greatest Common Factors in both sound and mathematical expressions.

- Students should have mastered the skills in Music Multiples lesson #1 (Skip Counting Patterns) and Music Multiples Lesson #3 (Multiple Families) for the multiples being studied. In the case of this example, they would need to be familiar with the multiples of 3, 6, and 12.
- Generate or display the visual graphic of the multiples being studied, i.e. 3, 6, & 12 in this example. (See Music Multiples Lesson #1)
- Have students perform one or more of the multiples using body percussion. Two or more multiples can be performed simultaneously.
- If desired, have a classroom percussion instruments highlight the last beat of each body percussion set, i.e. triangle plays on every multiple of 3, tambourine on every multiple of 6, and drum on every multiple of 12. Listen for patterns in the sounds.

Repeat steps 3-4, adding the following elements from Music Multiple Lesson #2 (Multiple Families) for each multiple being performed:

- One or more students make one tally mark for each completed body percussion pattern. If you are doing more than one multiple at time (i.e. 3’s and 6’s and 12’s), then have one student make tally marks for the 3’s and another make tally marks for 6’s and another for the 12s. Or you may do the activity three times, once for 3’s and another time for 6’s, and another for 12s, as long as you stop on the same number each time.
- The class watches the teacher to signal when to stop counting.
- The teacher gives the stop signal exactly when one of the common skip counting numbers is spoken and writes that number on the board or document camera display.

Depending on time allotted for the lesson, do one of the following activities:

- Look for patterns among multiples of the various factors and discuss the patterns, linking them to the terms LCM or GCF, or
- Students can use the numbers generated by this activity (number of beats in the body percussion pattern, number of tally marks, and the number on which they stopped counting) as members of factor fact families to generate mathematical expressions or representations. They must be able to identify what each number in their expression represents. This process must be completed for each multiple (i.e. 3’s, 6’s and 12’s) so the factor families of the various numbers can be compared so that patterns can be discovered.

- Depending on the specific objectives of the lesson, the teacher may choose to have students explore as many written representations as possible or focus on representing specific concepts.
- Enjoy singing or listening to the music again while performing the body percussion.

Note: It may be instructive to repeat the activity with a number that is not as closely related, such as 5, to contrast the patterns. In that case it would be necessary to use different music for the pattern in 5.

- INTEGRATION INFORMATION
- ESSENTIAL QUESTIONS
- DIFFERENTIATION
- VOCABULARY
- HISTORICAL ELEMENT
- ASSESSMENT STRATEGIES
- OTHER INFORMATION

This lesson builds on the fundamental relationships of equal units and repeated patterns in both music and math that were explored in Lesson #1. If students regularly practice the body percussion skills learned in that lesson as applied to a variety of numbers, then they will be fluent in multiples and these follow-up lessons will be exceptionally efficient and effective. The body percussion practice can be tucked into little snippets of classroom time or incorporated into daily classroom routine as a transition activity.

What relationships can be found among the different factors and multiples being studied?

Choose music that is at a tempo that the students are able to perform accurately. Being too fast or too slow can make it difficult for children. It is also important that the beat maintain a steady tempo, or speed.

This lesson can also be adapted for use by individuals or small groups to meet individual needs.

This lesson can also be adapted for use by individuals or small groups to meet individual needs.

- Beat
- Rhythm
- Meter
- Multiples
- Factor
- Product
- Dividend
- Divisor
- Quotient
- Least Common Multiple (LCM)
- Greatest Common Factor (GCF)

Historical content of each lesson will vary according to the music used.

MUSIC:

Students’ accurate performance of the body percussion patterns without rushing (speeding up).

MATH:

Accurate identification of Least Common Multiples and/or Greatest Common Factors.

Students’ accurate performance of the body percussion patterns without rushing (speeding up).

MATH:

Accurate identification of Least Common Multiples and/or Greatest Common Factors.

This lesson can be taught well in a short period of time if students are fluent in the skills and concepts in the previous Music Multiple lessons. It will be most effective if students have frequent, enjoyable, ongoing practice with performing the patterns in Lesson #1.

- One or more recordings of music at a steady tempo in meters that match the factors being studied.
- Music playback equipment
- White board or document camera
- Optional: simple percussion instruments to emphasize the skip counting numbers.