Common Multiples: IM 6.7.17
[url=https://im.kendallhunt.com/MS/teachers/1/7/17/preparation.html]“Common Multiples”[/url] from IM Grade 6 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 6.7.17
- IM 6.7.17 Lesson: Common Multiples
- Practice 6.7.17
- IM 6.7.17 Practice: Common Multiples
IM 6.7.17 Lesson: Common Multiples
What do you notice? What do you wonder?
A florist can order roses in bunches of 12 and lilies in bunches of 8. Last month she ordered the same number of roses and lilies.
If she ordered no more than 100 of each kind of flower, how many bunches of each could she have ordered? Find all the possible combinations.
What is the smallest number of bunches of roses that she could have ordered? What about the smallest number of bunches of lilies? Explain your reasoning.
The least common multiple of 6 and 8 is 24.
What do you think the term “least common multiple” means?
Find all of the [b]multiples [/b]of 10 and 8 that are less than 100. Find the least common multiple of 10 and 8.
Find all of the multiples of 7 and 9 that are less than 100. Find the least common multiple of 7 and 9.[br]
What is the least common multiple of 10 and 20?
What is the least common multiple of 4 and 24?
In the previous two questions, one number is a multiple of the other.
What do you notice about their least common multiple?
Do you think this will always happen when one number is a multiple of the other? Explain your reasoning.
[size=150]Lin’s uncle is opening a bakery. On the bakery’s grand opening day, he plans to give away prizes to the first 50 customers that enter the shop. Every fifth customer will get a free bagel. Every ninth customer will get a free blueberry muffin. Every 12th customer will get a free slice of carrot cake.[/size][br][br]Diego is waiting in line and is the 23rd customer. He thinks that he should get farther back in line in order to get a prize. Is he right? If so, how far back should he go to get at least one prize? Explain your reasoning.
Jada is the 36th customer.[br]Will she get a prize? If so, what prize will she get?
Is it possible for Jada to get more than one prize? How do you know? Explain your reasoning.
How many prizes total will Lin’s uncle give away? Explain your reasoning.
IM 6.7.17 Practice: Common Multiples
A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time?
A red light blinks every 12 seconds and a blue light blinks every 9 seconds. When will both lights blink at the same time?
Explain how to determine when 2 lights blink together.
List all multiples of 10 up to 100.
List all multiples of 15 up to 100.
What is the least common multiple of 10 and 15?
Cups are sold in packages of 8. Napkins are sold in packages of 12.
What is the fewest number of packages of cups and the fewest number of packages of napkins that can be purchased so there will be the same number of cups as napkins?
How many sets of cups and napkins will there be?
Plot and connect these points to form a polygon. (-5, 3), (3, 3), (1, -2), (-3, -2)
Find the lengths of the two horizontal sides of the polygon.
Rectangle ABCD is drawn on a coordinate plane. A = [math](-6,9)[/math] and B = [math](5,9)[/math]. What could be the locations of points C and D? You can use the applet below to help you.
A school wants to raise $2,500 to support its music program.
If it has met 20% of its goal so far, how much money has it raised?
If it raises 175% of its goal, how much money will the music program receive? Show your reasoning.