Exploring patterns

What do you notice about the following numbers?

Did you notice any patterns in the groups of number given?

Using factors and multiples to solve problems

In this learning activity we will be using Greatest Common Factor (GCF) and Lowest Common Multiple (LCM) to solve problems.

When we compare the factors of two different numbers such as 12 whose factors are: 1, 2, 3, 4, 6, 12 and 16 whose factors are: 1, 2, 4, 8, 16, we look at both sets of factors and determine which is the largest factor. In this case, that is 4. That means the GCF (Greatest Common Factor) is 4.

When we compare the first 7 multiples of two different numbers such as 2, whose first 7 multiples are 2, 4, 6, 8, 10, 12, 14, … and 3, whose first 7 multiples are 3, 6, 9, 12, 15, 18, 24… we find the first number that appears in both lists. In this case, that would be 6. That means the LCM (Lowest Common Multiple) is 6.

Funfair activity

Part A

Ms. Keyoto’s Grade 7 class is helping with the School and Community Fun Fair. They are having a barbecue and selling burgers. They hope to sell at least 120 burgers.

The students need to buy supplies for the barbeque. Burger patties are sold in boxes of 6 and the buns are sold in packages of 8.

How many packages of buns and boxes of patties do the students need to purchase so they don’t have any leftover buns or patties?

How many complete burgers can they make?

Record your strategies and responses in an audio recording, on paper, digitally, or in a notebook.

Part B

The Grade 7 and 8 students helping with the barbecue need to be divided into helper groups so that tasks can be divided. The more groups there are, the better the tasks can be divided.

The Grade 7s have 16 students that need to be equally divided into the helper groups. How many different groupings can be made?

The Grade 8s have 24 students that need to be equally divided into the helper groups.

What is the maximum number of helper groups that can be formed?

What other size groups can be formed?

Record your strategies and responses in an audio recording, on paper, digitally, or in a notebook.

Reflecting back

When we needed to determine the number of packages of burgers and buns to buy, we used our understanding of multiples to help us calculate the correct number of each for the Funfair. Then we applied our knowledge of common factors to help us create groups to divide the Funfair tasks.

Which strategy will you choose to help you solve these two scenarios?

Choose one of the following scenarios to complete.

1. Two grade 7 student helpers are decorating for the barbecue and are hanging balloons on the fence surrounding the school yard. The balloons come in their school colours of white and orange and some of the balloons are star-shaped! They decide to create a pattern with the balloons: every 5th balloon is going to be orange and every 7th balloon is going to be a star shape. How many balloons will they need to hang until they reach an orange star balloon in their pattern? Show your work in whatever representation is best. Explain your thinking.

2. The next day, Ms. Keyoto wants to treat the class for all their dedicated work organizing the fundraiser barbecue with some cupcakes and cannoli from the local bakery. The bakery prepares boxes with mixed pastries in them. That morning 84 cannoli and 120 cupcakes were made. How can the baker fill the greatest number of boxes, so that each box has the same number of cupcakes and the same number of cannoli? This does not mean any box has the same amount of cupcakes and cannoli.

Let’s practice

1. What is the difference between a factor and a multiple of a number? Use an example to show your thinking.
2. A radio station you listen to is giving out prizes in the next 5 minutes. Every 5th caller wins a music gift card. Every 7th caller wins tickets to an upcoming concert. You are the first caller to win both prizes. What caller number are you?

Reflection

As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.

Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.

When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.

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