Students will explore the relative frequency of different jelly bean flavours found in one bag of jelly beans. 

In this task, students will be introduced to a relative frequency table. They will use the table to compare different quantities of jelly bean flavours relative to the entire bag of jelly beans. In today’s task, we will start the notice and wonder with a bag of 100 jelly beans. This will allow students to make connections between fractions and percent. In the productive struggle, the bag will contain 20 jelly beans only. This will require students to reveal a rate or scale the ratio in order to determine relative frequency out of 1 or 100%.
Some of the big ideas that may emerge in today’s task include:

• Frequency is the number of times a category or event occurs within a data set. 
• A relative frequency table shows each category expressed as a fraction of the total quantity or frequency.
• Relative frequency can be represented using fractions, decimals, or percents. 
•  Fractions, decimals, and percents can all represent relationships to a whole.
• The sum of the relative frequencies is 1 or 100%

Show students the following video:

Then, ask students:

What do you notice?
What do you wonder?

Give students 60 seconds (or more) to do a rapid write on a piece of paper.

Then, ask students to share with their neighbours for another 60 seconds.

Finally, allow students to share with the entire group.

Some of the noticing and wondering that came up in a class recently included:

• I notice a bag of jelly beans.
• I notice there are a lot of jelly beans.
• I notice different colours.
• I wonder what flavour they are.
• I wonder how many there are of each colour.
• I notice that there are more blue jelly beans than any other colour.

At this point, you can answer any notices and wonders that you can cross off the list right away.

Next, share the following short animation or visual prompt and ask the following question:

The red jelly beans make up what fraction of the entire bag of jelly beans?  

Without counting, make an estimate.

We can now ask students to make an estimate (not a guess) as we want them to be as strategic as they can possibly be. This will force them to use reasoning to try and come up with a reasonable fraction.

Monitor student thinking by circulating around the room and listening to the mathematical discourse. Encourage students to use precise mathematical language and listen for the use of both fractional language and percent to describe the quantity of red jelly beans relative to the whole. Some students will likely communicate the fractional amount out of 100 jelly beans. Others may determine that red represents one fourth of the bag. This is an opportunity to discuss equivalence. 

Allow students to share their estimates with neighbours first, then with the class. Write down their estimates on the chalkboard/whiteboard/chart paper so students feel their voices are being heard and so they feel they have a stake in solving this problem.

Share the following animation.

Discuss the information shared in this relative frequency table about the red jelly beans. Relative to all 100 jelly beans in the bag, red makes up one-fourth of the bag, or 25% of the 100 jellybeans in the bag. When determining relative frequency, it is helpful to think of the whole as 100. Luckily in this scenario, there are 100 jelly beans in the bag.

Encourage students to discuss how they would complete the table for the other colours in the bag. 

Since you have already taken some time to set the context for this problem and student curiosity is already sparked, we have them in a perfect spot to help push their thinking further and fuel sense making.

Share the following silent animation.

You can verbally share the following prompt with students:

Complete the table to display the number of each colour of jelly bean relative to the total number of jelly beans in the bag. 

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Show students the following reveal video:

Provide students an opportunity to reflect on their learning by offering these consolidation prompts to be completed independently.

Consolidation Prompt #1:

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Consolidation Prompt #2:

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We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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