In today’s task you will continue investigating the case of the missing batteries. Today, you will explore a pack of 100 batteries. From each pack, the same quantity of batteries are missing. Students will need to determine the total number of full packs of 100 batteries that can be made.

In this task, students explore the context of decimal hundredths leveraging the hundred-frame model. You will notice that we are using the same model as day one, however now, each part within the ten-frame has been partitioned into ten, creating one-hundred parts altogether. It is important for students to understand this relationship, that one-hundredth is a tenth of one-tenth.

Or inversely, that one tenth is ten times greater than one-hundredth. When all hundred items are there, that would be equal to one whole pack of batteries. However, if one or more of those items are missing, we are again left with a fraction of a pack. Because the model is partitioned into one-hundred parts, the fraction can be represented using decimal notation. Using similar strategies that were revealed on day one, students will combine the partial packs in order to determine the total number of full 100 battery packs that can be made.

Some of the big ideas that may emerge through this task include:

• Fractions can be represented in a variety of ways;
• Fractions (and their decimal representation) represent values relative to a whole (for example, one whole pack);
• Quantities represented as a decimal are fractions limited to base ten denominators (i.e.: tenths, hundredths, thousandths, etc.);
• One tenth is one-tenth of one whole, one is ten times greater than one-tenth;
• One hundredth is one-tenth of one-tenth, one-tenth is ten times greater than one-hundredth;
• Multiplication can represent “groups of”, or multiple copies of the same quantity;
• Multiplication is an extension of counting, skip counting and repeated addition.

All tasks within this unit are intended to be completed without the use of a calculator to support reasoning and thinking.

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. Be sure to write down these noticings and wonderings on the blackboard/whiteboard, chart paper, or some other means to ensure students know that their voice is acknowledged and appreciated.

Some of the noticing and wondering that may come up includes:

• I notice a display of batteries.
• I wonder what store this is.
• I notice the battery brand is Power-Up.
• I notice there are different types of batteries and different quantities.
• I notice different prices.
• I notice that the bundle pack costs $29.99.
• I wonder how many batteries they are going to buy.

At this point, you can answer any wonders that you can cross off the list right away. For example:

• The store is (share the name of your local store).
• The person taking the video works at the store.
• They are going to restock this display.
• In particular, they are going to be restocking the bundle pack of AAA batteries.

Prompt students by stating:

How many batteries do you think are in the bundle pack of AAA batteries? Draw a model to represent your estimate.

The purpose of this prompt is to encourage students to visualize the array and an opportunity to build flexibility with multiplication.

After students have had an opportunity to share their models, reveal that the batteries are arranged 10 by 10 by sharing the following image.

Prompt students with the following story script:

The store clerk was restocking this product, and noticed that four of these 100 packs of batteries only had 55 of the advertised 100 batteries, or fifty-five-hundredths of a full pack.

The store manager agreed it would be unfair to sell packs with missing batteries and asked the clerk to use the four partial packs to make full packs of 100. How many packs of 100 batteries can he make?

In summary, we are asking students:

Four of these 100 packs of batteries only had 55 of the advertised 100 batteries, or fifty-five-hundredths of a full pack.

How many full packs of 100 batteries can be made with the four incomplete packs?

At this time, you may want to provide students with this copy of blank hundred frames that mirror the 100-pack of batteries.

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After you have consolidated the learning by making connections across different student approaches, share the following reveal video to confirm their solutions:

Here is the final frame of the reveal video:

Answer: 2.2 boxes.

Provide students an opportunity to reflect on their learning by offering this consolidation prompt 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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