Upon opening ten-packs of batteries, it appears that every pack only has 8 out of ten batteries. Each pack has eight-tenths of the total number of batteries per pack. Students will be encouraged to regroup the batteries in order to make full packs of ten batteries.

In this task, students explore the context of decimal tenths leveraging the ten-frame model. When all ten 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 left with a fraction of a pack. Because the model is partitioned into ten parts, the fraction can be represented using decimal notation. Students will then realize that they have multiple copies of that fractional pack to work with. They will be asked to determine the total number of full packs.

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.);
• 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 of a 10-pack of batteries with 2 batteries missing:

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 batteries.
• I notice it says 10 AAA.
• I see a “plus” and “minus” sign.
• I notice there are only eight.
• I wonder what happened to the other batteries.
• I wonder if the package is open.
• I wonder how much they cost.

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

• This is a ten-pack of AAA batteries.
• The brand is POWER-UP.
• They cost $14.99.
• The package is not open.

In the video, students will likely wonder how this package is not open, yet missing 2 batteries?

You might want to engage in a discussion about what may have happened here. It is possible that there was an issue at the factory where the batteries were put into packages and the manufacturer didn’t notice!

Prompt students by stating:

How can this particular pack of batteries be represented as a quantity?

Through this prompt, you are trying to ask purposeful questions to elicit the idea that the quantity can be represented as eight-tenths, or 8/10 or 0.8. If a whole pack has ten batteries, then the quantity in the pack shown on the video is less than a whole pack.

This discussion will create an opportunity to reveal that a decimal notation is a fraction with a unit fraction limited to base ten denominators. In this case, we are working with tenths.

Prompt students with:

Twenty of these ten-packs of batteries were purchased at the store. Each one had only eight out of the ten batteries that were promised in a full pack due to an error at the factory.

With these twenty packs of batteries that are only eight-tenths full, how many full packs of ten can you make?

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Show students the reveal video that is a replay of the consolidation silent solution video #1 that matches student approach #1:

Here is a screenshot of the final frame showing 16 full packs and 4 packs empty:

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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