Today, we will revisit the piggy bank. Students will notice that the meter now demonstrates a range from -2 to 2. This is because the piggy banker will be depositing coins into their bank, and also withdrawing. This will create an opportunity to explore separating subtraction (one of the subtraction structures), or possibly adding a negative (depending on how the student interprets the action and represents it symbolically).

Students will also observe the piggy banker depositing multiple coins at once, all coins of the same value. This will introduce the idea of multiplying by a whole number, and the use of brackets in standard notation.

In this task, students will continue exploring the relationship between fraction and decimals. Students have been adding decimals and fractions over the last two days, today we will introduce subtraction and multiplying by a whole number. This task should be completed without the use of a calculator. The introduction of multiple operators will incite a need for the order of operations.

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 dollar);
• Quantities represented as a decimal are fractions limited to base ten denominators (i.e.: tenths, hundredths, thousandths, etc.);
• Standard representation of coin values are expressed as decimal hundredths;
• Quantities can be represented using a variety of symbolic notations and maintain equivalence;
• When the order of operations is not considered, the solution can vary;
• The order of operations can be revealed through the context;
• Multiple expressions can be used to represent the same value;
• Removal subtraction of a positive value or adding the negative of that same value has the same result, i.e., 6 – 2 = 6 + (-2).

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 the same piggy bank.
• I notice a bar on the side, but it is different. Now it says -2 to 0 to 2.
• I notice that every time the person drops a coin, the bar goes up.
• And when they took a coin out, the bar went down. Below zero.
• I wonder if there was already money in the bank.
• I wonder what the black and the red mean.
• I wonder how much money is in the piggy bank.

At this point, you can answer any wonders that you can cross off the list right away. For this particular spark, you will want to keep most of the information hidden at this time. By sharing too much information, you may rob students of their thinking. You can confirm that the piggy bank was empty before the first deposit. 

After we have heard students and demonstrated that we value their voice, we can land on the same question that we explored on Day 1:

How much money is in the piggy bank?

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 spatial reasoning alone to try and come up with an initial estimate and to share it with their neighbours by trying to articulate why they believe their prediction is reasonable.

Consider asking students to think about a value that would be “too low” and a value that would be “too high” before asking for their best estimate in order to help them come up with a more reasonable estimate.

Let them chat with their neighbours and challenge them to an estimation duel or a math fight.

Monitor student thinking by circulating around the room and listening to the mathematical discourse.

Encourage students to use precise mathematical language. You will likely hear students discussing coins using the names of the coins (quarter, dime, nickel), as well as the number of cents. Based on the movement on the meter, pay close attention to the use of fractional language. For example, “I think the meter increased to one-fourth between 0 and 1”. Some students may also begin talking about positive and negative values. For example, “when the bar was above zero, it was black, but when it was below zero, it was red”. “I think the red means that they took money out, so it’s negative”.

After students had an opportunity to share their best guess, tell them that you will share some information with them that might help to refine their estimate.

Show students the following image:

Prompt students with:

Based on the meter readings for all seven transactions, determine the value of all of the coins deposited or withdrawn, and the total amount in the piggy bank.

Write a single equation to represent this scenario using decimal or fractional notation for the value of the coins.

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Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

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Show the following reveal video to empty the piggy bank and reveal the coins: 

Alternatively, you could show this reveal image:

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

Consolidation Prompt:

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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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