Students will predict how long it will take for a candle to burn out completely.

In this lesson, students will collect and organize two-variable data in order to make predictions based on the relationship between the variables. We will emerge the idea of correlation and in particular, linear correlation through the context of a burning candle over a period of time to predict when it will burn out. 

Some of the big ideas that may emerge through this problem based, real world math lesson include:

• A relationship can exist between two (or more) varying quantities.
• Observing how one quantity behaves as another quantity changes can help us determine if the quantities are related.
• Quantities that can change (or vary) are called variables.
• If a cause and effect relationship is observed between two variables, the variable causing the change is known as the independent variable while the variable experiencing the effect of the change is known as the dependent variable.
• While constructing a table to compare the change in the independent variable has on the dependent variable can be helpful, constructing a graph known as a scatter plot or line plot can provide an opportunity to make visual predictions leveraging a line of best fit (or curve of best fit). 
• Making predictions within the domain and range of the given set of data is known as an interpolation.
• Making predictions outside the domain and range of a given set of data is known as an extrapolation.
• Relationships that appear to follow a straight line are said to have a linear correlation. 
• A linear correlation can be described as increasing (rising to the right), decreasing (falling to the right), strong (very close to following a linear path), or weak (following a linear path more generally).
• The equation of the line of best fit can be used to algebraically make interpolations and extrapolations.

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.

Replaying the video can be helpful here.

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 noticed a candle.
• What is being used to hold the candle?.
• The candle was lit.
• The walls are a copper colour.
• I wonder how long they’ll keep it lit for?
• I wonder how long it will take for the candle to burn out?
• And many more.

At this point, you might comment on some of the things students noticed and potentially answer some of the questions students had, if you can.

Verbalize the following prompt and share it on the projector for students:

How long will it take before the candle burns out?

Make an estimate.

We can now ask students to make a prediction based on their intuition and prior experiences involving candles.

Do your students typically light candles when celebrating a birthday? An important meal? Celebrating a religious holiday? Encourage students to use their prior experiences to make an estimate. Given the lack of information given about this particular candle, you can expect a wide range of estimates to be shared. Highlight how we might be able to use mathematics to help us become more precise with our estimates.

Show the following video that will begin revealing the height of the candle at various points in time as it burns.

Now that students have been given some data relating the height of the candle and time it is lit, ask students to update their estimates.

How long will it take before the candle burns out?

Update your estimate.

Be sure to remind students that they are not to use a calculator (at least not yet) to update their estimate for how long the candle will take to burn out. Encourage students to use some type of mathematical model in order to communicate their thinking and convince others of their thinking.

Facilitator Note: While there will be an opportunity to provide students with a lesson template that provides a table and grid for graphing in the Consolidation section of the lesson, we want to ensure students are given enough time to use their own strategies and tools to leverage and strengthen their problem solving skills.

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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.

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 students the following reveal video:

Here is an image of the final frame of the 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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Consolidation Prompt #3:

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Consolidation Prompt #4:

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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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