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# Placing Toothpicks Part 3

## Patterning and Partial Variation Linear Relations

• LR2.02 – I can construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools for linearly related and non-linearly related data collected from a variety of sources.
• LR2.03 – I can identify, through investigation, some properties of linear relations and apply these properties to determine whether a relation is linear or non-linear (by rate of change/initial value when described in words, by first differences in a table, straight/curved graph, degree of terms in equation).
• AG1.01 – I can determine, through investigation, the characteristics that distinguish the equation of a linear relation (straight line) from the equations of non-linear relations (curves).
• LR2.04 – I can compare the properties of direct variation and partial variation in applications, and identify the initial value when described in words, represented as a table, a graph, or an equation.

## Act 1 & 2- Revealing The Task

Show the students the video below:

If you have already used the Placing Toothpicks and Placing Toothpicks Sequel, asking them what questions they have might be a bit redundant. Sure, I could change what figure number I want them to find, but this process might be more forced than it is worth.

As we did in the previous toothpick tasks, the question(s) I want students to think about are:

How many toothpicks are in the 6th term? … the 11th term?

I would likely have students figure this out on their own, using any strategy and then consolidate the task. The following math task template might be a good option to consolidate student thinking:

## Act 3 – Reveal the Solutions

You can now let students see their solution in action!

## Student Exemplars

Here’s some work I captured when I tried this task for the first time the other day.

Have you tried this task? How can we make it better? Share your thoughts in the comments below!

## New to Using 3 Act Math Tasks?

Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

## Share With Your Learning Community:

I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.

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