Another post from Tap Into Teen Minds. Enjoy!
Patterning and Partial Variation Linear Relations
This task is a follow up to the Placing Toothpicks and Placing Toothpicks Sequel tasks I posted recently. The first task was proportional, followed by a quadratic in the second. This task is going to extend the original task from a proportional (direct variation) linear relation to a partial variation linear relation. That means this task could be used for patterning in elementary or for linear relations in grade 9 academic and applied. Here’s the grade 9 academic expectations we can make connections to:
- 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:
Can’t see the video? Click here.
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!
Act 3 – Watch the Solution
Can’t see the video? Click here.
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!
Download Resources For This Math Task
Click on the button below to grab all the media files for use in your own classroom:
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