This past week I did an activity inspired by Fawn Nguyen’s Visual Patterns work. The last time I did this activity, I blogged about it here.

Pattern:

Notice & Wonder:

 What do you notice (facts)? What do you wonder (Qs)? each step the cubes increase how come the reds arent increasing? How many blue blocks will they add on the 4th step Each step, more cubes are added Why is there always 3 red but the blue always increases? Why Do we only have 3 reds There are 3 steps in the picture there are red and blue cubes how much the sides go up each time The number of blue blocks increase as the number of steps increase. why isnt red increasing? Cubes, there is steps How many cubes added every step? I notice there a step 1 , step 2, step 3 Why does the blues always increase and the red stays the same Always 3 red in the middle the outside length increases by 1 each time Why is the red not increasing – The number of blue cubes increase each step. (2, 8, 18, etc) – The number of red cubes stay the same each time. – How many blue cubes will there be at step 10? – What is the formula? 3 red squares on each step , There’s always 3 red in the middle How much blue cubes will it be in step 4 the red blocks stay they same but the blue blocks increase every time how much the blue blocks are going up by

Estimate:

Solve:

Groups used tables to start. Then, most could see the pattern of the two squares on each end with a side length equal to the step number and they used this pattern to calculate the number of blocks for step 57.

A follow up question in the Pear Deck slides asked them if the pattern was linear, quadratic or neither. We discussed how we can determine this, and I sent students back to their boards to find the first & second differences.

The next question in the slides asked them to use Desmos to find the curve of best fit and its equation. I reviewed how to do both linear & quadratic regression on Desmos on the board for them. After students found the equation with Desmos, they were asked to go to their boards one last time and use their equation to verify how many cubes would be needed in step 57.

We then had a whole class discussion on how the terms in the equation represented the visual pattern.

Individual practice on quadratic relations was assigned from Khan Academy; different exercises depending on whether or not they had finished their homework from the last time we worked on quadratics.

Activity available here.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)