This is my 2nd or 3rd time doing this activity, but hadn’t yet blogged about it. So here goes … I made lots of changes, even from one period to the next.

**Prompt**:

**Notice-Wonder-Estimate:**

**Solve**:

At your boards (whiteboard / chalkboard) in groups of 2-3 randomly assigned (VNPS & VRG).

Most groups started calculating the cost per person for each teacher. I stressed to them multiple times that all 3 teachers were paying along the same formula or “price plan”. They really struggled with how that could be. In first period there was 1 group whose board had a table on it & they had started using 1st differences to calculate the rate of change. I called all the groups over & led a discussion about the strategy and asked about what sort of deposit (a cost for 0 people) might have to be made by the teachers & sent all the groups back to continue, strongly urging them to explore the table idea. In 3rd period, none of the groups started the table, so I called all the groups over to some spare board & said “here’s something I saw in 1st period” & proceeded to have the same conversation with them.

Here are their boards:

We got to the point on day 1 where everyone solved for the cost for 150 guests. Time ran out, & bell rung.

Between periods 1 & 3 today I added some extra slides & questions to my slide deck to make it better.

**Day 2:**

Yesterday I added a slide asking students to graph the 3 points from the original data set in the original prompt. Today we started on that slide in Pear Deck :

I asked them if this was linear or nonlinear. Why? In 1st period this also resulted in a conversation about 1st differences when the x values don’t have a constant increase.

I asked if the line of best fit would pass through the origin?

I then sent groups to their boards with the task of using Desmos to find the equation for the line of best fit . Their boards:

Once they had done a linear regression to find the equation, I asked them to use their equation to solve for the number of guests I invited if my party cost $3545 at the banquet hall. I coached a few groups through the proper format in which to show their work when solving an equation.

The rest of the period was dedicated to individual practice on a Khan Academy problem set called “Slope intercept equation from graph“.

Find the whole lesson here (the unassociated file is Pear Deck).

As a final note, this whole problem-based teaching can be hard for the student to grasp sometimes. Today this happened:

How do you handle it when students question your teaching skills or pedagogy? Let me know in the comments below!

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

I suppose something can be said about direct instruction being a pedagogy that doesn’t create frustration and anxiety in students.

I would say there are moments when direct instruction is needed. That the timing of it is an important pedagogical choice.