## Day 10 – Buggy Whiteboards

Physics 11 – I did a lot of talking again today, which was expected but still a bit disappointing.  It was the first board meeting I had with one class, and they were very quiet and unsure of what to say, ask or critique.

The top picture shows some good analysis and you can see the influence of math in the notation. We later talked about better symbols to use, and why a decimal is better than a fraction in this context.  The bottom picture is a screen grab from the consensus we came to for making whiteboards and models.  This class didn’t have anyone generalize the model, so I had to go over that part.

Next the students will have some practice moving through different representations (words, graphs, motion maps), which will highlight how they all apply to the same model.

## Day 9 – Adding Integers Again

Math 8 – All my grade 8’s had their timetables changed so I was essentially starting with a new class today. About 2/3 of my students were new to me.  Having already done a constructivist review lesson with adding integers, today I took a faster more direct route because the first half of the class was spent going over class business (books, course outline, expectations, etc).

I quickly reviewed two methods for adding and subtracting integers, using modeling and a number line.  From what I saw on Wednesday, almost all kids are comfortable with this.

The situation that is hardest for them to understand and the hardest for me to explain is when you subtract a negative number. For this, I had students fill in the 6 – n table shown above.  Students were confident that the pattern was correct and would hold for subtraction.  From this, we reasoned then that 6 – (-1) = 7, 6 – (-2) = 8, etc.

I get kids to explicitly state their reasoning each time.  It’s repetitive but I want to reinforce that answers come from reasons, not tricks.

From the data table and the equations we developed, I asked students to write down a rule on how to subtract a negative. Most students give rules #1 and #2. I ask around until we get to rule #3 (we had already covered the definition of an “additive inverse”). I then asked the students to give the pros and cons of each rule and we generally agree that rules 1 and 2 don’t give any explanation and they can also be confusing.

Most kids do have a rule for this situation. They say you turn one negative around and put it on top of the other negative, which makes it a positive. Excuse me while I gag…

Next day I will offer an analogy for adding and subtracting integers:a hot air balloon where positives are helium and negatives are weights.  It’s the best analogy I’ve come across that fits with subtracting a negative (if you remove a weight, the balloon rises / gets more positive / does the same thing as if you added  helium).  I might make a Scratch game/simulation for this.

One last note… I had students return some Plickers voting cards since they weren’t going to be in my class anymore. One student was walking away when she stopped, turned around and said, “I really liked your class. It’s the most fun math class I’ve ever had.”

So that goes in the win column.

## Day 8 – Buggy Whiteboarding

Physics 11 – Today was the students’ first shot at whiteboarding models that they’ve developed.  The photo above is interesting because during their presentation, this group realized that the direction on their graph was wrong.

The group below has a valuable statement on possible errors in data:

And the group below were the only ones that got to point of getting a mathematical model of the buggy motion. They had some good things to say with their presentation, more than what is shown here.

## Day 7 – Adding Integers

Math 8 – Classes started off as a quick review of adding integers but it turned into an in-depth review.

The class was asked to give examples and non-examples of natural numbers and then integers.  They were then asked to give examples of equations with integers.  I then formed groups and asked each group to come up with at least one strategy for solving an equation with integers.  All names and groups were generated randomly.

The most common strategy the kids came up with was using a number line, along with some examples using modeling/grouping.  Several kids say they “just do it using my brain.”  They have a harder time explaining their strategy as they learn proper language to describe what they do.  We then went over the strategies together.

It was common to see students solve something like 3 + (-8) using a number line.  When I then challenge them to do 3 – (-8) it gets much more difficult.  I encouraged them to use an inverse operation so that 3 – (-8) = 3 + (+8).

Using proper language is awkward at times, since it is easy to say “instead of subtracting, add the opposite”, but that doesn’t quite describe what is happening mathematically.

At the end of the day we had bad news: all of the grade 8 classes are being rescheduled.  So the first three classes we did with problem solving and creating a thinking classroom has to be re-done.

## Day 6 – Project Specifications

Engineering Physics  – Today the class was given their first project.  I created randomized groups of 4, in an effort to hopefully spread the different skills of students.  In other words, I wanted to make sure that the 5 buddies that were good with building things with their hands weren’t all in the same group.  I gave the students a challenge from an old UBC Physics Olympics pre build competition.

Having gone through a 10-step design process, I asked the students to clearly write down the projects criteria (goals) and constraints. As you can see in the above example, there is a wide range of opinion on what is a criteria and what is a constraint! We’ll need to do some work on this next class.

## Day 5 – Gauss 1 to 100

Math 8 – Today the kids tackled Gauss’ 1 to 100 problem.  How can a person add up the numbers from 1 to 100 in seconds?  What is the strategy?

This was a tough problem.  Two “hints” help the process along.  If kids write down all the numbers from 1 to 100, they can piece together  the strategy easier.  One thing I did was wait for kids to start grouping numbers, and then point out how grouping seems to help.

One interesting brain thing is that no one thought to add 1 + 100, 2 + 99, 3 + 98, for sums to 101. This includes myself. I think people are much more tuned and comfortable with 100, it’s less “outside the box.”

Next day we will do some formal work on integers and I will bring in the associative property of addition, using this problem as an example.

## Day 4 – Spaghetti Towers

Engineering Physics – Today the class was challenged to the classic “marshmellow on a tower of spaghetti” challenge. We then discussed the different parts of their design process, what was good, and what went wrong.  I’ll follow up on this with some formal design plans/procedures and then the students will be given a more significant design challenge.