Algebra – We started the week on Tuesday (Monday was a holiday) with the lesson “comparing delta y and delta x”. I love that CPM talks about slope as “change in y over change in x” and then moves on to using delta y and delta x rather than “rise over run”. This was a really good lesson, but since Tuesday’s are our short days the period was only 39 minutes so we didn’t get to finish. I started Wednesday doing a problem from Tuesday, and after talking about homework too we didn’t get to finish all that I wanted to from Wednesday! So on Thursday we finished another problem from Tuesday, and one from Wednesday, and then started summarizing how we can go from a table to an equation, and from a situation (story or pattern) to an equation. We didn’t get to the graph to an equation in both classes. Today was the first half of the lesson on Slope as Rate of Change. It was a fun lesson – 3 girls were doing the first heat of a competitive tricycle race and we graphed their lines based on the story given, then wrote the equations. We then saw when the one girl caught up to another, and proved that algebraically by putting in the x and y values of the point into both equations (and they were both true!). Then we looked at the graph to see who won the race if it was 20 meters long, and proved that by putting 20 into each equation and finding who had the shortest time (x values). WooHoo! Here’s what the graphs looked like:
We also had a Participation Quiz today – I walked around listening to what the groups were saying and how they were working together. Both classes did such a good job! Here are some samples: “Does someone else want to read?” “Did you just divide to get that rate?” “So it’s 4/14, right? Right. Right, 2/7.” “Can we use 20 again?” “Wait, what are you talking about?” “Okay, do you want me to read? Wait one sec.” “Okay, we’re going by 2’s, right?” “Okay, so we need to reduce, right?” “Is it seconds?” “Wait, how many meters?” The last question was about a clown riding his tricycle with the equation f(x) = 20 – x. Some were confused so I suggested changing the equation around to -x + 20. Then I heard kids saying “Oh, he’s riding backwards!”. We graphed the clown’s line after talking about what the 20 represents – he started from the finish line and rode to the start!
Math 7CP – We started the week with Clothesline Math (I need to go put it up again, brb). See Andrew Stadel’s post on what Clothesline Math is. We put up a lot of numbers between -3 and 3 and discussed the placement. I need to spice it up a little for next year. I’m looking forward to doing double number lines for equations though! Thursday we did another number line – but this time they had to figure out what the increments were and find the missing numbers. A lot of the increments were straight forward, 1/2, 1/3, 1/5 but a couple of them were harder – 2/3 and 2/5!
It helped some kids to make a box between the numbers given, and then separate it into sections based on the increments. The denominator was the number of sections (they could easily see that) and the numerator was the difference between the numbers on the edges of the box.
Friday we started with the kids putting up fractions between 0 and 1. Most kids could do it without any problem, but a couple need help – 0.8 and 0.9 initially next to 0, and 1/6 next to 1. The class helped them put the numbers in the correct place and I’ll need to work more with them! Then we drew different number lines to represent the different number sets (natural, whole, etc) within the set of Rational Numbers (is ‘set’ the correct term? idk idc either lol).
I had wanted to use all different colors (pic on left) but ended up using red and black (which are actually the colors of CSUN, where I graduated…coincidence? I think not). I really like this way of presenting the sets – it seems better than doing the “boxes” like I’d done in the past.
7 Accelerated – Tuesday and Wednesday we did an activity called Newton’s Revenge – which is about a roller coaster that people are starting to not ride because they are wary of the low ceiling in the tunnel. Is it safe for tall people to ride??? The kids “collected, organized and analyzed data” by measuring themselves at 2 stations – height and reach when sitting. Then they input their data into Desmos and plotted it on a graph I had for the class (which is scaled badly on purpose).
The second day they had questions to answer about the graph – why had the teacher scaled it that way, could they just use their numbers as the increments, why had the teacher started at 0. I passed out graph paper and we did the axes together (excuse – I wanted to make sure they had everything I wanted the first time). While they plotted their points and another table’s points I wrote an equation for the line on Desmos, then we looked at it and figured out if Yao Ming (he is referred to in the book) could ride the ride based on the line of fit. It was pretty fun.
Thursday and today we worked on deciding if the situation was proportional either by making a graph or table, also finding the unit rate. The situations varied from a puppy gaining weight, an investment, mowing the lawn, buying ferret food, the tomato plant growing, buying videos with shipping costs and more. I think they’re good on proportional relationships! And finding unit rate!