MEL3E Day 24 – Shortest Routes with Desmos

Warm Up: Estimation 180

Since last week we did the 1/4 cup of candy corn today we looked at estimating how many would be in the big bag.

We remembered that there was 19 candies in the 1/4 cup. For their too high and too low today I also had them find how many scoops of candy that would be. For example, Joey said too high might be 1000. So I had them determine how many scoops of 19 that would be. I then asked if this now still seems too high?

After all students had voiced their best guess and how many scoops it would be I showed the answer:

I asked them how Mr. Stadel determined the answer of 893 if he didn’t count. I let them study the info shown. Shanice piped up, “there was 47 scoops….so 19 x 47 = 893.”

Today we switched strands from Saving & Borrowing to Travel and Transportation. They all got out an iPad and went to this Desmos Activity.

The first problem has students drawing a route from our school to a Tim Horton’s. I asked them to try to draw the shortest route possible.

This had them hooked. Each wanted their route to be the shortest.

I took time here to show different routes students had drawn.

As a class we moved to the next screen where we estimated the actual distance.  A student pointed out that the map image had a scale in the bottom right corner. A small section was labeled to be 200m. They used that to help estimate the distance for their routes. But we needed a better way to determine who would have drawn the shortest route! Moving to screen 3 we used the points to determine the “map distance” for each section of our route.

Students filled in a description of each leg of their route and the distance in map units.

We measured the scale at the bottom to create a scale factor for this map.

I demonstrated how to use the scale factor to determine the actual distances in metres and kilometres. We went around the room voicing how far our routes were to see who had the shortest!! Moving to the 4th screen showed what Google would say.

That was problem 1 out of 5 in this Desmos activity. We started problem 2 but did not finish it. Tomorrow’s work!!

Having the students guess the shortest route first allows them to try something informal before we try to formalize it with actual distances. Desmos’ sketch tool allows them to draw, erase, undo, and re-draw those routes. The ability to wipe away their trials is so valuable. It allows them to take risks. It allows them to get deeper into their understanding.

Give it a try. I feel I’m missing some extension questions, or questions that dig a little deeper. Can you help me out and leave me some feedback in the comments? Thanks.

MEL3E Day 22 & 23

Day 22

Warm up today was from Would You Rather:

The groups blew my expectations out of the water on this one. They asked for the weights of the coins and then went to work.

One group looked at using copper pennies vs. zinc pennies in comparison to the quarters.

Most groups wanted the quarters regardless of the money…less to carry around.

We picked up where we left off from the credit card scenario bills. As we progress through the bills students saw what happens when you don’t pay off your entire bill. As a class we worked out interest charges added to the new bill, new statement amounts, and minimum payments for a variety of scenarios. We still did not complete all problems before class ended.

Day 23:

Warm up:

We brought up the Clock app on our iPads to help answer this problem. We reviewed converting times from the 24 hour clock and looked at timezones across the world.

Next, we worked on solving Robert Kaplinsky’s “Is Gas Cheaper With Cash or Credit Card” problem.

I showed this image:

Students noticed a variety of things including that gas here seems to cost more if you use a card. It was a no-brainer that they would choose to purchase with cash. Like in Robert’s lesson, I handed them a paper credit card and asked, “If you use this card does that change your mind?”

We discussed what cash back meant. Students worked on the boards to see if getting 2% back (2% off the price) changed their initial decision. They calculated this for each of the three gas types. I was caught up in good discussions with them and I forgot to take pictures of their work.

For the remainder of class they worked and submitted their credit card scenarios.

Random Winner Game – MEL3E Day 6

I’ve decided to spread some skills (expectations) around as warm ups. Today our warm up involved pay schedules.

They highlighted every two weeks on their sheet to indicate pay days…..and seeing which months had 3 payments allowed us to have a short discussion on making budgets around our pay cheques.

We picked up where we left off from yesterday’s practice sheet with percent. We talked again about different ways to get paid, including an example of getting paid by commission. I brought in the random winner game to give a little more excitement to just practicing. I usually use the Smartboard and sticky notes but this always ends up with a huge waste of expensive stickies. This time I re-used the 100 grid from the Explain Everything file from yesterday.

I assigned each person a colour (I only have 13 students—-otherwise assign each pair a colour). Each time they get their question checked by me and it’s correct they earn a tile. If it’s incorrect give them some feedback and ask to try again. WHEN correct they go to the iPad and randomly choose one of the squares to cover. At the end of class we randomly chose one of the squares….and whoever is covering that square is the winner!

Now since we’re dealing with teenagers…..this excited some of my students and for others……not so much. Although one student didn’t want to place any tiles on the grid she still had all her answers checked by me for feedback.

Tomorrow will be our first mastery day. We’ll spend the day working on skills from the week plus a quiz.

Grab the Explain Everything File

Percent Pile Up – MEL3E Day 5

Today I wanted to see what my class’s prior knowledge was around percent. Since they are 16-17 year olds they have been exposed to percent quite a lot. But since their math skills are operating anywhere between a grade 5 level through to a grade 9 level I wanted us all on the same page.

I started off with an Explain Everything file I put together. The slides start at a basic level but then creates a need to determine equivalent values that match a certain percentage.

Slide 1:

Getting the explain everything file onto each students iPad, or getting them connected to the wifi, or showing them how to type in a URL can take some time…..so slide 1 is an easy intro that students who are waiting can work on.

Slide 2,3,4

I wanted to make sure that when we know the whole is 100 that just counting the tiles covered gives us the percentage. These were too easy for my students but it gave us some time to review writing a fraction as a decimal and as a percent. I asked students to tell me the percentage they covered and then we converted to a decimal and fraction. They had the option to record what they were thinking.

Slide 5,6,7

Right away almost all students covered 10 squares. I then asked them to convert their new fraction (10/50) into a decimal to see if we get 0.1 ….and then some shock on their faces appeared. Some students then knew their mistake and made some corrections. But we spent some time here going over the visual interpretation …..10% means that 10/100 are covered. This board had been cut in half so only 5 must be 10%.

Slide 8-12

This is where we generated a need for an algebraic (proportion) method. The students could estimate how tall he could be….but they had a hard time determining with accuracy how tall he would be. So this is where I stepped in and showed them how to calculate. The remaining slides with Fido and then with piles of gold and then finally with no visuals at all were to practice this method.

After all slides were finished they started on some more practice questions on paper. We’ll finish those tomorrow as most students just started it.

Grab a copy of the Explain Everything project file