# Two Trains…

How many of you have seen a problem like this one?

I’m a fan of taking a problem like this, one that you would assign for homework (in the “application” section of the exercises….and one that very few students even attempt….and someone will ask you to take it up next class) and bring it to the start of my lesson. I’ll teach our concept/idea through this problem. But we can’t just throw this problem up on the board and say “Let’s solve it”……because no will want to. There is no drive for any of us. Like Dan mentions here….who cares!

Who cares about the trains travelling…who cares that they are even trains….they could be bicycles, or cars playing chicken….but is changing the context really going to change how engaging the problem is to students? Dan argues no. I agree.  Before you read about this lesson check out this post on Real vs. Fake world….and the Circle Square lesson on 101qs.com which was an inspiration for changing the Two trains problem around.

Here’s my go at this one:

Show them this video:

ask What do you notice? What do you wonder?

Have students guess WHEN the two dots would meet?

Have them guess on WHERE the dots will meet?

Have a discussion on what will be needed to determine the times and distances. Spend some time here on speed. Go over the relationship between distance, time, and speed.

Show them this image and have them makes some guesses on where the dots are now.

then reveal

Calculate the speeds of the dots. Have students go back to their original guess on time and find how far each dot would travel.  Who in the class is closest? Did anyone guess right?

Now help them generalize…

Create the equations

If our lesson is on solving this using an algebraic technique we can teach them that here. Or maybe we want to show them the graphical solution. Either way we have taken the tougher question from homework that no one cares about and used it to set up and teach a skill.

and finally,

I’m sharing this lesson now (before I teach it) with you hoping to get some feedback. Writing these lessons here also help me work out the details. This is week 4 of the #MTBos blogging initiative and its focus is lessons. I won’t get a chance to teach a lesson this week. Our school had final exams and then PD days in preparation for second semester. Good luck to all those starting up again!!

# Trashketball – A Spiralled Lesson!

This was our multi-day, curriculum-spiralled, activity this week!

### Day 1 – Filling the Bin!!

Let’s get curious!!…..I showed this video from Andrew Stadel, and took questions & wonderings:

We settled, (I chose) on the question on how many paper balls would fill a bin! They made predictions, too high, too low and right on!

They made paper balls and found their diameter. We agreed that each ball could be different so we recorded everyone’s diameter and averaged them to give the “average ball size”

# Distance-Time Graphs – Gallery Walk

The last few semesters I ran this two-day lesson on distance-time graphs. Today I added a new twist on Day 2.

Recap: Day 1 – A few prediction videos on water height in a cup vs. time. Then WATERLINE by Desmos!

Day 2:  Today

Warm Up – We reviewed the previous day’s work by choosing one of the cups from the picture and drawing a water-height vs. time graph.

Not surprisingly, no students chose to draw the graph for the Stanley Cup. After they make their sketches we dove into using the CBR Rangers from Vernier just like on Day 2 from the previous post. They walked in front of the Ranger taking various different walks and we all saw their distance-time graphs in real-time. For each walk the students made prediction graphs on their whiteboards before seeing the live graph.

I wanted more predictions from them so I showed them a video I made. They were to watch the video and make a prediction graph of my distance away from the camera vs. time.

After take up of this graph they were to create their own video on the iPads. Each pair of students we’re given a scenario to film that described motion.

Here are two motion videos they filmed: Very basic to start!

They had to create their distance-time graph and hide it under the flap on the vertical whiteboards.

Pairs then went on a gallery walk. They watched each student made video, graphed the matching distance-time graph and then checked the answer under the flap.

Kids enjoyed it and they practiced lots of different distance-time graphs.