The original idea for this lesson came from Al Overwijk. Thanks again Al!
The possible Ontario overall curriculum expectations covered in the activity:
Grade 10 applied:
graph a line and write the equation of a line from given information
Grade 9 applied & academic:
solve problems involving proportional reasoning;
apply data-management techniques to investigate relationships between two variables;
demonstrate an understanding of constant rate of change and its connection to linear relation
solve problems by using proportional reasoning in a variety of meaningful contexts.
demonstrate an understanding of proportional relationships using percent, ratio, and rate.
demonstrate an understanding of relationships involving percent, ratio, and unit rate.
Act 1: Turbo Texting:
I started with “I was with my brother one afternoon and I needed to text my wife. After texting her, my brother informed me that I was a ‘terrible texter’. He said I was soooooo slow. I on the other hand disagreed. Then we decided to settle this once and for all—- race!!!”
ME: “Use any method you choose to determine: Who is the faster texter?” I allowed them time here to work on a strategy. I watched carefully what strategies they used or didn’t use.
Seeing the different strategies gave us a nice discussion the importance understanding what rate we are determining and how to interpret it to answer the problem.
I showed this picture next:
and this piece of info…
Students completed this problem and we discussed the assumptions we needed to make.
How do your students compare to Jon and Kevin? Have them time each other while texting the 165 character message. Have them determine their texting speed to see who the fastest texter is in the class.
ME: “Now you may have texted that message in 18 seconds, but would you do this all of the time? Would you keep that same rate for a shorter message? Longer message? We better keep this experiment going.
I set them off to text various messages of different lengths using this handout (I modelled the handout format after Mary Bourassa’s Spegettini and Pennies handout – thanks Mary).
Click to download a copy
Students used Desmos and the regression tool to create a linear model. They used that model to predict how long it would take to text 140 characters, 200 characters, and this message: “Dear Mom and Dad I promise to never text and drive.” They finally timed themselves to compare the calculated time and the actual time.
Extension: Compare the relationship between the number of words in a message and the time to text the message. How would the equation change? Is it still proportional?
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?
Give some more info
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.
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.
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!!
One of my favourite lessons to do with my grade 9 applied students is the Fast Clapper! I first saw it on Nathan Kraft’s virtual filing cabinet! My main goal here was to solve proportions through algebra.
We started class like this:
ME: Hey guys get ready…..I want you to clap as fast as you can……Ready…..Set……..GO!
Class: They clapped. Some students gave it their all….some not so much.
ME: Ok….That’s enough. Now let’s make a competition out of this! I want you to clap as fast as you can for 10 seconds….count how many claps you make! …Ready —– GO!
Class: This time all of them gave it their all!!
ME (after 1o seconds): STOP! Great job! Quick, write down how many claps you made in those 10 seconds. Who thinks they had the most.
James: I did….I had 37 claps
Josh: Nope, I’ve got that beat……48 claps.
Shylynn: I did 56
ME: OK….now find how many claps you made in 1 second!
They did this pretty easily and we went around the room again….still seeing Shylynn with the highest!
ME: Great job…..now watch this guy….
Hayden: Wow!!! that guy can clap
ME: I know….Let’s watch again. This time watch the video and try to see something you didn’t before.
We watched a few times. Each time students would notice something different. We noticed:
He closes his eyes
The record is 721 claps per minute — “I wonder if he’ll beat the record”
He clapped 58 or 60 times in the video
The video only showed the first few seconds
ME: Let’s take the suggestion to discover if he beats the record. Who thinks he’ll beat the record? Who thinks he’ll tie the record? Who thinks he won’t beat the record?
We took a vote and recorded it.
ME: In order to see if he beats the record we’ll need some of that info from the video…..but we better be exact. Why?
Janice: If we’re off by a clap in the first few seconds….it could be huge after a minute.
ME: Ok, let’s be exact.
Jake: We could pause the video on the last moment to see.
Judy: He claps 63 times in 4.6 seconds.
ME: OK….go for it. Work together to see if he beats the record.
They got going and I needed to work with a few groups to discuss how to get started. “IF you could find how many claps in 1 second how could that help?”
After some time I stopped them and showed some students’ solutions
We then showed the rest of the minute!
We moved into re-solving the problem using ratios and proportions. I went through slides to show how to set up the proportion and how to solve it with algebra.
I’m a strong believer in letting the students struggle and persevere through problems. I want them to use their prior knowledge to solve the problem in any way they can, any way that makes sense to them. I can see their understanding when they have to explain their thinking to me and the class. After they solve the problem in their way…..I take what they have done use it to explain the “math teacher” way.
Today one of my grade 10 academic students was solving a problem and I could see some good thinking on the page….but he also wrote: I don’t know how to start this. I asked him right there why he wrote that when he had almost a full answer on his page. He said “I know that’s not the way you want me to solve it!” I jumped on that quick and said….”I want you to solve problems that make sense to YOU. Just show me your thinking” He went on to solve the problem with in a great way.
We need to build our students confidence up. We need to promote and value their solutions instead of forcing our solutions on them.
So, back to Fast Clapper: I used their solutions to help explain why the math teacher way also makes sense. Here is a silent version of the slides I used.