Today I made our go to snack…..peanut butter bites. My kids eat these up like crazy. I turned the making into a math task.
Ask for what they notice and what they wonder?
The intended question here is: How many energy bites will be made?
Have them guess. Too high…too low….best guess.
Ask for what information we would need.
They may notice that the ball is not quite lined up right. How will the adjust?
Is the bite a perfect sphere? Will a sphere be good enough? Give them the volume of a sphere formula. Let them work.
You students may notice the dimensions of the bowl…..or also may notice that its filled up to the 500ml mark. An interesting task will be to calculate the number of bites using either the volume using the dimensions or the volume using the measuring cup.
Act 3: The reveal
Possible sequel question:
What would be the diameter of the giant Peanut Butter Ball if all 22 were mashed together?
And now for the recipe….as requested by Meg Craig!
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.
School is just right around the corner for us up here in Ontario and I can’t stop thinking about that first day. As for my grade 9 applied class’ first day I have ran the R2D2 problem in the past with great success.
Now, over the summer I’ve seen great improvements in Pear Deck and wanted to get into it! Also Desmos has been busy and released Activity Builder!! So let’s mash these two apps up with some R2D2!!
So here is the R2D2 problem presented with Pear Deck and an extensions with Desmos….
Act 1: The video
and this is what Pear Deck will show after you insert the video…..love how the video will be displayed on the projector and not on each individual device!!!
I like using Pear Deck here for asking for wonderings and notices because it allows students who normally won’t shout out answers to have a voice in the room. Students get to input their responses and the teacher can show them on the projector.
For generating estimates I absolutely love how they put our Too high and Too low guess on a number line…..it gives us the visual of where our actual estimates will lie.
Act 2: Gathering the Info
In the new version here I get students to draw their estimates of the dimensions of both the board and the post it note…..this pushes them into drawing diagrams.
Revealing the dimensions….
Students are ready to solve….
Act 3: Revealing The answer
The Extension: How many rectangles can we make that have an area of 609 post it notes?
To extend I want students draw out different rectangles and label their dimensions! They can use Pear Deck’s white board!
But then they can enter them into Desmos through a pre-made activity I created in Activity Builder. (the Pear Deck file links to the Desmos activity).
For each rectangle the student can come up with they find the perimeter and plot the length vs. perimeter in the Desmos graph. The teacher on the projector can use the Overlay function and show all the different rectangles students are coming up with…essentially showing the pattern that emerges! Using the pattern students can read off the minimum perimeter!
If you have a Pear Deck account Grab and download the file below!