As part of my day to day warm up series in my grade 9 applied class we are solving Solve Me Mobiles. Like what VisualPatterns does for my students and learning and discovering linear relations — Solve Me Mobiles is having students solve equations without really knowing it.
Puzzles are presented with minimal distraction and with clarity. Puzzles require no explanation. Students know exactly what its asking for.
Today we started on Puzzle 12 and completed up to puzzle 14 (first 15 minutes of class).
As students explain their strategies to the class I translate their words into small equations…. All with the goal in mind of sneaking in equation solving.
Jill easily solved a 1-step equation on the left side…and then used pictures to help solve the 2-step equation on the right.
I knew that I wanted to give this a try for this semester! What I especially love about this activity other than students experiencing rates of change is that this is an activity that can span multi-grades!
Here is what we did,
Generating Curiosity
I found this video on YouTube and asked the class to think of great questions we could ask about what we see!
Great questions from the kids and we all agreed to look at
How does the sucking time affect the radius, circumference, volume, and surface area?
How long will it take until the lollipop is all gone?
Let’s investigate those relationships starting with the easy to measure (circumference) and also estimate how long it will take until the lollipop is no more!
We had guesses : ranging from 10 minutes through to 35 minutes.
Gathering Data
I handed out one lollipop per pair of students, along with some dental floss for measuring circumference. We set our timer for 30 seconds and began sucking and capturing data!
We recorded the circumference every 30 seconds up to 7 minutes like Al’s and Janice’s instruct in their lesson Plan.
They also have a great handout for tracking the circumference over the 30 second intervals.
Analyzing the Data
So we first looked at the Time vs. Circumference and Time vs. Radius relationship
We discussed its linearity and why. Students predicted with more accuracy when their lollipop would run out.
Up to this point this task is great for grades 7, 8, 9, or 10!! (Just edit the file to exclude the average and instantaneous rates of change).
Grade 7 & 8: Practice plotting points and reading/interpreting graphs.
Grade 9 & 10: Find lines of best fit and first differences.
We found the average rate of change for each 30 second interval and discussed what this meant. We used the last column to talk about narrowing the interval down to estimate the instantaneous rate of change, and noticed that it’s about the same for all values. Why does this make sense???
We moved on to looking at Time vs. Volume and Time vs. Surface Area
Great talks around how Volume and Surface aren’t deceasing at a constant rate! It changes! Students can see these changes and see in their tables where the volume is changing the fastest.
Overall a great intro activity to get students thinking about narrowing intervals to approximate instantaneous rates of change.
Next up: We’ll relate what we did here with the tables to the graphical interpretation of rates of change (secant and tangent lines) and then on to the algebraic!
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!
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.
