Thanks for inviting me to learn with you at the York Catholic District School Board for a day full of math professional development! The group was energetic and excited to learn about meaningful manipulative use, sparking curiosity and building conceptual understanding in grade 9 applied mathematics.
Here’s a summary of what we explored today. Looking forward to connecting again soon!
How many seats are there?
In the airplane problem, we made predictions and made connections to multiplication and the order of operations by writing expressions. There are extensions to this task that we did not explore today, but are applicable for grade 9 applied.
We briefly discussed the importance of counting and quantity principles, but focused on the importance of unitizing. A full summary is below:
After break, I shared Would You Rather?, a website created by John Stevens that provides all kinds of great warm-up problems for a range of grade levels including grade 9 applied:
Here’s a visual animation of the second problem we did involving fractions:
— Kyle Pearce (@MathletePearce) April 28, 2017
Exploring the Progression of Multiplication
We made a leap from counting principles and unitizing to multiplication and specifically, using arrays and area models.
As an aside, you might consider looking at the “Japanese Multiplication” or “Stick Multiplication” which is derived from base ten block representation:
3 Act Math Task: Donut Delight
After lunch, we explored the Donut Delight 3 act math task where we played with multiplication to predict how many donuts there were in the “double hundred dozen” box and then used repeated subtraction to lead to a flexible division algorithm for division when we tried to find how many layers there were.
Progression of Division
We didn’t have time to dive into division with base ten blocks, but I thought I’d put that here for you to reference:
We attempted to summarize the use of manipulatives on a continuum called “Concreteness Fading”. While the name suggests that concrete manipulatives fade away over time, it is important to remember that they fade away with one layer of abstraction and then reappear as a new layer is “piled” on.
Here are some other tasks we explored as well:
How many packages of paper will it take to reach the ceiling?
The Stacking Paper Tasks are also available on iOS as a multi-touch book for iBooks:
Learn more about what’s inside the multi-touch book here.
Or, consider accessing these tasks in an interactive way via Google Sites.
3 Act Math Tasks: Curious Math iTunes U Course
Access over 30 tasks with all resources downloaded directly to your iOS Device to avoid streaming media in your classroom through the Curious Math iTunes U Course:
Other Useful iTunes U Courses to Check Out:
OR, you don’t want to download Jon’s Beautiful Functions book? Check out all of the links here on his blog.
Hope you folks found this YCDSB math professional development experience useful.
I’d be delighted to come back and learn alongside you all again sometime soon!