If you are looking for good “thinker” problems for your students, check out Brilliant.org. Brilliant has Problems of the Day on a variety of topics including Algebra, Geometry, Calculus, Number Theory and Logic.
I have to admit, I’m addicted to KenKen Puzzles. 🙂 KenKen Puzzles are a style of arithmetic and logic puzzle invented in 2004 by Japanese math teacher Tetsuya Miyamoto, who intended the puzzles to be an instruction-free method of training the brain. This puzzle game helps students improve their calculation skills, logical thinking and persistence.
Rules for Playing KenKen
Like Sudoku, no digit can be repeated in a row or column. In addition, the numbers must combine to form a target number using a specific operation.
- Fill in the numbers from 1 to the grid size. For example, this 4×4 KenKen puzzle uses digits 1, 2, 3 and 4.
- No digit may be repeated in a row or column.
- The numbers within each heavily outlined set of squares, called cages, must combine (in any order) to produce the target number in the top corner using the mathematical operation indicated.
- Cages with just one square should be filled in with the target number in the top corner.
- A number can be repeated within a cage so long as it is not in the same row or column.
Here are some resources if you would like to use KenKen Puzzles in your classroom.
During my spring break last week, I has the privilege of spending a day with some incredible educators, Dan Meyer, and the Desmos crew at the Desmos headquarters in San Francisco. We even got to enjoy a chat from Phil Daro during lunch. I learned so much from everyone I spoke and worked with! And Desmos knows how to give a good swag bag. 🙂
If you’d like the details, please view the notes from the day at bit.ly/descon16.
Here is the fruit of my labor for the day: The Tortoise & The Hare, Desmos style. 🙂
If you haven’t used the Desmos Activity Builder yet to create your own classroom activities, I encourage you to give it a try. I just started using the Activity Builder earlier this year, and it really is intuitive and easy to use. A good read before you start is Dan Meyer’s blog post, Desmosify Your Worksheet.
If you create an activity, please share in the comments!
I began using the Desmos graphing calculator with my students at Maryknoll in 2012 and have LOVED it, but I didn’t really explore the Desmos Classroom Activities in-depth until this year. It all began at our Northshore School District Summer Institute this past August with Dan Meyer when he had us do the Central Park activity. I was hooked.
At a district PD session last week, teachers started off with a quick Desmos graphing calculator overview and learned how to create sliders. Next we explored the iPhone 6s Opening Weekend Sales activity to see an example of a task that was adapted using the Desmos Activity Builder, and we read Dan Meyer’s post, Desmosify Your Worksheet. Then teachers choose a lesson of their own and turned it into a Desmos Classroom Activity. Here are a few examples:
- Graphing in Slope-Intercept Form!
- Absolute Value Graphs
- Conic Section Exploration (this one is mine 🙂 )
Teachers used these activities with students this week and were very happy with the results. One of the reported advantages was that graph windows are preset for students so they could focus on the mathematical concepts being studied rather than getting sidetracked by technical issues.
The sliders also made exploration MUCH easier. In the past, using these lessons with a standard handheld graphing calculator meant that students had to enter several equations to explore the effect a coefficient has on the graph. Now the sliders allow a student to view numerous graphs instantly.
Comparing Quantities (qualitative comparisons) is a classroom routine that make student thinking visible and supports the Standards for Mathematical Practice. It can be used at any grade level and with a wide range of content.
The basic idea is to give students two quantities, Quantity A and Quantity B, and ask students to decide if:
- Quantity A is great than Quantity B (>)
- Quantity A is less than Quantity B (<)
- Quantity A is equal to Quantity B (=)
- There is not enough information to determine (?)
Students make their conjecture and provide two reasons to support their conjecture.
Here’s a 6th grade example for ratios:
Comparing Quantities activities are most effective when they get at a big mathematical idea rather than just computation. In this 6th grade example, the big mathematical idea is understanding the difference between part:part vs. part:whole ratios.
If you are interested in using Comparing Quantities in your classroom, resources are available in this Google Drive folder. The folder contains activities for each grade level grade 5 through Algebra 2 as well as a blank template and lesson guide. If you have questions about these resources, just let me know!