Teaching in the Block

Our school district is preparing to transition to a block schedule for all secondary schools in Fall 2017. I spent approximately 8 years of my teaching career teaching in a block schedule. At Woodland High School, we had a 5-period modified block where block classes met for 80-90 minutes daily for a semester. At Maryknoll High School, I taught in a 3-period day on trimesters where each class met for almost 2 hours a day. Here are some of the things I learned from these experiences.

• DEPTH: One of the advantages of the block is that it allowed plenty of time for deep exploration and full investigation of a topic in a class period.
• REVIEW: My students needed more review in a block schedule than they did when taking math every day all year long. I had to find creative ways to incorporate review because we also needed time to learn new concepts. I tended to use warm-ups to refresh their memory about prior math they learned that we would need for the day’s lesson or lessons coming up in the near future.
• ENGAGEMENT: Students won’t stay engaged for 80-90 minutes of lecture! I tried to mix things up and incorporate movement so kids weren’t feeling stir crazy. Variety is the key to making the block work well.
• FORMATIVE ASSESSMENT: During a 90 minute class period, I needed to know where students were at in their learning way before the end of class. Using formative assessment throughout the class period helped me adjust and address misconceptions early.
• TECHNOLOGY: You may know by now that I LOVE using technology to support student learning, and teaching in the block allowed time for this. We could use technology to explore or investigate, to review, as a formative assessment tool, or as a way to capture student thinking through mathcasts.
• CLOSURE: Closure became crucial when teaching in the block. Since I didn’t get to see my students every day, I needed to ensure they all left class with the day’s learning solidified. I strongly recommend an exit routine that includes a way to summarize the day’s learning (which also works well as a formative assessment that will help you with the next lesson).

For some practical advice and strategies for teaching math in the block, I suggest reading Math Giraffe: Teaching on a Block Schedule.

What I Love About the Desmos Graphing Calculator

Desmos is a free online graphing calculator tool that is available through any web browser or as an app for iPad or mobile devices. It has most of the functionality of a TI with some added features that I love.

• Desmos is INTUITIVE: The Desmos graphing calculator is very user-friendly and intuitive. There aren’t many special commands to learn or to find buried within menus, like on some graphing calculators. If you want to trace a graph there is no special button, just click and hold on the graph to see the coordinates.
• Desmos TABLES: Desmos supports function notation, and tables link to function values. Type in the x-values you want, and see them appear on the graph.

• Desmos SLIDERS: Sliders are my absolute favorite feature! Sliders allow me and my students to easily see how a parameter affects a graph. It takes just seconds to build an interactive demonstration for your classroom! Visit learn.desmos.com/sliders to view a quick video tutorial or to take an interactive tour. 

Sliders are also a great way to animate graphs, which can be used to model a situation over time. I used sliders to create this animated Ferris wheel to model the distance of the rider from the ground over time.

• Desmos lets me SAVE & SHARE: Users can work on a problem, save their work, and share it with others. That means you can create a graph and then share the link with your students for them to access it. They can save their work and share it with you, or go back to their work later to add to it or revise. It also means that teachers can share graphs with each other instead of reinventing the (Ferris) wheel!

 

If you would like to learn more about the Desmos graphing calculator, please visit learn.desmos.com/calculator.

It’s been a whirlwind!

This school year has been a whirlwind so far! But things feel like they are settling in now and I’m finding my groove. 🙂 Here are a few things that I have in the works:

• New position: I accepted a new position as the K-12 Math Curriculum Specialist for my district. Expanding into the elementary grades is new for me and I’m looking forward to it!
• Math adoption: I am facilitating our district’s 6-8 math adoption and have been reviewing instructional materials. In this first year of our 2-year adoption process, we are focused on reviewing current research and exploring materials that align with our vision of student learning.
• Desmos Fellows: I’m thrilled to be a Desmos Fellow this year! I spent Veteran’s Day weekend at Desmos headquarters with a fantastic group of math educators, exploring and learning about Desmos. Great weekend, and I got more Desmos socks. 🙂 Read the Des-blog for lots of Desmos Fellows info and updates.
• More Desmos: I have been collaborating with a math specialist in a neighboring district to create Desmos PD for our secondary math teachers and am also planning PD about Desmos Activity Builder for elementary teachers.
• 3-Act Math Tasks: I’m continuing to support our teachers as they implement 3-Act Math Tasks in their classrooms. Secondary math teachers began this work after working with Dan Meyer in August 2015, and now we are expanding this into the elementary grades. I am providing after-school PD this year and full-staff PD at some of our elementary schools.
• Model lessons: I’ve been getting into classrooms and using Desmos and 3-Act Math Tasks with students! So far this year I’ve been able to use Sugar Sugar and Pentomino Puzzles Desmos activities with some junior high students and worked with teachers to use the Classroom Conversation Toolset in the Desmos teacher dashboard. I’ve also taught several 3-Act lessons; I used Nana’s Chocolate Milk with 7th graders after Thanksgiving, taught Thick As A Brick to 6th graders on Wednesday this week, and will be teaching The Cookie Monster to first graders on Monday.
• WA Math Fellows: This is my 4th year as a WA State Math Fellow. This year I have adopted a 7th grade class to work with. I administered the baseline task via Desmos and based on our analysis of their work, the classroom teacher and I used the 3-Act Math Task Nana’s Chocolate Milk to address some misconceptions students had about ratios and proportional relationships. We are now deciding next steps with these students but may use Thick As A Brick along with this Desmos calculator animation.
• NSD Math Fellows: This is my 3rd year facilitating our district Math Fellows program. Our focus will be Jo Boaler’s book, Mathematical Mindsets. I am currently planning our book study which will begin in January 2017.

Whew! That’s quite a list and it’s only December. 🙂 Stay tuned for updates!

A Brilliant Resource

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.

You can also download the Brilliant.org app for iPhone/iPad or Android.

Number Sense with KenKen Puzzles

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.

KenKen Resources

Here are some resources if you would like to use KenKen Puzzles in your classroom.

• Introduce KenKen puzzles as a classroom cooperative puzzle
• KenKenPuzzle.com
• Free Inky Puzzles
• KenKen Puzzles on NCTM Illuminations

Would You Rather…?

WouldYouRatherMath.com is a site with great comparison problems that require students to justify their choices mathematically. They even have a worksheet students can use to show their work for Would You Rather…? tasks. Like the Comparing Quantities tasks shared earlier this year, this is another great way to get students to justify their thinking using mathematics.

More Desmos!

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’m lovin’ Desmos Classroom Activities!

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.

If you haven’t yet explored the Desmos Classroom Activities or tried out the Activity Builder for yourself, I highly encourage you to do so!

Productive Strategy: Comparing Quantities

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!

I Feel a 3-Act Comin’ On…

My apologies to Chuck Wicks. 🙂

I took these pictures during my flight on the way home from AMLE 2015.

 

I feel a math task in here, something along the lines of a Dan Meyer’s 3-Act Math Task, and am trying to tease it out. If you’ve got an idea, I’d love to hear it!