What Would You Do With Two Extra Periods of Math Each Week?

My plan for this year

I have two extra periods of math class with my students this coming year, with very little directive except that the time isn't for core curriculum. This post is my tentative plan for what I'll do with that time. Reflecting on what I’ve come up with, I think it’s also a valuable window into my values as a teacher.

Context: last year I taught 7th grade math every day, 60 minute periods. That was three periods a day, and the other two periods were rotating quarter-length electives on math games, personal finance, and coding. This year I will teach 7th grade math every day, 54 minute periods. Then I will have every student twice a week in a "math enrichment class." I will have three sections of core math averaging around 22 students, and four sections of enrichment math averaging around 16 students. One requirement is that I don't teach core content during enrichment time because students will often be pulled out, mostly for special education or English learning services but also for other things. There is also a push to improve test scores. Our test scores are not good, and that is part of the reason for this change. While that push exists, we've had a lot of admin turnover and the current folks don't seem overly concerned. I feel good about my plan for core math — we use the Illustrative Math curriculum as a foundation, and I mix and match with some supplemental resources and stuff of my own creation. I need to figure out what to do with the enrichment time.

I have four goals for math enrichment:

• Give students positive experiences with problem solving and exploration

• Support core content by responding when students struggle with a topic

• Improve foundational skills

• Create time for practice, makeup work, and catching up

There’s also an implicit fifth goal that this doesn’t take me forever to prep each week. I’ve tried to pick activities that will be useful for students, but also aren’t too hard for me to put together and plan for.

Here’s how I hope to meet those goals.

Goal one, give students positive experiences with problem solving and exploration.

The key here is that the experience is positive. My goal isn't for students to solve really complex problems every day or become the best problem solvers in the world. My goal is for students to have time to explore in a safe, supportive environment, broaden what it means to do math, and experience success so that mathematical exploration becomes something they look forward to and feel good at.

I want to do this in two ways. First, one class a week will open with a Polypad exploration in a Desmos activity. I wrote a while back about some models for interesting questions in the Polypad + Desmos format. I've refined those over the last year. Each activity will have 3-5 questions to explore with manipulatives about numbers, factors, and fractions, then an exploration screen with some sort of math art or other interesting tiles to play with, and then an open exploration screen. The questions will repeat and build on each other week after week so students have a chance to get good at them. The goal is to see math as something you can play around with and manipulate, while also using this space to practice some arithmetic skills.

Second, one chunk of class will be a "problem solving block." I'm interpreting "problem solving" very broadly here. There will be some math skills involved, but I want to expand what my students see as "doing math." Here are some examples:

• Exploring problems from Play With Your Math like this one about stairs or this one about squares

• Playing a few rounds of a game like 101 and You're Done or Half Fraction Snake and then strategizing the best way to win

• Making Mobius strips, cutting them in different ways, and trying to predict what we will get

• Exploring problems from Youcubed like this one about squares in rectangles or this one about Pascal's triangle

• Playing with Rubik's cubes and learning different moves on the path toward solving them (my department has a class set of cubes)

• Making a paper-size Sierpinski triangle that we then combine with other students' to make a large Sierpinski triangle

• Playing different versions of Nim and trying to find good strategies

• Exploring a simple game coded in Scratch

Some of this will be what people typically think of as "problems" in math class, but we will also do math art, explore mathematical games, code things, make things, and more. Again, my number one goal is that it feels like a positive experience that broadens students' horizons. There will be lots of math built in, especially practice with arithmetic, but the goal is mostly to have some fun in a "problem solving" context.

Goal two, support core content by responding when students struggle with a topic.

I want to do this in two ways. First, one class each week will begin with a warmup that asks students to answer self-explanation prompts about what they've learned in the last week. A few samples from our first unit might be, "In your own words, what does scale factor mean?" or "How can you tell if one figure is a scaled copy of another?" or "What is the difference between a scaled copy and a scale factor?" Students take a few minutes to reflect, then I facilitate a share-out and also use it as a chance to reteach or clarify any issues I'm seeing.

Second, I give a short quiz once a week most weeks. My goal is to look at student work and either build a short mini-lesson to address common mistakes, or work with a small number of students if a large majority did well but a few had trouble. This will often be structured as a mini-whiteboard lesson. I’ll do a quick intro clarifying any issues I'm seeing, then a bit of practice on mini whiteboards to try and solidify their understanding with the flexibility to do a few more problems if we need.

Goal three, improve foundational skills.

Again, two pieces here. First, each class will begin with Mathigon/Math for Love's Multiplication by Heart flashcards. They're quick and I had students do this once a week last year. I like that the cards are visual, they gradually incorporate more challenging facts, and they adapt to revisit cards students get wrong. This will be the very first thing students do each day, before Polypad one day and before the self-explanation prompts the other day

Second, I've put together an assessment in DeltaMath (an online practice platform) that covers all the foundational skills I hope students come into 7th grade with. Think basic operations, fraction operations, factors/multiples, stuff like that. It's deliberately narrow. I don't care about multiplying two mixed numbers, I'm only including adding/subtracting fractions with like denominators or denominators that are multiples of each other, I don't care about 2x2 multiplication. But the foundational stuff is important! Students will take the assessment about once every two months. Then, I will design mini-lessons on skills students struggle with. If they have a hard time multiplying a unit fraction by a whole number, I'll design a quick lesson building a conceptual foundation then have students do a bit of practice on mini whiteboards, with the flexibility to add more problems or explanation if students need. Those skills will be included in the weekly practice students do to follow up and further solidify their understanding. I'm imagining these as very short, under 10 minutes most days, but responsive to what students are having trouble with. If students aren't making progress I can follow up with them individually.

Goal four, create time for practice, makeup work, and catching up.

Each period will end with a bit of study hall time. I assign a little bit of DeltaMath practice every day, and a set of mixed practice spanning a range of skills about once a week. Students have some time to work on this during regular class but often don't finish. Our school also has the same absenteeism problems as most other schools right now, so this time will also be helpful for makeup work and retakes. Finally, this gives me some time to check in one-on-one with kids who need extra support. I have challenge assignments, math games, puzzles for students who are finished everything.

In Summary

• Day one: Multiplication by Heart, Polypad exploration, foundational skills mini-lesson, quiz follow-up, study hall

• Day two: Multiplication by Heart, self-explanation prompts, problem solving block, study hall

I’m still figuring out some of the timing pieces. It looks like a lot, but every chunk except for the problem solving block should be under 15 minutes, and I think the balance of consistent routine and rapid transitions will be helpful for engagement.

A Final Thought

So that's my plan. I'm sure parts of it will change as it meets the reality of the school year. There’s also a lot of nitty gritty that will have a big impact on my success or failure — the problems I choose and the way I frame them for problem solving, my routines around teaching with mini whiteboards, the specifics of foundational skills practice, and more.

I have one final reflection, though. I think this plan is a good microcosm of my values as a teacher. I want to create time for exploration, and make sure that exploration is a positive experience for students. I want to make sure students are learning core class content, and follow up when they are having a hard time. I want to make time for foundational skills practice, and to target that practice toward the most useful skills. I've written a lot in the past few months about procedural fluency and I'm putting a lot of that thinking to work here. When I was writing those posts I would occasionally get snarky comments about how there's more to math class than skill fluency. I agree! I hope this post is a good illustration of that. We're doing lots of other stuff that I hope will be fun and creative and exploratory. But we will also work on fluency with skills. Part of the purpose of all that writing was to figure out how to teach fluency efficiently. Fluency matters, but it's not a good use of time to do fluency for an entire period. My goal is to be specific about which skills students need to be fluent and which they don't, be efficient in mini-lessons and practice, and then move on to all the other stuff we can do with math.