Teach Math with Spiralled 3-Act Tasks – a full course

This semester was my first go at spiralling a course through problems instead of units. Traditionally we teachers follow the chapters and sections from the textbook. Well why not? It’s all laid out and organized nicely….most times in 1 day chunks….no planning needed, am I right???

How exciting is it though? How much do students really need to think? Are they really solving problems and learning mathematics.

After reading about spiralling from Alex Overwijk and bouncing ideas back and forth with Kyle Pearce we decided to give spiralling 1P math with 3 act tasks a try.

Each day or two I would  introduce to a new 3-act math problem (read Teaching with 3-Act Tasks) to solve with students. We would use that to stimulate wonderings and finally narrow down to a particular goals I wanted to cover.  Each of these lessons is taught with a 4 part math lesson (From Kyle Pearce) which always has students working on solving problems on their own FIRST, and then we step in and teach skills (“math teachery” way) after.

We did not teach within units. We mixed up our 3-Act tasks and problems throughout the semester.

I kept a list of all lessons, and order I used, along with any resources like blog posts, video files, handouts, etc. I wanted to share that list below.

Spreadsheet design was by Kyle

The spreadsheet shows for each day,

  • the strand we covered,
  • the learning goal (LG – for my assessment sheet),
  • the topic, notes for planning,
  • the inquiry lesson portion (3-Act math problem(s))
  • connections to other strands (a place for me to remind myself to tie this piece to other strands)
  • the consolidation/practice resources/links
  • other resources like blog posts, handouts, links, tweets, etc.

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You may notice the bright pink row. These are our assessment/mastery days. We had one whole class each week for this.

The first half of an assessment/mastery day class was handing back of past paper assessments that look like:

Assessment

Each one consisted of 4 questions that covered the learning outcomes of the last week or so.  I wrote feedback for any question that weren’t completed perfectly. They were to read the feedback and re-do those questions.

I let them know that everything counts…..I consider all our conversations, my observations and anything they hand in for their grade.

Also during the first half of class students worked towards upgrading their skills. They access their customized spreadsheet which shows their achievement on each of the learning goals. They choose a learning goal to upgrade. Based on their prior achievement they are given another task to try. After I assess this new task I go and change the mark for that learning goal.

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Both Kyle and I have written posts on this sheet a few times. (here, here, and here). An idea we extended from Alice Keeler.

We spend a good chunk of time working at getting better on our skills always promoting growth!

The last half of the class we do this week’s paper assessment (that looks like the one above). I mark it and give it back so that next Tuesday we can do that all over again.

Here are some benefits I have noticed from both spiralling and teaching through problem solving:

  • Almost no need to review at the end of the year. We reviewed all through.
  • Students see how math connects together. (Proportional reasoning shouldn’t stand as a lone unit when you have linear relations and algebra to teach too!).
  • Students were more confident in math than I’ve ever seen them. (And for 1P’s too!). When teaching in units, students know that whatever problem we will solve today HAS to do with what we learned yesterday. When we teach through spiralling students are always wondering what math they can use to solve the problem at hand. My students became great at risk taking! They would try! How many times has it been where we give a new problem to our students they complain that you haven’t shown them how to do this. My students were given new problems everyday and they became great a trying strategies. Whiteboards help immensely with this too!
  • A time saver! You may think that I would run out of time teaching this way…..I couldn’t possibly teach through problem solving and still cover everything, let alone booking a whole day dedicated to growth EACH WEEK! We had lots of time. Since each lesson tied multiple expectations and learning goals together, we could cover more in one lesson than we could in two lessons the old way. The growth/upgrades each week allowed students to practice skills from all over the course. Around mid-term time I gave my students an old final exam to see how they would do, and they did great!!! I was amazed. We still had half a semester to go!

Since we are coming close to the end I wanted to share my experience! Feel free to check out my daily plan from grade 9 applied

As always, if you have any recommendations or feedback for me I would love to hear about it!

 

 

Proportion Explosion

Since we are spiralling the curriculum in grade 9 applied, my math task choice is getting very picky! I always want to uncover more that one expectation in a lesson/task! In this task we used volume of spheres, solving proportions, and properties of linear relations.

Act 1:

We took questions and wonderings and then settled on the problem of Let’s see that balloon explode and when is that going to happen?
We guessed and recorded the guesses on our whiteboard for future comparisons!

Act 2: What will we need!

There were good conversations on this piece! I’m always surprised by how much kids know! Someone asked for the rate of water!!!! Wowsers! I assumed I might have to dig to get them to ask for that one. They also wanted me to say how much a balloon will hold…..which is where I wanted to direct them first.

Info to give and record:

As always, I made them guess for it! After revealing 12 inches….we converted to centimeters. Next it was their turn to go ahead and find the volume of the balloon. I find it so valuable to have discussions on why use a sphere to model the volume? Will we be correct? Is it ok we’re wrong?

Volume of the sphere/balloon

Act 2: Rate of Water

 
This is where the kids got lost a bit! They weren’t sure how to use this part exactly after just finding the volume of the balloon.  I stepped in and used some direct instruction on how to set up the proportion. Handout prepared:

Handout

FullSizeRender 14

Solutions

Act 3: The reveal

The extension is how we practiced solving a few proportions. We solved for the volume when the time was 10 seconds, 20 seconds, until kids saw the pattern.

10 seconds

10 seconds

After filling the table out, we found the first differences, discussed direct vs. partial linear relations!

Grab all the files to run in your class:

Help us Make the Awesome Assessment Tool We All Need!

Our semester is now half over and the use of our spreadsheet and mastery learning has been amazing. I didn’t think that the spreadsheet system Kyle and I created back in January,  based on Alice Keeler’s Google Sheet’s and Gamifying the classroom, would have had this much of an impact on student learning. But it did!

We want to take our Assessment spreadsheet for growth learning to the next level!

Students are empowered! They are taking learning into their own hands. They can see on their student view each learning goal (expectation) and their achievement on that goal. They have specific feedback on what to do next! They can access the customized questions based on their skill level and improve! More than before they can see exactly what to do next to get better. Screen Shot 2015-04-16 at 4.20.29 PMHowever, we know that the Master View of the spreadsheet looks intimidating to set up and edit. Screen Shot 2015-04-16 at 4.34.56 PM We have shared this spreadsheet with many educators from all different subjects, and we get the same response “This looks awesome! but…..it’s scary ….what if I delete a cell here or there by accident? Would it mess it all up?”

Answer: It could!

We love this tool….we want to make it better and so much easier to use. That’s where we need help!

We are just regular’ ol’ math teachers.

We imagine this on the web.

We need the help of web programmers.

In the web version:

Students, parents, can log in access and view their achievement. Share it even! A place to capture their learning!

Teachers can log in, track marks, provide feedback, award mastery badges, give next steps, reveal new questions for mastery, point to extra help resources all in one place. They could capture and store student work. Teachers could share learning goals (even whole courses) and the activities/resources they have with other teacher users.

So many tools are out there for assessment. None of them are a complete system. This one is!

We have so many ideas on where this could go….but we are stuck. We need it to be more user friendly.

Please share this out! If you know of anyone who wants to partner up, share our passion and help make this happen as much as we do….show this post to them!

Kyle over on Tap Into Teen Minds has also written a post. Go on over there are read his too!

If you yourself are interested in partnering up with us fill out the form below Let’s make that assessment tool we ALL Need!

 

Ready for round 2?

Second semester is starting tomorrow and I just wanted to get down my ideas on things I will be changing and things I will be keeping…..

New things…

I’ll be using the spreadsheet I modified from @alicekeeler. Although I plan on using Kyle Pearce’s further modified version.

I have slightly modified old my assessment approach (again). I’ll share later.

Kyle and I have been Tweeting back and forth all weekend about spiralling our grade 9 applied classes. We have been teaching using an inquiry based approach (4 part math lesson) and thought that spiralling would fit right in. We’ll keep you posted. Here is my day-to-day plan by topic and task, so far .

I’ll Continue….

a ton of stuff….but here are a few

Keeping my students curious.

Strengthening the connection between algebraic representations and graphical representations using Desmos! 

Documenting my class by taking a picture/tweet for every school day.

Warm ups – To start every class we do a warm up / starter. Most of these starters are math related but for me the most important part is that the starters allow our class to “Gel”. My buddy @Regan_bio is an advocate for always saying we should show our students that we are human and remember they are human too. Take the first 5 minutes of class and be a good human with your kids…..maybe they will be more ready to do some math!

Recently Mary Bourassa has shared her great list of daily warm ups for her grade 10 applied class. Check out her warm ups.

Here’s what we have been doing…

Monday’sEstimation180 – As a class we complete one of these great challenges (10 minutes). We track our progress on Andrew’s / Michael Fenton’s provided handout.

Tuesday’s – Visual Patterns. I choose a pattern for us to determine the equation.

Wednesday’s – Pictionary – Our class is split into two teams. They take turns drawing and guessing objects, sayings, math ideas that I have picked out. Most of the time this is a non math game. (10 minutes)

Thursday’s – Throw Back Thursday — I choose a question / skill that my class has been exposed to in the past and we work on our whiteboards on this as a review question.

Friday’s – 20 Questions. — I pick something and the class has 20 yes or no questions to try and guess what I have picked. We then play a second round where the class together picks something and I try to guess. (10 minutes).

Have an exciting second semester everybody!