Formative Assessment & 3 Act Math Tasks

This post references the 3-act math task structure. If this is unfamiliar to you read about it here from Dan Meyer, and here from me.

A common question I get about using 3-act math tasks from teachers is “How do you assess that?” And I’ve found it’s both hard and easy to answer this question mostly because for the last few years I’ve felt like I’m ALWAYS assessing! 

Let me explain.

“3-act tasks are formative assessment machines.” They’re naturally structured to give you the teacher rich information about your students understanding and knowledge.

From Wikipedia,

Formative assessment is, “a range of formal and informal assessment procedures conducted by teachers during the learning process in order to modify teaching and learning activities to improve student attainment.”

Keys words: “during the learning” and “modify teaching

When I first started teaching I asked about the difference between formative and summative assessment. I was told to think of it like: formative assessments were quizzes and summative assessments were unit tests. Both of which were marks that got recorded in a markbook. It was like the going mantra was, “Why are we marking it if I’m not going to count it?”. I’ve grown to believe that formative assessment isn’t just a packet/booklet/worksheet/homework/quiz that we count or don’t count for marks…..Formative assessment should inform us.  It should give us information to use to help craft our next instruction.

3-Acts and Formative Assessment

A teacher while observing one of my lessons commented: “Wow! Your students were so engaged during that task with the movie.” Most teachers I see are seeing 3 act tasks as a way to engage our students. In my opinion thinking that the power of 3 act tasks starts and ends with student engagement greatly undervalues the task structure. As a teacher you can learn so much from what your students show you during those first two acts. You just have to listen.
Those acts are all about assessing where you students are and designing, on the fly, where to go next!! And I totally I agree, That is definitely hard! It’s hard to plan to be flexible.

“plan with precision so we can proceed with great flexibility.” – Tom Schimmer

Act 1 is about  Being curious, Wondering, Estimating, and being informal. Listen to their estimates. Insist on having students share their reasoning. Don’t let them off the hook when they say “I just guessed”. You gain valuable feedback on their ability to use our Mathematical Processes. Listening to their reasoning will give you insight into possible strategies they will use when solving the problem. It will help you prepare on the fly possible scaffolding questions to push your students thinking.
Act 2 is for watching what your students do. This is your chance to carefully craft a plan. What strategies did you see? What strategies need to be shared and discussed? What strategies didn’t see and need to be introduced and modelled? For me, gone are the days where I develop a “lesson plan script” that I follow for the first 25 minutes of class. I need to know where they are before proceeding.

Let’s consider the proportion problem Turbo Texting (See the whole lesson here). See the act 2 video below.

Have a look at the student work after showing act 2.

What do you see? What information does this tell you? What would you ask this student?
Does the student know why they divided? Do they know what the 0.1125 means? Can they interpret to see who is faster? How can you use this to help craft your instruction when you bring the class back together?

Then when you see this answer, it’s clear that they knew how to interpret their calculation, but also informs you that you’ll need make sure both of these solutions are shared to the class. A great class discussion can occur here on how each solution shows who is faster and why we would want to find each rate.
Without allowing your students try their own strategy here in Act 2 it is most likely that both of these calculations would never have popped out. It’s allowing your students to show what they know that allowed for this discussion to happen.
Or take this example from the popcorn pandemonium task (read here first). View Act 2 here:

and a student’s thinking,

and another,

If the learning goal is to “Connect various representations of a linear relation” then seeing this strategy from our students allows us to take what they know and connect it to something new! We should build on their understanding not dismiss or overrule it. This can be powerful in their learning process. But without seeing their thinking first you wouldn’t know exactly what to build onto. To help our students the most we should be continually assessing where they are and where they need to be then design our instruction to make that happen. 3 Act tasks are amazing structures to assist you in this journey, they’re not just videos to engage your students……they’re so much more than that. Go ahead…… plan with precision.

Further Reading.


MEL3E Day 20

Since it’s October I picked a candy theme estimate from Estimation180. We chatted for the first 5 minutes about our favourite Halloween candy.

After some Too high, too low, and best guesses we revealed the answer:

If you teach MEL3E you may know that regular attendance from some students is an issue. There always seems to be a few students you only see once or maybe twice a week. Years ago I used to give these kids hassle when they came to class. I would give them a lecture about attending regularly….and if you think of all the adult interactions that kid had that day most likely none of them were positive. And I contributed to that. Even though they made the decision to come to class that day. And you know what….most likely that kid wouldn’t be back for some time.

Now….with this group,  all interactions are positive. I want that student who comes only on Thursday to have at least one positive interaction with an adult that day. I want them walking out after the class thinking that my room is “good” place. I feel they will be more likely to come back to school even if it’s just for math class. If they are there some good will happen.

So, with different kids being absent on different days it becomes tough to get every kid the practice and learning they need. The mastery days and spiralling works well to address this. If a kid is away all week they won’t necessarily miss the whole banking unit. We’ll hit this again next cycle. Mastery days will allow kids to work on what they need.

Today wasn’t technically a mastery day, but the day was broken into a few tasks.

  1. Some students finished (or started) the transaction activity from yesterday.
  2. Some students practiced more with updating their account balances from transactions.
  3. Some students worked on past work (timezones, best deals, tax problems).

Tomorrow we’re on to credit cards.

MEL3E – Day 3

I was so pumped for today’s lesson other than the fact that it was 30+ degrees in my classroom. We all sweated together!

Again we started with a Would You Rather  problem…this time with earnings.

Most students started with the hourly rate and calculated correctly on their whiteboard the weekly wage. They needed a bit of help going from weekly to annually. A few students took the opposite route of dividing the $30000 up into weeks then hours!

I took up both solutions on the board as they would become useful for the next activity.

We had a brief talk on gross pay, net pay, deductions, and payment frequency. I handed out the first page of the Pay schedule matching activity.


Click the picture to download the Word file

Students were to sort the pay frequencies based on most pays a year to least and paste onto the tracking sheet.

We took this up together and then I created a hard copy of the frequencies on chart paper to post on the wall.

They distributed the job titles among the schedules in any way they liked. There was one job title left blank so they could create their own title. Once this was pasted on the master tracking sheet they had to distribute the hourly rates of pay and annual earning among the jobs….now each student had unique problems to work with. Their task was to fill in the remaining spaces–the gross pay per period and either the annual earning or hourly rate.

What I found was most students could find their hourly rate when given the annual earning as long as the job title listed the hours worked in a week. There was lots of struggling all around with finding the hourly rate any where else. I could see some confusion with calculating gross pay in almost all cases. As a group they did not complete all of this activity and we’ll pick it up again tomorrow.

If I had to run this again I think I’d modify the slips so that first there was all hourly rates and no annual earnings….which would keep the calculation moving forward in time. Then I would give a second activity on another day with only annual earnings and ask for gross pay.

My goal was to dive right in and work through confusion and struggles as they come up. I think we’re there….now to work with the confusion and struggles!!

As for tomorrow I’ll start with some problems involving calculating gross pay from annual earnings and then come back to this task.

Day to day 

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…’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!