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.

 

Turbo Texting

The original idea for this lesson came from Al Overwijk. Thanks again Al!
The possible Ontario overall curriculum expectations covered in the activity:
  • Grade 10 applied:
    • graph a line and write the equation of a line from given information
  • Grade 9 applied & academic:
    • solve problems involving proportional reasoning;
    • apply data-management techniques to investigate relationships between two variables;
    • demonstrate an understanding of constant rate of change and its connection to linear relation
  • Grade 8:
    • solve problems by using proportional reasoning in a variety of meaningful contexts.
  • Grade 7:
    • demonstrate an understanding of proportional relationships using percent, ratio, and rate.
  • Grade 6:
    • demonstrate an understanding of relationships involving percent, ratio, and unit rate.

Act 1: Turbo Texting:

I started with “I was with my brother one afternoon and I needed to text my wife. After texting her, my brother informed me that I was a ‘terrible texter’. He said I was soooooo slow. I on the other hand disagreed. Then we decided to settle this once and for all—- race!!!”

If you’re viewing this through email you may have to click through to see the video

What do you notice? What do you wonder? Allow students a few minutes on their own to jot down their ideas. Then share with partners, then the class.
Here are a few questions/tasks I asked them next. I wanted to slowly build into deciding if this relationship was proportional.
  • What relationships can you see? — Number of characters in a text vs. the time to text it.
  • Create a scatter plot sketch of how the number of characters in a text affects the time to text that message.
  • How does this graph look with both texters on the same grid?
  • Who is the faster texter? Predict. How does your sketch show who is faster?
  • Kevin finishes first does that mean he is the faster texter?
  • How will we determine who is the faster texter? What will we need to see?
We took our time with these questions so we could develop and understand the relationship between characters in a text and the time to text it.

Act 2

If you’re viewing this through email you may have to click through to see the video

ME: “Use any method you choose to determine: Who is the faster texter?” I allowed them time here to work on a strategy. I watched carefully what strategies they used or didn’t use.

Seeing the different strategies gave us a nice discussion the importance understanding what rate we are determining and how to interpret it to answer the problem.

I showed this picture next:

and this piece of info…

Students completed this problem and we discussed the assumptions we needed to make.

Texting Time

How do your students compare to Jon and Kevin? Have them time each other while texting the 165 character message. Have them determine their texting speed to see who the fastest texter is in the class.

Linear Modelling

ME: “Now you may have texted that message in 18 seconds, but would you do this all of the time? Would you keep that same rate for a shorter message? Longer message? We better keep this experiment going.
I set them off to text various messages of different lengths using this handout (I modelled the handout format after Mary Bourassa’s Spegettini and Pennies handout – thanks Mary).

Click to download a copy

Students used Desmos and the regression tool to create a linear model. They used that model to predict how long it would take to text 140 characters, 200 characters, and this message: “Dear Mom and Dad I promise to never text and drive.” They finally timed themselves to compare the calculated time and the actual time.
Extension: Compare the relationship between the number of words in a message and the time to text the message. How would the equation change? Is it still proportional?

Magic Rings

A good friend of mine Brian McBain showed me this construction with two paper rings taped together. I had two of my daughters predict what would be made from cutting down the middle of both rings. Watch below.

They also wanted to make a survey to see what you would predict. Can you do us a favour? Watch the start of this video. Pause the video and make a prediction. Enter your prediction on the google form below. Then watch to see what is created! Have fun.

Can’t see the video or survey? Click through to the post

The Orr team thanks you for participating. If you teach a class go ahead and share this with them. We would love to see what other kids predict.

Assessment in MFM1P – Update

Here’s a short update on my grade 9 applied course. I’ll try to explain this as clearly as I can…bare with me.

An integral part has been our weekly mastery days. I’ve written about those days along with the tools that make them possible here. These days have been so important to our learning and we will definitely be doing them again next semester.

Allowing For Differentiated Learning and More Student Accountability.

Having these days allows students to have more responsibility in their learning not less! We are using a web based and app based tool called Freshgrade (You can read about how I set that up for mastery days here – this post will be mostly about the benefits). On our mastery days students have to scan through their portfolio and decide which learning goals (expectations) to improve on….then, they, the student, has to go and make that improvement happen (Each LG in Freshgrade has links to questions for them work on). So our mastery day is filled with students all working on different expectations from the course — according to their need. With the encouragement I give them they know it’s up to them to work towards mastery on each learning goal.

Student view of a learning goal to improve:

An activity in Freshgrade I’ve called a learning goal. Each one shows student achievement and next steps to improve.

Capturing Growth Informs Instruction & Assessment

The portfolio tool in Freshgrade is amazing. It captures and holds all of their work. It provides me great insight into their learning. As students work to improve their learning goals (expectations) they upload pictures of their work through the app. I get to see that work and provide audio or written feedback also through the web/app or in person. What I love is that I get to see all that interaction for each learning goal (expectation) forever. I can see the growth that my students are making. My old spreadsheet tool never tracked past work…only most recent. I love being able to see a student’s thinking progression as they attempt problems. It makes me as a teacher more confident about that student’s ability on the course expectations.

For example, this student uploaded a picture of their work on solving a proportion. They were confused on the nature of proportional relationships. After a comment and talking with the student they made corrections and re-uploaded. Their next step is to attempt a new problem to show consistency. That progression of learning stays in their portfolio for us both to see!

A student view of their portfolio:

Can’t see the video? Click through to the post

Capturing all of their progress and achievement in Freshgrade also provides me a ton of data. Since I set up the categories in Freshgrade to be the strands from the curriculum and each learning goal is assigned to one of those strands I get to see my class’ achievement on those strands. For example, If I filter the activities (learning goals) to only see the ones for linear relations I can see if we need to work more on linear relations. This has been great in the spiralled course. We can spend more time on what we need.

Gradebook view showing learning goals and student achievement.

I hope I explained our mastery day process clearly……now, onto an updated day-to-day plan for MFM1P.

Planning:

Each semester I’ve spiralled I’ve kept a spreadsheet that outlines my day-to-day. In the links below you can see those outlines in detail. I’ve included each semester on it’s own tab.

Webpage view of the outline

Get your own copy of the Google Sheet (You’ll need a Google account).

Sign up for a free Freshgrade account