# Fuel Sense Making & Black Box Defrost

### Sparking Curiosity:

I put this video on infinite loop while the students filed into the class. I let it play and said “here is your warm up today”

I said nothing else. I was letting the curiosity build. After it looped and looped students started to work. Without saying a word about it students were trying to find how long it will take to defrost an item that weighed 3.5 pounds.

### Igniting MY Moves:

Since I routinely let students struggle to solve problems instead of showing them immediately a “how to”, I have to be ready to give feedback on what they try on the fly. I want to help push them in not only a direction that solves the problem but prepares them to see solutions that are not their own and solutions that attempt to address our learning goal for that day. That takes careful planning which is not an easy thing.
Plan with Precision so you can proceed with great flexibility” – Tom Schimmer.
When I first started teaching so much of my planning was solely focused on answering questions like, What topic? What examples?, and How long do I spend on it? Now my planning time is mostly spent trying to answer: How will the students solve this problem? How can I use what they will do to shape the lesson? What do their attempted solutions tell me about what they have learned so far? So my planning process has gone from examples like this where I was so concerned with WHAT….
to spending most of my time thinking about HOW. HOW will the students respond to the task? What does that look like? That takes a ton of anticipation. Anticipating their solutions and strategies puts me in a better position to understand their thinking and help shape that thinking. For each possible attempt I need to be ready to provide feedback to help them achieve our goals.
For the Defrost Black Box problem from above the learning goal I am hoping to pull out is “Relations can be represented in various ways” and “Problems can be solved in a variety of ways” I anticipated that some of my students would attempt to solve it with a unit rate.
Possibly some of my students may solve it with a table of values and linear relation.
Some may set up a proportion.

The book 5 Practices for Orchestrating Productive Mathematics Discussions has been an invaluable guide to help me re-design my planning time.

### Fuel Sense Making

Since my goal is for students to see “Relations can be represented in various ways” and “Problems can be solved in a variety of ways”
I need to be ready to fuel their sense making by linking the different student strategies together.
Here are some of what the students tried.

I did not anticipate students using seconds.

I also did not anticipate students using additive thinking with the unit rate.

We learn so much from our students by allowing them to show their thinking. Imagine all the missed conversations with my students from 2005 – 2013. Imagine how many of my students felt like they were failures because their brains didn’t tell them to solve those problems the same way the I did. When in reality they had so many good insights that just needed to be tailored.
Selected students presented their strategies to the class. Now it was time to show how their strategies connect together.
We showed how the unit rates that many of them found and used showed up the table solution.
We moved from there to show how this would be represented on our number lines.
Yes the planning that comes from Igniting My Moves and Fuel Sense Making takes time and it is not easy. But I can tell you that it is worth it.
On a side note: Help me settle a problem. A teacher said, “Students might find a real microwave more engaging than the fake one you have shown.”
Is version 2 of the Black Box Defrost more engaging or worth doing more because it is real? What are your thoughts?
Version 2: The More Real version

# Polygon Pile Up

When it comes to angles involving parallel lines, triangles, and other polygons I’ve always assumed my grade 9 applied students “get this”. I’ve felt that angles were an easy topic. I guess I thought this because most students seem pretty happy when solving angle problems and for the most part being doing pretty well on assessments. However, this year I noticed two inadequacies that I am trying to address.

1. Most of my students didn’t actually know what an angle measurement of 65 degrees really means.
2. They have a hard time determining what information is needed when solving multi-step angle problems. Lack of a good strategy.

When having students determine angles in triangles almost all of them knew that all three angles should add to 180 degrees. The trouble came when I saw some answers like this (from more than one student).

What bothered me was the location of the 40. I wondered why outside the triangle? I pressed this student for more info. I asked him to draw me any right triangle and label the three angles.

Hmmm…I asked him to point to one of the angles. He pointed to where he labeled the 85. What I found is that this student was mixing up length measurements with rotational measurements and he was not alone.

I found a great activity to hit this head on. Laser Challenge from Desmos worked wonders to get my students to understand and experience rotational measurements. Students have to enter values to rotate the laser and mirror to hit targets.

My students “felt” what 60 degrees is. Experiencing that rotation made all the difference to clear up what we were actually measuring. When second semester rolled around and my new crop of kids came in we started with this activity right away.

Most of our students struggle with solving complex problems where they have to think of a strategy. Before I gave them something like this,

I wanted to them to experience what information would be useful to know first. I decided to turn the problem around and inside out.

I gave them this.

I wanted them to think backwards….just like we need to do sometimes when solving longer problems. On the “easy” side most filled in 3 angles in the quadrilateral. What was great was that prepared them to think what we could leave out for the harder one. This simpler diagram challenged my class to think, plan, and strategize!

It was great to do this before we introduced this puzzle Jim Roesch, Kristyn Wilson, and myself created:

[There is a video embedded here — Can’t see it? Click through to the post page]

Here is the puzzle

And to really challenge yourself or your students here is a blank one. Can you fill it in so it’s “hard” to determine that indicated angle? What is the least amount of info you can give to bring out the most amount of thinking? Share them out!

# Peregrine Falcon – Fastest Animal Alive

I modified this video originally from Vox for a colleague and her math class.

Could you watch this short video on peregrine falcons with your students….

1. What do you notice? What do you wonder?
2. What questions will you work on with your students? Work on them.
3. You can watch the full video here to see/hear un-bleeped values.
4. Take pictures of any thinking your students show you. Send me comments & pictures on Twitter, email, or here.

I’ll update the post with your student’s work.

Thanks,.

# 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.