Peregrine Falcon – Fastest Animal Alive

I need your help…..

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….

and then Complete these tasks?

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.

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?

Perimeter Jumble

You’ve seen this problem before.

I was discussing this problem with a co-worker a week or so ago and they suggested I change the scenario to a fence around a skate park….”to make it more relatable to students.” I wasn’t sure that particular fix was going to make my students want to solve it more (more on that from Dan here, here, and here). Instead, “I want to make it more curious than that…and get my students to do most of the heavy lifting”.

The textbook and many teachers will tell you to break out the geoboards and bands. But I still feel like that is telling them what to explore. I wanted them to ask the question before we do the exploring. How can we make this topic more curious?

Here is my attempt at making this more curious:

Show them this and ask for what do you notice? What do you wonder?

Today, my students noticed: “The number of pieces stayed the same,” Different rectangles, squares were made,” “The rectangles were blue,”

Today, my students wondered: “What would the perimeter be?” “How big were the rectangles?” “Were they all the same area?” “Why are we doing this” “Which shape would be the biggest?” “How long was each piece?”

I circled the wonder: Which shape is the biggest? But I extended it…. I confirmed some of their other wonderings like…yes the number of lines didn’t change. How many did you see? Did you guess 24?

screen-shot-2016-12-20-at-1-35-17-pm

Draw one of those rectangles you saw on your whiteboard. Write the dimensions. Determine the area.

I asked each student what dimensions they had and the area. Who has the biggest? I extended the idea….”I wonder what would happen if we had a different number of lines, a different perimeter to work with?”

The rest of the lesson would flow much like all of those geoboards lesson (get their hands/minds working — the less I talk the more they learn).

I assigned each pair of students a piece of chart paper with a new perimeter to work with. Draw rectangles with your set perimeter. Record the dimensions and the perimeter.

img_5398

The recorded on the sheet:

screen-shot-2016-12-20-at-1-35-01-pm

I showed some pics of student graphs on the TV and we concluded together that squares were making the largest area!

The groups then turned to doing some practice problems of “Here is a perimeter…what dimensions will produce the max area” and the backwards questions…”If the largest rectangle has an area of ___ what would the perimeter be?” Some groups were given the problem where we only use 3 sides to enclose an area. What now will make the largest area?

Stripping this problem of context didn’t make them want to investigate less……in this case my students were engaged as much as I’ve seen them lately.

I wasn’t pushing them to memorize that it’s a square that will give the max area….I feel like the big idea here for us was taking our own wonderings and investigating them systematically to discover a relationship. For me that is the bigger take away for these grade 9 students.