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?

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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.

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The recorded on the sheet:

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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.

 

 

Really Big Lights – A math problem

Here’s a really big problem you can work on with your students this holiday season.

Act 1:
Show them this video and ask: What do you notice? What do you wonder?

After allowing them to voice their noticing and wonderings guide them to wonder: How big is that new light? How many times bigger is the big light compared to the old light? How many Really Big Lights would you have to put up to cover the same length as last year?

Act 2: Here are some images to help make some conclusions:

Guess: How long is the big light? How many times longer is the big light than the small light?

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Reveal:

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Guess: How many small lights are in one string that stretches 15 feet?

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Reveal:

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Work together to determine how many Really Big Lights would replace the string of 50 lights? What assumptions will you make?

Act 3: Reveal

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Why might your calculated answer be different from the answer shown?

If you had 50 Really Big lights how long would could they reach? How many cars could you put in that garage?

Grab all files for this activity

You can see more info about the lights over at http://reallybiglights.com/

Energy Bites! – 3 Act Math

Today I made our go to snack…..peanut butter bites. My kids eat these up like crazy. I turned the making into a math task.

Act 1:

Ask for what they notice and what they wonder?

The intended question here is: How many energy bites will be made?

Have them guess. Too high…too low….best guess.

Ask for what information we would need.

Act 2:

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They may notice that the ball is not quite lined up right. How will the adjust?

and

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Is the bite a perfect sphere? Will a sphere be good enough? Give them the volume of a sphere formula. Let them work.

You students may notice the dimensions of the bowl…..or also may notice that its filled up to the 500ml mark. An interesting task will be to calculate the number of bites using either the volume using the dimensions or the volume using the measuring cup.

Act 3: The reveal

Possible sequel question:

What would be the diameter of the giant Peanut Butter Ball if all 22 were mashed together?

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And now for the recipe….as requested by Meg Craig!


Link

Two Trains…

How many of you have seen a problem like this one?

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I’m a fan of taking a problem like this, one that you would assign for homework (in the “application” section of the exercises….and one that very few students even attempt….and someone will ask you to take it up next class) and bring it to the start of my lesson. I’ll teach our concept/idea through this problem. But we can’t just throw this problem up on the board and say “Let’s solve it”……because no will want to. There is no drive for any of us. Like Dan mentions here….who cares!

Who cares about the trains travelling…who cares that they are even trains….they could be bicycles, or cars playing chicken….but is changing the context really going to change how engaging the problem is to students? Dan argues no. I agree.  Before you read about this lesson check out this post on Real vs. Fake world….and the Circle Square lesson on 101qs.com which was an inspiration for changing the Two trains problem around.

Here’s my go at this one:

Show them this video:

ask What do you notice? What do you wonder?

Have students guess WHEN the two dots would meet?

Give some more info

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Have them guess on WHERE the dots will meet?

Have a discussion on what will be needed to determine the times and distances. Spend some time here on speed. Go over the relationship between distance, time, and speed.

Show them this image and have them makes some guesses on where the dots are now.

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then reveal

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Calculate the speeds of the dots. Have students go back to their original guess on time and find how far each dot would travel.  Who in the class is closest? Did anyone guess right?

Now help them generalize…

Create the equations

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If our lesson is on solving this using an algebraic technique we can teach them that here. Or maybe we want to show them the graphical solution. Either way we have taken the tougher question from homework that no one cares about and used it to set up and teach a skill.

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and finally,

I’m sharing this lesson now (before I teach it) with you hoping to get some feedback. Writing these lessons here also help me work out the details. This is week 4 of the #MTBos blogging initiative and its focus is lessons. I won’t get a chance to teach a lesson this week. Our school had final exams and then PD days in preparation for second semester. Good luck to all those starting up again!!