Pentomino Puzzles

A few years ago I was introduced to a series of activities (through my then districts math consultant) that builds a driving need for students to createscreen-shot-2016-09-30-at-8-14-39-am, simplify, and solve linear equations. I used the activity for a few years in a row while I taught grade 9 academic. Since then I had forgotten all about it (funny how that goes) UNTIL NOW!

The activity ran as a series of challenge puzzles around Pentominoes and a giant hundred grid chart.

Activity 1: Explore

Ask students in groups to choose this tile and place it on the hundreds chart so that it covers a sum of 135. The task seems so simple to start but unpacks some great math.

Allow them to determine this sum anyway they like.

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I circulate and listen to their strategies. I give them very little feedback at this point. After a few minutes I choose some of those groups I heard interesting strategies to share..then let any other group share out their strategy.

img_2198Activity 2: Keep Exploring

I have them use the same tile and try again. Place the tile so that it covers a sum of 420. Listen to those strategies! Most groups that didn’t have a strategy before will try to adopt a strategy they heard last round. At this point most students will catch the strategy “If I divide the sum by 5, being like the average then I should have the middle number in the shape.”

This is where I stop and have a formal discussion as to why dividing by 5 here works? Will this always work? Will this always work with other shapes? What other shapes will this work with then?

We formalize the strategy.

Our big problem to start is not knowing where to place the tile. Let’s say I label the middle square n. What will the square immediately to the right of n always be? The left? The top? The bottom? Have them check this out by placing the tile repeatedly back on the grid.

Now let’s add all of those expressions up

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The middle square must be a multiple of 5!!! I have them try this strategy out by throwing out another sum and have them place the tile.

Look at another tile!

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We go back and outline that we could have chosen a different square to label n. Which results in a new equation and solves for different value…..but results in the same placement of the tile!!

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We continue by me having them select different tiles, giving them sums, having them create equations and solving them. I love how hands-on this lesson is. Holding the tiles adds some “realness” which I feel drives the need to solve these equations.

However,

this year when I remembered this activity I wasn’t sure I still had the tiles kicking around (I found them later). I immediately made a digital version with Explain Everything.

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The digital version gives each student their own copy and while working in groups can chat about what strategy worked and what didn’t. Before on the paper version….only one student could hold the tile. Also, when students have to voice their strategy through Explain Everything they have to have careful thought. They think about the words they want to use. We this careful thought they get to make their thinking visible for me!

One new addition to the activity I get to make here is that they can create their own pentomino…..and then their own puzzle to share with their classmates.

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Since then I also created the activity with some help from the team over at Desmos

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Click to access and rune the teacher.desmos.com activity

I love their new conversation tools….I get to pause the class and discuss when needed!

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Students can even sketch their new tile and create an expression to match! screen-shot-2016-09-30-at-9-24-03-am

 

Desmos even added some nice extension questions. Love it! screen-shot-2016-09-30-at-9-24-23-am

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In the future the next time I explore this lesson I see a blend of hands on tiles with digital support. I think having the best of both worlds here can pack a powerful 1-2-3-4-5 punch!

Pick your favourite!

Download the Explain Everything Pentomino Puzzles .xpl file. 

Access the Desmos Activity

 

 

Random Winner Game – MEL3E Day 6

I’ve decided to spread some skills (expectations) around as warm ups. Today our warm up involved pay schedules.screen-shot-2016-09-13-at-11-52-17-am

They highlighted every two weeks on their sheet to indicate pay days…..and seeing which months had 3 payments allowed us to have a short discussion on making budgets around our pay cheques.

We picked up where we left off from yesterday’s practice sheet with percent. We talked again about different ways to get paid, including an example of getting paid by commission. I brought in the random winner game to give a little more excitement to just practicing. I usually use the Smartboard and sticky notes but this always ends up with a huge waste of expensive stickies. This time I re-used the 100 grid from the Explain Everything file from yesterday.


 I assigned each person a colour (I only have 13 students—-otherwise assign each pair a colour). Each time they get their question checked by me and it’s correct they earn a tile. If it’s incorrect give them some feedback and ask to try again. WHEN correct they go to the iPad and randomly choose one of the squares to cover. At the end of class we randomly chose one of the squares….and whoever is covering that square is the winner!

Now since we’re dealing with teenagers…..this excited some of my students and for others……not so much. Although one student didn’t want to place any tiles on the grid she still had all her answers checked by me for feedback.

Tomorrow will be our first mastery day. We’ll spend the day working on skills from the week plus a quiz.

Grab the Explain Everything File 

Percent Pile Up – MEL3E Day 5

Today I wanted to see what my class’s prior knowledge was around percent. Since they are 16-17 year olds they have been exposed to percent quite a lot. But since their math skills are operating anywhere between a grade 5 level through to a grade 9 level I wanted us all on the same page.

I started off with an Explain Everything file I put together. The slides start at a basic level but then creates a need to determine equivalent values that match a certain percentage.

Slide 1:

Getting the explain everything file onto each students iPad, or getting them connected to the wifi, or showing them how to type in a URL can take some time…..so slide 1 is an easy intro that students who are waiting can work on.

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Slide 2,3,4

I wanted to make sure that when we know the whole is 100 that just counting the tiles covered gives us the percentage. These were too easy for my students but it gave us some time to review writing a fraction as a decimal and as a percent. I asked students to tell me the percentage they covered and then we converted to a decimal and fraction. They had the option to record what they were thinking.

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Slide 5,6,7

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Right away almost all students covered 10 squares. I then asked them to convert their new fraction (10/50) into a decimal to see if we get 0.1 ….and then some shock on their faces appeared. Some students then knew their mistake and made some corrections. But we spent some time here going over the visual interpretation …..10% means that 10/100 are covered. This board had been cut in half so only 5 must be 10%.

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Slide 8-12

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This is where we generated a need for an algebraic (proportion) method. The students could estimate how tall he could be….but they had a hard time determining with accuracy how tall he would be. So this is where I stepped in and showed them how to calculate. The remaining slides with Fido and then with piles of gold and then finally with no visuals at all were to practice this method.

After all slides were finished they started on some more practice questions on paper. We’ll finish those tomorrow as most students just started it.

Grab a copy of the Explain Everything project file

Final Assignment – Estimation Challenge

For our final activity I started the off with this……

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we filled in too high, too low, and best guesses! Then we checked the answer…..

Completing this challenge got the students pumped and hooked into doing some math on our very last days of class (especially with some students exempted from the final exam). Our final assignment is to …

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We got out the iPads and I let the kids work….. here is what a few came up with:

A lot of kids did water filling or post it note covering estimates. Some kids ended up making an all-out 3 Act math problem.

Zack

How many caps will fill the marker?

Estimate & Answer

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Alexis

How many cups to fill the shape?
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Answer:

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Meghan

A 3- act task in Explain Everything:

How many post-its will cover this triangular wall:

Act 1: She put a photo and a small video in Explain Everything to start us off.
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Act 2: She provided us with a little more info after we made some guesses.
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and
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Act 3: Made a time lapse video and provided a screen shot with the answer

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Grab her Explain Everything File here

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Tiana

How many stickies to fill the door window?

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And hit us up with a time lapse video for the answer:

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Celina

How many water bottles will fill the hexagonal prism?

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and the answer

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Watch the water fill up by grabbing her Explain Everything File

A fun last few days….and I’ve got some new estimates for class next year.