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.

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.

Slide 5,6,7

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%.

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.

Last year around this time I shared out a Google Form for classes to record measurements around their pumpkins and make them explode! I shared that form on Twitter so that we could crowd source as many pumpkins as we could to make the sample size large enough. I was pretty shocked at how many schools from North America took on Pumpkin Time-bomb. By the time Halloween was over the spreadsheet had over 90 entries. That’s over 90 pumpkins exploded in the name of math and data collection.

This coming week let’s add to the data and use the it in our classroom to discuss: Scatterplots, Trends, Correlation strong, weak, no-correlation, lines of best fit, correlation coefficient, etc.

Here’s a sample lesson you could use on the day you make your pumpkin explode.

Generate Curiosity

Play this video which shows Jimmy placing rubber bands around his pumpkin.

How many rubber bands will make the pumpkin explode?
Have students write down a guess that is too low. Too high. Then estimate their best guess.

Show the Act 3 Video

Now Bring out your pumpkin for the class to see! Have them predict how many rubber bands it will take before it will explode. Repeat the estimation process. Have them save their guess till the end of class.

Making A Model

Throw out the question: “What measurements of the pumpkin changes how many rubber bands are used?” Let your students brainstorm a list of variables. Have a discussion on variables & relationships. Write all the variables on the board they come up with. Narrow down the list to items that are measurable with the pumpkin we have in the class. What affects the explosion the most? Height, diameter — circumference, thickness of the wall?

Have them choose a variable that they feel should have a relationship with the number of rubber bands. Fill out the prediction part of the handout.

Click here to grab a copy of the prediction handout

As a class measure all variables needed. Write them on the board for all to see.

Analyzing Data

Give students the link to the spreadsheet of all the pumpkins to date (You should copy and paste the data to your own sheet so you can filter/sort the results and share that sheet out to your students.)
Discuss with your students the lack of consistency in the selection of rubber bands from all over the country. How can we minimize this variable skewing our results? Filter the data with your students(or before hand) showing one type of rubber band (Most common is a rubber band of length 8.65 cm). This will only show all the pumpkins that have been destroyed using that type of band.
Get your students to grab the data that relates to their relationship.

For example:
If Kristen chose the relationship Circumference vs. Rubber bands she should copy and paste the circumference column and the rubber bands column into a new sheet side by side. Then copy and paste all that data into the pre-made Desmos File.
She can adjust the scale in Desmos as needed. Have her move the movable point and drop it where she thinks your class’ pumpkin will lie. Or you can have her find the line of best fit to help predict how many rubber bands it will take. Either way we want her to predict with more accuracy.

So Kristen would predict that if her circumference was 90.5 cm then it will take 272 rubber bands to blow up the pumpkin!

Now if Kristen chose a variable that it was clear there is no relationship then you get to have a discussion about correlation vs. no correlation. Have her choose new variables to predict on.

Once everyone in the class has a new prediction start wrapping bands around that pumpkin (You may want to start this as early as possible).

Watch your pumpkin explode and give congratulations to the student who predicted closest to the actual number of rubber bands.

Don’t forget to enter all your data to the sheet by filling out this form (you can also use the form to show the videos to the class).

So today I gave them this slide and said I want you to solve a puzzle!

They broke out their iPads and used the Algebra Tile app to put together the rectangle. The kids worked away and you could see them trying to put tiles in a way to make the rectangle
….and they soon found out that they had to fit a certain way!!
On take up we made sure everyone had either my rectangle or a rotated version.

Then we did this one…..

After we were done I asked the class: “If the combination of squares and rectangles makes up the area, what are the dimensions of the rectangle?” They had a little bit of a hard time here, but finally could see the x + 4 and the x + 2 as the length and the width. I then wrote …

And then I heard some “aaah”s. We had previously seen both versions of the quadratic expressions and discussed why the factored form helped us out quite a bit if we wanted to find the x-intercepts.

We stopped there….It only took us 15 minutes. Tomorrow we will do a few more…..always writing the factored form after. I will also try to get students to notice efficient strategies to make the rectangles.

Why did you put 4 x terms along the width and 2 x terms along the length?

How does that relate to the number of singles?

Where I hope to go with these warm ups is to factor all types of trinomials:

Perfect Squares

This time…..make a square

… and get this…

Trinomials of the Type ax^2 +bx + c

Completing the square too!!!!

This time…make a square

We’ll be definitely working our way out of the app and onto paper with area diagrams…

Factoring

Completing the square

Completing the square

I think working with these puzzles for the next few weeks first will give us a strong base when it’s time to factor to help solve equations and then complete the square. I think I’ll track all the warm ups we do like this and I’ll post them all!

For many years now my classes have been completing a course wide project on Picture Modelling. Before Desmos (B.D.) I use to send home copies of Geometer’s Sketchpad for students to generate a picture using only functions.
After Desmos showed up it was now super easy for students to generate art and access graphing software from any device.

The project has been so successful at engaging students to learn about various functions and their transformations I extended it to all grades! For the last few years the project spans grades 9 through 12. Each year learning new functions and creating art.

This summer while at the Apple Distinguished Educator Institute in Miami I started a project that would create a digital resource that would link the Modelling Functions with Art Project with function challenges created by Michael Fenton, Dylan Kane, and myself.

If you are in an one-to-one iPad room or have access to iPads the resources are in an iTunesU course and multi-touch book for iPadotherwise they are linked on this site for any device (see below).

Each chapter starts with linking patterns, tables, graphs and equations in pre-made Desmos graphs or in pre-made Desmos activities made using Activity Builder. Following that, activities ask students to match functions to specific criteria like Michael Fenton’s Match My Line or in my Match My Trig Function. Again the teacher can choose to use the activities in the Multi-touch book or from the pre-made Desmos activity.

Every so often in the challenges students are asked to show their thinking by uploading a picture of their work on a Padlet page. Students can crowd source different ways to solve the same problem.

Finally, at the end of each chapter students are to create a working piece of art and share it on a Padlet gallery page! Students can see each others work and comment.

Each chapter covers different functions but many chapters can be done in the same course: