# 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:
• graph a line and write the equation of a line from given information
• 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
• solve problems by using proportional reasoning in a variety of meaningful contexts.
• demonstrate an understanding of proportional relationships using percent, ratio, and rate.
• 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!!!”
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).

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?

# Reading Relationships – Literacy & Math

Friday last week was a PD day for us here in Chatham. We spent the day going over our OSSLT (Ontario Secondary School Literacy Test) results from last year and discussed how departments can make a difference. We came to a giant conclusion through the data that although OUR students could read…..they struggled with comprehension.

The OSSLT is a giant beast and most schools say “Literacy is a whole school issue.” I agree….but it can seem daunting to take on as a whole. Each of our departments decided to narrow their focus. Departments would choose a type of reading activity and incorporate that type into their lessons on a regular basis. We would own that type of reading assessment and use the data/results in June to see if we made a small difference.

Here is one sample lesson plan our math department created to do in our grade 9 & 10 classes.

## Generate Curiosity

Show students this Estimation180 challenge.

How many pages in this book?

Day 99 http://www.estimation180.com/day-99.html

Have them guess too high, too low, best guess (Grab Andrew’s tracking sheet)

I zoomed into the passage on the answer picture and asked students to read the passage silently to themselves and raise their hand when finished.

We discussed that different people read at different speeds. Students made sure to point out: “Just because I read slower doesn’t mean I understand less.” Connor wanted to go as far as saying that maybe if you read slower you will understand more.

These were great observations and I said let’s explore this more.

I had them guess how fast they read in words per minute. To help make this guess we counted up all the words in the passage above (51) and asked them if they thought it took a minute to read that passage. Some students agreed and predicted they read 50 words/min, some predicted much higher at 300 words/min. They all recorded ther prediction on their whiteboard.

Let’s discover our reading speed! We’ll explore the relationship between words read and the time taken.

## Predicting

Using the handout students predict what the relationship between time read and words read will look like.

## Finding our Speed

All articles are of appropriate length with questions that are of the same variety as the OSSLT. The key for us is the book also shows the number of words per article!!

I gave each student an article titled Jackie Chan Actor & Stuntman (1006 words) I also asked them to get out their phones to time how long it takes to read.

After reading, students are to answer questions based on the reading. We’ll take up and compare our score vs. Speed later.

They read, recorded their times and calculated words/min on the handout.

## Explore the Relationship.

We used this rate to introduce direct variation. We filled out a table showing words in 1 min, 2 min, etc. We showed it was linear and introduced terms initial value, rate of change, and direct variation.

I stole parts of Kyle Pearce’s template for our task Flaps for this handout

We went on to use our equation to answer the following…

Lastly after students answered the follow up questions from the reading we graphed our reading speed vs. our score on the reading. We’ll repeat this lesson again and again, each time adding to this graph…..trying to see if Connor’s statement — “does reading slower result in better understanding?”  —  true or false.

Run this lesson in your class:

Grab all Files Now

# Popcorn Pandemonium

My afternoon grade 9 applied class (as a group) is very outspoken, loud, and restless (maybe it’s because it’s the afternoon and they have been sitting at desks all day). They have been a challenge to keep on task. So….I  am trying to find opportunities for them to be outspoken, loud, and restless.

A few weeks ago I came across this post by John Berray. Using/eating marshmallows to compare rates of change. I loved his idea of “experiencing rate of change” I decided to re-purpose his lesson to meet our goal of—> “I can solve a linear systems of equations by graphing.” I also took his recommendation of using popcorn instead of marshmallows…..and it paid off!!

Here is the low down…. we start the “Math Dial” off low.

ME: OK you are going to have a good o’ fashion popcorn eating contest!

Here are a few from math tweeps

here are a few questions we can address with this problem.

• When will Tim and Don eat the same amount as Jon?
• Who will eat the most when the minute is up?
• Will there be a time when Tim and Don eat the exact same amount?
• When would Don eat more than Tim?

ME: Ok lets figure out who will eat the most in the 1 minute. But I want to recreate the video with you guys.

So I made a giant bowl of popcorn. (Don’t have time to make enough popcorn? — have kids give high fives to a timer instead)

Arrange groups of 2 or 3 and everybody grabbed some popcorn to start!

Round 1:

In each group kids are to choose who to mimic, Jon, Tim, or Don. They are to eat just like them! Allow them to ask about how fast each person is eating….or how much did each start with, etc.

Show Act 2 to answer those questions:

Tell them to get their timers ready….because they will eat just like one of those guys. Ready…..all you Tims and Jons eat your starting amount … Set….Go!

Start the timers and eat!

Question 1:
After they are finished, have them work out on their whiteboards who would eat the most in a minute.

Question 2:
When would Tim & Don eat the same as Jon if ever? (Great potential here for integer solutions talk).

Question 3:
During the minute, at anytime did Tim and Don eat the same?

If there was no time limit find when Tim & Don would eat the same?

Used this handout so they could create tables of values. Had them graph in Desmos!

The awesome thing was that my students were desperately trying to find the equations to match their graphs….they didn’t want to plot all the points. I visited each group helping them find the equations if needed. Once the equations were in desmos they knew where to look.

Act 3 – The reveal of who ate the most in a minute

Round 2: Do it all over again with new eating patterns!
Here are two possible eating pattern cards to give out:

Students who finished early worked on our Crazy Taxi  vs. a new Insane Cab

(@mathletepearce has a nice write up on using the Crazy taxi problem in class.)

Next day! Solving Multi-step equations…..will solve this systems of equations algebraically.

# Stacking Cups!

So we did Dan’s Meyer’s stacking cups lesson in class today!!!  I first saw this activity from Andrew Stadel in his 3-Act math collection. Not sure who first came up with it though. But thanks to both of you!

I started class by stacking the cups up in front of them…..allowed them wonder what was going on. They had questions like

“What are you doing?

“Are we having Hot Chocolate?”

“Are we going to use them to drink something?”

“How many cups do you have?”

and “How tall are you in cups?”

and bingo there we go!

I told them that is our task for today…To discover how tall I am in cups! I then had them estimate how many cups it would be! They were uncomfortable to start. They wanted to guess perfectly so they wanted to know how tall I was. They tried to put cups next to me as I walked around. They wanted me to lie down! I said just make an estimate to start off! I wanted them to guess so we had something to compare their final answers to. I wanted them to continually checking their work against their initial guess.

After a few minutes of estimating one group asked: “Are we stacking them like this…..

or like this…..

Awesome!!!! I said “Does it matter?” and they all yelled yes!!! So we then agreed that we had TWO problems to solve. So we put up two sets of estimates!!! We decided to stack them like the second picture first!

Estimates

“Did you need anything from me?”

they asked for: Rulers, my height, and Desmos!

I gave them all of those things…….everyone wrote frantically when I said I was 183 cm tall!!!

They worked! I saw groups stacking cups, recording values in Desmos, and measuring!

Almost all groups realized that the stack height was only changing by the lip amount and I saw a lot of this…

which had me excited!!! It gave me a chance to say: “Tell me about this, why do you think this is correct?” It was so interesting to hear their responses…..they were convinced they were right so I said let’s plot this in desmos and see if the equation matches the table

Oh!!

They knew they were wrong…..but what was awesome is that they knew how to fix it!!!! Desmos is awesome for this. It’s like a visual self correction machine! We discussed that the start of the line didn’t seem to match up with our points. Then the ahaa! happened.

“We didn’t use the zero row for our start value.” They fixed it and were visually rewarded with a correct answer.

After our equations were in desmos, the kids dragged their finger along the line until they reached a height of 183 cm and read off the number of cups! For the kids who seemed ahead of the game this was my chance to introduce solving equations by using opposite operations!

Finally we stacked the cups to verify.

Round 2: Stack the cups end to end.

Most groups divided my height with the height of 1 cup…..21 cups….give or take….So great! It gave us context when we discussed opposite operations when solving equations.

I found it was great that we had two problems in one! We are discussing how to distinguish between partial variation problems and direct variation problems. And here is one scenario where we got to look at each!!! Such a valuable activity!

Oh……did you want to know my height in cups (overlapped)??? —–> 128!

## [UPDATE: April 2015]

As an extension use the videos from Andrew Stadel to teach solving linear systems graphically! Access his task here

## Below are the list of Ontario Curriculum Expectations covered in this activity—-> Look at them all!!!!

• pose problems, identify variables, and formulate hypotheses associated with relationships between two variables
• carry out an investigation or experiment involving relationships between two variables, including the collection and organization of data, using appropriate methods, equipment, and/or technology (e.g., surveying; using measuring tools, scientific probes, the Internet) and techniques
• describe trends and relationships observed in data, make inferences from data, com- pare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses
• compare the properties of direct variation and partial variation in applications, and identify the initial value
• express a linear relation as an equation in two variables, using the rate of change and the initial value
• describe the meaning of the rate of change and the initial value for a linear relation arising from a realistic situation
• determine values of a linear relation by using a table of values, by using the equa- tion of the relation, and by interpolating or extrapolating from the graph of the relation.