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.

In math we chose reading informational texts and answering multiple choice questions based on those readings.

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)

And the answer.

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.

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Finding our Speed

A great reading resource is the series  Critical Reading Series. 

Screen Shot 2015-10-28 at 6.34.54 PMAll 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

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

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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.

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Run this lesson in your class:

Grab all Files Now 

Fast Clapper

One of my favourite lessons to do with my grade 9 applied students is the Fast Clapper! I first saw it on Nathan Kraft’s virtual filing cabinet! My main goal here was to solve proportions through algebra.

We started class like this:

ME: Hey guys get ready…..I want you to clap as fast as you can……Ready…..Set……..GO!

Class: They clapped. Some students gave it their all….some not so much.

ME: Ok….That’s enough. Now let’s make a competition out of this! I want you to clap as fast as you can for 10 seconds….count how many claps you make! …Ready —– GO!

Class: This time all of them gave it their all!!

ME (after 1o seconds): STOP! Great job! Quick, write down how many claps you made in those 10 seconds. Who thinks they had the most.

James: I did….I had 37 claps

Josh: Nope, I’ve got that beat……48 claps.

Shylynn: I did 56

Class: Whoa!!

ME: OK….now find how many claps you made in 1 second!

They did this pretty easily and we went around the room again….still seeing Shylynn with the highest!

ME: Great job…..now watch this guy….

Hayden: Wow!!! that guy can clap

ME: I know….Let’s watch again. This time watch the video and try to see something you didn’t before.

We watched a few times. Each time students would notice something different. We noticed:

  • He closes his eyes
  • The record is 721 claps per minute — “I wonder if he’ll beat the record”
  • He clapped 58 or 60 times in the video
  • The video only showed the first few seconds

ME: Let’s take the suggestion to discover if he beats the record. Who thinks he’ll beat the record? Who thinks he’ll tie the record? Who thinks he won’t beat the record?
We took a vote and recorded it.
ME: In order to see if he beats the record we’ll need some of that info from the video…..but we better be exact. Why?
Janice: If we’re off by a clap in the first few seconds….it could be huge after a minute.
ME: Ok, let’s be exact.
Jake: We could pause the video on the last moment to see.

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Judy: He claps 63 times in 4.6 seconds.

ME: OK….go for it. Work together to see if he beats the record.

They got going and I needed to work with a few groups to discuss how to get started. “IF you could find how many claps in 1 second how could that help?”
After some time I stopped them and showed some students’ solutions

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We then showed the rest of the minute!

We moved into re-solving the problem using ratios and proportions. I went through slides to show how to set up the proportion and how to solve it with algebra.

I’m a strong believer in letting the students struggle and persevere through problems. I want them to use their prior knowledge to solve the problem in any way they can, any way that makes sense to them. I can see their understanding when they have to explain their thinking to me and the class. After they solve the problem in their way…..I take what they have done use it to explain the “math teacher” way.

Today one of my grade 10 academic students was solving a problem and I could see some good thinking on the page….but he also wrote: I don’t know how to start this. I asked him right there why he wrote that when he had almost a full answer on his page. He said “I know that’s not the way you want me to solve it!” I jumped on that quick and said….”I want you to solve problems that make sense to YOU. Just show me your thinking” He went on to solve the problem with in a great way.

We need to build our students confidence up. We need to promote and value their solutions instead of forcing our solutions on them.

So, back to Fast Clapper: I used their solutions to help explain why the math teacher way also makes sense. Here is a silent version of the slides I used.

We moved on from here to solve Dan Meyer’s Sugar Packets problem and the Smart Car Smash to practice solving proportions with algebra.

And then used a Knowledgehook gameshow to practice some more…go ahead, give it a shot.

Introducing Trig through Slope

Here is our lesson today to introduce trigonometry for the first time. We had spent a few days with solving problems with similar triangles. We are spiralling and have done  lots of work recently using slope and the distance formula to classify triangles. I wanted to capitalize on that familiarity with slope to introduce the tangent ratio for the first time.

We started with this….again

Most students like last time chose A and their reason was it was less steep. So I asked “How much less?” “How do we measure that?”……SLOPE was the response and they calculated the slopes to verify.

Next I had them do this…
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I stressed supreme accuracy and added “Try to create a size of triangle you think no one else will make”……I had them measure their rise and run and enter them in this table on the board.

Table

I also kept a running table in Desmos…

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As more students added their triangles I could hear them say, “I bet all the slopes should be the same” , “They’re all similar triangles” We took a moment to discuss similarities and make it clear we all have similar triangles and that the ratio between the rise and the run should all be the same. We also discussed why some of our triangles did not have a slope of 1.7. I had them repeat the process with an angle of 45 degrees.

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I said out loud that MY slope ratio was 1….and I could see all their heads bobbing up and down….”Yep, we got 1 too”.

Next….

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I asked them again to create an angle/triangle (Had them keep the same orientation of the triangle as I did in my diagram) that no one else would.

Measure the rise and the run, then calculate your slope. Keep your triangle and slope hidden, especially from ME.

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Keeping their angles and ratios hidden from me I said…”When I point to you tell me your angle….and I’ll magically tell you your slope” Cue the Oooohs and aaaahs.

I played up the magic bit. I held my calculator up to shield the screen from them.

I pointed at one student they told me “34 degrees”. I punched on my calculator mysteriously and said…”0.67.” The student yelled out….”Hey that’s right”. I went around the room pointing at students and telling them their slopes (ratios). I could see it on their faces, they wanted to know how I was doing this……Boom Let’s talk about Trigonometry.

So I said:

“In math we have these things called functions….they’re like black boxes that take an input and do some number crunching and spit out an output. One function you have used already is the square root function. You give the function 9 and it spits out 3. We math people use a symbol for this function so we all know what is going on. There is another function that will calculate the slope of a right triangle if you give it the angle. So we could write something like this “(I used one of the students angles).

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“This is what I was doing when you gave me your angles….I was using the function to calculate your ratio between rise and run. But we don’t usually use the term slope when we talk about right triangles. We use fancy words.” I had them draw a right triangle in their notes and we labeled it with Hypotenuse, opposite and adjacent. Screen Shot 2015-10-08 at 5.07.34 PM

“Instead of using a slope function…..we use the word TANGENT. And instead of using the word rise we use the word OPPOSITE and instead of run we use ADJACENT. So we can write this tangent function equal to the rise/run = opp/adj.”

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“And we math people don’t like to write too much so we really use this version.”

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Then we practiced using the tangent button on our calculators. They pretended to be the magicians and checked each others ratios. We practiced using the inverse tangent button to find angles.

Once we were comfortable we moved into writing the ratio and finding the angle out. We also used this example to write the tangent ratio of the other angle.Screen Shot 2015-10-08 at 2.21.05 PM

and then one more for lengths:

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Since we are spiralling I gave them the homework set (Mary Bourassa Style) to work on….here.

Tomorrow I’ll introduce the Sine and Cosine function.

Using slope here to introduce trig allows us to take something familiar and make something new. Students could see the progression happen and not have trig just thrown at them.

Would to love to hear your thoughts on this. How do you introduce trig?

 

Sneak in Solving Linear Equations — SolveMe Mobiles

As part of my day to day warm up series in my grade 9 applied class we are solving  Solve Me Mobiles. Like what VisualPatterns does for my students and learning and discovering linear relations — Solve Me Mobiles is having students solve equations without really knowing it.

Puzzles are presented with minimal distraction and with clarity. Puzzles require no explanation. Students know exactly what its asking for.

Today we started on Puzzle 12 and completed up to puzzle 14 (first 15 minutes of class).

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https://solveme.edc.org/?mobiles=-12

As students explain their strategies to the class I translate their words into small equations…. All with the goal in mind of sneaking in equation solving.
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Jill easily solved a 1-step equation on the left side…and then used pictures to help solve the 2-step equation on the right.

Onto Puzzle 13,

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https://solveme.edc.org/?mobiles=-13

After Carl explained his strategy I used the opportunity to discuss opposite operations.

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https://solveme.edc.org/?mobiles=-14

Here’s what one student wrote to solve this one…

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And we translated that answer into this one.

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All this took about 15 minutes of class time….and then we were onto something else!

Work it in! —- SolveMe Mobiles

Other Warm Up Posts: