Day 164: Dandy Candies

Geometry tackled Dandy Candies today. This 3-Act has a great flow and I love the animations in the video.

Candy

I made a couple mistakes along the way in asking students to solve for both surface area and ribbon used at the same time; too much was happening at once for some of ’em. However, they were able to answer both questions by the end of the period. I sent them home work the extension question of “Is there a packaging method out there that uses even less cardboard than option B?”.

Another great question just came to mind: Will the option that uses the least amount of cardboard always use the least amount of ribbon? These questions are scary close to maximum and minimum values of functions… Nice.

More to come on this tomorrow.

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Day 150: Ticket Roll (Student Work)

Continuation from yesterday’s post.

There were some interesting ways students went about finding the total tickets, have a look.

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I have been working on transitions within 3-Act problems.They always start really well then student engagement and quality of work slowly decline. Folding a sheet of plain old paper into 6 regions and having a purpose for each region has helped quite a bit.

For those interested

  1. Estimate: Guess, low, high
  2. Info they need
  3. Game plan of how they will use that info
  4. Provided information
  5.  and    6.    Work

One strategy that worked well today was I had students share out their confident calculations. I threw ’em on the board and then whoever had the closest talked about their solution process.

The tail end of lessons seems to be a weak spot in my daily instruction, I’m interested to hear in what sort of closing routines you all have.

Day 149: Ticket Roll

Geometry took a concept test today and started on The Ticket Roll from 101qs.

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3-Acts are a lot of fun, I have been working on having students develop all aspects of the problem: from the initial question I shift their thinking to what information they need. Then before giving it to ’em I ask how they would use their desired info. Here is the list my class came up with.

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A couple students reached a final number but a majority took the problem home, I am looking forward to hearing their solution methods tomorrow.

Day 143: Two Triangles

Geometry is starting a chapter on area, at the beginning of the period I put this up.

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It was fun to see students expressions as they figured out that both large triangles have the same base/height and are also made up of the same pieces. The group was able to come up with the solution after about 5 minutes.

For the rest of the period they worked on Dan’s Coffee Traveler Three-Act.

Here are some of the end results.

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Day 52: Arithmetic Sequences

In Algebra I use Dan’s Super Stairs to introduce Arithmetic Sequences. I used this same activity in Geometry which can be found on Day 15 and wrote about how I work Three-Act problems here.

The highlight of the day was when two students from two different periods recognized the rule n(n+1) in a way that I was not expecting…

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Most students used a form of arithmetic sequence to add 1+2+3+4+…+21 then doubled it. When I asked for the total students for 1,000 stairs this method came up short and directed them towards different solution options.

Day 47: In-N-Out Part II

This is a continuation of Day 46

Today I started Algebra by asking students to create a rule to find the cost of an N x N burger. I saw quite a few students take .9(n) + 1.75 or .9(n) + 2.75

Misconceptions are so much easier to address when they are about cheeseburgers…

After a bit of questioning students realized they were double counting some burgers and modified the equations to .9(n-1) + 1.75 and .9(n-2) + 2.75.

I stopped after this point last year, but after looking at Robert’s post I had students model the 100 x 100 case using 4 different representations: Numbers, Pictures, Symbols, and Words.

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I probably helped students a little more than I should have. I am still uncomfortable having them set up their own graphs… what if they put 100 values in their table?!?! I am still learning.

My district has some English Common Core Writing Protocols, so after this point students wrote a short paragraph describing their solutions using those.

We also had a great discussion on why the table represents a function:

T: “Why does it make sense for the relationship we see in the table to be a function?”

S: …?

T: …. waiting….

S: Each number of patties is paired with a single cost?

T: Why does that make sense?

S: I don’t want to pay a different amount for a double double than someone else.

T: Yeah… that wouldn’t be fair.

I am excited to try this activity again next year!

My Reflections on this…

  • I liked using the video as Act 1 then revealing the 100 x 100 picture later in the lesson.
  • I used the modified receipt from Tim’s post in one class then decided to go back to the original (I got called out and it kind of halted the class).
  • I still helped students too much.
  • The four representations were a great way of bringing the activity full circle.

Here are a few other posts on this activity I came across.

Day 46: In-N-Out

Today students started Day 1 of In-N-Out by Robert Kaplinsky.  My whole department does this activity to kick off functions in Algebra 1. I did this activity last year and have made a few modifications…

We started by talking about our favorite fast food places. Since Montana doesn’t have any In-N-Out it is nice for a student to mention the place so it doesn’t come across as forced. Last year we started with the 100 x 100 pictures. I mixed things up this year and showed students a video instead.

At this point we dive into 3-Act world.

Write down the first question that comes to your mind.

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The +6 shows that 6 other students found that question interesting.

In this period the main question How much would a 100 x 100 cost? didn’t come up. That’s ok. I helped them along.

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We took estimates. Sometimes I get crazy low estimates and that doesn’t bother me. However, this year I have been feeling that students are starting to take advantage of the amount of openness they have in math… So I took a page from Andrew’s comment here and asked students “Take a minute to look at the range of estimates we have, convince why any of them might not make sense” 

I didn’t just blow off the fact that Alex’s name was attached to one of the estimates, after someone called him out, I gave him a chance to respond.

After I showed students what a cheeseburger and double double look like.

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And asked them what they noticed about each.

They came up with pretty much everything; same number of buns on each, same condiments, different number of patties and cheese.

Students created a wish list of information they wanted to answer the question:

46.4

I added a new piece here that I REALLY liked… by asking students: what would you do with this information?

I then gave them this picture and set them loose to answer the question.

46.5

About half the class was done in two minutes.

There were two main misconceptions I saw….

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Instead of showing these pictures right off the bat I asked students “I am seeing a lot of different calculations. If we use a double double to find the price, shouldn’t it be the same as using a single cheese burger to find the price?”

They agreed. Then we worked through $2.65(100) and $1.75(100). They weren’t the same. We talked about what they were calculating.

******A big difference this year… This incorrect answer seemed to be discouraging. Students weren’t even sure if the 100 x 100 existed. So at this point in time I showed them the picture

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I loved the reactions and students had a good idea of how they needed to calculate the price.

In some classes we reached final calculations and looked at the receipt. I am saving that for the continuation of this post… coming tomorrow!