Estimation

Filling it up!

by Jon Orr

In our grade 9 applied class we are finishing off linear relations and moving into solving equations. I want an activity that is hands-on, engaging, and shows a purpose to solving linear equations.

Here is some thoughts on an activity I want to try. Let me know what you think. Any feedback would be greatly appreciated.

Here it is: Filling it up!!

Show them this picture….

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Let them wonder, let them ask what that thing in the pitcher is.

ME:

“How many would be too much?”

“How many would be not enough?”

“How many is just right?”

Have them record the guess. “We’ll compare our answer to our guess”

Next,

ME: Let’s find out how many.

Organize them into groups of 3.

ME: What are we going to need?

We’ll need volume of the pitcher, volume of the cup, and volume of the weight.

Have discussion on:

What shape is the cup? …..is it more like a cylinder or a cone? Which is it closest to? What formula for volume will you use? Will you be right?

What shape is the pitcher? What shape is the weight?

Choose 1 member of you group to find the volume of the cup; choose 1 member for volume of the pitcher; choose 1 member to find volume of the weight.

Have the items around the room like stations:

IMG_2776

IMG_2775

IMG_2772Each member will find the volume of their object and bring it back to the group.

Allow the students to work

Here are some scaffolding questions I can use (Please feel free to give me some more)

  • What’s changing as you fill up the pitcher?
  • Does it start with zero volume? What volume of the pitcher is already taken up?
  • What volume is left after the weight?

Here is a possible solution….

IMG_2778

My idea is this could be great context for introducing solving equations using opposite operations! Use their technique  and show how the volume grows as the cups increase. Use Desmos and relate it to y = mx + b.

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show them how their strategy is the same as solving 5562 = 1511 + 335x. Boom! Context for solving equations!

My ideas for extensions would be to put objects like….

IMG_2781

in the pitcher. Count how many cups to fill the pitcher now. Use our equation to solve for the volume of the car. [Corresponding Grade 9 Academic learning goal: Find the y-intercept (initial value) of a linear equation given the slope (rate of change) and a point. ]

What do you think?? Think it would work? I would love some feedback!

The Best Estimates

by Jon Orr

So Dan sent out this tweet.

Wasn’t sure if he was asking Andrew to make a blog post or anyone, but I decided to share my thoughts!

If you’re not familiar with Estimation180…..become familiar quick!! The challenges/estimates have been great conversation starters, warm ups, and intros to math concepts in my classes for the last couple years!!!

So, to answer Dan’s question…..My favourite Estimates have been the ones that make the students do a double take! They make us say No Way!!! or How is that right?

Here is my favourite…

Day 52

It’s awesome because of the controversy! Very few kids guess that there are actually 12 ounces/355ml in that glass! Most think it must be more than the can! In my class we have had great discussion on reasons. Most say the camera angle in the picture is deceiving. They get angry because they think I tricked them. From this point on they are skeptical about all given information!! Awesome! Love it!

I love this whole line up of estimates. Great discussion come out of why the tall vase has the same volume as the Dessert Dish on day 54….

….and the glass on day 57

I think the kids get a kick out of watching the video answers too!

I’m a huge fan of these types of estimates too …. ”

How many small vases will it take to fill the large vase?

by these types I mean “How many of these fit in there?” These have worked wonders for some of our problem solving skills. After we reveal the the answer we take, for example the total ounces in the large container and try to work backwards and see if we can figure out how many small containers fit. (by dividing). By using these estimates as warm ups it has been an easy transition to solve problems like…

Screen Shot 2014-11-14 at 6.46.49 PMIn the past my grade 9 applied students have struggled with this type of problem. After using the “how many fit” estimates my students’ ability on this type have dramatically improved!

These are a few of my favourite things…

Again ….check this site out now…..Estimation180. Thanks Andrew Stadel!