## Redefining Mathematics Pedagogy with Contextual Tasks & Technology

### Tuesday August 1st, 2017

Thank you for joining me for some math geekery at the **Whittier California EdTechTeam Summit**! Please feel free to utilize the resources related to the day below for your future use. As always, please don’t hesitate to reach out in the future!

## Session #1: Sparking Curiosity to Promote Inquiry and Productive Struggle

During the first session of the morning, we discussed more strategies to spark curiosity in order to promote inquiry and productive struggle.

The task we focused on during this session was the Counting Candies 3 Act Math Task:

## Counting Candies [3 Act Math Task]

### How many candies should each person get?

Working With Fractions To Find Unknown Values In this task, students see a bunch of candies poured on the table. How many candies should each of four people receive if you know how many there are in two thirds of the whole? Act 1: Introduce the Problem https://youtu.be/S74d7yFoPG4 What's the question? In this case, we're looking at: How many candies should you receive if ...

After introducing the task, we also added a Desmos Custom Activity to the mix:

## [DESMOS] Counting Candies 3 Act Math Task

This activity supports the Counting Candies 3 Act Math Task in order to introduce the idea of systems of equations.

Access this activity in the following ways:

- As a student to try the activity.
- As a teacher to create your own session for your class.

## Session #2: Making Math Contextual, Visual and Concrete

Before jumping into the task, we discussed the two groups of students I (unintentionally) created in my class and the possible commonalities between students in both groups.

We also spent some time discussing the problem with rushing to the algorithm and used the Keurig Instant Coffee Maker commercial as a prime example of the rush to the algorithm.

The task explored during this session was the Stacking Paper 3 Act Math Task:

## Stacking Paper [3 Act Math Task]

### How many packages of paper will it take to reach the ceiling?

Real World Math in Proportional Reasoning and Linear Relations Here's a new Real World / 3 Act Math Task that is related to proportional reasoning and a direct variation linear relation with a partial variation sequel to boot! Please note that this is part one of three tasks in a series: Stacking Paper - Direct Variation (y-intercept equal to 0) Stacking Paper Sequel - Partial ...

Keep in mind that you might consider using Google Sites as an option to deliver this task:

You can also read a blog post about creating interactive tasks with Google Sites here:

## Creating Interactive Math Tasks With Google Sites

Recently, I wrote a post summarizing the Stacking Paper Tasks multi-touch book for iBooks. If you had a chance to download the multi-touch book, you'll notice that it is interactive and collaborative leveraging embedded padlet walls for students to share out their work. However, I've had some folks on Twitter asking how they could do something like this without an iPad: @MathletePearce Any sug...

I shared a Google Doc with a couple additional options as well such as Desmos Custom Activity Builder, Knowledgehook Gameshow, Recap! and GoFormative.

## Session #3: Creating Interactive Math Learning Journeys

In this session, we explored the **Four Stages of Learning (or Four Stages of Mastery)**, as I like to call them.

I then shared my vision for mathematics education that I have been refining for the past five years. Here is what it looks like currently:

We then jumped into a 3 act math task called “Walk Out“:

## Walk Out [3 Act Math Task]

### What does the distance-time graph look like?

Introducing Distance-Time Graphs & Graphing Stories This 3 act math task was created as a simple, yet powerful way to introduce distance-time graphs and other various graphs of linear and non-linear relationships between two variables. In particular, I'm looking to address the following specific expectations from the grade 9 math courses in Ontario: Grade 9 Applied LR4.02 & Grade 9 Acade...

After introducing the initial video and giving some time for you to notice and wonder, we soon added in a digital tool called Knowledgehook Gameshow to make the process interactive. As I mentioned in the session, I would spend time without any digital tool when introducing 3 act math tasks in your classroom to build a community of mathematical thinkers and discourse.

## Check Out @Knowledgehook’s FREE Gameshow Assessment Tool!

A Free Gamified Clicker Tool With Ready-Made Content! Knowledgehook’s Gameshow Beta Tool is a FREE Gamified Online Assessment Tool that does more than what Google Forms, Socrative and Kahoot can do by pushing the bar up with level-up experience (XP) points as well as FREE content teachers can use to run ready-made gameshows or customize their own! While this is just the beta version, I am impr...

We also explored how we can use Explain Everything and Desmos to make Interactive Math Learning Journeys:

## Explain Everything Math Learning Journey

Exploring Geometry By Discovering Angle Relationships *Wed Apr 8, 2015* - The Explain Everything Project File has been updated to correct an error. The Geometry portion of the grade 9 applied course is one that I have always struggled to make meaningful for my students. The curriculum has students exploring angle theorems, but really never goes deep enough for finding these angles to be...

## Explain Everything Angle & Triangle Journey (Part 2)

Kicking It Up A Notch With Visual Angle Proofs Yesterday, I posted about my first attempt at creating an Explain Everything Math Learning Journey by providing students with an Explain Everything Project File with some questions intended to have them discover some angle theorems. We began the journey today and I hope that we will have some video footage to share in the coming days. The stu...

## Desmos Math Journey: Representations of Linear Relations

Using Desmos to Create Interactive Math Investigations Just recently, I have really been extending the effectiveness of inquiry/discovery based learning in my classroom by having students work at the whiteboards around my room. Students in grade 9 applied math are usually disengaged in math class because they have likely struggled with mathematics in elementary school. While I'm thoroughl...

Another Desmos Activity we explored was Marbleslides: Lines.

## [DESMOS] Marbleslides: Lines

This activity supports the Counting Candies 3 Act Math Task in order to introduce the idea of systems of equations.

Access this activity in the following ways:

- As a student to try the activity.
- As a teacher to create your own session for your class.

Note that they have other Marbleslides versions including:

## Other Useful Math Tasks and Tools:

## Stacking Paper Sequel [3 Act Math Task]

### What is the height of the table?

Finding the Equation of a Line Given Slope and a Point This 3 Act Math Task is a sequel to the Stacking Paper Real World Math Problem I created a couple weeks back. In the previous task, students were asked "How many stacks of paper will it take to reach the ceiling?" That problem had a sequel that explored the scenario of stacking the paper on a table instead of on the floor in order to see i...

## Thick Stacks [3 Act Math Task]

### How tall is the table?

Finding the Equation of a Line Given Two Points This 3 Act Math Task is yet another sequel to the Stacking Paper and Stacking Paper - Sequel 3 Act Math Tasks where we look at linear relations with respect to a real world situation involving packages of paper stacked into a tower. While the original task begins with a direct variation requiring only basic proportional reasoning skills, th...

The Stacking Paper Tasks are also available on iOS as a multi-touch book for iBooks:

Learn more about what’s inside the multi-touch book here.

Or, consider accessing these tasks in an interactive way via Google Sites.

# 3 Act Math Tasks: Curious Math iTunes U Course

Access over 30 tasks with all resources downloaded directly to your iOS Device to avoid streaming media in your classroom through the Curious Math iTunes U Course:

## [DESMOS] Function Carnival

Access this activity in the following ways:

- As a student to try the activity.
- As a teacher to create your own session for your class.

## [DESMOS] Polynomial Equation Challenges

Access this activity in the following ways:

- As a student to try the activity.
- As a teacher to create your own session for your class.

## [DESMOS] Polygraph: Parabolas

Access this activity in the following ways:

- As a student to try the activity.
- As a teacher to create your own session for your class.

## Other interesting Desmos Activities to Explore:

**Will It Hit The Hoop? – Dan Meyer 3 Act Math Task**

Try as a student: Desmos Activity (Code: nax6)

Use this activity with your own class by clicking here.

## Other Useful Courses to Check Out:

Learn Pythagorean Theorem Through Exploration – Kyle Pearce

Stacking Paper Tasks – Kyle Pearce

Beautiful Functions – Jon Orr

OR, you don’t want to download Jon’s Beautiful Functions book? Check out all of the links here on his blog.