Student engagement is a funny thing.

On twitter I’ve been pretty critical about using extrinsic rewards to increase student engagement.

Today was our 100th day of school (as calculated by our students!) To celebrate we made 100 piece trail mix. Our trail mix included: cheerios, chex, raisins, and M&Ms. Candy! Talk about extrinsic student engagement! Before we dove in to the rewards food, I gave my class the following problem:

We have 4 ingredients to make trail mix. How many different combinations of ingredients can we have if our trail mix only has 100 total pieces?

The students persisted through their work on this word problem, until they arrived at various solutions based on their calculations and personal taste. For instance, one student is allergic to nuts and could only eat the cheerios and raisins, so that impacted his work on the problem. The students worked diligently and happily ate the trail mix once they had arrived at a reasonable solution.

However, after class I channeled Graham Fletcher and Dan Meyer to try to make this mathematical experience a more rich one for the students. So, here is a preview of the 3-act task we will be doing tomorrow in class…

# Why Count Your Money, When You Can Estimate?

The end of spring break means we are in the midst of our school’s spring financial literacy unit.  This is always a favorite of both students and teachers.  We ground our work in very concrete community related activities, such as going to the bank and going to the store.  Students love spending money and teachers love going on community walks in the spring and early summer. Everyone wins!

Before we start going on trips, I wanted to do some number sense work with my classes relating to the counting of money.  As we left for spring break I tweeted about an estimation idea inspired by counting money.

Right on cue, Graham Fletcher, who writes his own amazing blog here, gave me some sage advice.

I took Graham’s advice and ran with it.  As much as we like our money math standards to relate to identification of coins and bills and getting accurate counts on prices and change, estimation is a key skill in any “real world” financial transaction.  When was the last time you stood at the supermarket register counting out the entire pile of change you got from the cashier? Generally, we look at the coins in our hand and make a quick estimate as to whether we think it is the correct change or not.  So I used the idea from my tweet, took some inspiration from fellow math teachers Andrew Stadel and Joe Schwartz, and turned it all into a financial literacy lesson.

Here’s how it went…

# #MTBoS Mod: 3-Act Edition

One of the missions of this blog is to take the work of the amazing online community of math teachers known as the MathTwitterBlogoSphere (MTBoS) and to show what modifications are made for students with disabilities.  I call it the #MTBoS Mod(ification).  You can read the first two editions here and here.  This edition is about the lesson structure created by Dan Meyer known as a 3-Act Task.

#MTBoS MOD: 3-Act Edition

The 3-Act math task I chose was created by Graham Fletcher called It All Adds Up.  I chose this because in our spring trimester we focus solely on financial literacy.  As a teacher of students with disabilities we spend a great deal of time on the adaptive mathematics that is often over-looked or just simply considered  a “real world context” in the classes of typically developing students.  In the world of special education these tasks are known as Instrumental Activities of Daily Living (IADLs), which are complex skills needed to live independently.  IADLs are not to be confused with the Activities of Daily Living, which are basic self-care tasks.  At my school we call these skills the Mathematics for the Instrumental Activities of Daily Living.

As a pre-assessment for our “money unit” (as the students call it) I used “It All Adds Up.”  The goal was to see how comfortable the students were with identifying coins and counting different combinations of coin denominations.  I launched the task with three of my student groups.  The task is great for students at different computation levels.  At the simplest level the students can solve it by adding coins together to equal \$1.00.  At a more complex level students can look for patterns that can help them solve the problem more efficiently as well as reflect on the possibility of multiple solutions to the problem.  I gave this task to groups of students with a variety of different needs and modes of processing.  I’ve broken the three groups into the three stages of the Concrete-Representational-Abstract method of instruction.