Mind Reading with Algebra

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Objective

Students will be able to create, compare and simplify expressions created from number tricks.

Big Idea

Amaze your students with the mystical mind reading powers of algebraic expressions.

Warm up and Homework Review

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Mind Reading with Algebra, Video Narrative, Warm Up explains this lesson’s Warm Up- Mind Reading with Algebra which asks students to find the error in a fictional student's work simplifying an expression.

I also use this time to correct and record the previous day's Homework.  

Creating Algebraic Expressions off of Mind Reading Tricks

30 minutes

Trick Number 1:

This lesson begins with the announcement that I am going to read the minds of the entire class.  This introduction must be done with some drama for the best effect.  I tell them that doing so much mathematics has made my brain so powerful that I can actually read minds.  Here are the steps that will be followed:

  • Pick a number.
  • Add three.
  • Double it.
  • Subtract 4
  • Cut it in half.
  • Take off your original number.

With some flare, and fake mind reading, I state that everyone has the number 1.  I ask them to try it again with a new number.  

Now that they are all convinced that either I can read minds or, more likely, that something funny is going on, I  ask them to figure out why it works (Math Practice 1).  My students are placed into pairs already and that is who they will work with.  

I  walk around to provide support while they work.  A great scaffolding piece is to ask what we use to represent ANY number, since any number can be put into this trick.  Something to watch for will be students who do things like take (2x+2)/2 and get x+2.  Stamping out these types of student misunderstandings is one of the goals of this lesson.  Take them back to the steps using numbers and remind them that 2x+2 represents a number like 14 (if our original number was 6) so when you divide a number you must divide the whole thing not just part of it. 

They will probably end up with steps like this:

x

x+3

2x+6

2x+2

x+1

1

As soon as many or all of the groups have a decent idea, I ask for a volunteer to come to the board and share their reasoning (Math Practice 3) Making sure that they fully explain their work.   I ask the other students if they have any questions for the volunteer.  If no one does, and there needs to be some further clarification, I ask some questions myself.  I  look for further volunteers who may have taken a different approach and allow them to share as well.

As long as no one brought it up, I ask the students to write all of the steps as a single expression.  They will get some time to work on this and then I have someone share their solution with the class.  Once the class has agreed on a single expression, I have them number the steps to the trick within that single expression (Math Practice 7). Finally, they will simplify the expression.  Obviously, they should get 1. 

We conclude this portion by discussing which method is better, the single expression or the list of algebraic steps.  They must provide justifications for the support of one or the other.  Some may say things like the list is easier or the single expression is all in one place. 

Trick Number 2:

I tell them that this is one that will really impress their friends. 

—  Pick a number.

—  Add 6.

—  Double it.

—  Subtract 2.

—  Cut it in half.

I do the trick with the class and then ask someone about their their final number.  Since the simplified expression is x + 5, let them know their original number.  I do this for a couple of people without letting in on the secret and then have them discuss with their partner to see if they figure out how I did it without writing out the expression.  This is discussed as a class and then the students make the list and expression just like the previous problems.  

Trick Number 3:

The next mind reading trick has these steps:

—  Pick a number.

—  Square it.

—  Add the square to the original number.

—  Divide it by the original number.

—  Add 17.

—  Subtract your original number.

Once I have performed the trick, I have the students write both the list of algebraic steps and the single expression.  This one will be a bit trickier with the square.  Some students may need to be reminded that x2/x is x. Once they have the single expression, I have them identify each step of the trick and then simplify it.  This one simplifies to 18.

Writing a Mind Reading Trick off of an Expression

8 minutes

The final problem asks the students to write the steps to a number trick using the following expression: (2x+10)/2 - x (Math Practice 7).   This one is interesting because if they factor the 2x + 10 into 2(x+5) they will get different steps that lead to the same conclusion (which is 5).  

Please see Section 2 for the PowerPoint.

Exit Ticket

2 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

Today's Exit Ticket asks the students to simplify an algebraic expression involving a parenthesis within a fraction.  Order of operations and combining like terms are two important skills to ensure that students have mastered. 

Homework

1 minutes

The first part of this homework gives the students a mind reading trick and asks them to analyze it algebraically (Math Practice 2).  They are then given an expression and asked to write a mind reading trick off of that expression.  Finally, they are asked to write their own trick as well as an expression based off that trick.