When I train new math and special education teachers I explain that teaching math should be like feeding a hot dog to a baby in a high chair. Cut up the hot dog into bite-sized pieces. The baby will still consumer the entire hot dog. Same with math. Our students can consume the entire math topic being presented but in smaller chunks.

My approach to doing this is through a task analysis. This is very similar to chunking. It is a method to cut up the math into bite-sized pieces just as we would break up a common task for students with special needs.

While waiting for my coffee order at a Burger King I saw on the wall a different version of a task analysis. It was a step by step set of directions using photos on how to pour a soft cream ice-cream cone. I thought it was amazing that Burger King can do such a good job training its employees by breaking the task down yet in education we often fall short in terms of breaking a math topic down.

9 thoughts on “Cutting Up the Math Into Bite-sized Pieces”

So I tried to break down a task my scholars are doing in Alg 2 just now, finding the axis of symmetry and the vertex of a given quadratic.

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Consider the task of “find the axis of symmetry and vertex of f(x)=2x^2+5x-1

!st cut remember the general form f(x)=ax^2+bx+c
2nd cut identify the values of a,b and c.
a=2, b=5, c=1
3rd cut remember the equation of the axis of symmetry. x=(-b)/(2a)
4th cut substitute the values into the equation of the axis of symmetry.
x=(-5)/(2*2)=-5/4 x+-5/4 is the axis of symmetry
5th cut the vertex is at the point (-5/4,f(-5/4))
6th cut calculate f(-5/4)
7th cut f(-5/4)=2(-5/4)^2+5(-5/4)-1=(-50/16)-25/4-1=(-50/16)-(100/16)-16/16=(-166/16)=(-84/8)=(-42/4)=-21/2

The Axis of symmetry is x=(-5/4) and the vertex is at ((-5/4),(-21/2)
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Somehow the 7 bites from the 7 cuts don’t seem bite size…..but I can’t think of how to make the cuts smaller…..

So I tried to break down a task my scholars are doing in Alg 2 just now, finding the axis of symmetry and the vertex of a given quadratic.

———————————————————————————————————-

Consider the task of “find the axis of symmetry and vertex of f(x)=2x^2+5x-1

!st cut remember the general form f(x)=ax^2+bx+c

2nd cut identify the values of a,b and c.

a=2, b=5, c=1

3rd cut remember the equation of the axis of symmetry. x=(-b)/(2a)

4th cut substitute the values into the equation of the axis of symmetry.

x=(-5)/(2*2)=-5/4 x+-5/4 is the axis of symmetry

5th cut the vertex is at the point (-5/4,f(-5/4))

6th cut calculate f(-5/4)

7th cut f(-5/4)=2(-5/4)^2+5(-5/4)-1=(-50/16)-25/4-1=(-50/16)-(100/16)-16/16=(-166/16)=(-84/8)=(-42/4)=-21/2

The Axis of symmetry is x=(-5/4) and the vertex is at ((-5/4),(-21/2)

——————————————————————————————————

Somehow the 7 bites from the 7 cuts don’t seem bite size…..but I can’t think of how to make the cuts smaller…..

Hey Doug, here is what I came up with. It has some conceptual steps, some definitions (e.g. symmetry) and some prerequisite skills (fractions) https://www.facebook.com/plugins/post.php?href=https%3A%2F%2Fwww.facebook.com%2Fctspedmathdude%2Fposts%2F2151456128226279&width=500

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