## Monday, August 29, 2016

### 10 Days of Number Talks for High Schoolers

This summer I read a book called "Making Number Talks Matter" by Cathy Humphreys and Ruth Parker.  It was outstanding.  It really called me to action.  I highly recommend it.

Also, I read a great blog post regarding Number Talks by Sara VanDerWerf @saravdwerf called "Secondary Number Talks"  Sara challenged me to give Number Talks 30 times in a year and also for 10 days in a row (I'm trying it for the first 10 days of school)

Number Talks are short mental math problems given to students to work out individually and then discuss as a whole group.  They are fascinating and fun.  Mostly it reverses the typical way a math class is run.  You give the problem with no introduction and no explanation and no hints.  Then you discuss the many different ways students solved the problem.  It is amazing the different thought processes that happen in with this method.  The students are set  free from the boundaries of whether they did it the same way as the teacher.  They relish in the coolest and fastest way.  They oooh and aaahh at the different methods.  The most amazing part is that the students start to see the connections in math that we have been trying to beat over their head for so long.

Typically this is how the Number Talks have gone.

1. You will be given a problem and time to work out the problem mentally.
2. You will be given some time to share your idea with someone near you and get feedback.
3. As a whole class we will share out potential solutions.
4. Then as a whole class we will share out methods for those solutions.
5. Depending on time, we will use one or more methods on a new problem.

Here are my Ground Rules

Everyone's voice matters.  Be respectful when someone is giving their opinion.
Everyone will be asked to take risks and be uncomfortable. Being uncomfortable is OK.  It is a part of growth and learning.
If you find one way to figure out the problem, then see if you can find a different way.
Try to think of a visual method of solving and explaining your solution.

Here is the one I gave DAY 1 (I got this problem from @joboaler ICTM 2015 keynote)

Simplify

POSSIBLE DISCUSSIONS and SOLUTIONS

Here is another thing that I think would be great to start doing on day 1.  EQUATIONS

5(18)=90
5(10+8)=90

5(18)=90
5(20-2)=90

5(18)=90
5(2)(9)=90

5(18)=90
2(5)(18)=2(90)

5(18)=90
18(2+2+1)=90

10 DAYS OF NUMBER TALKS
DAY 1 TOPIC: Multiplication
Simplify

DAY 2 TOPIC: Subtraction
Simplify
DAY 3 TOPIC: Visual Pattern
How is this growing?
What does step four look like?  How many small squares are in step four?
What does step 43 look like?  How many small squares are in it?
What does the xth step look like?  What is the equation for it?

DAY 4  TOPIC: Fractions
Simplify

DAY 5 TOPIC: Visual Pattern
What does step 10 look like and how many mini squares are in it?  What does the xth step look like?  What is the equation for it?

DAY 6  TOPIC: Division

DAY 7 TOPIC: Visual Pattern
What does step 43 look like and how many squares are in it?  What does the xth step look like?  What is the equation for it?

DAY 8  TOPIC: Multiplication
Simplify

DAY 9 TOPIC: Visual Pattern
What does step 43 look like and how many squares are in it?  What does the xth step look like?  What is the equation for it?

DAY 10 TOPIC: Percents
Simplify
25% of \$200

Here is what I give to the students
Day Topic URL (to copy to your drive)