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Oh, now I get it!. What Kids Can Do When we get out of their way . . . Will show us what they know . . . Will help us guide our instruction . . . To improve student learning!. Robert Preston CUSD Math Coach. Let me talk!. This is what I do know. My Intentions. To motivate To encourage

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robert preston cusd math coach

Oh, now I get it!

What Kids Can DoWhen we get out of their way . . .Will show us what they know . . . Will help us guide our instruction . . . To improve student learning!

Robert Preston

CUSD Math Coach

Let me talk!

This is what I do know.

my intentions
My Intentions
  • To motivate
  • To encourage
  • To open your mind to new possibilities
  • To get you to try on someone else’s thinking
  • To leave you feeling empowered

Standards alone will not improve schools and raise student achievement, nor will they narrow the achievement gap. It will take implementation of the standards with fidelity by school leaders and teachers to significantly raise student achievement.

Implementing the Common Core, 2013

instruction that is student centered
Instruction That Is Student Centered

“Instruction involves posing tasks that will engage students in the mathematics they are expected to learn. Then, by allowing students to interact with and struggle with the mathematics using THEIR ideas and THEIR strategies – a student-centered approach – the mathematics they learn will be integrated with their ideas; it will make sense to them, be understood, and be enjoyed.”

“Teaching Student-Centered Mathematics”; John Van de Walle, 2006


Start Now: Instructional Shifts

Some have called the shifts expected by the CCSS monolithic in scope . . . implementing the CCSS is not about thinking out of the box. It is about transforming the box itself.

Implementing the Common Core, 2013

let do some math division anyone
Let Do Some Math: Division Anyone?
  • CCSS Domains? Grade level?
  • Requisite skills? Grade level?
  • Success rate? Why?
  • Work with a partner.
  • You have $37 dollars. You just spent $15 on breakfast. How much do you still have?
care to number selection
Care to Number Selection
  • Start simple . . . Increase cognitive demand gradually
  • Keep context
  • Bill choice . . . Why?
  • When do I add other bill denominations?
the videogame
The Videogame
  • You have $123. The videogame you desire is on sale on Amazon for $91. If you make this purchase, how much will you have remaining?
  • How was this one different?
  • Decomposition and re-composition of number.
  • Math Practice?
you and 3 friends
You and 3 Friends
  • That lost dog really was lost. You and your 3 friends just picked up the reward; $300. Since you originally decided to share the reward fairly, how much will each person get?
  • Partitive or Quotative? What?

Partitive or Fair Sharing Division:

determines the number in each group, number of groups is known

Quotativeor Measurement Division:

determines the number of groups, chunk size known

birthday party
Birthday Party
  • Your mother promised you a birthday party for you and some of your friends at Cal Skate. She said she will spend up to $75. If each person costs $13, how many friends could you invite to your party?
  • Partitive or Quotative?
the puppet shows
The Puppet Shows
  • The 4th grade classes at Glendale School put on puppet shows for their friends and families. Ticket sales totaled $532, which the four classes are to share equally. How much should each class get?
the last two problems
The Last Two Problems

Were they different?

Did one required a greater cognitive demand?

Does this approach differ from how division is traditionally taught?

Who is doing engaging in the mathematics?

our role shifts
Our Role Shifts
  • We do less
  • We talk less
  • We listen more
  • We facilitate their learning
  • We make those ah-ha moments explicit for all
5 practices for o rchestrating p roductive mathematics discussions
5 Practices for Orchestrating Productive Mathematics Discussions
  • The 5 Practices
    • Anticipating
    • Monitoring
    • Selecting
    • Sequencing
    • Connecting

Stein and Smith, 2011


Anticipating: what students will do--what strategies they will use--in solving a problem Monitoring:their work as they approach the problem in class Selecting:students whose strategies are worth discussing in class Sequencing:those students' presentations to maximize their potential to increase students' learning Connecting:the strategies and ideas in a way that helps students understand the mathematics learned

switch our representation
Switch Our Representation
  • Base-10 blocks
  • Why important?
  • Why second?
Again . . .
  • Show me 37 . . . Take away 15 . . . How did you do it?
  • Show me 123 . . . Take away 91 . . . How did you do it?
linking back to division
Linking Back to Division
  • 300 shared between 4 bags (circles, boxes, tubs). What actions are taken? How do they link to one another?
base 10
Base 10

11 378 becomes


Where do you see any 11’s?

Other good divisors . . . 9, 5, 4

Start where they start . . . It tells you where to go

base 101
Base 10

11 378 becomes

11 100 +100 + 100 + 70 + 8

Where do you see any 11’s?

Other good divisors . . . 9, 5, 4


Sequencing the Sharing

Anna’s Thinking