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Mathematical Openers
Dan Finkel @mathforlove Math for Love
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Christopher Danielson
Goals
1. Learn some openers! 2. Explore how to use openers to support thinking, discourse,
and numerical fluency. 3. Choose one you’ve never tried to use in your classroom.
CCMP1 Make Sense of Problems and Persevere in Solving Them
Openers make problem solving and sense making the immediate priority when students walk in the classroom
CCMP 3 Make Viable Arguments and Critique the Reasoning of Others
Ask students to defend their thinking.
Model skepticism, and motivate explanations.
What is numerical fluency?
In groups of 3, write down 3 traits of numerical fluency.
What does numerical fluency look like?
•numbers/equations and representations are connected.
•estimations are natural and helpful
•student can arrive at answers quickly and correctly
•understanding is robust; changes in a question don’t throw student off
What does numerical fluency look like?
•numbers/equations and representations are connected.
•estimations are natural and helpful
•student can arrive at answers quickly and correctly
•understanding is robust; changes in a question don’t throw student off
The central move of Number Talks:
Replace “what’s the answer” with
“How many ways can you figure out the answer?”
Here’s how Number Talks work:
1. Teacher poses the problem - simple enough for mental math.
2. Students mentally solve the problem in as many ways as they can.
3. Students share their answers. (teacher lists them all) 4. Students defend their solutions/explain their thinking. 5. Discussion and consensus. 6. Followup problem
As students grow, Number Talks do too.
From dots…
As students grow, Number Talks do too.
to operations…
160 ÷ 5
You can often use the demonstration problem in your curriculum as a number talk.
Tips for Talks:
1) Always be encouraging!
•Start with topics that feel too easy, and move forward from success.
•Say yes to your students’ ideas.
Tips for Talks:
2) Your first job: interpret, record, and clarify student thinking.
Tips for Talks:
3) Later, connect different approaches, & compare their efficiency
Tips for Talks:
4) This is formative assessment
Tips for Talks:
5) Lots of short talks > a few long ones
Unit Chats
Like a Number Talk, with different options for what unit we’re counting with respect to.
Malke Rosenfeld
Splats
Same or Different
Peter Morris
Games and other challenges
What Qualities Make a Great Game?
1. Has a choice for the student to make.
2. Math is the engine of the game.
3. It’s simple to learn and quick to play.
A Teacher-led Game: Penny - Nickel - Dime
I’ll roll the die 7 times. For every roll, you get to take that many pennies, nickels, or dimes.
Whoever gets closest to $1 without going over wins.
Target Number
12 = …
Goal: 21
The Broken Calculator
Goal: 33
The Broken Calculator
For the future:
1. Try out a new opener this week!
2. A good goal: do 2 - 3 openers per week(for 5-10 minutes each)
Mathematical Openers at mathforlove.com/lesson-plan
•Number Talks •Target Number •Penny Nickel Dime •Don’t Break the Bank •Dollar Digit •Broken Calculator (early version)
Mathematical Openers
•Estimation 180 estimation180.com •Would You Rather wyrmath.com •Visual Patterns visualpatterns.org •Fraction Talks fractiontalks.com •Same or Different samedifferentimages.wordpress.com •Splats stevenwyborney.com
•Visible Thinking visiblethinking.weebly.com/daily-routines.html
Find more unit chat images by searching #unitchat
Daniel Finkel @mathforlove
mathforlove.com dan@mathforlove.com
math love + θ8(
[
!=
%{ }<
zxy
)2
31
05
9 7
7
n6ϕ
∫ ∞Ω
t∑
λψ
4
π
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