Crafting and Implementing
Open Ended Questions!
David Sladkey twitter @dsladkey
Email: dsladkey@gmail.com
Scott Miller twitter @smiller229
Email: smhawkeye@gmail.com
David Sladkey @dsladkey
High School Math Teacher Naperville Central High School
Married with 3 grown
children + 2 grandchildren
Scott Miller @smiller229
Math Instructional Coordinator Naperville Central High School
Married with 3 grown children
Target
Empower teachers to create open ended questions.
Find a shoulder partner and...
-
Find the coordinates of two points that produce a slope of
(100, 22) & (107, 20)
(0, 0) & (1, -2/7)
(4.4, 2019) & (70.4, 1999)
2
7
“People are naturally curious, but we are not naturally good thinkers; unless the cognitive conditions are right, we will avoid thinking.”
-Daniel Willingham
After
Before
Find the slope of the line between the coordinates (4,3) and (-3,5)
Before
After
Find the coordinates of two points that produce a slope of
2
7
-
Find the slope of the line between the coordinates (4,3) and (-3,5)
Before
After
Find the coordinates of two points that produce a slope of
2
7
-
Find the coordinates of two points that produce a slope of
Your coordinates may not be on an axis.
One coordinate must be in the 1st quadrant.
One coordinate must be in the 2nd quadrant
2
7
-
What does the data show?
93%
A question I constantly ask myself
“Who is doing the thinking in the problem?”
-Jana Sebestik
How we changed our practice
Graph f(x)= x2+3x-4
Before
Find an equation that might look like...
After
Find an equation that might look like...
After
The teacher puts up an expression/equation for students, working in pairs, to create a
Truth (equivalent)
or Snare (non-equivalent).
TRUTH or SNARE
Equivalent
Thumbs Up
TRUTH or SNARE
Non-Equivalent
Thumb Down
TRUTH or SNARE
Unsure
Thumb Sideways
TRUTH or SNARE
Theme Polynomials
6x2 - 4x
Find 2 Truths
Find 2 Snares
TRUTH or SNARE
Theme Polynomials
6x2 - 4x
6x3 - 4x2
TRUTH or SNARE
Theme Lines
x - y = 3
TRUTH or SNARE
1
2
Picture of students at the board
Pair number 1
Pair number 2
Pair number 3
“Sometimes I think that we, as teachers, are so eager to get to the answers that we do not devote sufficient time to developing the question.”
-Daniel Willingham
Instruction
Instruction
What do you notice? What do you wonder?
x - 18 = 0
x2 - 18 = 0
x2 +7x - 18 = 0
Practice
Before
Practice
11.Create a quadratic equation in standard form with -3 as one of the solutions.
After
Instruction
What do you notice? What do you wonder?
What do you notice? What do you wonder?
What do you notice? What do you wonder?
Notice and Wonder
Annie Fetter
Resources
Open Middle
Visual Patterns
Maths Venns
Desmos
Open Middle
Before
Directions: Solve the equation
43 + x = 17
Open Middle
Directions: Use the digits 1 to 9, at most one time each, to create two equations: one where x has a positive value and one where x has a negative value
After
negative value.
Open Middle Calculus
Open Middle
Robert Kaplinsky
Nanette Johnson
Visual Patterns
What does the Step 4 step look like?
What does Step 10 looks like?
How many squares are in Step 43?
How many squares are in Step x?
Visual Patterns
Here are some ways
students found the xth term…
(x+1 + 3x) (4x+1) (4(x-1)+5)
Visual Patterns
What does the Step 1.5 step look like?
Visual Patterns
Before
Visual Patterns
After
Visual Patterns
Fawn Nguyen
Maths
Venns
Maths
Venns
Maths Venns
Craig Barton
Before
After
Before
After
Stand and Talk
What are 10 things that you notice or wonder about this diagram?
Class Discussion
Stand and Talk
Create an open ended question on a piece of paper or on the screen.
Stand up. Nothing in your hands
In a minute you will be finding a partner and looking at the question on the paper. No groups of 3.
Find 10 things that you noticed or wondered about.
Sit back down and discuss as a class.
Via Sara VanDerWerf @saravdwerf
Stand and Talk
Positives about this activity
Choice
Active
Wonder
Discussion
Questions
Curiosity
“If I want students to learn how to communicate mathematically, I need to ask them to communicate.”
-Dan Meyer
Stand and Talk
Sara Vanderwerf
Back to Front
Back to Front: Given Words
1. One student faces the back of the room and one faces the front facing each other.
2. The ‘front’ student sees a word on the screen and must make a drawing that represents the word without talking. The ‘back’ student tries to guess the word.
Back to Front: Given Words
Back to Front: Given Picture
1. One student faces the back of the room and one faces the front facing each other.
2. The ‘front’ student sees a picture on the screen and must instruct the ‘back’ student to draw it accurately. (you must decide how if the ‘front’ student can see the drawing)
Back to Front: Given Image
What your partner needs to draw
Back to Front: Given Image
What your partner needs to draw
Desmos
Desmos
Desmos
Assessment
Given the graph, write an equation of a line perpendicular to the given line.
What mistakes do you anticipate?
Assessment
Assessment
New Resources
I have a question!
“I am inclined to think that most teachers believe they should teach principles rather than facts, that they should aim at mental
power rather than knowledge of details. At the same time many teachers seem to think they are compelled by one circumstance or another to sacrifice their ideals and best judgment.”
“If the material is poor or comes to us in any stage poorly prepared we have simply to make the best of it and that is surely not done by aiming at facts but by aiming at principles and methods and to obtain as much mental power as possible.”
-W H Metzler, NCTM Annual Meeting
1908
We know the Before
We will reach the After?
Thanks So Much
Please say hello on twitter
@smiller229 @dsladkey
Digital Textbooks that we use