SLIDE 1 STEM Workshops 2014
Welcome!! Sandra Scott Jeanne Villeneuve Virginia Horowitz
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SLIDE 2 Agenda
Project Goals and Desired Outcomes
Critical Thinking & Standards of Mathematical Practice
Since I started teaching….
Big Problem “A Storm is Coming”
Journals
Culminating Task
Big Problem “Museum Exhibit”
Journals
Smaller Problem “Planet Ork”
Wrap up
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SLIDE 3 Workshops and Project Goal
Prepare students for STEM education and careers through applied academics
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SLIDE 4 Desired Outcomes
Critical Thinking Skills
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Standards of Mathematical Practice Effective Teacher Behaviors Student Behaviors Student Engagement Strategies
SLIDE 5
Desired Outcomes
Participants will:
Increase their familiarity with the Standards of
Mathematical Practice
Strengthen their inclusion of Critical Thinking Skills in
their teaching
Reflect on & incorporate reach-based effective teacher
practices
Increase the use of appropriate student engagement
strategies in their teaching
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SLIDE 6 Critical Thinking
from Scheffer and Rubenfeld, 2001
- 1. Analyzing (Separating a whole into its parts)
- 2. Synthesizing (Bringing parts together to form a whole)
- 3. Applying Standards or Judgment
- 4. Discriminating (Similarities and Differences)
- 5. Information Seeking (Searching for evidence, facts and
gathering data)
- 6. Logical Reasoning (Drawing Inferences or Conclusions)
- 7. Predicting (Envisioning a plan and its consequences)
- 8. Transforming Knowledge (Changing or converting concepts
from one context to another)
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SLIDE 7
Some Student Engagement Strategies
Small Group Discussions Thumbs Up/Down/Sideways Traveling Salesman Journals/Reflection Papers Quick Writes Hands-on Real World Applications Whip-around Exit Slips
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SLIDE 8
Teacher Behaviors
Organization & Planning Begin with the end in mind. What do you want your students
to understand, to know and to be able to do?
Use Open-ended questioning strategies. Be prepared with a
set of good questions that further your students’ Critical Thinking Skills. Anticipate misconceptions and stumbling blocks.
Use highly effective teaching strategies (e.g. Marzano’s 9) Model Thinking Aloud Make your expectations clear—at the beginning Think about your core beliefs about teaching and learning and
do your best to “live them”
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SLIDE 9
Grouping of Practices 9
SLIDE 10
Since I Started Teaching…
Life has been like…
choose a book, movie, TV show, etc.
because…………….
SLIDE 11
Since I Started Teaching
Life has been like “A Thousand Splendid Suns” because ………… You can’t wait to see what each new day holds.
SLIDE 12
Since I Started Teaching
Life has been like Seinfeld because…………… Weird personalities have dominated my days
SLIDE 13
Since I Started Teaching
Life is like “Yellow Submarine” because……. My department is really coming together.
SLIDE 14
Since I Started Teaching
Life is like a Monster commercial because .....
https://www.youtube.com/watch?v=npQC7v73TXg
SLIDE 15 A Storm is Coming
An auger falls off a combine during harvest because the ball bearing failed. The
steel balls fell off the machine onto the field over several yards making it impossible to recover and count the original number of balls needed to repair the auger. The parts store is several hours drive away, the harvest needs to be completed ASAP as a storm is predicted to hit in about 10 hours, you don’t have any measuring tools, and no time to return home to get measuring tools. You need to improvise. How can the number of steel balls be estimated to get an accurate count, go to the parts store, return, and repair the equipment before the storm?
Bearing: A part of a machine that bears friction Ball Bearing: A bearing consisting of a number of hard balls running in grooves (called a race) in between two concentric rings. Ball Bearing Uses: Car wheels, skateboard wheels, roller blades, manufacturing equipment, farm implements, etc.
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SLIDE 16 Collect and graph the data
Due to the high cost of the bearing balls, you want to order only what you’re sure you
- need. In your truck you have some tubing and duct tape, as well as miscellaneous
items in the glove compartment (your teacher will hand you a bag of these items). Additionally you are able to gather about 35 bearing balls from the ground. Decide with your group what unit of measure you will use to measure the ball bearing
- provided. You may use any of the items listed above, or anything on your person. With
your group, determine how many “marbles” it takes to line each of the round items you have or can create. Record your data, then graph it. Use the graph to make a reasonable prediction for how many ball bearings you will need to purchase. Inspiration for this problem: http://searchingformath.com/2012/06/01/how-many-ball- bearings/ and Sandra Scott
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SLIDE 17 Journals
How might this problem be used in your classroom? What question(s) could you ask to increase students’ critical thinking during this exercise?
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SLIDE 18
Using Graphing Calculators to determine linear regression. Follow the handout in the binder to enter your data and find the line of best fit.
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SLIDE 19
Where, How and Why Could You Increase Your Use of Big Problems?
Please Journal Your Response ...
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SLIDE 20
Culminating Task – Workshop #3
Look for a familiar problem or one you would like to try
with students—applicable to your grade level/course
Teach this piece of a lesson to the group so that you
apply what you have learned in the two workshops and reflect on your work
Identify the CT Skill(s) and SMP(s) and the Student
Engagement strategies you use
Can work alone or with a partner—10 to 15 minutes per
demo
Questions?
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SLIDE 21
M3
The Museum of Modern Mathematics plans to feature a
new exhibit in the hall of Pi. They plan to hang an 8 foot diameter circle, filled with glistening round stones. The stones are each ¾ in diameter. How many stones will be needed to cover as much of the circle as possible without any overlap or any excess hanging outside the circle?
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SLIDE 22 Find a Pattern
Your group has several circles. Measure the diameter
- f each circle in inches (input), then cover the circle
with as many pennies as possible (output).
Record your data on the chart at the front of the room. Graph your data, and use it to predict how many stones
would be needed for the museum’s exhibit.
Can you create an equation that models your data?
Try it here ________________________________________
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SLIDE 23
Alternatives and Variations
Change the size of the circle to make the problem more
manageable
Use a graphing calculator to determine the equations of
the: line of best fit, parabola of best fit, exponential of best fit.
Online Version: https://class.desmos.com/pennies Inspiration: Dan Meyer, and Desmos
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SLIDE 24
The Lab Rats
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SLIDE 25
Journaling
Write down the critical thinking skill(s) and SMP(s) you would focus on when you use this Big Problem.
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SLIDE 26 Planet Ork
Welcome to the workshop! Please read the problem below, and determine which clique each inhabitant was from. Be prepared to justify your answer.
Mork took Mindy to the Planet Ork. One day, while sightseeing, they
happened upon an odd looking township. Mork explained to Mindy that the inhabitants of this township all belonged to one of two cliques: The truth tellers (who always tell the truth) and the liars (who always lie). Just then, three of the inhabitants walked up to Mork and Mindy.
“We’re all liars” said the first. “Just one of us is a truth teller” claimed the second of the three. The third did not speak.
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SLIDE 27
WHY The Warm-up Problem?
Warm-ups are an easy way to begin making changes in
your curriculum.
Problem solving often allows different types of students
to “shine”
This problem requires reasoning and construction of
viable arguments
Students can test and debate their solutions in small
groups
Mathematics Arithmetic
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SLIDE 28
Whip Around and Evaluation
You have the following handouts:
1.Student Engagement Strategies 2.SMPs 3.Critical Thinking Skills 4.Effective Teacher Behaviors
Pick one item from one of the lists that you will pay attention to between now and our next workshop. Be prepared to announce it during our “Whip Around”.
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SLIDE 29
Next Workshop: Friday, April 4th
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SLIDE 30
What Grouping of Practices Are You Most Comfortable With? 30
SLIDE 31
What Grouping of Practices Are You Least Comfortable With? 31
SLIDE 32 Who’s Your Favorite Bidder? 32
Barry
SLIDE 33
How Many Years of Teaching Experience Do YOU Have? 33
SLIDE 34
Standards of Mathematical Practice 34
SLIDE 35
Wake UP!!! – Part 1
It is your job to order new cups for Wake Up, the coffee
shop you work for. The computer is down, and the boxes that the cups come in have all been recycled, but you did notice the box was about the same height as your manager, Mrs. V. The operator at the Cups Are Us warehouse can take your order, but they don’t know how many cups come in a box. Discuss what information and tools you will need to figure out how many cups come in a box.
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SLIDE 36
Wake-Up --- Part 2
Now that you have the information and tools you
requested, graph a set of data that represents the situation.
Next, determine an equation that would represent the
height of a stack of cups, and determine how many cups each box holds.
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SLIDE 37 Wake-Up Part 3
Your manager is very market savvy, and wants all the
cups to be stacked so that each stack is the same
- height. Obtain a new cup from your teacher, and
determine how many small cups and how many large cups would be in each stack so that they are the same
- height. Also, if the box for the large cups is the same
size as the box for the small cups, determine how many large cups come in a box.
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SLIDE 38 Traveling Salesman
- 1. What do x& y represent in your equation?
- 2. What are the physical representations of the x & y
intercepts?
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SLIDE 39 Wake-Up Part 4
Write up a solution for this set of problems. Include equations and graphs, and answer the following questions, using complete sentences.
1.What do x& y represent in your equation.
What are the physical representations of the x & y intercepts?
2.What does the slope represent in terms of the situation? Explain how you know this. 3.At any point during the tasks did your group disagree on any of the questions
above? If so, how did you reach an agreement? If not what misconceptions do you think might have occurred in another group or class?
4.What place does rounding have in this situation? What would you round to…the
nearest…what?
5.How far off was your initial guess from the actual answer? Look at the guesses on
the board, and explain why they might be such a broad range.
6.Look back at your graph. Did you connect the dots? Why or why not? Do you think
you should revise your graph? Explain.
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SLIDE 40
Resources For This Big Problem
For a complete lesson, including a scoring rubric see
website (link)
Source: Inspiration for this lesson came from Dan
Meyer http://blog.mrmeyer.com/?p=692
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SLIDE 41 Putting It All Together
American Idol Viewership in Millions by Season Number: Cost of a 30 second Superbowl Ad, in years after 2007:
0.5 1 1.5 2 2.5 3 3.5 4 2 4 6 Cost in Millions of a 30 Second Superbowl Ad Years after 2007
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SLIDE 42 Student Assessment
The assessment is a practical demonstration with written documentation.
Find your own linear relationship… Now that we have explored linear relationships in class, find and model another real
life linear relationship. Provide the following:
The context of the linear relationship along with the definition of your independent and dependent variables.
The equation of the line.
Explanation of the slope and y-intercept in the context of the problem.
Explanation of whether or not the relationship is continuous or discrete relative to the context of the problem.
A graph of the relationship/line with axes appropriately labeled.
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