Middle School Mathematics Initiative
Linda Lucey, Ph.D
Senior Associate
International Center for Leadership in Education
Gold Seal Lesson Agenda
•
•
•
•
•
1. Creating a Gold Seal Lesson
2. Process of Editing a Gold Seal Lesson
3. Performance Task
4. You become the content editor!
5. Review your lessons
Steps to Create a Gold Seal Lesson
•
•
•
•
•
•
Review the Rigor/Relevance Framework
Begin with a Big Idea
Find an idea
Brainstorm real-world situations
Research the idea
Develop the lesson
A
GOLD-SEAL LESSON
HAS:
RIGOR
AND
RELEVANCE
THAT SOUNDS
INTERESTING, BUT MY
STUDENTS NEED TO PASS
THE FCAT!!
MY KIDS TAKE SO MUCH
CLASS TIME JUST TO
MASTER THE BASIC
CONCEPTS!!
IF I MAKE MY LESSONS
MORE RIGOROUS, MY
STUDENTS WILL ALL
FAIL!!
BESIDES, MAKING GOLDSEAL LESSONS SOUNDS
HARD!!
USING THE TEXTBOOK IS
EASIER.
PRESSURES:
•TIME
•DIVERSE LEARNERS
•EMPHASIS ON TESTING
•REMEDIATION
•LITERACY
•NUMERACY
BENEFITS:
•INCREASE UNDERSTANDING
•MAXIMIZE TIME ON TASK
•MINIMIZE RE-TEACHING
RIGOR
EVALUATION
MEANS
SYNTHESIS
FRAMING
LESSONS AT
ANALYSIS
THE HIGH
END OF THE
APPLICATION
KNOWLEDGE
COMPREHENSION
TAXONOMY.
KNOWLEDGE
A LESSON WITH RIGOR ASKS
STUDENTS TO:
EXAMINE
PRODUCE
CLASSIFY
DEDUCE
GENERATE
ASSESS
CREATE
PRIORITIZE
SCRUTINIZE
DECIDE
Math Teachers Beware!
Evaluate
• Let x= 4 and y = 3
10x – 2xy
RELEVANCE IS THE
PURPOSE OF THE LEARNING:
ACQUIRE KNOWLEDGE
APPLY KNOWLEDGE
INTERDISCIPLINARY
REAL WORLD PREDICTABLE
REAL WORLD UNPREDICTABLE
A LESSON WITH RELEVANCE
ASKS STUDENTS TO:
USE THEIR KNOWLEDGE
TO TACKLE
REAL-WORLD PROBLEMS
THAT HAVE
MORE THAN ONE SOLUTION.
A PROCESS FOR EDITING A
GOLD-SEAL LESSON
PERFORMANCE TASK —
Overview
1.a. Plot the following points on your coordinate system. Remember
that the first coordinate of the pair names a position going right or
left in the horizontal direction, and the second coordinate names a
position going up or down in the vertical direction.
(1,1), (5,1),(6,2),(7.2),(7,1)(8,1),(9,2)
(9,4),(7,4),(6,5),(5,5),(1,3),(0,3),(1,1)
b. Connect the points in the order they are shown in 1a. What is the
result?
c. Add -10 to the first coordinate of each point. What happens?
Add 2 to the first coordinate and add -5 to the second coordinate of each
point. What happens?
e. What should you do to the coordinates if you want to move the
drawing up three units and to the right five units?
A PROCESS FOR EDITING A
GOLD-SEAL LESSON
REVIEW THE LESSON IDEA –
Plot a picture with given coordinates.
Add the same number to the xcoordinate and re-plot the figure.
Observe the translation effect.
A PROCESS FOR EDITING A
GOLD-SEAL LESSON
BRAINSTORM REAL-LIFE
SITUATIONS THAT USE
TRANSLATION. SEARCH THE
INTERNET FOR IDEAS.
Marching band formations?
Flip book animation?
What Is Cartoon Rendering?
Cartoon rendering (sometimes referred to as cel-shading) has two
major constituents: painting and inking. In the traditional sense,
painting is filling a cartoon object with areas of color. A simple
cartoon will use solid colors for different objects (flat-shading), but
more complex cartoons use two or even three colors for each
material. This is often called stepped-shading because the color
"steps" dramatically from the shadow color to the highlight color.
The stepped-shading effect looks quite different from realistic
rendering techniques as there isn't a smooth gradient between the
shadowed and highlighted areas of an object.
Game Programming Beginners Guide
by Dave Astle
I often get asked how someone with little or no
programming experience can get started in game
development.
I will walk you through the things you need to do to
get to the point that you can make your own games.
The first thing you will need to do is to choose a
language to program in. You have a lot of choices,
including Basic, Pascal, C, C++, Java, etc. I'm going
to recommend starting with C and C++. Some
people will say that those languages are too
advanced for beginners, but because I started with
C++ myself, I tend to disagree. In addition, C/C++ is
the most widely used language today, so you will be
able to find a wealth of resources and help
.
A PROCESS FOR EDITING A
GOLD-SEAL LESSON
USE THE VERB LIST TO
FRAME AN ACTIVITY THAT IS
HIGH IN RIGOR.
Create, judge, evaluate, generate,
examine, decide, produce,
assess, prioritize, classify . . .
A PROCESS FOR EDITING A
GOLD-SEAL LESSON
THINK OF AN ACTIVITY THAT
IS INTERDISCIPLINARY OR
BASED ON THE REAL WORLD
AND HAS MORE THAN A
SINGLE SOLUTION.
Make sure it relates to the
learning standard!!
A PROCESS FOR EDITING A
GOLD-SEAL LESSON
USE AN ASSESSMENT
METHOD THAT IS BASED ON
EVIDENCE OF STUDENT
LEARNING.
Often, this means to create a
rubric.
OPERATIONS & COORDINATES
Plot the following points on your coordinate system. Remember that the
first coordinate of the pair names a position going right or left in the
horizontal direction, and the second coordinate names a position going
up or down in the vertical direction. Connect the points in the order
shown. You should see a picture of a wooden shoe.
(1,1) (5,1) (6,2) (7,2) (7,1) (8,1) (9,2) (9,4) (7,4)
(6,5) (5,5) (1,3) (0,3) (1,1)
6
Add -10 to the first coordinate of
each point in the list shown in a.
Write the coordinates, then plot
the figure on the same set of
axes as used for “a”. Use a
different colored pencil.
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
FLIP BOOKS
FLIP BOOK ANIMATION
Learn how mathematics can be used to animate
cartoon figures – it’s all about translation!
1. First you must learn a little about the mathematics involved. On a sheet
of graph paper, draw a large set of coordinate axes. Label the x and yaxes and label some points.
a) Plot the following points on your coordinate system. Remember that the
first coordinate of the pair names a position going right or left in the
horizontal direction, and the second coordinate names a position going
up or down in the vertical direction. Connect the points in the order
shown. You should see a picture of a wooden shoe.
(1,1) (5,1) (6,2) (7,2) (7,1) (8,1) (9,2) (9,4) (7,4)
(6,5) (5,5) (1,3) (0,3) (1,1)
FLIP BOOK ANIMATION
Learn how mathematics can be used to animate
cartoon figures – it’s all about translation!
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
b) Add -10 to the first coordinate of each point in the list shown in a. Write
the coordinates, then plot the figure on the same set of axes as used for “a”.
Use a different colored pencil.
Write a sentence or two to describe what happened to
the wooden shoe image:
FLIP BOOK ANIMATION
Learn how mathematics can be used to animate
cartoon figures – it’s all about translation!
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
c) Add 2 to the first coordinate and add -5 to the second coordinate of each
point. Write the new coordinates on the lines below, then plot the points on
the same set of axes, using a third colored pencil.
Write a sentence or two to describe what happened to the original wooden
shoe image:
FLIP BOOK ANIMATION
Learn how mathematics can be used to animate
cartoon figures – it’s all about translation!
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
d) How should the coordinates be changed if you
want to move the drawing up three units and to the
right five units?
FLIP BOOK ANIMATION
Learn how mathematics can be used to animate
cartoon figures – it’s all about translation!
6
5
4
3
2
1
0
0
e)
1
2
3
4
5
6
7
8
9
10
Work with a partner to clearly write a set of just
three rules that a person could use to translate a
figure vertically, horizontally or diagonally.
Integrate the web
Lesson 1: The Infernal Bouncing Ball.
NOTE: I wrote this tutorial in 2000, and intended it for students learning traditional,
hand-drawn animation. Nevertheless, the principles can be adapted to Flash or 3D
animation. The main tutorial page is here (there's a walk cycle tutorial, and I'll be
adding Flash lessons soon).
This exercise will teach you the most important principles of animation, namely:
Arcs.
Timing/Spacing.
Squash and Stretch.
Volume.
This is the first lesson taught to any animation student. You can pay through the
nose to learn it at a school, but I am giving it to you for free, so behold! Look at the
bouncing ball scene below:
Florida Middle School Mathematics Initiative | International Center for Leadership in Education
2a) Now you will be making a FLIP BOOK to animate a point. The point
will look like it is rolling across a table and falling off of the edge onto the
floor. Once you learn how to animate a simple shape like a point, you
will be able to use this technique to animate more complicated figures.
There are two websites that do a good job of explaining the first lesson
that a beginning animator is taught. Visit these websites before you
begin your own animation experiment in 2b:
http://www.idleworm.com/how/anm/01b/bball.shtml
http://www.cartoonster.com/
We will be using translation to animate our “ball”.
The websites referenced above did not use our
strict mathematical definition of translation to
animate their balls.
Write two reasons why the previous
sentence is a true statement.
(7, 0)
(7, 0)
(5.5, 0)
(5.5, 1)
(6, 1)
(5.5, 1.8)
GIVE STUDENTS A WORKSHEET
ABOUT ANIMATING A BALL USING
GIVEN COORDINATES.
ASSIGNMENT:
a)Create a flip book that uses one or
more transformations to animate an
object.
b)Show your flip book to your group.
Explain the transformations used.
c)The group judges whether the
animation actually used that
transformation.
ASSESSMENT: RUBRIC
Score each of the following
characteristics on a scale of 4 to 0, where
4 = surpasses expectations;
3 = high quality performance;
2 = satisfactory performance;
1 = minimum quality performance;
0 = does not meet expectations.
ASSESSMENT: RUBRIC
The student is able to accurately plot
points in the coordinate plane.
•Evidence shows that the first wooden
shoe was plotted correctly.
•Evidence shows that the second and
third wooden shoes were plotted
correctly.
ASSESSMENT: RUBRIC
The student can describe the relationship
between translating a point and the
changing coordinates of the point.
•Evidence of this is provided in the
answer to 1d.
•Evidence of this is provided in the
answer to 1e
ASSESSMENT: RUBRIC
The student can apply transformation
concepts to animate a shape using a flip
book.
•The flip book is complete and done on
time.
•The flip book actually does animate a
figure using transformation.
Performance Task
• Includes an overview and a description.
• The overview is a description of how a student
is expected to demonstrate learning
(understanding, knowledge and skills). The task
may be a product, performance of extended
writing that requires rigorous thinking and
relevant application. It is usually written in the
third person describing the learning to other
educators.
• The description is the teacher procedures,
including instructional strategies, and literacy
strategies.
• The overview includes:
–
–
–
–
Student work that will be produced or performed
Specific learning context
Whether group or individual
Resources students will be provided or have to
acquire
– Setting where students will complete the work
– Conditions (often real-world) under which the work
will be done
• The overview does not include:
–
–
–
–
Assessment. It implies but does not specify
Specific direction to the student
Specific equipment list
Homework or reading assignments
Sample Overview
Students will create a flip book
animation. Students will work
individually and in pairs to search the
internet for animation instructions,
use graph paper and a teacher
generated template. Flip book
animations will include the translation
of images on a coordinate plane.
Florida Middle School Mathematics Initiative | International Center for Leadership in Education
Student Work
Students will create a flip book
animation. Students will work
individually and in pairs to search the
internet for animation instructions,
use graph paper and a teacher
generated template. Flip book
animations will include the translation
of images on a coordinate plane.
Student Work
Specific Context
Students will create a flip book
animation. Students will work
individually and in pairs to search the
internet for animation instructions,
use graph paper and a teacher
generated template. Flip book
animations will include the translation
of images on a coordinate plane.
Student Work
Specific Context
Students will create a flip book
animation. Students will work
individually and in pairs to search the
internet for animation instructions,
use graph paper and a teacher
generated template. Flip book
animations will include the translation
of images on a coordinate plane.
How
Student Work
Specific Context
Students will create a flip book
animation. Students will work
individually and in pairs to search the
internet for animation instructions,
use graph paper and a teacher
generated template. Flip book
animations will include the translation
of images on a coordinate plane.
How
Resources
Student Work
Specific Context
Students will create a flip book
animation. Students will work
individually and in pairs to search the
internet for animation instructions,
use graph paper and a teacher
generated template. Flip book
animations will include the translation
of images on a coordinate plane.
How
Resources
Conditions
Lesson Components
• 1. Instructional Focus Statements
• 2. Student Learning: what students will be
doing during the lesson (the math)
• 3. Essential Skills (from International
Center List)
• 4. Scoring Guide
• 5. Handouts
• 6. Standards
Performance Task Handout
Sample Overview
Students will write a report describing
how automobiles have been
improved to prevent accidents.
Students will work in pairs to collect
reaction time data and use Internet
resources. The report will include
sample reaction times, explanations
for stopping distances, and
calculations using formulas.
Student Work
Students will write a report describing
how automobiles have been
improved to prevent accidents.
Students will work in pairs to collect
reaction time data and use Internet
resources. The report will include
sample reaction times, explanations
for stopping distances, and
calculations using formulas.
Student Work
Specific Context
Students will write a report describing
how automobiles have been
improved to prevent accidents.
Students will work in pairs to collect
reaction time data and use Internet
resources. The report will include
sample reaction times, explanations
for stopping distances, and
calculations using formulas.
Student Work
Specific Context
Students will write a report describing
how automobiles have been
improved to prevent accidents.
Students will work in pairs to collect
reaction time data and use Internet
resources. The report will include
sample reaction times, explanations
for stopping distances, and
calculations using formulas.
How
Student Work
Specific Context
Students will write a report describing
how automobiles have been
improved to prevent accidents.
Students will work in pairs to collect
reaction time data and use Internet
resources. The report will include
sample reaction times, explanations
for stopping distances, and
calculations using formulas.
How
Resources
Student Work
Specific Context
Students will write a report describing
how automobiles have been
improved to prevent accidents.
Students will work in pairs to collect
reaction time data and use Internet
resources. The report will include
sample reaction times, explanations
for stopping distances, and
calculations using formulas.
How
Resources
Conditions
Activity
Student work
Context
Students will design a poster of a circle graph on the
topic of “Healthy Snacks in Snack Machines” based on
a survey of at least 100 students regarding which
snacks they prefer. Make recommendations to the
principal about which snacks should be put into school
machines, using data and graph.
How they will
work
Resources
Conditions
Activity: Healthy Snack
Student work
Context
Students will design a poster of a circle graph on the
topic of “Healthy Snacks in Snack Machines” based on
a survey of at least 100 students regarding which
snacks they prefer. Make recommendations to the
principal about which snacks should be put into school
machines, using data and graph.
How they will
work
Resources
Conditions
Activity
Student work
Context
Student pairs will use the playground’s seesaw to
determine where they each need to sit in order to make
it balanced. They will use scales to measure their
weights and rulers to measure distances. Using the
data collected, students will make predictions for where
they would need to sit if a different student sat across
from them.
How they will
work
Resources
Conditions
Activity: Gold Seal Lesson Editing
• Read the lesson.
• Review Rigor/Relevance Framework
– Knowledge taxonomy verb list
– Relevance level
• Write a performance task
Contact Information
Linda Lucey
Linda@SPnet.us
518-399-2776 ext. 224
1587 Route 146, Rexford, NY 12148
E-mail - info@LeaderEd.com
www.LeaderEd.com
Phone (518) 399-2776
Fax
(518) 399-7607