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Mr. Bill Lombard's approach
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1bill.lombard@gmail.com http://mrlsmath.comwww.tttpress.com
“Building mathematical skill on a foundation of understanding”
STAR Testing: Prepare Stress-Free Students and Teachers Easily
A tool to help meet the California Mathematics Standards
presentation by Bill Lombardsome graphics from
http://en.wikipedia.org/http://commons.wikimedia.org
2bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
I view the STAR test as an
opportunity, not a burden,
since it allows schools and
teachers to focus on the
curriculum contained within the
test.
3bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
When I present content in class, the
focus is on concepts first, then
problem-solving and algorithms.
When students can see the big
picture, they have the opportunity to
grasp concepts that lead to future
success in subsequent coursework.
4bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
If they only learn how to “push
symbols around a page”, or imitate
the instructor without real
understanding, the scope of their
mathematics is somewhat limited.
5bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
1. Start early
2. Set a clear target
3. Be consistent
4. Make STAR prep part of daily routine
5. Add variety to your preparation
6. Get students to the point of automaticity
7. Confidence in a job well done
6bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Here’s an example of using the STAR 5th
Grade materials – see question 38, which
says:
If N = 4, what is the value of 6 x N – 3 ?
7bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
When students are shown only how to
solve this specific problem, they are not as
flexible as when shown how to solve the
entire class of similar problems.
If they are shown only one way to relate to
this problem, their problem-solving
abilities are not as strong or versatile as if
they can see this problem in Multiple
Representations.
8bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
1. Let’s set this up in a t-table format.
Since 6 x N – 3 is an algebra expression
that varies according to the value of N,
looking at a series of values brings this
problem into clearer focus.
Our number sense gains strength this way.
9bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
2. Let’s use language, the operating
system of our brains:
The pattern in the t-table can be
expressed as, “Starting with – 3, add 6
each time.”
10bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
3. Let’s graph it. We can see the rate of
change as the slope.
We can see the starting point as the y-
intercept. Most importantly, we have a
picture.
11bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
When we are all done with this problem,
our students have tools to work with for
future problems, not just an answer to a
single STAR question.
It’s important to view a problem within the
larger context, not in isolation.
12bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Here’s an example of using the STAR 5th
Grade materials – see question 38, which
says:
If N = 4, what is the value of 6 x N – 3 ?
13bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Here’s an example of using the STAR 5th
Grade materials – see question 38, which
says:
If N = 4, what is the value of 6 x N – 3 ?
14bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
1. Start early
First week of school is a great time to begin
15bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
1. Start early
First week of school is a great time to begin
Good teachers set the classroom climate in the first few days of school
16bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
1. Start early
First week of school is a great time to begin
Good teachers set the classroom climate in the first few days of school
Begin STAR prep with the simplest questions to build the "Can Do" attitude
17bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
1. Start early
First week of school is a great time to begin
Good teachers set the classroom climate in the first few days of school
Begin STAR prep with the simplest questions to build the "Can Do" attitude
You can even begin with questions from a lower grade level
18bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
1. Start early
2. Set a clear target
19bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
2. Set a clear target
Let students know where to aim
20bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
2. Set a clear target
Let students know where to aim
Let students know your expectations
21bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
2. Set a clear target
Let students know where to aim
Let students know your expectations
Coaches look at game films of opponents
22bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
2. Set a clear target
Let students know where to aim
Let students know your expectations
Coaches look at game films of opponents
Share a multitude of potential questions
23bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
1. Start early
2. Set a clear target
3. Be consistent
24bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
3. Be consistent
Master the fundamentals
A, B, C, . . .
John Wooden, famous UCLA basketball coach, used to begin each season with showing his players how to properly tie their shoelaces.
25bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
3. Be consistent
Master the fundamentals
Students thrive on daily routine
Shawn Johnson competes ––>
26bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
3. Be consistent
Master the fundamentals
Students thrive on daily routine
Toolkit of skills
Four forms of a straight line: slope-intercept, point-slope, standard,
intercept
27bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
3. Be consistent
Master the fundamentals
Students thrive on daily routine
Toolkit of skills
Four forms of a straight line
Six ways to write direction of a line:
m, slope, rate of change, rise/run, y/x, (y2-y2)/ (x2-
x1)
28bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
3. Be consistent
Master the fundamentals
Students thrive on daily routine
Toolkit of skills
Four forms of a straight line
Six ways to write direction of a line
Properties of geometric figures
29bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
1. Start early
2. Set a clear target
3. Be consistent
4. Make STAR prep part of daily routine
30bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
4. Make STAR prep part of daily routine
Warmup
31bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
4. Make STAR prep part of daily routine
Warmup
Homework questions
32bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
4. Make STAR prep part of daily routine
Warmup
Homework questions
Quizzes/tests
33bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
4. Make STAR prep part of daily routine
Warmup
Homework questions
Quizzes/tests
Confidence through skill growth over time
34bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
SnagIt process of cutting/pasting to make new
materials
35bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
1. Start early
2. Set a clear target
3. Be consistent
4. Make STAR prep part of daily routine
5. Add variety to your preparation
36bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
5. Add variety to your preparation
Build a library of prep materials
37bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
5. Add variety to your preparation
Build a library of prep materials
2x + 3 = 11
3x + 4 = 25
38bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
5. Add variety to your preparation
Build a library of prep materials
2x + 3 = 11
3x + 4 = 25
Ax + B = C
39bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
5. Add variety to your preparation
Build a library of prep materials
Ax + B = C
40bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
5. Add variety to your preparation
Build a library of prep materials
Ax + B = C
PROGRAM: LINEAR: Prompt A: Prompt B: Prompt C: (C – B) ÷ A –>A: Display A
41bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
5. Add variety to your preparation
Build a library of prep materials
Modify questions
Randy has $100 and saves $20 per week.
In how many weeks will he have $300 ?
42bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
5. Add variety to your preparation
Build a library of prep materials
Modify questions
Randy has $100 and saves $20 per week.
In how many weeks will he have $300 ?
Randy has $__ and saves $__ per week.
In how many weeks will he have $___ ?
Use templates
43bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
5. Add variety to your preparation
Build a library of prep materials
Modify questions
Incorporate language
44bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
EZ-Write Ideas
What is the key step in this process?
What would you tell a classmate who was absent?
Best done after lesson/activity and a few problems
45bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
5. Add variety to your preparation
Build a library of prep materials
Modify questions
Incorporate language
Backward/Forward Mapping
46bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Grade 4 sample test question
47Grade 4 sample test question
bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
48Grade 4 sample test question
bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
49bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
5th grade STAR test sample
50Grade 6 sample test question
bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
51Grade 7 sample test question
bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
52Grade 7 sample test question
bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
53Algebra 1 sample test question
bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
54Geometry sample test question
bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
55Algebra 2 sample test question
bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
56bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
5. Add variety to your preparation
Build a library of prep materials
Modify questions
Incorporate language
Backward/Forward Mapping
Print and Cut up
Tremendous staff development activity !
57bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
Group Project
58bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
1. Start early
2. Set a clear target
3. Be consistent
4. Make STAR prep part of daily routine
5. Add variety to your preparation
6. Get students to the point of automaticity
59bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
6. Get students to the point of automaticity
Math facts and concepts
3(x + 5) = 3x + 15
L
W
60bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
6. Get students to the point of automaticity
Math facts and concepts
Building blocks
61bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
6. Get students to the point of automaticity
Math facts and concepts
Building blocks
a 2 + b
2 = c 2
What does this really mean?
62bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
6. Get students to the point of automaticity
Math facts and concepts
Building blocks
a 2 + b
2 = c 2
but only in a right triangle !
63bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
a 2 + b
2 = c 2
Classic Greek demonstration
64bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
a 2 + b
2 = c 2
Algebraic proof
65bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
a 2 + b
2 = c 2
Even President Garfield can do it !
66bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
6. Get students to the point of automaticity
Math facts and concepts
Building blocks
State the Quadratic Formula:
67bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
6. Get students to the point of automaticity
Math facts and concepts
Building blocks
If ax 2 + bx + c = 0,
68bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
6. Get students to the point of automaticity
Math facts and concepts
Building blocks
If ax 2 + bx + c = 0,
then
2 4
2
b b acx
a
69bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
6. Get students to the point of automaticity
Math facts and concepts
Building blocks
Proof of the Quadratic Formula
“A real mathematical mountain to climb”
70bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Proof of the Quadratic Formula
Takes 9 – 15 steps
Takes several days of constant teacher
attention
Takes modeling in class at least eight
times
Covers & reinforces many important
concepts
Gives students a real feeling of
accomplishment
71bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
72bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
6. Get students to the point of automaticity
Math facts and concepts
Building blocks
Game type format
73bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Game type format
Four In a Row
– from Simply Great Math Games, Teacher to Teacher Press
74bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Game type format
Traditional Bingo
– from Simply Great Math Games, Teacher to Teacher Press
75bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Game type format
Universal Math Book Bingo
– from Simply Great Math Games, Teacher to Teacher Press
76bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Game type format
The Tax Collector
– from Simply Great Math Games, Teacher to Teacher Press
77bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Game type format
Streets and Alleys
– from Simply Great Math Games, Teacher to Teacher Press
78bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
6. Get students to the point of automaticity
Math facts and concepts
Building blocks
Game type format
Revisit/Reteach/Review
79bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
Revisit/Reteach/Review
How do you get to Carnegie Hall?
80bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
Revisit/Reteach/Review
How do you get to Carnegie Hall?
Practice, practice, practice . . .
81bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
Revisit/Reteach/Review
You can’t expect students to
• Learn
• Master
• Remember
concepts & skills when you only do it once !
82bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
1. Start early
2. Set a clear target
3. Be consistent
4. Make STAR prep part of daily routine
5. Add variety to your preparation
6. Get students to the point of automaticity
7. Confidence in a job well done
83bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
7. Confidence in a job well done
Refine your preparation process
Think, think, . . .
Plan, plan, . . .
Create, create, . . .
84bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
7. Confidence in a job well done
Refine your preparation process
Confidence is contagious and builds excitement
85bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Seven Keys to Success
7. Confidence in a job well done
Refine your preparation process
Confidence is contagious and builds excitement
86bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com
Teaching:
the hardest job you’ll ever love
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