do now: fact family worksheets!
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×. +. Do Now: Fact Family Worksheets!. +. ×. Work your way through the various Fact Family Worksheets See if you can identify the Fact Families being practiced ~ Answer sheets are at the back of your packets ~. –. –. ÷. ÷. CITY YEAR CHICAGO. CITY YEAR CHICAGO. CITY YEAR CHICAGO. - PowerPoint PPT PresentationTRANSCRIPT
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++ Do Now:Fact Family Worksheets!
• Work your way through the various Fact Family Worksheets− See if you can identify the Fact Families
being practiced
~ Answer sheets are at the back of your packets ~
+
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CITY YEAR CHICAGOCITY YEAR CHICAGOCITY YEAR CHICAGO
Math 203Session Developer: Mari Mermelstein
City Year Chicago
Putting Idealism to WorkPITW #2 “Every battle is won or lost before it is fought.”
This 2500-year-old insight from the Chinese strategist Tsun Tsu (pronounced
“Sun Soo”) is the most important rule of implementation for idealism.
All of City Year needs to be built on it. It means that setting clear and correct
goals, and preparing an effective plan to meet those goals, are the critical
elements to success. Almost any glitch or failure can be traced directly to poor
planning or preparation. Another way of saying this rule: “For better or worse, you
always get the result you planned (or failed to plan) for.”
There are three steps to winning battles before they are fought. First, visualize a
final result — a great service project, an outstanding event, a successful
fundraising activity; second, think backwards step by step from that imagined great
result, until you understand all the steps and every single detail it will take to
succeed — including contingencies for what could go wrong — like “what do we do
if it rains?”; and third, only then begin to implement each step forward.
Overview• Tutoring at a Glance
• Activity Planning Worksheet
• Computational Fluency− Review− Computational Fluency Tracker
• Data-Informed, Content-Derived Instruction (DCI) − Introduction− Graphic Organizers
• Example Tutoring Session
Tutoring at a Glance1) Plan Tutoring Session
– Use Activity Planning Worksheet
2) Tutoring Session:
– Welcome
– Computational Fluency (record results)
– DCI (take notes on student progress during
session)
– Close
3) Write up notes
– Student Progress Log and Comp Fluency Tracker
Activity Planning Form
Welcome
Computational Fluency
Data-Informed Content Derived Instruction
Close
Computation Fluency - Review
Computational Fluency
Computational Fluency• The ability to efficiently and accurately compute addition,
subtraction, multiplication and division problems
• Focus on Whole Numbers and Fact Families
• Advance Computational Fluency will focus on Commutative, Associative, and Distributive Properties
• Number One Rule…
…No Calculators!!!!
Computational Fluency Ideas
• Mental Math Strings
• Online Worksheet Generators
• Math GAMES!
• Other ideas?
Comp Fluency Tracker"Fact Families" Mastery Scores
Assessment Date Fact Families Score Specific Fact Family Assessed Common Errors Aimline (90%)
9/13/2011 71.00 Subtraction 1-20 4-9's 90.009/15/2011 68.00 Subtraction 1-20 4-9's 90.009/17/2011 73.00 Subtraction 1-20 3's, 4's, 7's, and 8's 90.009/21/2011 75.00 Subtraction 1-20 4's, 5's, 7's, and 8's 90.009/23/2011 80.00 Subtraction 1-20 5 - 9s 90.009/25/2011 88.00 Subtraction 1-20 6's and 7's 90.009/28/2011 81.00 Subtraction 1-20 5 - 9s 90.009/30/2011 89.00 Subtraction 1-20 6's and 7's 90.0010/3/2011 92.00 Subtraction 1-20 7's 90.0010/5/2011 96.00 Subtraction 1-20 all good 90.00
DCI
Data-Informed Content Derived Instruction
Data-Informed, Content-Derived Instruction (DCI)
Data-Informed: means we will take formal and informal data to
make meaningful decisions about what supports the students need.
Types of data: (including, but not limited to)
– course grade
– classroom test/quiz scores
– class work samples
– information the student or teacher tells you
Content-Derived: means that the content comes directly from
what the students are studying in class. We are not simply restating
what the teacher has said verbatim, but we model what we do based
on what the students are familiar with to help them gain a deeper
understanding of the content.
Graphic Organizers
• Acronym/Mnemonic Organizer
• Venn Diagram
• Procedure Notes Organizer
• Concept Definition Organizer
• Sequence Organizer
• Top Hat Organizer
• Vocabulary Knowledge Rating
Concept Definition Organizer
(aka 3 column definitions)• Useful at the beginning of a unit to build a
strong foundation for understanding concepts
• Good for visual learners
• Provides formative data about your student
General Concept/Chapter/Unit
Concept DefinitionMath/Visual Illustration
E X AMP L E
Venn Diagram• Useful for visually representing the similarities and
differences between two concepts or items.
• Can be used during any part of the learning process− Beginning: (formative data) tells you what the student
already knows
− During: (formative data) tells you what the student has
learned so far/still needs clarity on
− End: (summative data) tells you what the student has
learned
EXAMPLEDivisible by: 2 3
Bank of Numbers: 1, 2, 3, 5, 6, 7, 9, 12, 13, 14,
e 22, 24, 27, 32, 36, 39,
42
EXAMPLEDivisible by: 2 3
2 3
22 6, 12 9
14 24, 36 27
32 42
39
Bank of Numbers: 1, 5, 7, 13 (not used)
Acronym/Mnemonic Organizer
• Do not create these just to create them. Create them
because the student needs a support.
• Helps students remember an instructional sequence.
• Use during a unit of learning – this is a tool to help
students solve problemsTopic (Acronym or Mnemonic Device)
L Description
E Of
T What
T Each
E Letter
R Stands
S For
Word Problem:
TK is running at a pace of 6 miles/hour. His goal is to run 10 miles. How
long will it take him (in minutes) if he keeps up this pace the whole time?
Solving Word Problems (GUESS)
G Givens
U Unknowns (what are we solving for?)
E Equation
S Substitute
S Solve
EXAMPLE
Solution Steps:Step 1: Givens (G)
TK’s pace is 6 miles/hour
Step 4: Substitute (S)10 miles = 6 miles/hr · time
Step 3: Equation (E)D = r · t
Step 2: Unknowns (U)Time – in minutes
Sequence Organizer• Used to help students recall the steps involved
in solving specific problem types.
• Use during a unit of learning –help students
organize/plan problem solving
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:
EXAMPLE
Evaluating a Function at a Specific ValueWrite out the entire function
Substitute the value in
Eval using O of Ops
Simplify each term
Simplifying All
Answer!
Vocabulary Knowledge Rating
• Used to gauge a student’s understanding of
vocabulary
• Should be used at the beginning of a unit (to
gain baseline) and/or end of a unit (to assess
progress)
Topic
Vocabulary Term
I’ve never heard of the term
I’ve seen this term before,
but can’t explain it
I’ve seen and used this term
before
I know the term and can explain
it
1 2 3 4
1 2 3 4
Topic: Adding Fractions
Vocabulary Term
I’ve never heard of the
term
I’ve seen this term before, but can’t explain it
I’ve seen and used this term
before
I know the term and can
explain it
Fraction 1 2 3 4
Numerator 1 2 3 4
Denominator 1 2 3 4
Common Denominator 1 2 3 4
Simplify 1 2 3 4
Reduce 1 2 3 4
E X AMP L E
Procedure Notes Organizer• Allow students to organize their notes, determine
common procedures and the rationale behind
those procedures.
• Use near the beginning of a unit to set up the
student for success as the unit progresses
Write Equation (or Problem) here
Steps Calculations Reasons
E X AMP L E
Top Hat Organizer• Can visually represent the similarities and
differences in two concepts or procedures.
• Use to compare the problem solving process
of two equations, comparing word problems,
and comparing statistical data.
• Use during the unit to assess continuing
student need / check for understanding
• Use after to reflect / gauge student learning
x
xx
EXAMPLE – adding/subtracting fractions
xNeed to have COMMON DENOMINATORS
Have 1 completed problem and 1 problem for the student to do
Adding Problem Adding Problem
Adding Problem Subtraction Problem
Subtraction Problem Subtraction Problem
Have 2 problems for the student to do
Reality Check
Picture yourself in class
working with a student…
What concept are you covering?
What is that student struggling to understand?
What tool do you wish you could
magically pull out of your pocket to help
that student?
Create Your Own!
Activity: Select one of these graphic organizers
that you think would be most effective for
working with that student…
and CREATE IT!
• Acronym/Mnemonic Organizer
• Venn Diagram
• Procedure Notes Organizer
• Concept Definition Organizer
• Top Hat Organizer
• Sequence Organizer
• Vocab Knowledge Rating Organizer
Share Out• Group yourselves by Graphic Organizer type
• Talked about what CONCEPT you are covering and
WHY you chose that Graphic Organizer
• Select ONE person to be your spokesperson:
Be ready to tell the group:– Which Graphic Organizer you have
– The top 2 concepts people used it for
– If there was a general reason people chose that Graphic
Organizer
Putting it all together!
• How do I plan my tutoring session?
– Talks with your teacher
– What concepts are you covering in class?
– Do your students need time to complete class work or can you
use this time to provide conceptual support?
• What does my tutoring session actually look like?
– What documents do I need?
– What do I do during the session?
– What do I do after the session?
E X AMP L E
Card Multiplication• Computational Fluency Component
• Rounds 1-5: Multiplier = 4
• Rounds 6-10: Multiplier = 7
Keep track of student(s) score in the Notes section on
the Activity Planning Worksheet
Notes/Next Steps: Take time to reflect: How did they
do? Are they ready to move on or do they need
more practice? How did the activity go? Did they like
it?
Warm up to DCI
Transitions
student(s) from
Computational
Fluency to DCI.
Mental Math String
Data Informed, Content-Derived Instruction
• Use the results of the warm up to guide an
initial conversation with the students.
– Ask them to identify specific areas of confusion
– If they are unable to identify specifics, talk them
through a problem and see if they understand
each step. (see questioning guide)
1Identify the Problem.
Can you tell me what you are having trouble understanding/solving?
2Check for
Understanding.What can you tell me about this
problem? What are you being asked to solve?
3 Check for Knowledge of appropriate skills.What strategies or operations can
you use to solve this problem?
4Check for Application.Okay, let’s try the first step. What
should we do first? (Do it.) Second? (Do it.) Third…
1AShow me a problem or equation that you
are having trouble solving.
2BIt looks to me that you are solving a ___ problem, let’s try strategies that would work when
___ing
2AHave we
worked on similar
problems? How did you solve them?
3AThis looks like ___.
We worked on
problems like that __. Let’s look at those notes…
If Yes
If No
If Answered correctly.
If Answered correctly.
If Cannot answer correctly.
If Cannot answer correctly.
If answered no or cannot answer correctly.
Questioning
Strategy
• Step 1) Pre-Work: Identify specific areas of confusion
• Step 2) I DO: Re-explain concept(s). Model one or
two example problems (in Think-Aloud style)
• Step 3) WE DO: Fill out a Procedure Notes Graphic
Organizer and do 2 problems together
Data Informed, Content-Derived Instruction
Simplify 3(2x2 + 5x) - 7 - 3x + 1 - x2
Steps Calculation Reason
1. Rewrite the expression
3(2x2 + 5x) - 7 - 3x + 1 - x2
2. Distribute
Order of Operations: Multiplication and division should be solved before addition and subtraction. Always work from right to left.
6x2 + 15x – 7 – 3x + 1 - x2
3. Gather like terms together 6x2 – x2 + 15x – 3x – 7
+ 1Ensures proper simplification
4. SimplifyOrder of Operations: Addition and subtraction from left to right, do whichever operation appears first.
5x2 + 12x – 6
Make sure you are doing the correct problem
• Step 1) Pre-Work: Identify specific areas of confusion
• Step 2) I DO: Re-explain concept(s). Model one or
two example problems (in Think-Aloud style)
• Step 3) WE DO: Fill out a Procedure Notes Graphic
Organizer and do 2 problems together
• Step 4) YOU DO: Student works on problem set.
Have them do at least on one problem as a Think-
Aloud to gauge comprehension (use questioning guide)
Data Informed, Content-Derived Instruction
Activity
Work-
sheet (revisite
d)
After the Session• Student Progress Log:
– Facilitates the sharing of information between CMs and
the teacher
– Provides the teacher (and yourself) with detailed
information about the progress of students during the
tutoring sessions.
• How to use:
– Fill it out after EVERY tutoring session.
– ONE student per page
– Use your notes from the APW to fill in the information
– Write in comments you want to share with your teacher
– Write down ideas from your teacher meetings to help plan
for future tutoring sessions.
Comp Fluency
DCICM
Notes Section
Teacher Notes Section
Example Student Progress Log
Comp Fluency
DCI
CM Notes
Section
Teacher Notes Section