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 ~

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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 share:– 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?

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)

• Step 1) I DO: Identify specific areas of confusion to

know what concept(s) to re-teach. Model one or two

example problems (in Think-Aloud style)


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 2) WE DO: Fill out a Procedure Notes Graphic

Organizer and work on 10/26 course work using the

graphic organizer.


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 2) WE DO: Fill out a Procedure Notes Graphic

Organizer and work on 10/26 course work using the

graphic organizer. Students will work on problem sets

individually. (Have students do at least on problem as a Think-Aloud)

• Step 3) YOU DO: Have students complete mental

math string. do at least on one problem as a Think-

Aloud to gauge comprehension (use questioning guide)


YOU DO:Use this time to

assess individual

student comprehension:

–Think-Alouds

–Mental Math Strings

Mental Math String

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

Do Now: Fact Family Worksheets!

Documents

Transcript of Do Now: Fact Family Worksheets!