ADD+VANTA

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WHY ADD+VANTAGE?

• Focuses on foundational mathematical thinking for all students

• Common language across the whole school

• Daily routines in the classroom along with more intensive focused instruction for struggling students

• Logical mathematical thinking and flexibility

• Screeners to assist with diagnosis of mathematical deficiency in order to target appropriate instruction

• Sequence for learning about number, counting, addition, subtraction, multiplication and division.

• Helping students gain a meaningful understanding of number going from unitary to composite strategies

ADD+VANTAGE MATH DOES NOT…

• Replace core curriculum

• Teach algorithms

• Guarantee students will “catch up” with classroom scope and sequence through an intervention time….HOWEVER, it does fill foundational gaps that are preventing the student from accessing grade level math curriculum.

INFORMED ASSESSMENT

Where are they

now?

Where do I want

them to be?

How will they get there?

How will I know when

they get there?

Teaching &

Learning Cycle

Screeners allow teachers

to pinpoint student’s stage and

levels

Screeners allow teachers to

pinpoint student’s stage

and levels

Teacher knowledge as

a developmental continuum of mathematics

Informed instruction

that develops underlying

strategies & skills

LEARNING FRAMEWORK IN NUMBER

• Six Categories • Number Words• Numerals• Additional & Subtraction• Structuring Numbers• Place Value• Multiplication & Division

• Students develop in all categories simultaneously• Students having gaps in earlier foundational skills will struggle and continue to fall further behind

Number Words NumeralsAddition and Subraction

Structuring Numbers

Place ValueMultiplication and

Division

Chapter 3 Chapter 3 Chapters 4 & 6 Chapters 5 & 7 Chapters 8 & 9 Chapter 10

Forward/Backward Number Word

Sequences to 10Numerals to 5

Emergent Counting(learning to count

visible items)

Early Spatial Patterns and Finger

Patterns   

Forward/Backward Number Word

Sequences to 30Numerals to 10

Perceptual Counting(can count, but not

when hidden)

Facile Structures of 5   Initial Grouping

Forward/Backward Number Word

Sequences to 100Numerals to 20

Figurative Counting(can count, but not

“counting on”)

Intermediate Structures to 10    

  Numerals to 100        

Forward/Backward Number Word Sequences for

Composite Units

Numerals to 1000 and beyond

Initial Number Sequence

(Counting-on and Counting-back)

Facile Structures to 10 Tens and Ones Perceptual Counting

in Multiples

      Intermediate Structures to 20

Tens and Ones with Materials (Jump

&/or Split)

Figurative Composite Grouping

Forward/Backward Number Word

Sequences to 1000 and Beyond

 

Facile Number Sequence

(uses range of non count-by-one

strategies)

Facile Structures to 20

Tens and Ones without Materials (Jump &/or Split)

Repeated Abstract Composite Grouping

       

Mental computation involving addition

and subtraction with 2- and 3-digit

numbers

Multiplication and Division as Operations

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UNITARY COMPOSITE

• Students functioning in the “unitary” construct is one-to-one only• They count by ones as a strategy to solve• Often, these are PreK- 1st grade students, developmentally appropriate• For older students, this becomes a problem• They may have memorized algorithms to appear as though they are using

composite thinking, but typically are using only unitary strategies• Accurate but slow • Place value problems• Struggle with multiplication, fractions, decimals, word problems, multi-

digit problems, etc.• Don’t recognize when an answer clearly is wrong

• Composite Thinking – • Can use more than one strategy• Multiple mental math strategies• By 1st or 2nd grade, should be developing• Critical for future successful learning of mathematics

Structuring Numbers (Levels 0-5) : Finger Patterns / Spatial Patterns / Combining and Partitioning

Written Labels: Numerals (Levels 0-5) and Numeral Sequences, Recording Symbols

Addition and Subtraction Arithmetical Strategies• Unitary

Constructs 0-3

Addition and Subtraction Arithmetical Strategies• Composite• Constructs 4-

5

Multiplication and Division Arithmetical Strategies• Composite

Constructs 0-5

Place Value Base-Ten Arithmetical Strategies• Composite

Constructs 0-5

Unitary Strategies Composite StrategiesThe Learning Framework in Number

Forward and Backwards Number Word Sequences

related to Composite Units

Forward and Backward Number Word Sequences by Ones

(Levels 0-5)

OUR GOAL

• Develop foundational skills for all students• Most core curriculum address these steps, but it often moves too

fast• Most of these strategies are not paper/pencil activities

• Know and understand the continuum of mathematical learning

• Analyze and diagnose how students are thinking about math

• Target instruction to extend mathematical thinking and apply to core curriculum

• Target instruction to fill gaps for struggling students

SCREENERS

GENERAL INSTRUCTIONS FOR SCREENERS

• Should focus on responses and strategies rather than right or wrong answers – the goal is to learn about the child’s thinking and strategies.

• The key, is watching the strategies the student is using to solve

• The follow-up for every question is….• How did you figure it out?

• Give neutral responses to answers…not great job, you got that one, that was close, etc.

• Should not repeat or re-phrase the question, unless you’re sure it’s necessary.

• Make sure you give plenty of wait time in order for them to think through

• Avoid the temptation to talk to the student when they are engaged in solving the task

• Watch closely for lip, finger, head, body movements – those will give you important clues as to what strategies they are using.

• Avoid having students check every answer.

• Make sure you have all of the materials you need.

KINDERGARTEN MATH SCREENER

• Constructs assesssed:• Forward Number Word Sequences 0-10• Numeral Identification 0-10• Addition and Subtraction – count visible numbers

BIG QUESTIONS:

1. Where is my student performing?

2. What is their next step?

3. If you’re screening a class….where are most of my kids?

1ST GRADE SCREENER

Constructs assessed:

• Forward Number Word Sequence (1-22)

• Backward Number Word Sequence (from 10)

• Numeral Identification (up to 20)

• Addition & Subtraction

• Structuring Numbers

(*subitize means to perceive at a glance the number of items presented)

BIG QUESTIONS:

1. Where is my student performing?

2. What is their next step?

3. If you’re screening a class….where are most of my kids?

2ND GRADE SCREENER

Constructs Assessed:

• Forward Number Word Sequences

• Backward Number Word Sequences

• Numeral Identification

• Addition & Subtraction (screened/covered)

• Structured Numbers

BIG QUESTIONS:

1. Where is my student performing?

2. What is their next step?

3. If you’re screening a class….where are most of my kids?

3RD GRADE SCREENER

Constructs assessed:

• Backward Number Word Sequences

• Numeral Identification

• Multiplication and Division

• Addition and Subtraction

• Place Value Base-Ten (no paper/pencil, mental math only)

• Structuring Numbers

BIG QUESTIONS:

1. Where is my student performing?

2. What is their next step?

3. If you’re screening a class….where are most of my kids?

4TH GRADE SCREENER

Constructs assessed:

• Forward Number Word Sequences

• Backward Number Word Sequences

• Numeral Identification

• Multiplication and Division

• Place Value Base-Ten (no paper/pencil, mental math only)

BIG QUESTIONS:

1. Where is my student performing?

2. What is their next step?

3. If you’re screening a class….where are most of my kids?

5TH GRADE SCREENER

Constructs assessed:

• Backward Number Word Sequences

• Numeral Identification

• Multiplication and Division

• Place Value Base-Ten (no paper/pencil, mental math only)

BIG QUESTIONS:

1. Where is my student performing?

2. What is their next step?

3. If you’re screening a class….where are most of my kids?

YOU’V

E SCREENED…

NOW

WHAT

?

NEXT STEPS GUIDE

• Addvantage Math Next Steps Guide – by Grade• Aligns specific strategies based on screening results

• Instructional Activities are explained:• Teaching Number in the Classroom (purple book)• Includes how to vary the activities

• DENS – Developing Efficient Numeracy Strategies (posted on the web)

CLASSROOM ROUTINES BY GRADE

This is a menu of SHORT routines for daily work.  A few minutes daily working with each of these areas will reap HUGE benefits, especially as students become older.  Pick a few from the list in each skill area - it is not necessary to do all areas every day.  Whatever you do forward, also do backward.  For example, structuring fluidly is essential for success in algebra.

PUTTING IT ALL TOGETHER

• Classroom Routines for all students• Transitions between activities• Lining up, ticket out the door, have a few minutes • Redirection strategies• Math warm-up• Align with the Math Big Ideas for your grade that will be coming up

• Screener • Primary – helpful to do with all students• Intermediate – should do at least those for whom you have

concerns

• Small groups in the classroom /Interventionist/parent volunteer, etc.• Targeted games or activities

WHAT’S YOUR PLAN FOR NEXT STEPS

1. Identify at least 3 classroom routines you will begin using. Gather materials, practice, decide when, etc.

2. What screeners would you use? With which students? Gather materials, decide which students, practice, etc.

3. Recognizing that you have not yet completed the screeners, what kind of focus areas do you anticipate needing to meet student needs? After screening, debrief and plan targeted instruction.

4. How will you progress monitor students? Frequency?