OLD DOGS, NEW MATH ARIZONAS COLLEGE AND Kyrene S chool Di strict - - PowerPoint PPT Presentation

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OLD DOGS, NEW MATH ARIZONAS COLLEGE AND Kyrene S chool Di strict - - PowerPoint PPT Presentation

May 08, 2023 570 likes •1k views

OLD DOGS, NEW MATH ARIZONAS COLLEGE AND Kyrene S chool Di strict CAREER READINESS M arch 2 6, 2 0 15 STANDARDS (AZCCRS) Alison Gaedke Math Coach *Lagos *Mariposa http: p://w /www.kyrene ne.org/Page/333 3365 MAIN TOPICS 1) What are

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Kyrene S chool Di strict M arch 2 6, 2 0 15

Alison Gaedke

Math Coach *Lagos *Mariposa

OLD DOGS, NEW MATH

ARIZONA’S COLLEGE AND CAREER READINESS STANDARDS (AZCCRS)

http: p://w /www.kyrene ne.org/Page/333 3365

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MAIN TOPICS

1) What are these new strategies and why are we teaching them? 2) What can I do at home to support my child in math?

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WHY DO WE DO IT “DIFFERENTLY” NOW?

EXHIBIT A

Find the sum.

298 + 26

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WHY DO WE DO IT “DIFFERENTLY” NOW?

EXHIBIT B

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 Move from just learning a single technique (HOW) to understanding the math behind it (WHY). given directions vs given map

THE TRANSITION

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 Standard Algorithm - a step-by-step procedure

  • Carrying the 1 in addition – not taught until 4th Grade (4.NBT.B.4)
  • Borrowing in subtraction – not taught until 4th Grade (4.NBT.B.4)
  • Carrying in multiplication – 5th Grade (5.NBT.B.5)
  • Long division – 6th Grade (6.NS.B.2)

 Strategies – build to an understanding of the operations used in solving problems - FLUENCY

ALGORITHM VS. STRATEGIES

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FLUENCY

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 Direct Modeling – model the action or structure of problem, also described as ‘Counting All’ Most basic level (preK and Kinder)

ADDITION STRATEGIES

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 Counting On – able to start at first number/largest number and count up from there It is okay for a child to use fingers to count at this stage.

ADDITION STRATEGIES

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 Incremental Adding (using decomposition & friendly numbers)

ADDITION STRATEGIES

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 Decomposing using an Open Number Line – break apart one number into smaller, friendlier numbers (whatever makes sense for the child!)

ADDITION STRATEGIES

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 Adding by Place Value – break apart (decompose) numbers into tens, ones, etc. and add like place values

ADDITION STRATEGIES

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 Compensation – making the problem simpler by adjusting to a friendly number

ADDITION STRATEGIES

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Begin with using objects, pictures to represent both numbers

  • Direct Model

Move into using fingers to keep track of counting

  • Counting On

Use simpler facts to solve problem

  • Add by Place Value, Decomposing, Incremental

Adding, Compensation

ADDITION SUMMARY

Most efficient strategy to use depends on both the child and the problem.

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 Direct Modeling – represent action or structure of problem

SUBTRACTION STRATEGIES

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 Counting Down – start at larger number and count back, may use fingers or tallies to keep track of counting

SUBTRACTION STRATEGIES

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 Incremental Subtracting (uses decomposing & friendly numbers)

82 82 – 49 49

82 – 10 = 72 72 – 10 = 62 62 – 10 = 52 52 – 10 = 42 42 - 9 = ___ 42 – 10 = 32 so it is 1 more, 33 33

SUBTRACTION STRATEGIES

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 Counting Up - using addition to find the distance/difference between the two numbers

SUBTRACTION STRATEGIES

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SUBTRACTION STRATEGIES

 Counting Up (using larger numbers)

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 Counting Back Using an Open Number Line and Decomposition

SUBTRACTION STRATEGIES

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 Subtracting by Place Value

SUBTRACTION STRATEGIES

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 Compensation – using friendlier numbers and adjusting answer

SUBTRACTION STRATEGIES

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Begin with using objects, pictures to represent both numbers

  • Direct Model

Move into using fingers to keep track of counting

  • Counting Down, Counting Up

Use simpler facts to solve problem

  • Incremental Subtracting, By Place Value,

Compensation

SUBTRACTION SUMMARY

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 Direct Modeling – draw picture of problem, read ‘x’ sign as “groups of”

3 x 4

(3 groups of 4) Add up all dots to find answer.

MULTIPLICATION STRATEGIES

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 Repeated Addition – skip counting, with or without number line

MULTIPLICATION STRATEGIES

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 By Place Value– decompose number based on place value to use simpler facts to build to answer

13 x 4 (10 x 4) + (3 x 4) 10 x 4 = 40 3 x 4 = 12 Add products up… 40 + 12 = 56 56 MULTIPLICATION STRATEGIES

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 Area Model – decompose larger numbers into smaller, friendlier numbers based on place value

MULTIPLICATION STRATEGIES

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 Related Facts: using facts students already know to solve problems; other patterns that students discover such as Double & Half

MULTIPLICATION STRATEGIES

DOUBLE & HALF 5 x 6 is the same as 10 x 3 14 x 4 = 7 x 8

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 Direct Model – use pictures/objects to model the total being divided into groups (“dealing out”)

DIVISION STRATEGIES

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 Repeated Subtraction – subtract divisor repeatedly to find how many times it can be subtracted

DIVISION STRATEGIES

At-home practice:

Skip-count forwards AND backwards

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 Area Model – connect division as multiplication problem

DIVISION STRATEGIES

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 Big 7 – help understand long division process by using smaller known facts to reach the solution

  • The number of steps taken to solve the problem will vary based on

students estimation skills and number sense.

DIVISION STRATEGIES

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 Decomposing – breaking apart the larger number into smaller, friendlier numbers, basis of distributive property place value simpler facts (24÷4=6)

DIVISION STRATEGIES

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 Related Facts – using facts students already know to solve problems

DIVISION STRATEGIES

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Begin with pictures, objects to represent problem.

  • Direct Model, Repeated Addition/Subtraction

Use simpler problems to build up to given problem

  • Decomposing, Area Model, Related Facts

MULTIPLICATION AND DIVISION SUMMARY

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 http://www.kyrene.org/Page/2770

PARENT RESOURCES

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 Attitude

  • Help your child develop a “growth attitude” about math.
  • Feedback – resist the temptation to give them the right
  • answer. Instead ask them to talk through how they worked it
  • ut and lead them to the spot of the error.
  • Ask questions when they get the answer right, too!
  • Patience – learning doesn’t happen in an instant.
  • Make math a natural part of life instead of just a subject in

school.

  • #1 rule - NEVER describe yourself as hopeless in math!!

HOW CAN I SUPPORT MY CHILD IN MATH?

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 Dreambox - can be accessed at home

HOW CAN I SUPPORT MY CHILD IN MATH?

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 Dreambox – PARENT ACCOUNT

Review your child’s academic progress with a DreamBox Parent

  • Account. Please follow these steps to create your free Parent Account:
  • 1. Go to http://www.kyrene.org/Page/32735 and click on Dreambox.
  • 2. Select your child’s school and have your child log in to their profile just

as he/she would at school.

  • 3. Click Setup Parent Access at the bottom of the page.
  • 4. Follow instructions to create a new login and password.
  • 5. Read Terms of Use and Privacy Policy.
  • 6. Click "Submit".

Log into your home account after set up:

  • 1. Go to http://play.dreambox.com
  • 2. Enter your email address and password.
  • 3. To see student progress, click the "Parent Dashboard" button.

HOW CAN I SUPPORT MY CHILD IN MATH?

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 Math Props – “talk math” and incorporate math into everyday life

  • Digital and Analog clock – skip-counting by 5’s
  • Traditional Wall Calendar – skip-counting by 7’s, patterns
  • Measuring Cups/Tapes – customary and metric
  • Dried beans, macaroni, M&M’s – counting, direct modeling
  • Coin jars – dump out & count
  • Indoor/Outdoor Thermometer – compare temperatures
  • Money – cash back, estimating total, estimating tax

HOW CAN I SUPPORT MY CHILD IN MATH?

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 Play Games! !

  • Dart board (Velcro darts) – addition, doubling, tripling
  • Outdoor Games – Bean Bag Toss, Ladder Golf
  • Board games with dice and/or spinners
  • Regular deck of cards – endless games to play!

**Have them keep score!

HOW CAN I SUPPORT MY CHILD IN MATH?

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CARD GAMES!