old dogs, new math - kyrene school district · 2015. 3. 26. · math coach *lagos *mariposa old...
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K y r e n e S c h o o l D i s t r i c t
M a r c h 2 6 , 2 0 1 5
Alison GaedkeMath C oach
*Lagos
*Mar iposa
OLD DOGS, NEW MATH
ARIZONA’S COLLEGE AND
CAREER READINESS
STANDARDS (AZCCRS)
http://www.kyrene.org/Page/33365
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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 4 th Grade (4.NBT.B.4)
Borrowing in subtraction – not taught until 4 th 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 – 49
82 – 10 = 72
72 – 10 = 62
62 – 10 = 52
52 – 10 = 42
42 - 9 = ___
42 – 10 = 32 so it is 1 more, 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
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
out 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 cl ick on Dreambox.
2. Select your chi ld’s school and have your chi ld log in to their profi le just as he/she would at school.
3. Cl ick Setup Parent Access at the bottom of the page.
4. Fol low instructions to create a new login and password.
5. Read Terms of Use and Privacy Policy .
6. Cl ick "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, cl ick 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!