Transcript Direct Model

PARENT MATH NIGHT
ARIZONA’S COLLEGE AND CAREER
READINESS STANDARDS (AZCCRS)
Sierra
November 21, 2016
Amy Ordonez
Math Coach
* E st re l l a
* S i e r ra
http://www.kyrene.org/Page
/35162
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?
WHY DO WE DO IT “DIFFERENTLY” NOW?
EXHIBIT A
Find the sum.
298 + 26
WHEN KIDS USE “OLD MATH”
“Insanity – doing the same thing over and over again and
expecting dif ferent results.” –Albert Einstein
THE TRANSITION
 Move from just learning a single technique (HOW) to
understanding the math behind it (WHY).
given directions
vs
given map
ALGORITHM VS. STRATEGIES
 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 – 5 th Grade (5.NBT.B.5)
Long division – 6 th Grade (6.NS.B.2)
 Strategies – build to an understanding of the operations used
in solving problems - FLUENCY
FLUENCY
ADDITION STRATEGIES
 Direct Modeling – model the action or structure of problem,
also described as ‘Counting All’
Most basic level (preK and Kinder)
ADDITION STRATEGIES
 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
 Incremental Adding (using decomposition & friendly numbers)
ADDITION STRATEGIES
 Decomposing using an Open Number Line – break apart one
number into smaller, friendlier numbers ( whatever makes
sense for the child!)
ADDITION STRATEGIES
 Adding by Place Value – break apart (decompose) numbers
into tens, ones, etc. and add like place values
ADDITION STRATEGIES
 Compensation – making the problem simpler by adjusting to a
friendly number
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
Most efficient strategy to use depends on
both the child and the problem.
ADDITION
SUMMARY
SUBTRACTION STRATEGIES
 Direct Modeling – represent action or structure of problem
SUBTRACTION STRATEGIES
 Counting Down – start at larger number and count back, may
use fingers or tallies to keep track of counting
SUBTRACTION STRATEGIES
 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
At-home
practice:
Skip-count
forwards AND
backwards by
10’s and 5’s
SUBTRACTION STRATEGIES
 Counting Up - using addition to find the distance/difference
between the two numbers
SUBTRACTION STRATEGIES
 Counting Up (using larger numbers)
SUBTRACTION STRATEGIES
 Counting Back Using an Open Number Line and Decomposition
SUBTRACTION STRATEGIES
 Subtracting by Place Value
SUBTRACTION STRATEGIES
 Compensation – using friendlier numbers and adjusting
answer
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
MULTIPLICATION STRATEGIES
 Direct Modeling – draw picture of problem, read ‘x’ sign as
“groups of”
3x4
(3 groups of 4)
Add up all dots to find answer.
MULTIPLICATION STRATEGIES
 Repeated Addition – skip counting, with or without number
line
MULTIPLICATION STRATEGIES
 By Place Value (partial products) - 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 = 52
MULTIPLICATION STRATEGIES
 Area Model – decompose larger numbers into smaller,
friendlier numbers based on place value
MULTIPLICATION STRATEGIES
 Related Facts: using facts students already know to solve
problems; other patterns that students discover such as
Double & Half
DOUBLE & HALF
5x6
is the same as
10 x 3
14 x 4 = 7 x 8
DIVISION STRATEGIES
 Direct Model – use pictures/objects to model the total being
divided into groups (“dealing out”)
DIVISION STRATEGIES
 Repeated Subtraction – subtract divisor repeatedly to find how
many times it can be subtracted
At-home
practice:
Skip-count
forwards AND
backwards
DIVISION STRATEGIES
 Area Model – connect division as multiplication problem
DIVISION STRATEGIES
 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
 Decomposing – breaking apart the larger number into smaller,
friendlier numbers, basis of distributive property
place value
simpler facts
(24÷4=6)
DIVISION STRATEGIES
 Related Facts – using facts students already know to solve
problems
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
PARENT RESOURCES
 http://www.kyrene.org/Page/2770
HOW CAN I SUPPORT MY CHILD IN
MATH?
 “Do’s”
 #1 - Help your child develop a “growth attitude” about math.
 Recognize there is more than one way of solving a problem.
 Ask questions when they get the answer right, too! (handout)
 Pretend you don’t know – have you child teach you.
 Play games & puzzles (develop numeracy & logic skills)
 SET, Mancala, Yahtzee, Mastermind, Blokus, Guess Who?, Dartboard
 Brainteaser puzzles (problem-solving, critical thinking)
 Lego blocks, K’nex (spatial reasoning)
HOW CAN I SUPPORT MY CHILD IN
MATH?
 “Don’ts”
 Focus on speed (i.e. flash cards)
 Just give them extra math work
 Simply give the correct answer. Try to give f eedback – ask your
child to talk through how they worked it out and lead them to
the spot of the error.
 Expect them to “get it” after you’ve explained it once – Be patient!
 #1 rule - NEVER describe yourself as hopeless in math!!
There is no such thing as the “math gene”!
HOW CAN I SUPPORT MY CHILD IN
MATH?
 Dreambox - can be accessed at home
HOW CAN I SUPPORT MY CHILD IN
MATH? DREAMBOX-PARENT ACCOUNT
HELPFUL BOOKS