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

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

WHY DO WE DO IT “DIFFERENTLY” NOW?

EXHIBIT B

Move from just learning a single technique (HOW) to

understanding the math behind it (WHY).

given directions vs given map

THE TRANSITION

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

FLUENCY

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

ADDITION STRATEGIES

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.

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

SUBTRACTION STRATEGIES

Counting Up - using addition to find the distance/difference

between the two numbers

SUBTRACTION STRATEGIES

SUBTRACTION STRATEGIES

Counting Up (using larger numbers)

Counting Back Using an Open Number Line and Decomposition

SUBTRACTION STRATEGIES

Subtracting by Place Value

SUBTRACTION STRATEGIES

Compensation – using friendlier numbers and adjusting

answer

SUBTRACTION STRATEGIES

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

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

Repeated Addition – skip counting, with or without number

line

MULTIPLICATION STRATEGIES

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

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

MULTIPLICATION STRATEGIES

DOUBLE & HALF

5 x 6

is the same as

10 x 3

14 x 4 = 7 x 8

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

DIVISION STRATEGIES

At-home

practice:Skip-count

forwards AND

backwards

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

DIVISION STRATEGIES

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

http://www.kyrene.org/Page/2770

PARENT RESOURCES

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?

Dreambox - can be accessed at home

HOW CAN I SUPPORT MY CHILD IN

MATH?

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?

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?

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?

CARD GAMES!