Teaching Students to Think Mathematically and Algebraically By Greg Tang (www.gregtang.com): Here is a summary of a better approach to some basic math skills that you can start using right now today to help your student to be smart in math. When they are smart in math they will actually enjoy it. As soon as a student masters a strategy encourage them do it FASTER and then MOVE THEM ON… (Down each column) Addition Skills

Subtraction Skills

Multiplication Skills

Division Skills

Traditional Algorithms

Count

Count down

Identity Property

/2 half

Make 10

Skip count to add

Make ten

X2 double

/4 half of half

Base 5

Double

Make tens

X3 Double and add 1

/6 /2 and then /3

Base 6

Turn arounds, commutative property

Make 100

X4 Double twice

/8 half 3 times

Base 2

Double +1,+ 2,+3

Make 100s

X10 just add zero

/9 how many 9’s?

Base 3

Doubles -1

Partial Differences

X5 half the x10

/10 drop the zero

Base 4

Shift a few

Partial Partial Differences

X9 start with x10 and then subtract

/5 double and divide by 10

Base 2-4

Make 10, make 10’s, add 10, add 9

Add up

X6 think in groups of 3 (x3 twice)

Divide by chunking – do in parts then add

Base 7

doubles +10, make 100, partial sums

Make 99

X7 add x5 and then x2

Reduce to divide

Base 8

Partial partial sums

Round to Subtract

X8 add two x4

Place value division: tens and ones only

Base 9

Bigger partial sums

Estimation

X11 insert the sum 11x45 = 4_5 = 495

DMSB: dirty monkeys smell bad

Base 7-9

Look for 10’s

Place Value

X12 x10+x2

Base 2-9 Converting

Place Value

X15 x10+x5

Base 2-9 Regrouping

Regrouping horizontally

X50 half x100

Regrouping Vertically

Partial products/ (Distributive property) Double half Place Value Multiply horizontally and then vertically