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