Fractions, Ratio, and Proportion Sequences

Make use of tens

4 1/2 * 50 = (4 * 10 * 5) + (1/2 * 10 * 5)
(40 * 5) + (5 * 5)
200 + 25

Halve and doubles

4 1/2 * 50 =
50 doubled once = 100 and doubled again = 200
1/2 of 50 = 25

or
double 4 1/2 and 1/2 50
9 * 25

Get rid of the fraction

double 4 1/2 and half 50
9 * 25

Use all the factors in pretty ways.

4 1/2 * 50 = 9 * 25 = 225
Or (4 * 50) + (1/2 * 50) = 200 + 25
Or (5 * 50) - (1/2 * 50) = 250 - 25 = 225
2 1/4 * 100
2 1/4 * 120
4 1/2 * 60
15 1/2 * 36 = (10 * 36) + (5 * 36) + (1/2 * 36) = 360 + (1/2 * 360) + 18 = 360 + 180 + 18
15 1/2 * 4 1/2 =

Multiplication and Division of Fractions Sequence

Developing strategies for computation with decimals

All the strategies for whole numbers can work with decimals.

Friendly numbers

71.87 + 28.2 = 72.07 + 28 (compensation subtract .2 and add .2)

71.87 + 28.2 = 71.07 + 29 (compensation subtract .8 and add .8)

71.87 + 28.2 = 72 + 28 + .07

Using money

.20 * 9 = (5 * .20 = 1.00 and 4 * .20 = .80) 1.80

.20 * 9 = ((.20 * 10) - .20)= 1.80

.25 * 9

16 * .25 = 4

How many students would know that a 4 x 4 array of quarters is 4 dollars?

Using fractions and decimals interchangeably

75 * 80 = 3/4 * 80 * 100 ( because 75 was treated as 75/100, divide 100 need to multiply 100)

1/4 * 80

.25 * 80

25 * 80

1/2 * 60

.5 * 60

.50 * 60

.50 * .60