Mental Math Strategies

We have been learning about the Front End Strategy and Compensation Strategy in math. 

(Grade 6 Math Outcome: B12 calculate products and quotients in relevant contexts by using the most appropriate method). We are using these strategies with multiplication and division  as well as whole and decimal numbers.

1. Front End Strategy:

We want to break up our number into smaller more manageable parts by creating "nice to work with" numbers.  We use the "front" of the number to help us caluculate quickly in our heads

 

1A.  Front-End Multiplication Strategy

This is usually used when one factor is a single digit and there is no regrouping.

For example, 3 x 2313 = 6000 + 900 + 30 + 9 = 6939

 

1 B. Break Dividend Into Parts Strategy

For many simple computations, divide the dividend into parts and divide.

For example, 1515 / 5 = (1500 / 5) + (15 / 5) = 300 + 3 = 303.

 

2. Compensation Strategy:

The compnesation strategy is a "cashier" method. 

 

2 A. Compensation Strategy for Multiplication

As with addition and subtraction, work with “friendly” numbers. 

For example, 5 x 29  becomes  5 x 30 (turning 29 into 30 because it is easier to work with 30)

multiply 5x30 = 150

then SUBTRACT  5 (because we had to add 1 when we rounded 29 to 30.  1 x 5=5) 

Our Answer:  145

 

2B. Doubling Strategy: Never Divide by 5 Again!

Use the double and half strategy to simplify all division by 5.
For example 520 / 5 is the same as 1040 / 10.
The Answer: 104