Arithmetic Grade Five

Lesson Forty-two: Count-bys

Count-Bys

Often count-bys are called multiples. Multiples and count-bys are the same thing. The multiples of 10, for instance, are the count-bys of ten: 


  10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110 ...
You can count by any number. Here are a few examples: 

  11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121 ...

  12, 24, 36, 48, 60, 72, 84, 96, 108, 120 ...

  15, 30, 45, 60, 75, 90, 105, 120, 135, 150 ...

A good way to memorize your basic facts is as a sequence of count-bys. Doing advanced work in multiplication is much easier when you know your basic facts by memory. If you have to stop to recall a basic fact you will have a more difficult time with advanced forms of multiplication.

You should also be able to identify the missing number in a sequence. Here are some examples: 


  20, 25, ___, 35  (missing number: 30)

  12, 18, 24, ___, 36  (missing number: 30)

  10, 20, ___, 40  (missing number: 30)
 
  28, ___, 32, 34, 36  (missing number: 30)

  ___, 40, 50, 60  (missing number: 30)
You can figure out what you are counting by through inspection of the numbers in the sequence. For instance, in the last example shown above we are counting by 10. When we are counting by 10 the number before 40 will be 30.

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