Patterns: Number patterns

Lessons

In this lesson, we will learn:

• How to find the rule for a number sequence and write an expression for it
• How to predict the next term in a number sequence

Notes:

• Number patterns can also be called number sequences
• A number sequence is a list of numbers (or terms) in order
• The order of number is decided by a mathematical rule
• The same operation (+, –, ×, ÷) is used between each term.


• An expression can be written for any number pattern/sequence
• The expression states what the first number in the list is, and what the rule is
• “start at _[#]_ and _[operation]_by_[#]_ each time.”
• For example,

• The rule is to add 3 and the expression is to “start at 1 and add by 3 each time”

• If a rule for a number pattern/sequence is known, you can predict the next terms
• Using the previous example,

• The next two terms in the sequence are 13 and 16

• Always find the rule by using two consecutive numbers (right next to each other) in the sequence
• For example,

• The rule is to add 4, therefore the entire sequence should be completed as: 6, 10, 14, 18, 22, 26

• Introduction
  Introduction to Number Patterns:
  a)

  How to describe and predict the pattern in a number sequence
  
  

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• 1.
  Next Number in the Pattern
  Write the next two numbers in the pattern. Then, describe the pattern with an expression.
  a)

  1, 4, 7, 10, ___, ___
  
  
  b)

  3, 6, 12, 24, ___, ___
  
  
  c)

  30, 25, 20, 15, ___, ___
  
  
  d)

  128, 64, 32, 16, ___, ___
  
  

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• 2.
  Fill in the Blanks for the Number Pattern
  Fill in the blanks for the pattern. Then, describe the pattern with an expression.
  a)

  60, 50, ___, 30, 20, ___
  
  
  b)

  ___, 11, 17, 23, ___, 35
  
  
  c)

  1, $\frac{1}{3}$, ___,$\frac{1}{27}$ , ___
  
  
  d)

  2, 10, ___, 250, 1250, _____
  
  

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• 3.
  Special Number Patterns
  Write the next 4 numbers in the special pattern below. Look at how much each term is increased by to find the rule.
  a)

  0, 1, 1, 2, 3, 5, 8, 13, 21, __, __, __, __
  
  
  b)

  1, 1, 2, 4, 7, __, __, __, __
  
  

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• 4.
  Number Patterns - Word Problem
  Natalie is doing swimming training so that she can hold her breath underwater longer. On the first day, she is only able to hold her breath for 30 seconds. On the second day, she can do it for 45 seconds. On the third day, she can do it for 60 seconds.
  a)

  If this pattern in her progress continues, how many seconds will she be able to hold her breath for by the 7^th day?
  
  
  b)

  Describe the pattern with a sentence expression
  
  

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