PATTERNS AND RELATIONSUnit 1

IN THIS UNIT YOU WILL INVESTIGATE PATTERNS AND RELATIONS.

You will describe, extend, and explain patterns, use patterns to make predictions, and show patterns on graphs.

You will learn how to use variables to translate simple statements into algebraic expressions (which you will then evaluate) or equations (which you will then solve).

YOUR GOALS… To recognize number patterns in tables. To be able to extend a table of values using a

pattern. To describe the relationships among terms in

a table. Divisibility rules- to recognize divisibility

quickly with numbers other than 2 or 5… the “easy” ones!!

KEY MATH LEARNINGS IN THIS LESSON: Patterns in numbers can be used to find

divisibility rules. Some divisibility rules depend on the digits at

the end of a number.

78, 27, 35, 410, 123, 2100, 4126, 795 You will find these numbers at the top of the

page in your textbook on page 6.

What does it mean for a number to be divisible by 2?

Answer: When you divide the number by 2, there is no remainder.

Circle the numbers that are divisible by 2.

78, 27, 35, 410, 123, 2100, 4126, 795

DIVISIBILITY RULES: (FOR 2) Any number whose ones digit is

even, is divisible by 2.

Multiples of 2 are even numbers: 2, 4, 6, 8, 10… ALL even numbers are divisible by 2.

(FOR 5) Any number whose ones digit is 0 or 5 is divisible by 5.

Here are some multiples of 5: 5, 10, 15, 20, 25…

The ones form a repeating pattern: 5, 0, 5, 0…

DIVISIBILITY RULES CONTINUED (FOR 10) Any number whose ones digit is 0,

is divisible by 10.

Here are some multiples of 10: 10, 20, 30, 40…

Do you see a pattern?

RULES FOR 4 & 8… A BIT TRICKIER! (FOR 4) Any number whose last 2 digits are

divisible by 4.

Mental math… this rule works because 100 is divisible by 4.

In your own words… How can you check if a number is divisible by 4?

If the number has 2 digits, I have to divide by 4. If the number has more than 2 digits, I divide the number formed by the last two digits by 4. If there is no remainder, I know the number is divisible by 4.

EXAMPLE: 1192 (FOR 8) We know 1000 is divisible by 8:

1000/8=25

So, we only need to check if 192 can be divided by 8.

Use mental math: 192/8=24

192 is divisible by 8, so 1192 is divisible by 8

ALL MULTIPLES OF 1000 ARE DIVISIBLE BY 8 2192 3192 4192 5192 … are all divisible by 8.

A number that is divisible by 8 is also divisible by 2 and 4 because 8 = 2 X 4

ANOTHER IMPORTANT IDEA ABOUT DIVISIBILITY: If two different numbers (28, 34) are each

divisible by the same number (4), then their sum is also divisible by that same number.

28 / 4 = 7 32 / 4 = 8

28 + 32 = 60

60 / 4 = 15

REVIEW VENN DIAGRAM PAGE 8 A Venn Diagram illustrates relations.

Practice, Page 8 & 9, Questions 1 to 7.

Use mental math. Use a calculator to check your answers.