Welcome to Math 6 Our subject for today is… Divisibility.

The Connector… To be successful in Math 6, you must have a strong grasp of all the skills introduced in Math 5, 4, 3, 2 and 1. So I will frequently discuss concepts that you may already have learned before.

KEY VOCABULARY FOR THIS LESSON Divisible- means that a number can be divided by another number with no remainder. Example: “6 is divisible by 3” Divisibility- the capacity of being evenly divided, without a remainder.

DIVISIBILITY RULES There are certain rules that we can use to tell if a number is divisible by another number.

Question: Why review divisibility? Answer: The rules for divisibility are useful in many instances, such as when looking for common factors, finding equivalent fractions, or finding equal ratios.

OBJECTIVE: Each student will:  State the rules for the divisibility of 2, 3, 5, 6, 9 and 10.  Apply the rules for the divisibility of 2, 3, 5, 6, 9 and 10

During this lesson, I will explore some of the divisibility rules. You probably already know some of these rules. But I’ll begin with the simplest rules.

A number is divisible by: 2 if the digit in the ones place is even. (If it ends in a 2, 4, 6, 8, 0.)

Examples: 3978 Is divisible by 2, Since it’s an even number Is not divisible by 2, since it’s an odd number.

A number is divisible by: 5 if it ends with a 5 or a 0.

Examples: These numbers are divisible by 5: ,875 These numbers are not divisible by 5: 48,568 2,374

A number is divisible by: 10 Only if it ends with a zero. (If there is a zero in its ones place.)

Examples: 900 is divisible by 10 10,960 is divisible by is divisible by 10 49,123,983 is not divisible by 10

Take another look at the last two rules. If a number ends with 5 or 0, it’s divisible by 5. If a number ends with a 0, it’s divisible by 10. So every number that is divisible by 10 must also be divisible by 5.

A number is divisible by: 3 if the sum of the digits is divisible by 3.

Examples: 315 is divisible by 3 since 3+1+5=9, and 9 is divisible be is not divisible by 3 since 1+3+9=13. and 13 is not divisible by 3.

A number is divisible by: 6 If it is divisible by both 2 and 3.

Examples: 330 is divisible by 6, 3+3+0=6; and 6 is divisible be 3. AND It is also divisible by 2 since it is even.

Examples: 233 is not divisible by is not divisible by 3 because 2+3+3=8. 8 is not divisible by 3. And it is not divisible by 2 because it is an odd number.

Those are the simplest rules All of the other rules are a bit less obvious. Next comes the rule for 9.

A number is divisible by: 9 When the sum of its digits is a number divisible by 9.

Examples: 3,330 is divisible by 9. Since =9, and 9 is divisible by 9. That example seems pretty simple. Lets look at another example of this rule.

Examples: 9,315 is divisible by 9. Since =18, and 18 is divisible by 9.

Notice Look at these basic math facts: 9 x 1=9 9 x 2=181+8=9 9 x 3=272+7=9 9 x 4=363+6=9 9 x 5=454+5=9 9 x 6=545+4=9 Add the digits in the product and you will get 9.

Here’s something pretty interesting… You can take the rule for 9 a step further… For every number divisible by 9, if you keep adding the digits together, you will eventually get a sum of 9.

If you keep adding, You will eventually get a sum of 9. Examples: 9,999 is divisible by =36 and 3+6=9 59,238 is divisible by =27 and 2+7=9. It always works.

Question: What about 4, 7 and 8? Are there divisibility rules for those numbers too? Answer: Yes. But we will cover those in a future lesson. For now, let’s apply the rules we have covered so far.

Guided Practice: Tell whether 610 is divisible: a. by 2 ___________________ b. by 3 __________________ c. by 5 ____________________ d. by 6 ____________________

Guided Practice: Tell whether 610 is divisible: a. by 2 Yes, its and even number b. by 3 __________________ c. by 5 __________________ d. by 6 __________________

Guided Practice: Tell whether 610 is divisible: a. by 2 Yes, its and even number b. by 3 No because 6+1+0=7 (7 is not divisible by 3) c. by 5 __________________ d. by 6 __________________

Guided Practice: Tell whether 610 is divisible: a. by 2 Yes, its and even number b. by 3 No because 6+1+0=7 (7 is not divisible by 3) c. by 5 Yes because it ends in 0 d. by 6 __________________

Guided Practice: Tell whether 610 is divisible: a. by 2 Yes, its and even number b. by 3 No because 6+1+0=7 (7 is not divisible by 3) c. by 5 Yes because it ends in 0 d. by 6 No, since it isn’t divisible By 3

Guided Practice: Tell whether 387 is divisible: e. by 2 ___________________ f. by 3 ____________________ g. by 6 ____________________

Guided Practice: Tell whether 387 is divisible: e. by 2 No. It has a 7 in the ones place (It’s and odd number) f. by 3 ____________________ g. by 6 ____________________

Guided Practice: Tell whether 387 is divisible: e. by 2 No, it has a 7 in the ones place (It’s and odd number) f. by 3 Yes because 3+8+7=18 which is divisible by 3 g. by 6 ____________________

Guided Practice: Tell whether 387 is divisible: e. by 2 No, it has a 7 in the ones place (It’s and odd number) f. by 3 Yes because 3+8+7=18 which is divisible by 3 g. by 6 No, because it must be divisible by both 2 and 3

Guided Practice: Tell whether 387 is divisible: h. by 9 ____________________ i. by 10 ____________________

Guided Practice: Tell whether 387 is divisible: h. by 9 Yes because 3+8+7=18 which is divisible by 3 i. by 10 ___________________

Guided Practice: Tell whether 387 is divisible: h. by 9 Yes because 3+8+7=18 which is divisible by 3 i. by 10 No, since it does not have a 0 in the ones place

Independent Practice: Tell whether each number is divisible by 2, 3, 5, 6, 9, and Make a chart as seen on the next slide…

Pause the lesson while you work Write yes or no in each box

Yes No 217No 247No 189No Yes No Yes No Independent Practice Answers

Conclusion: Divisibility rules of whole numbers are useful because they help us to determine quickly if a number can be divided without doing long division.

Assignment 1 Make up your own divisibility table like the one we used during the Independent Practice. (You can use the blank table on the next slide.) Let someone else try to complete the table.

Write yes or no in each box

Assignment- 2 Tell whether the statement is true or false. Explain your answers. a. All even numbers are divisible by 2. b. All odd numbers are divisible by 3. c. All even numbers are divisible by 5

Complete the exercise on the next slide “Divisibility for 3, 6 and 9. (A)” Assignment 3

Assignments-

Final thought… Learning new things in Math, as in any subject, can sometimes take lots of practice. But you will eventually succeed if you have patience. Some things will come easily, some things may not. You definitely will need persistence along the way.

I hope you enjoyed the lesson today. Look back over it many times so you can master the points we covered. Also: be sure to complete all of the assignments. See you next time.