1. Divisibility Tests for 3 and 9
Lesson

2. Factors List all the factors of each number.𝟐𝟗 𝟖𝟎 𝟑𝟎 𝟓𝟓 𝟏𝟖 𝟐𝟕
Factors List all the factors of each number.
answers

3. Factors List all the factors of each number.𝟐𝟗
(1,29) 𝟖𝟎
(1, 2, 4, 5, 8, 10, 16, 20, 40, 80) 𝟑𝟎
(1, 2, 3, 5, 6, 10, 15, 30) 𝟓𝟓
(1, 5, 11,55) 𝟏𝟖
(1, 2, 3, 6, 9, 18) 𝟐𝟕
(1, 3, 9, 27)
Factors List all the factors of each number.
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4. Multiples Find the first 3 multiples of each number.𝟏𝟖 𝟑𝟔 𝟗𝟎 𝟒𝟐 𝟐𝟏 𝟒𝟖
Multiples Find the first 3 multiples of each number.
answers

5. Multiples Find the first 3 multiples of each number.𝟏𝟖
18, 36, 54 𝟑𝟔
36, 72, 108 𝟗𝟎
90, 180, 270 𝟒𝟐
42, 84, 126 𝟐𝟏
21, 42, 63 𝟒𝟖
48, 96, 144
Multiples Find the first 3 multiples of each number.
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6. The area of a rectangle is the product of its length and width
The area of a rectangle is the product of its length and width. If a rectangular board has an area of 30 square feet, what are the possible measurements of its length and width?
Application Problem

7. The area of a rectangle is the product of its length and width
The area of a rectangle is the product of its length and width. If a rectangular board has an area of 30 square feet, what are the possible measurements of its length and width?
I know that l have to think of two factors with a product of 30 – a factor pair of 30. I’ll make a table.
The possible measurements of the board are 1 x 30; 2 x 15; 3 x 10; and 6 x 5.
Application Problem 1 30 2 15 3 10 6 5

8. , , ,940 2 4 5
Opening Exercise Place each number in the circle(s) that is/are a factor of that number. 8 10

9. Let’s look at and discuss the divisibility rules for each number.
Divisibility rule for 2: If and only if its last digit is 0, 2, 4, 6, or 8.
Divisibility rule for 𝟒: If and only if its last two digits are a number divisible by 4.
Divisibility rules for 𝟓: If and only if its last digit is 0 𝑜𝑟 5.
Divisibility rule for 𝟖: If and only if its last three digits are a number divisible by 8.
Divisibility rule for 𝟏𝟎: If and only if its last digit is 0.
Discussion

10. Let’s discover two new divisibility rules
What do the numbers 12, 18, 30, 66, and 93 all have in common?
They are divisible by 3.
Calculate the sum of the digits for each given number. For example, the sum of the digits in the number 12 is 3 because 1+2=3.
What do all these sums have in common?
When the sum of a number’s digits is divisible by 3, the entire number is divisible by 3. Now let’s examine a different set of numbers: 27, 36, 54, 72, and 99. What do these numbers have in common?
They are divisible by 9.
Let’s discover two new divisibility rules

11. Let’s discover two new divisibility rules
Calculate the sum of the digits for each given number.
What do all the sums have in common?
They are divisible by 9.
When the sum of the digits is divisible by 3 and 9, the entire number is divisible by 9.
Let’s try to use this knowledge to determine if a large number is divisible by 3, 9 or both. The number 765 is divisible by both 3 and 9.
Find the sum of the digits.
Are 3 and 9 both factors of 18?
Calculating the sum of a number’s digits helps us to determine if the number is divisible by 3 or 9 or both.
Let’s discover two new divisibility rules

12. Divisibility rules for 3 and 9
Divisibility rule for 𝟑: If the sum of the digits is divisible by 3, then the number is divisible by 3.
Divisibility rule for 𝟗: If the sum of the digits is divisible by 9, then the number is divisible by 9.
If a number is divisible by 9, it is also divisible by 3.
Divisibility rules for 3 and 9

13. Practice 1 Is 378 divisible by 3 or 9? Why or why not?
What are the three digits in the number 378?
What is the sum of the three digits?
Is 18 divisible by 9?
Is the entire number 378 divisible by 9? Why or why not?
Is the number 378 divisible by 3? Why or why not?
Practice 1

14. Is 3,822 divisible by 3 or 9? Why or why not?
Practice 2

15. Circle ALL the numbers that are factors of the given number
Circle ALL the numbers that are factors of the given number. Complete any necessary work in the space provided. Explain your reasoning for your choices.
Is 2,838 divisible by ?
Is 34,515 divisible by ?
Is 10,534,341 divisible by ?
Is 4,320 divisible by ?
Is 6,240 divisible by ?
Exercises 1 - 5

16. Exercises 1 - 5 Is 2,838 divisible by 3 9 4 ?

17. Without completing the division, how can you determine if a number is divisible by 3?
If a number is divisible by 9, will it be divisible by 3? Explain your answer.
If a number is divisible by 3, will it be divisible by 9? Explain your answer.
Math Talk

18. Lesson Summary To determine if a number is divisible by 𝟑 or 𝟗:
Calculate the sum of the digits.
If the sum of the digits is divisible by 𝟑, the entire number is divisible by 𝟑.
If the sum of the digits is divisible by 𝟗, the entire number is divisible by 𝟗.
Note: If a number is divisible by 𝟗, the number is also divisible by 𝟑.
Lesson Summary

19. Is 26,341 divisible by 3? If it is, write the number as the product of 3 and another factor. If not, explain.
Is 8,397 divisible by 9? If it is, write the number as the product of 9 and another factor. If not, explain.
Explain why 186,426 is divisible by both 3 and 9.
Exit Ticket