Transcript Divisibility by 3

Sample Factor Game
The winner of this game is the one with the most number of points.
Players take it in turns to choose a number.
The player whose turn it is receives the number of points equal to the number they chose;
The opponent is also awarded points equal to the sum of all of the factors of the chosen number
The example below shows how this works:
Amy is Player One and chooses the number 20
(20 has factors: 1, 2, 4, 5, 10)
Her points from her turn are therefore 20
Jayson is Player Two he gets the sum of all of the
factors of Amy’s chosen number …1 + 2 + 4 + 5 + 10 = 22
His points from Amy’s turn are therefore 22
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Continued on next slide…
It is now Jayson’s turn, note that all the previously used factor squares are now out of play.
Jayson chooses 18
(18 has factors 1, 2, 3, 6, 9)
Amy gets 3 + 6 + 9 = 18
She does not get factors 1 and 2 as points as they have
already been used.
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Amy now has 38 points:
Jayson now has 40 points:
20 points from round one and 18 from round two.
22 points from round one and 18 from round two.
Additional Rules:
If a player picks a number that has no remaining factors on the board that player misses a turn.
The first number chosen can not be a prime number.
It is the responsibility of each player to identify the factors (points) they are to receive. Factors that are not identified
remain ‘in play’.
The game finishes when the remaining numbers have no factors left on the board.
Using Your Calculator – Factor Game
It is possible to expedite the ‘factor – finding’ process using the
calculator.
The screen below shows that 11 is a factor of 55 since no remainder is
present for 55  11.
Furthermore, this calculation helps reinforce the ‘factor pair’ concept
and will lead to subsequent identification that numbers such as 25, 36,
49… are different.
Game Board 1
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Game Board 2
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Optional Calculator Use
Additional functionality on the TI-30XB MultiView™ X can
expedite the factor finding process.
Suppose a student wishes to search for factors of 36.
Begin by entering an equation:
Press the  key.
Type in the expression: 36  x
Press  once for x.
Press  to store the equation: y = 36  x
Select ‘Ask – x’ followed by OK.
Type in values for x to see the result.
This shows the factor pairs for 36: 2  18 and 3  12 etc…
Teacher Notes – Factor Trees
Some number divisibility techniques
Divisibility by 2: The number is even.
Divisibility by 3: Add the digits in the number together.
If the sum of these digits is divisible by 3 then the original number is also divisible by 3.
Example:
Consider the number 1278. This number is divisible by 3 since 1 + 2 + 7 + 8 = 18.
The digits in 18 are also divisible by 3.
The number 1279 is NOT divisible by 3. 1 + 2 + 7 + 9 = 19 and 19 is not divisible by 3.
Divisibility by 5: The unit’s digit of the number must be a 0 or a 5.
Divisibility by 7: Double the last digit of the number and subtract if from the rest of the digits,
repeat this process for larger numbers. If the result is 0 or is divisible by 7,
then the original number is divisible by 7.
Example:
Consider the number 882; 2  2 = 4 and 88 – 4 = 84.
The number 84 is divisible by 7 since 7  12 = 84.
Consider the number 5922, 2  2 = 4 and 592 – 4 = 588.
This number is still relatively large so the process is repeated. 8  2 = 16, and
58 – 16 = 42; 42 is divisible by 7 therefore 5922 is also divisible by 7.
Note: This divisibility rule is more complicated than 2, 3 and 5. Students will most likely use their
calculator to check divisibility in this case.