cm2 prime time 1.1 playing the factor game

7/27/2019 CM2 Prime Time 1.1 Playing the Factor Game

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Emue$tESatitlttFactors andProductsCfu*i" is 12 years old. Her cousin,Emilio, is 2 years old. Her brother,Cam, is 3. Her neighbor, Esther,is 8.The following numbersentences say that Jamie is

6 times as old as Emilio.12:6xZ

;l times as old as Cam.12:4X3

and times as old as Esther.172:11r. s

Notice that each of the whole numbers 2,3,4, and 6 can be multiplied byanother whole number to get 12.For this reason,2,3,4,and 6 are calledwhole-number factors, or whole-number divisors, of t2.Although 8 ls a whole number, it is not a whole-number factor of 12because you cannot multiply 8 by another whole number to get12.To save time, we will simply use the words factor and divisor to referto whole-number factors and whole-number divisors of a number.

5 Prime Time


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,Playing the Pactor GamePlaying the Factor Game is a fun way to practice flnding factors of wholenumbers. If you pay close attention, you may learn some interestingthings about numbers that you didn't know before!To play the game,t'ou need a Factor Game Board and colored pens, pencils, or markers.

The Factor Game

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Factor Game RulesPlayer A chooses a number on the game board and circles it.Using a different color, Player B circles all the proper factors of PlayerA's number. The proper factors of a number are all the factors of thatnumber, except the number itself. For example, the proper factors of 12are 1-,2,3,4, and 6. Although 12 is a factor of itself, it is not a proper factor.Player B circles a new number, and Player A circles all the factors ofthe number that are not already circled.The players take turns choosing numbers and circling factors.If a player circles a number that has no factors left that have not beencircled, then that player does not get the points for the number circledand loses the next turn.The game ends when there are no numbers left with uncircled factors.Each player adds the numbers that are circled with his or her color.The player with the greater total is the winner.

:::i; y* ,ss:il i-rsontine q"* \For: Factor Game ActivityVisit PHSchool.comWeb Code: amd-1 101

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lnvestigation 1 Factors and Products


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The First Five Moves of a Sample GameThis table shows the flrst flve moves of a game between Cathy and Keiko.The first column describes the moves the players made. The other columnsshow the game board and the score after each move.

ActionCathy circles 24.Keiko circles 1,2,3,4, 6, 8, and 12 (theproper factors of 24).

Keiko circles 28. Cathycircles 7 and 14 (thefactors of 28 that arenot already circled).

Cathy circles 27.Keiko circles 9 (theonly factor of 27 thatis not already circled).

Keiko circles 30.Cathy circles 5,10 and15 (the factors of 30that are not alreadycircled).

Cathy circles 25.All the factors of 25are circled. Cathy doesnot receive any pointsfor this turn and losesher next turn.

Score

Cathy Keiko3620I30o

24212730o

Game Board% % % 5& 7 e 9 1011 & 13 14 1516 17 18 19 2021 22 23 q$ 2526 27 28 29 30

& % % 5% @&

I 101'.1 13 6i 1516 17 18 19 2021 22 23 e4 2526 27 & 29 30% { b 5fffi % 1011 & 13 fiB 1516 17 18 19 202'.1 22 23 es 2526 EB % 29 30

% pm % jp&tr* @@@1 m 1316 17 18 19 2021 22 23 @ 2526 es & 29 &% {pm % (5)& {m @11 & 13 E 6B16 17 18 19 2021 22 23 e, @:26 a* % 29

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Problem W Einding Proper FactorsA. Play the Factor Game several times with a partner. Thke turns makingthe flrst move. Look for moves that will give you more points thanyour opponent. As you play, write down any strategies or patterns youflnd.B. How can you test to determine whether a number is a factor ofanother number?C. If you know a factor of a number, can you find another factor? Explainyour thinking.D. Give an example of a number that has many factors and an example of

a number that has few factors.E. Make a list of the factors of 18. Make a list of the divisors of 18. Arethe factors of a number also divisors of the number? Explain yourthinking.F. How do you know when you have found all the factors of a number?ACm ] Homework starts on page 14.

11} Playing to llllin the E'actor GameIliO you notice that some numbers are better than others to choose for thefirst move in the Factor Game? For example, if you choose 22,yo:u get22 points and your opponent gets only 7 + 2 * 11 : 14 points. However, ifyouchooselS,yougetlSpoints,andyouropponentgetsl + 2 + 3 + 6 +9 :21. points!Now you will make a table to analyze the Factor Game and look forpatterns. Your table might start like this:

First Move Proper Factors My Score Opponent's Score1 None Lose a Turn 02 1 2 13 1 3 14 1,2 4 3

9nvestigation 1 Factors and Products

cm2 prime time 1.1 playing the factor game

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