10.

Gordon's Games - Section D (Addition and Subtraction)
(original copyright,1977, by Gordon R. Scott, under the name "Two-Up".)

The Adding Game ( 6+ ): This is the game to study or play first. It is described at length for two players, although more could play.
&nbspEach player needs something to write on and write with.
  The players first decide on their order of play, the point at which the game will stop, and the range of goal choices. (0 to 18 is the full range, but younger children, for example, may start out with 0 to 10, or older children with 10 to 18.)
  Then the cards are shuffled and placed, face down, in rows of 4 or 5.
  After this each player, in turn , must choose and write down a number from 0 to 18 as a first goal.
  This goal is the possible sum of the numbers on two cards to be turned up later. It must be different from any goal chosen by any player during the game.
  After both/all players have written their goals so all can see, the first player starts the game by turning over two cards and leaving them in their original place, visible to all.
  The first player then adds the two numbers on those cards and tells the other(s) what he/she believes it to be. If the first player believes the sum to be the same as his/her goal number, a line is drawn through that goal number to show a point has been made.
  If any other player believes a mistake has been made, they must protest right away. If there is a protest the cards are not touched until it is settled. If the first player is proven wrong the goal number must be circled and rewritten.
  If there is no protest, the two cards are turned over before the first player writes a second goal, different from any other goal.
  The first player then turns up any two cards and goes on as before.
  If the first player does not make a goal with the two cards up, the cards are turned down in their original place and the second player starts his/her turn.
  This goes on until all the goals have been made, or some time agreed upon before the start has been reached, or an authority figure stops the game.
Note: There is no penalty for protesting the sum announced by a player.
  So another player has time to protest, the cards up cannot be turned over until their sum has been announced and a line has been drawn through the number.
  Only after the cards have been turned over is it too late to protest.
  If a player wishes to change an unmade goal, when it is his/her turn they may circle that goal and write a new one. He/she then passes the turn on to the next/other player immediately. Losing a turn is the penalty for changing a goal.
  See the next page for a sample run through of this game.

11.

For example, The Adding Game:

  B and C decide to play until one reaches 5 points, and B is to be first.

  B writes down 11 as a goal. C then writes down 6. Both allow the other to see their goal.

  B then turns over two cards, a 7 and a 2. Seeing these do not add up to 11, B allows C to look at the cards and then turns them over again.

  Now C begins and turns up a 4. C remembers the 2 that B found and turns it up.

  C's 4 and 2 make the goal of 6 so C says, "six", and draws a line through the 6 written as a goal to show one point has been made.

  C then turns over the 4 and 2 cards and, after that, writes down 7 as a second goal.

  This done, C turns up a 3 and tries to turn up the 4 found before. Instead C turns up a 5.

  Seeing that 3 and 5 do not make the goal of 7, C turns the cards back over.

  B turns over a 7 and the 5 C found. Thinking that 7 and 5 make 11, B says, "eleven", and draws a line through the 11 written as a goal.

  C quickly protests that the sum of 7 and 5 is 12.

  B checks this and agrees. B circles the 11 with the line through it to show a point has not been made, and writes 11 again.

  The two cards up are turned down and C takes the turn.

  C finds an 3 and a 4 this time, says, "seven", and draws a line through the goal of 7. C next turns over the 3 and 4. That done, C writes down 12 as a third goal. Then C turns up the 7 and 5 cards B found.

  C announces the sum is 12, draws a line through that goal, turns over the 7 and 5, and writes down 10 as a fourth goal.

  Next C turns up the 7 again and tries for the 3, but misses and gets an 8.

  After these are turned over, B has a turn and the game goes on until one player has reached 5 points and is the winner.

Note: The protest was made quietly and both were good sports.

12.

Making Nines ( 6+ ):

  This is a game which provides practise with the numbers that have the most different sets of one figure parts. That is, 9 is made from 0+9, 1+8, 2+7, 3+6, 4+5. 18 is only made from 9+9.
  It is easier to teach and to play than The Adding Game .

  The rules are the same as The Matching Game except the pairs picked up will be two numbers which add up to 9, such as 0 and 9, 1 and 8, etc.

Note: The game can be 'Making Eights', or 'Making Tens', but there will be two cards left at the end of either game.


The Adding Game with two or three cards (6+ ):

  This is played just like The Adding Game, except that a player may choose to pick up a third card if the sum of the first two cards up is less than the playerÕs goal.
  The goals are still chosen from the range of 0 to 18.

Example: B's goal is 16. B turns up a 7 and an 8. B says, "fifteen" and may then turn up another card. If it is a 1 then B says,"sixteen", and has made a goal.


The Adding Game with plus ten (6+ ):

  This time the players may choose to add 10 to the first of the two cards turned up. Cards must be turned over one at a time since this option is not open after the second card is turned up.

  If the player chooses to add 10 to the first number, this cannot be reversed.

  The player choosing to add 10 must say aloud the sum of 10 and the first number, before turning up the second card. Until turned over again, the number continues to be thought of as 10 more than it is.

  Goals for this game may be chosen from 0 to 28.

Example: B's goal is 15. B first turns up a 2. B says, "twelve", and then turns up a 3. B says, "fifteen", to make the goal and one point.


The Adding Game with three cards ( 7+ ):

  In this game the players must turn up three cards for each turn. Points are only made when the sum of all three numbers turned up equal the player's goal.

  Goals for this game may be from 1 to 26.

Example: C's goal is 16. To make it, C may turn up a combination such as a 7, and 8, and a 1. C might also turn up a 7, a 9 and a 0 to make 16.

13.

The Adding Race ( 7+ ):

Note: The Counting Race and The Adding Game should be read or played first.

  This, like The Counting Race, can only have two players. It is played like The Counting Race and like The Adding Game. Unlike The Counting Race, players do not take the cards away from their original spot and they may be trying to make the same numbers as their opponent. For this reason it is best if they start at different points and/or move through the numbers in different directions. (Since the cards are staying in one place it would be too easy to just copy what an opponent had already done.)

  These players do not choose goals. They choose a set of goals to be made in a certain order. They must decide how the race will be played. (Of course, someone might dictate what the rules of the day are.)

The options are:

   a. Any range from 0 to 18 can be chosen. Players might choose to race from 5 to 15, or 15 to 5, for example. 18 and 0 will be the hardest to get.

   b. Players might decide to race from 10 (the easiest to make). For example, one going towards 5 and the other towards 15. They might do just the opposite to see who can get to 10 first. Whatever is decided it must be remembered that the range must center on 10 to be fair.

  Goals are made, one at a time, in the order decided on, over the range decided on, until one player makes their last goal and wins.
Before they start, the players must write down, in order, the numbers they will have to make to win.

This may sound complicated, but it really isn't.

Example: The players decide to race away from 10. B will go towards 5, and C will go towards 15.
  B writes down 10, 9, 8, 7, 6, 5. C writes 10, 11, 12, 13, 14, 15.

  B goes first and finds a 6 and 4. B is away!
  B draws a line through 10 and turns over the 6 and 4. B still has the turn and next turns over 5 and 3. B turns them back over.

  C turns over the 6, but can't remember where the 4 is and turns up a 2. C turns the 6 and 2 back over and B starts.

  They go on like this until the first one to cross out all his/her goals wins.

  This game could be played like any of the three variations on The Adding Game, but that would be more complicated.

14.

The Adding to Fifty Game ( 8+ ):

  This and the next two variations are quite different from the previous adding games.
  Players in this game do not choose goals and may only look at two cards each turn. It is best played with two players. The deck is set out in the usual 4 x 5 way.
  They need a common place to record numbers.
  The first player turns up two cards and writes their sum and, beside it, his / her initials.
  After the cards are turned down, the second player turns over two cards and adds their sum to the first player's sum. The new sum is then written down with the second player's initials beside it. The cards are turned face down again.
  The first player then adds the sum of two chosen cards to the second player's sum and initials the latest sum.

  This continues until one player is able to bring the sum to exactly fifty, or is forced to go over it. The winner is the player who reaches fifty exactly, or is closest to fifty when someone goes over fifty.

Example: Players B, C, and D have brought the common total up to 42.
  B takes the turn and a 0 and 6 come up. B's latest sum becomes 48. B writes down 48 and initials it.
  When the cards are face down, C takes the turn and finds a 0 and 1 making C's latest sum to be 49. C writes down 49 and initials it.
  The cards are turned down again and D turns over a 0, tries for the 1, but turns up a 6. The total is 55 and the game is over.
  C is the winner since C brought the total closest to 50 without going over.

Note: Some players may prefer to rule that the cards are taken out of play as they are turned over . This would mean they would be placed to one side and the players would have to choose from the cards remaining face down.


Adding to Fifty Race( 8+ ) :   This variation is much like The Adding to Fifty Game, except that it can be played by two to four players who keep their own separate totals of the sums of the cards they turn up and can only win if they make exactly 50.
  So that their own totals will not exceed 50, the players may at any time decide not to add on the sum of the two cards they turn up, but they may not add to their total the value of just one of the cards up. They add the sum of both or nothing at all.

Example: B is up to 35. C has 32. B turns up a 7 and 5 to make a total of 47. C turns up the 7 and a 6 to make 45. B then turns up a 2 and 4 and does not add these on. C turns up the 2 and a 3 to make 50. C wins.

15.

The Fifty or Under Game ( 7+ ) :

  This is not a game where the cards are set out like any of the others, but the play is similar to The Adding to Fifty Game. Luck plays a very small part in this game .
  Two players each take a set of cards from 0 to 9 and place them face up in front of themselves so each can see the other's cards.
  The players take turns pushing forward one card at a time from their set.
  As each card is pushed forward the number on it is added to the total formed by adding all the other cards out.
  The player making the total go to 50, or having a total under 50 when the other player has to go over, is the winner.

N.B. The game could be played to some number other than 50, providing that number is less than 90. Changing the 50 to 20 could make the game more suited to the youngest players.

Example: The cards 9, 5, 3, 4, and 5 are out to make a total of 26 when the goal is to make 30.
  C, not having a 4 and knowing B doesn't have a 3, pushes out a 1 to make 27.
  B, seeing C doesn't have a 1, pushes out a 2 to make 29.
  C is desperate and pushes out a 0, but it will do no good.
  B wins by pushing out a 1.

16.

The Subtracting Game ( 7+ ) :

  This is played just like The Adding Game, but the goals chosen represent the difference between the two numbers up. Players must choose goals from 0 to 9.

Example: B has written 3 as a goal. If B turns up a 2 and a 5 then B can subtract the 2 from the 5 to make the goal of 3.

  C has chosen the goal of 0. If C can turn any two numbers up that are the same, C can make this goal.


The Subtracting Game with Plus Ten ( 7+ ) :

  This is played just like The Subtracting Game, except the players have the option of adding 10 to either of the two numbers they turn up.
  Goals range from 0 to 19.

Example: B chooses 7 as a goal. If B turns up a 4 and a 1, this goal can be made providing B calls out, "eleven", for the 1 card. B would then subtract the 4 from the 11 to make the goal of 7.
Note: If B had called out, "fourteen", it could not be changed and the goal could not be made.


The Subtracting Race ( 7+ ) :

  This is played like The Subtracting Game and The Adding Race.
  Two players start at opposite ends of the 0 to 9 goal set.
  The first to make all the goals in their order is the winner.
  Once during the game the players may have the same goal at the same time.

Example: B is racing up. B writes down 3, 4, 5, 6 as C has agreed to limit the game to four points. B must first turn over two cards with numbers having a difference of 3. Once that is done, B must draw a line through the 3 written down, and turn over the two cards up. Then B can try to turn over two cards having a difference of 4. If B fails to do so, the turn goes to C.
  C has written 6, 5, 4, 3 as a goal set. C must first turn over two cards with numbers having a difference of 6. If C fails to do so the turn goes back to B.
  The game goes on like this until one has finished his/her goal set and is the winner.

Start Section ABC Section D2 Section E 0 TO 9 FOR CARDS Home Page
Booklets Terms Start Simple Math Start Not So Simple Math Start Not Just Math CENTER