Mary Behr Altieri
P/NW BOCES
SW BOCES
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The Solution Game
Purpose: Mental math practice, use of properties of operations to solve problems.
Materials: One deck of regular playing cards with picture cards removed.
Set-up:
• The cards are placed in a stack at the center of the table (face-down).
• Five cards are removed from the stack, one at a time, and placed in a row
face- up.
• A sixth card is removed from the stack and placed face up below the row of
five. This card is called the “solution card.”
Object of the Game: Find a path to the solution card using as many cards in the
row as possible with any arithmetic operations. (Each card may be used only
once.)
Play: The first person to see a possible path to solution says, “SOLUTION!” and
tells the rest of the group what his/her path is. If he or she is correct, he/she wins
the cards used for the path to solution AND the solution card itself. Replace all
cards that have been taken (won) by new cards from the center stack. Play
continues in this fashion until no cards are left.
The player with the most cards at then end of the game is the winner.
Variations:
• Use all the cards from ace through 6 and only half the cards from 7-10. This
makes the game a little easier.
• Require a minimum number of cards used for solution. Only solutions using
at least three (or four, or five) cards is accepted.
• Create a deck of cards as follows. Make 3 cards for each of the numbers
from 1 through 8; 2 cards for each of the numbers
• from 9 through17; and one card for each of the numbers from 18 through 25.
(This last variation is based on a card game called KRYPTO. For decks
already printed like this, buy the KRYPTO deck from a company called, “Making
People Happy” at makingpeoplehappy.com. There is also a fraction
supplement to the regular deck. )
The variations allow for differentiation. Small groups can be playing different
versions at the same time.
1
FROM HERE TO THERE
These games are rather quick ones that provide practice in counting by various units. There are
some strategies involved that become rather sophisticated but knowing the strategies is not
required to play the games. Strategy just enhances the chance of a win.
They are all two-player games.
Game One: Getting to 100.
Each player starts with ten dimes and ten pennies. Players take turns contributing one, two or
three coins to the “pot”. On placing the coins in the pot, the player calls out the cumulative total
after each coin s/he places. The person who puts in the coin to make the total value of the pot
exactly one dollar is the winner. (Each player must place at least one penny in the pot during
the course of the game—which keeps it from being just a game of dimes and counting by tens.)
Variations on this game:
• Play on a one-hundred chart that is big enough to place the coins right on the chart. Both
players are placing their coins on the same chart.
• Play on a one-hundred chart by crossing out the numbers that are called. Each player uses a
different color crayon and are crossing out the numbers are the same chart.
• With only plain or lined paper, write the numbers underneath each other in a list, each player
using a different color, playing on the same list--again writing one, two or three
numbers. Each of the games above practices counting by tens and ones, which is a
valuable skill for all elementary students. The younger ones need to have reinforced the
idea that when adding tens, the number in the ones place does not change. Although we
may think this is obvious, to many of our students it is not and is worth discussion.
• Game Two: Getting to 1,000. This game is played without coins. Students play as in the third
variation of game one, placing numbers on a list in two different colors. Players may
choose to add one, two or three numbers, using ones, tens and hundreds. The player
who is able to place exactly 1,000 on the list is the winner. Variations on this game:
• Start at a number greater than one and have the target number be greater than 1,000.
• Make the counting units 25, 50 and 100.
• Play with decimals rather than whole numbers (tenths, hundredths).
•
Play with fractions (quarters and halves).
Mary Altieri, 2007
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All of these games are variations on an original game where the units are all the
same. The first one I saw was played with twelve toothpicks. Players on alternate
turns pick up one or two toothpicks on a turn. The person to pick up the last
toothpick was the winner (or the loser). Playing this simpler game can help us
develop generalized winning strategies for all such games.
More Variations for “From Here to There”
The first two variations come from: Trimathlon, by Sally & Sally.
1. Race to 100—There are many games with this title, but I found this one more
interesting than most!
It is played the same as the basic game introduced in “From Here to There”, but in this
game each player can choose any number from 1 to 10 to “put in the pot”. This game is
just played with pencil and paper or even just verbally. (Not so easy for the young
ones—think of all the practice they can get adding one digit numbers to two digit
numbers—very often bridging a ten!)
2. Sally & Sally have also suggested changing the range of numbers on each round of
the game. On a first round, each player can choose a number between 1 and 10 to add.
On the next time around, each player can choose a number between 1 and 11; the next
round between 1 and 12.
Alternately, decreasing the range of the numbers players can choose adds another
possible variation.
Mary Altieri, 2010
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Thank!you!for!participating!in!the!KenKen!Classroom!Program!!
There!are!many!ways!to!use!KenKen!with!your!students,!including!playing!
interactively!online!or!using!larger!puzzles!for!teamwork!solving.!
!
!TABLE!OF!CONTENTS!
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3x3……………...…..……….…..……………………….……Page!2!
4x4….….………..………….…….......……………………….Page!3!
5x5……………..….……….……...…………………….…….Page!4!
6x6………………..……..……..…………………..…....…….Page!5!
7x7,!8x8…………………….………………………..………Page!6!
Bonus!Puzzle…………………………………………...….Page!7!
Rules…….…………………………………………………….Page!8!
Answer!Key………………………………………………...Page!9!
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THIS!WEEK’S!KENtertainment™,,
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Sweet
Tooth
A
piece
of
cake
and
an
ice
cream
sundae
cost
two
and
a
half
dollars
($2.50)
between
them,
but
the
cake
costs
a
dollar
more
than
the
sundae.
How
much
does
each
cost?
Play
free
games
at
www.kenken.com
Find!the!solution!at!the!bottom!of!the!answer!key.
For more KenKen of all sizes and difficulty levels, visit www.kenken.com
!
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KenKen® is a registered trademark of Nextoy LLC, ©KenKen Puzzle LLC. All rights reserved. This work is
licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a
copy of the license visit http://creativecommons.org/licenses/by-nc-nd/3.0/!
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3x3!
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1-1
1-2
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1-4
1-5
1-6
For more KenKen of all sizes and difficulty levels, visit www.kenken.com
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4x4!
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1-7
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1-10
1-11
1-12
For more KenKen of all sizes and difficulty levels, visit www.kenken.com
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3!
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5x5!
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For more KenKen of all sizes and difficulty levels, visit www.kenken.com
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1-15
1-16
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6x6!
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For more KenKen of all sizes and difficulty levels, visit www.kenken.com
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1-17
1-18
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7x7,!8x8!
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For more KenKen of all sizes and difficulty levels, visit www.kenken.com
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1-19
1-19
1-20
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Bonus!Puzzle!
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There!are!several!ways!to!enjoy!KenKen.!Try!this!variant!!
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KenKen!Twist:!Instead!of!using!the!numbers!from!1!to!the!size!of!the!grid,!use!the!
numbers!indicated!at!the!top!right!of!the!puzzle.!!
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For more KenKen of all sizes and difficulty levels, visit www.kenken.com
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RULES!
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HOW!TO!PLAY!KENKEN®!
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1. Fill!in!each!square!with!a!single!number.!In!a!3x3!grid,!use!the!numbers!1!
through!3.!In!a!4x4!grid,!use!the!numbers!1!through!4.!In!a!5x5!grid,!use!the!
numbers!1!through!5…and!so!on.!!
2. Do!not!repeat!numbers!in!any!individual!row!or!column.!For!example,!in!a!
3x3!grid,!each!column!and!each!row!should!be!filled!in!with!the!numbers!1,!
2,!and!3,!with!no!duplication.!!
3. Each!heavily!outlined!set!of!squares!is!called!a!“cage.”!The!numbers!in!each!
cage!must!combine!(in!any!order)!to!produce!the!target!number!indicated!
in!the!top!corner!by!using!the!mathematical!operation!next!to!the!target!
number.!
4. A!number!may!be!repeated!within!a!cage!as!long!as!it!is!not!in!the!same!row!
or!column.!
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HINTS!
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1. First!fill!in!single!box!cages,!called!“freebies,”!with!the!number!in!the!top!left!
corner.!
2. Note!the!candidates!(all!possible!numbers!for!each!square)!for!each!
remaining!square!and!then!determine!the!correct!numbers!by!math,!logic,!
and!process!of!elimination.!
3. Each!puzzle!has!one!unique!solution.!
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Hello,!I’m!Lulu,!the!KenKen!Guru.!
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Did!you!know!the!Japanese!word,!
Kengaeru,!means!“to!think”?!
For more KenKen of all sizes and difficulty levels, visit www.kenken.com
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ANSWER!KEY!
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1-1
1-2
1-7
1-3
1-8
1-13
1-9
1-14
1-17
1-18
Bonus Puzzle:
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This Week’s Kentertainment:
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1-4
1-5
1-6
1-10
1-11
1-12
1-15
1-16
1-19
1-20
Sweet
Tooth
Cake
=
$1.75
Sundae
=
$0.75
For more KenKen of all sizes and difficulty levels, visit www.kenken.com
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9!
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KEN KEN FOR THE CLASSROOM
Any educator can join for FREE at
www.kenkenpuzzle.com/teachers
Mary Behr Altieri
P/NW BOCES and SW BOCES
[email protected]
Thank you for coming. Enjoy the rest of your conference!