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Do the Math: Making Math Memorable
Bill Atwood,
617-686-2330
www.collinsed.com/billatwood.htm
What do we know?
1. Learning is changing long term memory
2. To change long term memory: think, retrieve, practice
3. Practice is better when: frequent, mixed, spaced, feedback-driven
How?
1. Relational activities
2. Whole brain (active, visual, verbal…)
3. Fun—no pressure with lots and lots of quick repetitions, less “teachy”
4. Games that a tiny bit strategic—not just luck, not too competitive
5. For more traditional skills—give a clear, repeatable focus
Tonight:
1. Vocabulary
a. Charades; Mile a Minute; 10,000 Pyramid
2. Card and Dice Games for fluency and strategy
a. Spit; War; Cover Ten; Martinetti
3. Restaurant, airport, and car games
a. Poison; Counting; Categories; Fingers, Product/Sum Game
4. Problem Solving
a. KNSA and Mini White Boards
5. Other: Sorts, Best Commercially produced games
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A. Anytime games for groups:
Activities
1. Follow the Leader; Charades; Simon Says; Mile a Minute, Celebrity
Why? The goal of this game is to build math vocabulary and have fun.
When/where? You can play Simon Says after dinner to see who has to clear the table. You
can play it as charades or as the name game (celebrity where you mix in celebrities and other
famous people with math terms).
How? Simon Says: Show or develop gestures for different math terms. Play Simon Says,
teacher vs. class (How many outs can you get? This way no one gets out.)
(For words see collinsed.com/billatwood.htm) Celebrity: Give each person 10 small pieces
of paper or index cards and have them neatly write the name of a famous person or a math
term on it and fold it one time. Put cards in bowl. Form two teams and then one person from
each team either acts or describes (or both) the item on the card. Get your team to say as
many as you can in 40 seconds (pick a time). Repeat until all cards are gone. Then play
again. Only three words the second round. Then no words.
B. Restaurant Games with little or no materials needed
1. Five Down Five Across.
Why? Builds strategic thinking and a concept of area (the amount of square units inside a
closed figure)
Who: All ages. Two players.
When/where? Anytime and anywhere you have a pencil and some time.
How? Make a simple board by drawing an array (like a square) of five dots across and five
dots down. (See attached)
2. Bridges
Why: Builds strategic thinking and sense of line and space.
Who: All ages especially good for younger players (4 and up)
When/where: Anytime you have a pencil and the board. (see attached)
How: Choose who is x’s and who is o’s. Take turns connecting your symbols. You can
connect any two you want. No diagonals! First to make a bridge across wins.
3. Poison (Nim game, developed in ancient China)
Why? Builds logical thinking, patterns, number sense. Who: ages 4 and up. Two players. When/where? Anytime, anywhere! Pencil or 10 objects
(coins, rocks, bits of paper…) How? See directions on hand-out.
Also see Target Addition
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4. I’m Thinking Of…
Why: builds logical thinking and number sense
Who: all ages, two players or more taking turns
When/where: Anytime, anywhere. Good in the car. No materials needed (a number line can
be helpful for young players)
How: Pick a target range for the numbers: 1-10; 1-100; 1-1000 1-2 (with fractions halves,
thirds, fourths, sixths and eighths) or play with a time (between noon and midnight) or a 3
letter word. Then, first player (clue giver) thinks of a number (make them write it down to
avoid cheating). Next player guesses (also can write it down or mark it on line). First player
says higher or lower. Repeat until answer if found. Try to guess in as few guesses as
possible. For the 3 letter word version say, “Closer to front of alphabet or closer to back.”
Also you can always play with animals (20 yes or no questions)
5. Fingers
Why: builds sense probability, number sense, counting on
Who: Everyone best with four or more
When/where: Anytime, anywhere (in a line at amusement park, restaurant…)
How: Each person puts their hand behind back or under the table in a circle. Then, each put
out some number of fingers from 0 to 5. Play proceeds clockwise around table with one
person saying, “I think there are at least 4 (or some number) of fingers under the table.” The
person to the left must either challenge the prediction or continue by saying, “I think there are
5 (or some higher number) of fingers.” If he or she challenges, they signal the challenge by
putting out their fingers and then watching as each other person around the table/circle does
so (go in order around the table). The fingers are all counted and if there were at least 4 (or
the number predicted) of fingers then the challenger is out and play begins again to the left.
Last person alive wins. Note: The only person who can challenge is the person to the left of
the predictor. (If cheating is huge problem, have each person put between 0-5 toothpicks,
coins, sugar packets, or wads of paper in their closed hand.)
6. Bizz Buzz
Why: improves number sense and concentration.
Who: Ages 7 and up
When/where: Anytime.
How: Group sits in circle facing in. In a clock-wise direction, player count up from 1.
Instead of 7 and all multiples of 7, and all numbers that contain 7, say 'Buzz'. And the order
changes directions. For example, 1, 2, 3, 4, 5, 6, Buzz,(switch directions) 8, 9, 10, 11, 12, 13,
Buzz (switch), 15, 16, Buzz (switch), 18, ... if there is a mistake, start over at 1. Once it is
going well and the group has reached 50 or so, stop them and add 'Bizz' to the game. Now,
substitute 'Bizz' for 5. For example, 1, 2, 3, 4, Bizz (switch), 6, Buzz (switch), 8, 9, Bizz
(switch), 11, 12, 13, Bizz Buzz (double switch), 16, Buzz, 18, 19, Bizz, Buzz, 22, ... If the
number is a multiple of 5 and 7, or has 5 and 7 in it, like 35 or 57 or 70 or 75, say
'Bizz/Buzz'! Try for a group record or reaching 100.
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C. Games with Playing Cards
War (Compare), Spit, Clock, Pyramid, Cover Ten
Why: builds number sense, fluency, operations, beginning steps of telling time
Who: all ages
When/where: anytime but play in short bursts over time
How: See attached directions
D. Games with Dice
1. Snake
2. The Sum what Was (also called Close the Box)
3. Marinetti
4. Liar’s dice
E. Board Games
1. Checkers (thinking and grids)
2. Chess (thinking and grids)
3. Stratego (thinking and grids)
4. Connect Four (thinking and grids) 5. Battleship (coordinate grids)
6. Blokus (spatial awareness)
7. Clue (logic) 8. Mastermind (logic)
9. Guess Who (logic)
10. Yahtzee (probability, counting, operations)
11.Monopoly (number, real estate, taxes, counting, making change…)
12.Mille-Bournes (1000 miles, learn French and math)
13.24 Game (number sense and order of operations)
14.Chutes ladders (counting) 15.CandyLand (counting)
16. Pente, Othello (thinking) 17. Rat-a-tat Cat (counting, strategic thinking)
18. Magna-Tiles (3-d Shapes and engineering)
Resources: Family Math by Stenmark, Thompson, Cosse
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Measuring
meter
yard
area
perimeter
inch
liter
kilogram
temperature
12:00
Number sense
fraction bar
½
digits
hundreds place
multiple
column
difference
sum
part part whole
Geometry
parallel
perpendicular
intersect
face
edge
congruent
ordered pair
trapezoid
symmetry
Algebra/Data
number sentence
greater than
pattern
tally mark
key
line plot
range
median
mode
Talk a Mile a Minute or Charades
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5 Down 5 Across
Object: To capture and label as many of the 16 small 1x1
squares as you can (more than your opponent).
How to play: Decide who goes first. First player connects
any two dots that are next to each other with a line. You
cannot connect two diagonal dots! Next the second player
connects another two dots. Play continues until someone
has formed a square and labels that square with his/her
initials. When you form a square you must go again, taking
an additional turn. Play continues until there are no dots left
to connect. Most squares wins!
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Poison
In poison, you receive 10 (or more) chips/coins/tokens. Place them in front of
you and a partner. Take turns removing 1, 2 or 3 pieces (this can vary) from the
set until there is only one left-- the poison piece. If you take this last piece you
must suffer and die from poisoning. You must learn the rules quickly.
Rules
A. When it is your turn, you can take 1, 2, or 3 pieces, but you may not pass.
B. You must switch off, rotating who goes first.
Your task is to answer some of the following questions:
1. At what point can you know for sure that you have won or lost?
2. With 10 pieces in front of you, is it better to go first or second?
3. If it is your turn, can you find a strategy to always win with 10 pieces?
4. Given that you can choose to go first or second, can you find a strategy to
win with 20 pieces? Any number of pieces?
5. Can you write a mathematical rule to describe how to know if you should
go first or not, with any number pieces on the board?
6. How does your rule change if you can pick up 4 apples? 5 apples?
6 apples?
7. How does your rule change if the rule becomes, “Take the last piece and
live forever?” What strategy should you use now?
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Card Games That Build Number Power War: (Compare or Top It)
Deal out the cards in one deck. Aces are high, followed by King, Queen,
Jack, Ten… Each player puts down one card. Higher card wins and get the two
cards. Repeat. If the cards are the same it’s a WAR. Player must put two more
cards face down and then turn one over. Higher card wins both the original cards
plus the face down cards. Play until one player is out of cards or until you need a
break. Option: Jokers are wild cards.
Multiplication War:
Prepare the decks: To work on the most difficult facts you can remove the
easy facts: aces, 2’s, and 10’s. If kids know the 5’s and 9’s take some of these
out as well.) If you are just working on 5’s, 9’s, 2’s and squares then load up the
deck with these cards!
Explain to students that each player will put down two cards face up. Each
player multiplies the cards and must announce the product. The higher product
wins the two cards.
Show players that if the products are within 5 (for example 5x5=25 and
6x4 = 24), then it is a “war.” Players must put down two cards face down and
then two more face up. Find the products and highest product wins all!
Play with integers, red cards are negative and black cards are positive.
Remember positives are always higher than negatives.
Play with fractions: Each player puts down 4 cards then arranges them into a
fraction multiplication problem. Lowest fraction wins! This works great with
simplifying as players can put the four cards wherever they want and use commutative
property to rearrange numerators for simplifying (factoring). Also, play with
Adding or Subtracting War:
Explain to students that you follow the same rules as above, just add the two
cards. Sums within 1 are WAR! Or play red cards are negative and black cards
positive. Higher sum wins. If the absolute value is equal, it’s a war.
Show students how to “make a ten.” 8 + 6 = 8 + 2+ 4 = 14. The spots on
the cards are a useful manipulative. Show students that it’s easy to combine.
With integers, you can think of red cards as “bad guys” and the black cards as
good guys. They have battle. Show how the cards can cancel each other out
(make a zero).
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Other Versions: Play with 3 or 4 cards. Or play with a rule: add two and subtract one.
Or find difference and lowest wins.
ADVANCED TOP IT called: War (or TOP IT in your Hand)
Deal out all cards. Then each player takes top 7 cards for their first hand (or other
number) and keeps the rest in front of him/her. Take turns going first but then
whoever wins round must go first on next round. (It’s a disadvantage to go first.)
When it is your turn put down two cards from your hand onto the table (the kitty) and
say the sum of the 2 cards. Play goes around to the left. After everyone puts down a
pair of cards and announces their sum, the highest sum takes the whole group of cars in
the kitty.
The winner must go first in the next round. If there is any war, all players put down
just 1 tie-breaking card even if the war is among two lower cards. This is a variation
which you can decide not to use, but it adds much more strategy and keeps the players
(with a terrible hand of mostly low cards) involved in the game! When any war
happens, whoever puts down the last warring card has to play the deciding war card
first! (If players run out of cards in their hand, draw a new one from their pile.)
Whoever has the highest war card wins. (Note, if there is a tie among war cards, for
example 2 sixes: then the highest suit wins (to determine lowest suit you use alphabet:
clubs is lowest followed by diamonds, hearts, spades (C.D.H.S.). If you are playing
with a double deck (with multiple six of spades for example) then the warring parties
must draw an additional card from deck to see who wins.
Remember, the highest takes all the cards in that round. Take another 7 cards and
repeat until deck is finished. Highest total wins. (or shuffle and keep playing)
Examples: (Each player has 7 cards in their hand)
I.
Player A puts down 7 + 8 (says “fifteen”)
Player B is thinking he can’t win, so player B puts down 4 + 3 (says, “seven”)
Player C realizes she can’t win but goes for the tie: and plays 6 + 1 (says “7 WAR!”)
Player D plays 5 + 2 also and (says “7 war”!).
All 4 players, must put down an additional card to decide the war, but player D has to
play the card first because he was the last to call the WAR! If everyone has the same
card, then it goes by suit: clubs lowest, then diamonds, then hearts, and spades is
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highest (it’s alphabetical). If there are no cards left in the hand of seven cards, deal out
another card from each players stack. NO PEEKING!
II. Players keep playing unless they have run out of cards and if so, each takes a
new set of 7 cards.
Player A puts down 7 +8
Player B realizes that he can’t win the round. Wants to save 9 of diamonds, puts down
4 + 3
Player C realizes she can’t win either so decides to WAR with B. Plays 6 + 1
Player D also has 7 (5+2) but doesn’t want to be included with the war and have to go
first when putting down war card, so she plays 3 + 1. C must go first with the War
Card, and D waits to see what happens, saving his 9 of spades to try and win pot!
Fraction War:
Prepare the decks: include all cards 1 through 10 to start
Each player puts down 2 cards then arranges them into a a fraction. Lowest or highest
fraction wins! You can also put down three cards for highest mixed number wins.
Show students some of the strategies available to them. Use greater than or less than
half, convert to percent, think about missing part, same numerator, same denominator,
estimate, use a calculator. LEARN THEIR DECIMALS!
Four Quadrant War:
Prepare a large coordinate grid for each player. Use cards 1-10. Reds are negative,
blacks are positive. Goal is to fill out 4 quadrants with a point. Each player turns over
two cards and decides what order to put them (i.e. red 4 and black 9) Player plots the
point and moves the cards to either quadrant II (-4, 9) or Quadrant IV (9,-4). The
opponent does the same on his/her turn. First player to have a point in each of the
four quadrants wins all cards on the board. If you cannot play on your turn because
quadrant is already full, return cards to a discard pile which can be reshuffled and
reused in later rounds.
Other versions: Plot points to be the first person to make a square. Or, plot points to
make the largest rectangular area possible. You can also play in just the first quadrant
for grade 5, in which case you could use two dice instead of red/black cards.
Flash:
Prepare the deck (select the facts you most want to practice)
Explain to students that in this game they will have to use quiet voices. And
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they may have to put themselves on a delay if they are playing with a partner
who isn’t as quick. Each player turns over a single card (at the same time!) and
whoever says the product (or sum or difference) first wins the two cards. First
answer only! You can look at 7 and 8 and say “54” and then say “No 56!” If
players say it at approximately the same time, they don’t fight, you just split the
cards.
Spit and Multiplication or Addition Spit:
Spit is the game where two players put down four cards, face-up in front of
them. Then, you “spit” by playing a new card above your four cards in a small
pile between you and your opponent. Your opponent does the same. Players try
to get rid of their cards by grabbing one of the four face up cards and playing
them on top of either of the two spit piles. Typically, in Spit, you can play a card
if it is one higher or one lower than the card. Kings can be played on Aces.
Aces can be played on top of two’s, two’s on top of three’s…etc. Each time you
play a card from your face up cards, you replace it with a new one. When a player
is out of cards, he/she gets to choose one of the two Spit piles for the next round.
If neither player is out then whoever has fewer cards in front of them (or if still
tied, whoever has a smaller sum) gets to pick the Spit pile for the next round.
Continue playing until one pile is completely empty, or until some agreed upon
time is up.
Multiplication or addition spit follows the same rules as the traditional card game,
Spit. However in multiplication spit, you must say the product when you put
down your cards. Addition spit you must say the sum. You can allow black on
black, red on red, or same number on same number. Or you can use the same
rules as spit, consecutive numbers on consecutive numbers. The key here is that
you add or multiply each card before you can lay another one on top. If it feels
too fast for some players, have them take turns each time. If a player does
not have a play the other player can go again.
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How to Play Cover Ten
Object: To get rid of all the cards in the deck by covering up the 10’s.
Game could be called: COVER TEN
1. Lay out 12 cards in a 3 by 4 array. If any face cards or tens come up, put
them on bottom of deck and replace with new cards from Ace to 9.
2. Once you have 12 cards (Ace to 9) face up you can begin the game.
3. Look out at the array. Do you see any pairs that sum to ten? Cover them
with 2 new cards from your deck. Cover them by placing 2 new cards (from
the deck in your hand) face up on top of the two cards that made ten.
4. Do you see any pairs that make ten now? Cover them again with two new
cards from the deck.
5. Keep covering until there are no cards left in the deck.
6. If a ten comes up or a face card, then that spot in the array is CLOSED and
you can no longer use it. Eventually, many of the 12 spots will be closed and
the number of 10 possibilities will run out.
7. When there are no more pairs of ten to cover, the game is over. Your
score is how many cards are left in your hand. What’s your lowest ever?
Here you could cover the two
fives or the seven and three or
the six and four.
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Clock Solitaire
Deck: A standard 52-card deck.
Goal: Complete all other four-of-a-kind sets before the fourth King is revealed.
Setup: Shuffle the deck. Deal the cards, face down, into 13 piles of four cards
each. The piles should be arranged to mimic the numbers on a clock, with the
extra pile in the middle of the circle. The "numbers" of the piles (1 through 12 on
the clock; the middle pile is 13) are important.
How to play: Turn the top card on the 13 pile face up (that's the pile in the
middle of the circle). Place it, still face up, under the pile of that card's number.
For example, a 4 would go under the 4 pile. An Ace would go under the 1 pile.
Face cards are placed as follows: Jack under 11, Queen under 12, King under 13
(pile in middle). Then turn the top card on that pile face up and place it, still face up,
under the appropriate pile. Continue in this manner until the game ends (see
"Winning" below). If the final face-down card in a pile belongs to that same pile,
continue the game by turning the next (moving clockwise) face-down card face up.
Winning You win if all 13 piles become face-up piles of four-of-a-kind. However,
you lose if the fourth King is turned face up before all the other sets are completed.
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Card Layout
Pyramid Solitaire
Pyramid is played with a single, well shuffled pack of 52 playing cards. A pyramid of cards
is dealt, consisting of 21 cards formed from six overlapping rows. Each card in the top five
rows are blocked by two cards in the row beneath. Both of these cards must be discarded
before releasing the card above, making it available for play. The six exposed cards in the
bottom row of the pyramid are available for play immediately. Six cards are dealt to a reserve
below the pyramid, each card of which is available for play.
Objective Pairs of exposed cards that total 13 are removed and placed in a single discard pile at the top
left of the play area. The object of the game is to discard all 52 cards, demolishing the
pyramid in the process. Aces count as 1, Jacks 11, Queens 12 and Kings total 13 in
themselves and as such, are discarded as a single card rather than as a pair.
Pyramid Rules Cards are turned from the stock one card at a time. If the card cannot be paired with another
available card, it is discarded to a waste pile, the top exposed card of which
is always available for pairing. At any time, any pair of available cards that total 13, or single
exposed kings may be transferred to the discard pile. Available cards are any cards that are
completely exposed and include any of the six reserve cards, the last card turned from the
stock, the top card of the waste pile and any completely uncovered card in the pyramid. Only
the six cards in the bottom row of the pyramid are available at the start of the game, and as
they are removed, they make cards higher up in the pyramid available. For a pyramid card to
be available, it must be completely exposed by removing the two cards covering it. When the
stock has been exhausted and no more pairs of 13 can be found, the game is over. (Can also
be played with sums of 10)
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Playing Martinetti
Goal: Get up to 12 and back again!
1. Roll three dice.
2. You can use the pip(s), or any of the
sums that you get from adding pips. (you
can also play differences or products)
3. Move to each square one at a time, but
you must say out loud how you got there.
4. When you can’t go further, your turn is
over.
5. You can also play as a team. How many
rolls did it take you to get to 12 and back?
1
2
3
4
5
6
7
8
9
10
11
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Snake Why: Builds counting skills and a sense of probability
How to Play: Make the SNAKE Board. Choose add (or multiply). Start
under the column S. Roll the dice.
1. Students will add the two numbers. They write the sum under the S
column.
2. Roll again. Students continue to write the sum under the S column. 3. After each roll of the dice students may decide to go out of the game.
After 5 seconds, students must decide if they want to go out of the
round. If so, they must completely sit on the ground.
4. The round ends whenever you roll a single 1 on the die.
5. Any student who is sitting out, when you roll a 1, may keep their
points for that round. Any student still in the game has to cross out all
their points for that round.
7. If you happen to roll SNAKE EYES (two 1's) any students still in
that round, lose points from ALL (previous and current) rounds!
8. After a 1 or snake eyes, all students come back into the game for the
next round. For the second round you start in the N column, third round
A column, and so forth. You never know when that 1 will be rolled,
second toss or tenth toss! It is a game of odds, staying in is risky.
9. At the end of the game students will count up all the points they have
collected from all the rounds they earned points. The student with the
highest point total wins!
*Note- sometimes you might roll a 1 for the first roll of the round. I
always re-roll so at least we have something to go by for that round.
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How to Play Product Game
Materials: Game board, 2 players each has a different colored pen, 2
paper clips (or other place holder).
Object: Get 4 in a row on game board (across, up and down or
diagonally) just like in Connect Four.
Playing: First player uses places paper clips on any two numbers
(factors) at the bottom of board. Player finds the product and uses
his/her colored marker to color in that square from the game board.
Next player can move one or the other paper clip but not both! After
he/she moves the clip, he/she finds the product and colors in that
square. Game continues until there is a winner! Note: You can put
both paperclips on the same number. (For example, covering 9 and 9
gives the product of 81.)
Beginning of a sample game:
Player 1: Moves clips to 6 and 5 creating 6 x 5 and covers the 30
square.
Player 2: Moves the clip on 6 to the 4 creating 5 x 4. Covers 20.
Player 1: Moves the clip on 5 to 7. Creates 7 x 4. Covers 28.
Player 2: Moves the 7 clip to the 8. Creates 8 x 4. Covers 32.
Player 1: Moves the 8 clip to the 4. Creates 4 x 4. Covers 16.
Play continues…
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Questions for the Product Game _____________________
1. What are some of the best first spaces to cover? Where should
you put the markers? Why?
2. Which squares are easy to cover and which ones are hard to
cover? Why?
3. What should you be thinking about when it is your turn?
4. John is red and it’s his turn. Which shape should he move (square
or triangle) and where should he move it? Explain.
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Sum Game
This is the same as the product game
except with sums. It follows the same
rules. The only difference is the board.
There are numbers which are repeated.
When you move two paper clips at the
bottom onto two addends to make a sum,
choose a sum from the board above. Then,
the next player can move ONE OR THE
OTHER of the two paper clips to make
another sum. The goal is to get 4 in a row!!
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I’m The Greatest
Object: Get the Largest Number You Can
1. Use or make a board for playing. You can make a
number with 3 or more digits or a sum or difference
problem by drawing lines on your paper.
2. Draw a card or roll a dice.
3. Everyone must decide where to put the number on
their board. You can’t change it later!!
4. Keep playing until the board is full. Whoever has
highest is “The Greatest!”
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Total Score
Thousands, Hundreds Tens Ones
A.
Highest
Possible
Thousands, Hundreds Tens Ones
B.
Highest Possible
Thousands, Hundreds Tens Ones
C.
Highest Possible
Estimate the difference between your number and the highest possible number.
Write the approximate difference below. This is your score for the round.
Estimate the
difference between
your number and the
highest possible
number. Write the
approximate
difference below.
This is your score for
the round.
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I’m the Greatest Sum
Adding and probability game for 2-4 or more players
Materials:
1. Playing boards (2 digit sums, or 3 digit sums)
2. Pencils (or slide sheet into transparency sleeve and use white
board markers)
3. 20 playing cards (2 aces, 2 ones, 2 twos… up to 2 tens) for
each team playing.
4. If needed: hundreds chart or base ten blocks or other
manipulative for students who need extra support adding
Object of game:
Get the most points. Get 1 point if you make a higher sum than
your partner(s) or if you tie your partner. Get 1 bonus point if
you make the highest sum possible.
Or play as a team: 1 point if the team gets the highest sum
possible. How many rounds did it take to get five points?
How to play:
Youngest player is the dealer for the first round. Dealer turns
over one card from the deck of 20 cards. (Aces = 1 Tens = 0).
After the card is turned, each player places that number into a
place value position on their mat. They can put the number into
any position (i.e. hundreds, tens, or ones) in either the top
addend or the bottom addend on the left side of each player’s
game board. For example: a card showing 6 is turned over.
One player might decide to put that 6 in the tens place of the
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top addend on her mat while another player might place the 6
into the ones place on his mat. Players cannot change the
position of the number once they have placed it.
Dealer turns over a second card. Everyone places that digit in
a place value position. Continue until all place value positions
are filled.
Then, each player finds the sum of their number and checks it
with the team to make sure it is correct. Get 1 point if you have
the highest sum or if you tie your partner.
Next, arrange the dealer arranges the cards to show the
addends that would make the highest sum. Players record that
sum on the right side showing the digits to find the greatest
possible sum. Compare this sum to your own. Get 1 additional
point if you match the highest possible sum. Mark down your
score with tally marks.
Play another round. Play to 10 points or until time is up.
Players can pass in sheets to teacher or leave for next group.
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I’m The Greatest Sum 2 digits
Points: 1 point beat your group. Bonus 1 point if highest possible.
Total points:
Tally marks:
Your number: Highest possible:
Round 2
+ +
+ +
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I’m The Greatest Sum 3 digits
Points: 1 point beat your group. Bonus 1 point if highest possible.
Total points:
Tally marks:
+ +
+ +
Your number: Highest possible:
Round 2
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I’m The Greatest Difference 2 digits
Points: 1 point beat your group. Bonus 1 point if highest possible.
Total points:
– –
– –
Tally marks:
Your
number: Highest
possible:
Round 2
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I’m The Greatest Difference 3 digits
Points: 1 point beat your group. Bonus 1 point if highest possible.
Total points:
Tally marks:
– –
– –
Your
number: Highest
possible:
Round 2
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COUNTING TO BUILD FLUENCY
Bill Atwood
In his workshops to improve math fluency, Math Expert, Mahesh
Sharma, advocates for time practicing counting everyday. Students
can hear and see patterns as they count and build a deeper
understanding of math. Counting does not have to be limited to
multiples. In fact, students should get practice counting in a variety
of ways.
Many students will need supports in the beginning. These can be
chips, number lines, base ten blocks, hundreds charts, clocks, coins,
fraction circles or pattern blocks…
Consider have student practice counting in pairs or in groups of three.
Set a target number and then make students go backwards down to
zero (or to some negative number). After some practice, ask them to
count in front of another group, the teacher, or the whole class. How
smooth can they get? How far can they go? When they finish an area
they can cross it off their list and move onto a new area.
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Things to count by
1. Even numbers, odd numbers
2. Multiples of 2, 3, 4, 5…
3. 10’s but start at 3: 3, 13, 23, 33… (up to 153 down to -127)
4. 20’s or 25’s: up to 200 down to -200
5. 15’s: up to 150 down to -150
6.
‘s up to 5 and down to negative 5
7.
‘s up to 3 and down to negative 3 (or
‘s)
8. Doubling: (powers of 2) 1, 2, 4, 8, 16, 32… (get to 1,024)
9. Square numbers: 1, 4, 9, 16, 25… (up to 202= 400)
10. Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
11. Decimals like 0.2 (two tenths…) or 1.5 or 0.125
12. Common families of percent families : 12.5%; 25%; 37.5%;
50%; 62.5%…) or count by 12 ½ or 33
13. factor pairs of numbers like: 24: 1, 24, 2, 12, 3, 8, 4, 6, 1, 24, 2,
12, 3, 8… First person says smallest factor, next person gives the
other paired number… or each person alternates giving each pair in
order.
14. Time: start at 12:00 and add 15 min (or some other quantity) or
add 20 minutes…
15. Place value names (ones, tens, hundreds… and back down to
decimals)
16. Units by size: mm, cm, dm, m, Dm, hm, km
17. Units by size: ounce, cup, pint, quart, ½ gallon, gallon
18. Polygons by sides: triangle, quad, penta, hexa, septa, octa,
nona, decagon
19. Months: Jan, Feb, Mar…
20. Decades: 1962, 1972, 1982, 1992, 2002, 2012…
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What do I know? What is the key information? What else do I know from my memory of math that relates to this?
What do I (need) to find out? What is the problem asking me to do?
What steps do I need to do to answer the problem or question? Did I show all the steps it takes to find the answer?
Did I the answer? Did I include units (ft., in., cm
2, etc.) in the answer?
Did I double-check my answer to make sure it makes sense?
K N
S
A box
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name________________________
Using KNSA
In the following problems, underline what you KNOW, and use parenthesis to identify what you (NEED) to find or do. Part A has been done for you. Bonus: Show what you know and need to find with a fractional ratio. A. In grade 7, there are 2 teachers for every 20 students. If this is a constant rate, how many students would there be for 1 teacher? B. The average heart rate of a mouse is 500 beats per minute. How many beats would there be in 10 minutes? C. At his top speed, Usain Bolt, the Jamaican sprinter, can run 23 miles per hour (60 minutes). At this rate, how far could he run in 10 minutes? D. Many people tip waiters and waitresses at a rate of 15 cents per dollar. How much would the tip be for a meal that costs $20? E. If it takes you 1 ½ minutes to read a page of the book, The Hate U Give, how long would it take to read 10 pages?
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