(Not Just) Math Games Activities for Supplementing Curriculum Without Breaking the Budget Created and Compiled by Christopher Nelson! !
Version 1.0
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Table of Contents Preface................................................................... 2
Disc Games A Sea of Chips ........................................................ 5 Keys to the Puzzle ................................................. 7 Don’t Rock the Boat ............................................... 9 Mathematician Ammunition.................................. 11
Dice Games The Top of the Mountain....................................... 15 Toe the Line ......................................................... 17 Honey Comb Home ............................................. 19 A Master of Chance ............................................. 21
Card Games A Simple Trick....................................................... 25 I’ve Got Your Number .......................................... 27 Dart-less Darts ...................................................... 29 That Number Suits You........................................ 31
Logic Games A Lofty Figure....................................................... 35 Moving Mountains................................................. 37 Figuring Out the Combination .............................. 39 A Sorted Affair...................................................... 41
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Preface This compilation is designed with the sole intention of augmenting the reader’s bank of fun and engaging math activities suitable for all primary school ages, while relying entirely on implements and materials either already present in a common Caribbean classroom or else easily attainable. Whether the reader is a math instructor, a mathematician, or simply a learner, the author hopes that these activities are suitable to meet both the facilitator’s needs for new, fresh ideas and the classroom-tested plans accompanying them, as well as the students’ needs for external motivation in learning important foundational mathematical principles. The reader will notice that each activity is categorized by three groupings: Curriculum Topic, Suitable Ages, and Anticipated Time. While the curriculum topic is generally hard-line, barring an overhaul of the entire activity, the other two groupings are much more subject to easy alteration at the discretion of the classroom instructor. In fact, despite the Suitable Ages designation, nearly all of the activities can be tweaked to accommodate any primary or secondary grade level – check the “Variations” section of the activity for ideas. In addition, please observe the section designated “Notes.” This is left blank in order for instructors to write in their own observations of successful and unsuccessful elements, variations, or additional necessary preparations the author unwittingly overlooked.
What This Book Can Do This manual is full of both completely original and recirculated classroom math activities that have been selected based on three specific criteria: the ability to engage students’ interest and thus enhance learning, the relevancy of the curricular principles, and the quality of encouraging universal participation by limiting noncontributory downtime. Thus, the goal of each activity is to provide a classroom facilitator with the plan to carry out an attractive game that students will be eager to participate in, all while reviewing basic math principles.
What This Book Cannot Do This manual is not intended to substitute classroom instruction on any of the topics covered. The material, while directed in nature, is not designed to facilitate foundational learning of mathematical concepts, but rather create an enjoyable classroom atmosphere suitable to introducing a new concept, reinforcing instruction of a recently-learned concept, or reviewing an old concept.
Good Luck and Keep Learning! !"
DISC GAMES
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Chips at Sea CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Addition, Subtraction
6 – 10 years
15 min.
PREPARATION
Place a towel or bed sheet, preferably blue in color, down on the floor where all the students can see it. (While it takes part in the activity, this is essentially to expedite cleaning up the chips at the end of the activity.) Place a small pile of chips, say 10-20, at the center of the sheet. Keep a container of many more chips near at hand.
ACTIVITY
Explain to students that the sheet represents the ocean, and the pile of chips in the center represents a collection of ships. Tell students how many chips are in the pile, and have them remember the number. Then add 2 or 3 chips to the pile, allowing all of the students to see how many have been added and clearly speaking the number added. Inquire to the students how many “ships” are now at sea – has the number grown larger, and by how many? Continue in this manner for a time. Then remove 2 or 3 chips from the pile, allowing the students to see how many have been removed and clearly speaking the number removed. Inquire again to the students as to how many “ships” are at sea. Gently correct students if they declare an incorrect total. Allow students to use whatever mental tallying method they are comfortable with, like finding the sum or difference using their fingers. Continue in this manner until students lose interest or the arithmetic becomes too complex.
OBJECTIVE
Students engage in corporate learning and through collective imagination and story telling. Students develop mental arithmetic skills used every day.
TIPS
If so inclined, the instructor may compose a story ahead of time that shapes the lesson and gives students increased incentive to focus on the changes in the pile of chips. For example, the first pile may be traders at sea, coming to collect sugar from the West Indies; the second pile might be pirates trying to stave them off. It is recommended to not allow the students to engage the counting chips themselves, since playing with them on the blanket will most likely prove to be a distraction from the activity.
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VARIATIONS
DIAGRAM
NOTES
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For older classes, students themselves may want to participate by adding or taking away their own handfuls of chips, all the while maintaining a mental tally of the chips in the pile. Also for older classes, introducing the element of adding more piles of equal chips or dividing the piles into smaller piles of equal chips will help to introduce the topics of multiplication and division.
Keys to the Puzzle CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Numeracy
8 – 14 years
20 min.
PREPARATION
On ! chips, attach a different 3-digit number to each chip, such that each subsequent digit is not consecutive (e.g. 728). On the chalkboard, draw ! + 1 connected puzzle pieces in a large rectangle. Fill each puzzle piece with a 7digit number such that each number contains exactly once a 3-digit number from a chip. In order to guarantee no overlap, when creating 7-digit numbers, simply hide a 3-digit number inside 4 digits consecutive to the adjacent digits (e.g. 6567289) Leave the centermost puzzle piece blank. The chip with the number 728 then pairs with a puzzle piece with the number 6567289. Make sure the centermost puzzle piece remains with no pair, and fill this piece with either a class reward or a clue about the next activity.
ACTIVITY
At the beginning of the activity, give each student one “key,” one of the chips with a short number on it. Explain to students that their goal is to clear all of the puzzle pieces from around the centermost piece, but they must start from the outside and work their way in. In order to clear pieces, students must pair outermost pieces with their “keys,” taking turns identifying which puzzle piece pairs with their own “keys,” and submitting their keys to the instructor. Upon a student successfully pairing his “key” with an outermost puzzle piece and correctly reading audibly both numbers, the instructor will erase the image of the piece from the board and congratulate the student on his contribution. Continue until all pieces around the centermost piece have been cleared.
OBJECTIVE
Students develop numeracy through identifying matching digits and reading large numbers. Students contribute individually towards reaching a collective goal.
TIPS
To save time, the drawing on the board need not be puzzle pieces, but can be squares or rectangles as well. In order to engage students who have a key to a dormant piece, or have already used their key, try having them politely help students having difficulty pairing their keys. For smaller class sizes, two keys may be used per student.
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VARIATIONS
DIAGRAM
NOTES
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For younger students, the length of numbers on the chips can be reduced to two digits, and the numbers on the puzzle pieces can be reduced to three, four or five digits. For older students, “keys� may have arithmetic expressions and pair with their equivalent answers on the board. This activity can even be extended into literacy, using words and parts of words instead of long and short numbers.
Don’t Rock the Boat CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Open
10 – 18 years
30-45 min.
PREPARATION
Prepare around 10 challenge problems, with difficulty such that, while entirely possible to solve, they may at first appear intimidating to students. Select one of these challenge problems, and write it on the board. Place a bowl full of chips on the right half of a table at the front of the classroom, and a single stack of 3 chips in the center of the left half.
ACTIVITY
Designate a queue so that students, one at a time, approach the table, collect exactly one chip from the bowl, and place it on the chip stacks, with the following restrictions: (1) Students may only place a single chip on top of an existing stack, but it may be any stack of their choosing. (2) Students may begin a new stack, but only if they correctly answer the challenge problem currently on the chalkboard. If a student incorrectly answers the challenge problem, leave the problem on the board and have that student attempt to place his/her chip on an existing pile. Alternatively, if a student correctly answers the problem, allow that student to begin a new stack anywhere in the stacking area. Replace the problem on the board with a new one, and continue. If, at any time, a student places a chip that causes a stack to fall, designate that student “out,” passing his/her turn in future rounds. Have students immediately replace all of the fallen chips back into the bowl. Continue in this manner until either the participants have dwindled to just one, or time for the activity has run out.
OBJECTIVE
Students make critical decisions, subconsciously weighing the statistical odds of potential outcomes. Students contribute individually but are subject to a collective pressure to not fail. Students use mental math skills in a highpressure, high-visibility situation.
TIPS
The ordering of students is critical here. In order to avoid students decrying a bias, perhaps make the order follow a previously established meritocracy, e.g. grades on the last exam.
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VARIATIONS
DIAGRAM
NOTES
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To add an element of additional competitiveness have students that correctly answer the question on the board also replace it with their own new challenge problem, in addition to beginning a new stack. Alternatively, in order to reduce the inherent competitiveness of the activity, simply ignore the element of having students sit out after felling a stack – instead, when time for the activity has run out, award the class based on the number of standing stacks.
Mathematician Ammunition CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Open
12 – 18 years
30 min.
PREPARATION
Prepare approximately 15 review problems, and for each one think of one or two misleading incorrect answers. Gather plenty of counting chips, enough so that every student in the class could potentially have as many chips as review questions. Place a pot at the front of the room and a line on the ground about six feet away from the pot. Choose a small, plentiful material reward for students to earn at the end of the activity.
ACTIVITY
Explain to students that the class will be presented with one review question at a time, and each question will have a correct answer and an incorrect answer on the board at the same time. Students will be expected to simultaneously vote for the answer they believe is correct. Ask students to all together quietly raise their hands when indicating their choice. Students that choose the correct answer earn one reward chip; pass out one chip to each student who had their hand raised for the correct response. Continue in this manner until the review questions are exhausted or until students lose interest. At this point, have one student at a time stand behind the line on the ground and attempt to toss one chip at a time into the pot at the front of the room. Offer students a reward for every chip they successfully toss into the pot.
OBJECTIVE
Students are involved in reviewing previous material and have an interest in participating. Students contribute collectively but are rewarded based on individual efforts.
TIPS
When students become accustomed to the two-choice format, throw in a trick question – put two incorrect answers on the board. Reward any students that did not raise their hands for either answer with a chip. For classes with too many chips being earned, progressive rewards is an option; for example, every chip tossed in the pot earns a sticker up to 4 chips, and every 5 chips tossed in the pot earns a piece of candy in lieu of 5 stickers.
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VARIATIONS
DIAGRAM
NOTES
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If the instructor is concerned about the tossing of chips taking too long, students may be asked to toss 2 chips at a time, or simply rewarded based on their sum of chips collected and the tossing portion skipped entirely. Alternatively, to introduce a competitive factor for smaller class sizes, have students all stand equal distance from the pot in a circle, and toss chips into the jar in volleys. After a time, reward the few students that still have chips remaining with a special reward, and reward the class as a whole based on the number of chips in the jar. For older classes, adding a third choice (a second incorrect answer) may provide more of a challenge. For an alternative response method, rather than students quietly raising their hand, have students stand up from their desks and move to one side of the classroom, whichever side is closer to their answer on the chalkboard.
DICE GAMES
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The Top of the Mountain CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Elementary Statistics
1st and 2nd
20 min.
PREPARATION
Gather two dice and a shoebox lid to roll them in. On the chalkboard, draw a results histogram, with a column for each roll outcome number, as in the example. With a different color of chalk, draw 7-10 horizontal dashed lines at regular intervals on the histogram. Above the last horizontal line, approximately in the middle of the histogram, draw a smiley face or attach a picture of a reward for the class upon successful completion of the activity.
ACTIVITY
Have students take turns rolling one die in the shoebox. Explain to students that the class will be recording the results of each roll. Initially, the instructor should mark results on the chalkboard by filling in one box above the respective number. When one entry in the histogram has reached the top, inform students that the class will be starting over the activity using two dice, and students themselves will be expected to record the results on the board. At this point, add the reward symbol at the topmiddle of the histogram. Have students take turns rolling two dice in the shoebox, and approaching the chalkboard and adding one box above the respective number. When one entry in the histogram has reached the top line, give to the class the prearranged reward. Discuss with the class the difference in the shapes of the single-die graph and the twodice graph.
OBJECTIVE
Students learn how to make and read bar graphs, and recognize discrepancies in distributions. Students contribute collectively toward a preset goal.
TIPS
The first part of the activity is primarily to introduce to students the procedure of recording roll outcomes on a graph; if students grasp the concept quickly, the instructor may choose to move on to the more advanced second part of the activity: adding a second die. When discussing the shapes of the graphs with the class, call them different names: the single-die graph might be like the shape of the dock at Basseterre, or Bay Road, whereas the two-dice graph might look like Nevis Peak.
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VARIATIONS
DIAGRAM
NOTES
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For large classes, have students roll the dice just once each, and on the histogram write the students’ names in the block that corresponds to their roll. At the end, basic percentages over the whole class can be calculated and recorded above the respective outcome columns. For older students, begin the exercise with two dice and end the exercise with three dice. For much older students, add an averaging step at the end of the exercise, where students are asked to find the average roll using a calculator. To find the average roll, add up all of the roll outcomes, then divide by the product of the number of dice and rolls, i.e. 189 á (3 ! 18) = 3.5. That is, after rolling 3 dice 18 times, the sum total of all the rolls comes to 189. Find out the average for twodice results and three-dice results, and discuss with students why the average is always near 3.5.
Toe the Line CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Number Parity
2nd and 3rd
15 min.
PREPARATION
On the chalkboard, draw a number line, enumerating all the integers from !20 to +20, such that “0” is in the center. In different colored chalk, label arbitrary integers apart from 0 with arrows and one of the colors of the rainbow, such that all six colors are represented once on the number line. Collect a number of items equal to the number of students that are suitable to be used as placeholders on the chalkboard, or else draw stars in differently colored chalks; place these near the 0 on the number line. Set a box lid with a single die in it at the front of the classroom.
ACTIVITY
Explain to the students that each one has a placeholder, or “marker” on the board that represents them, and that their goal is to move that marker to the integer on the number line that shares a spot with their favorite color. Have the students then approach the box with the die, one at a time, and roll. Students are allowed to move either forward, i.e. positive, or backward, i.e. negative, but must move the number of integers equal to their roll on the die. Students will most likely not reach their intended target on the first roll, so after moving their marker one time, students return to the back of the queue and await their turn. When students reach the integers corresponding to their favorite color, they are finished with the activity and may return to their seats.
OBJECTIVE
Students perform critical decision-making in a very lowpressure environment. Students review basic numeracy, specifically number line dynamics and negative numbers.
TIPS
A simple, small reward to be distributed when students reach their intended destinations would be suitable to give a material incentive to the activity. Remind students that it is perfectly fine and expected that they may move past their intended target, as they can reverse the direction of their movements on their following turn.
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VARIATIONS
DIAGRAM
NOTES
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For classrooms with too many students to make this activity viable, break up students into six groups, depending on what their declared favorite color is. Then have a different representative from each group take turns rolling the die. Alternatively, if students waiting in the queue are too distracting, the activity could be made into an all-day or allweek event, such that when students display a merit-worthy behavior, or contribute positively in class, they earn the right to roll the die towards earning different rewards, which are in turn scattered around the number line. To add a competitive element, keep track of the order students reach their intended destination.
Honey Comb Home CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Open
3rd and 4th
20 min.
PREPARATION
On the chalkboard, draw a “honeycomb” of 19 planar hexagons, as shown in the diagram. To one side, add the guide showing which dice rolls pair to edges of a given hex. Attach two different pictures or draw two different-colored shapes inside the centermost hex; these will be used as team markers.
ACTIVITY
Split students into 2 groups. Designate one student from each group to be responsible for rolling the dice for her team. Explain to students that their goal is to be the first team to reach the exterior border and move their “honey bee,” their marker, beyond the outermost ring of hexes, leaving “the comb.” Quiz students, one group at a time, on subject material. When a group correctly answers a question, the designated roller will roll 2 dice and move her team’s marker to an adjacent hex, the direction determined by the dice roll as designated in the diagram’s direction guide. For example, in the event the designated roller for Team 1 rolled a “7”, she would move Team 1’s marker to the hex immediately adjacent on the right. If there is no hex to the right to move to, her team wins.
OBJECTIVE
Students use simple addition skills. Students are exposed to simple planar shapes and simple distributions of statistical outcomes. Students develop appropriate team-based competitive behaviors.
TIPS
Designated dice rollers may be students who have earned a reward for good behavior, or perhaps have been deemed exempt from answering quiz questions. Make sure all students understand how dice rolls determine the direction of moves before beginning the activity. Be prepared to explain why the selection of roll outcomes is evenly distributed around the guide hex. In the event the activity is taking too long, the instructor may adjust the rules ad hoc such that the students may choose the direction they want to move their marker.
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VARIATIONS
DIAGRAM
NOTES
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Students may be split into 3 or more groups, depending on the size of the classroom and number of students. Questions for quizzes may be of non-related material, as in history facts or science questions. For classes that wish to only use one die for the activity, simply adjusting the guide hex such that each direction is marked with each number from 1 to 6 is sufficient.
A Master of Chance CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Arithmetic
5th and 6th
60 min.
PREPARATION
Gather three dice and a shoebox lid to roll them in. On the chalkboard, write all of the numbers from 1 through 36. Gather several different colors of chalk.
ACTIVITY
Separate the class into teams of no less than 2 and no more than 4 students. Designate one of the teams “Team 1,” and subsequent teams in the same manner. Explain to students that they will attempt to claim as many of the numbers on the board for their team as possible. Students claim a number by first rolling three dice, and with any valid arithmetic operations that they can muster, arranging an arithmetic expression using exactly all three numbers of the roll outcome to equal an available number on the board. For example, if Team 1 rolled a 2, 2, and 4, this could be arranged 2 ! 2 ÷ 4, which is equivalent to 1. If the number 1 on the board is currently unclaimed, then Team 1 could claim the number 1. Else, if the number 1 was already claimed, then Team 1 could arrange the numbers 4 " (2 ÷ 2), which equals 3, and subsequently claim the number 3 instead. Alternatively Team 1 could arrange the numbers 42 ! 2, which equals 32, and claim the number 32. Any standard and valid arithmetic expressions are acceptable, and creativity is encouraged, especially when reaching for higher totals. Students should audibly declare their constructed expression to the class, and claim the number by circling it with their team’s color of chalk. Conversely, if a team is, in a set amount of time, unable to legitimately claim a number, or incorrectly claims a number that does not match their proffered expression, then the chance to use that roll passes on to the following team (i.e., Team 2 after Team 1, etc.). Teams take turns rolling the dice and claiming numbers, and play continues until either all numbers are claimed or a complete round takes place with no numbers being claimed. The team with the most claimed numbers at the end of play wins.
OBJECTIVE
Students combine creativity and arithmetic skills to create standard expressions as a means to an end goal. Students contribute in small collectives where group dynamics play a small yet significant role. !"#
TIPS
DIAGRAM
NOTES
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The instructor should enforce classroom participation rules to prevent shouting answers out of turn or other disruptive behaviors. The numbers 26 – 33 will most likely be the last numbers to be claimed, so the instructor may use hints or offer help when teams roll high numbers that are suitable for claiming one of those difficult numbers. For classrooms with large numbers of students, and thus many teams, having two sets of dice pass between teams will speed up play as teams deliberate. Just be sure each team ends up with equal chances to claim numbers."
CARD GAMES
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A Simple Trick CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Spelling, Counting
1st and 2nd
10 min.
PREPARATION
Arrange a deck of cards by value, such that the top card is an Ace, face down on the stack, and from there the values follow Ace, Ace, Ace, Two, Two, Two, Two, Three, Three, etc., through Tens, Jacks, Queens, and finally Kings.
ACTIVITY
Ask students to spell the names of the cards in order; that is, say aloud with the students the letters A-C-E. For each letter you speak, place a card face down in front of everyone. On the last letter, in this case “E,” place the card face up, instead. For each value, i.e. Ace, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, Jack, Queen, and King, the value of the upturned card will be the same as was just spelled. So, for example, as students spell T-E-N, two cards will have been set face down, and the third will be set face up, displaying a 10. Then, as students spell J-A-C-K, three cards will have been set face down, and the fourth will be set face up, displaying a Jack. Continue in this manner until all 52 cards have been spent. Students may want to see it again, and you can go through the activity as many times, quicker each time, until they are satisfied. When finished, discuss with students why a prepared deck works out this way.
OBJECTIVE
Students engage in a passive learning environment. Students must unravel two related principles that, at first, appear unrelated. Students refresh basic spelling skills and basic addition skills.
TIPS
Present the activity as a sort of card trick; allow the students to see that the deck has been pre-arranged, if they inquire. In order to solve the mystery of why it works every time, the instructor may choose to write the letters of each value on the board, and count with the students the number of total letters in the list.
VARIATIONS
For older students, inquire if it is possible to perform the same trick, but in reverse order – that is, reading a deck from King, Queen, Jack, …. to Three, Two, Ace. Discover together why this is not possible.
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DIAGRAM
NOTES
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I’ve Got Your Number CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Algebra
2nd and 3rd
10 min.
PREPARATION
Select a number of playing cards from a standard deck equal to twice the number of students in the class, leaving out face cards and 10s. If the class is larger than 9 students, it is recommended to have each value represented in the selection at least once. Prepare as many simple algebraic equations as desired, leaving out a single term of value 1 through 9.
ACTIVITY
Distribute exactly two cards of any value between Ace and Nine to each student. If one student draws two cards of equal value, have her swap with a neighboring student so that every student has two differently numbered cards. The instructor will then write one of the prepared equations on the chalkboard, leaving a blank where the term of value 1 through 9 should go. Students are then asked to raise only the card whose value they believe correctly satisfies the equation. For example, for an equation that reads 9 + __ = 11, all the students who are holding cards of value “2” would be expected to raise their card. Ask students to applaud correct contributions from their classmates.
OBJECTIVE
Students learn algebraic principles by mentally solving for unknown variables. Students contribute in a collective and passive environment with little performance pressure.
TIPS
As there are only four cards of any one value in a standard deck, no one equation should elicit more than four correct positive responses from students. When students become too familiar with the setup, shuffle the cards and redistribute them to students. Having a collective goal, say, 5 straight equations where all the students with the correct responses participate, gives incentive for students to focus on the activity even when their number is not being called. It is at the discretion of the instructor to actively develop a system where a student is empowered to seek help from his classmates in a non-disruptive fashion.
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VARIATIONS
DIAGRAM
NOTES
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For older students, distributing more than two different card values to each student yields a stronger challenge. Ask students to raise only the one card that correctly fits the equation. For much younger students, algebraic equations may be replaced with simple expressions or even audibly saying the name of a number. To add a perceived degree of randomness, or to engage students that are struggling or reluctant to participate, students may also be asked to contribute additional elements of the equation via the numbers on their cards or spontaneous suggestion. For example, a three- or four-term equation with two blanks can be solved by replacing one blank with the number on one of the student’s cards, and then solving for the last blank.
Dart-less Darts CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Addition
3rd and 4th
5 min. per Round
PREPARATION
Shuffle a standard deck of 52 cards.
ACTIVITY
Divide the class into two teams. In front of the class, deal all of the cards into two stacks of 26 cards each. Hand each team a stack of cards, and allow them to search through the stack. Explain to the class that their team earns points when their stack has more cards of a particular value than the opposing team’s stack. Point values are based on the face value of cards, with Jacks worth 11 points, Queens worth 12 points, and Kings worth 15 points. For example, if team one has three “9s” in their stack, and team two has one “9,” then team one earns 9 points toward their total. Moreover, if team two has four Kings in their stack, and team one has no Kings, then team two earns 15 points toward their total. Lastly, if team one has two Queens, and team two has two Queens, then it’s a push, and neither team earns points for that value. For every round, the points for each team are totaled and the winner of the round is the team with the most points.
OBJECTIVE
Students rely on mental addition of multiple terms. Students develop mental shortcuts to assist in carrying out rules.
TIPS
When students become familiar with the rules of the game, expect a few students to identify shortcuts to scoring the game, e.g. noting that having three cards of a value is sufficient to infer they receive points for those cards. When they do, ask those students to contribute by informing the class of their observations. In the event of a tie, randomly select one suit and ask students to count how many cards of that suit their stack contains. The team with the most cards of that suit wins. This activity is best implemented in combination with another groupwise activity, where the winning team of a round is designated with some benefit that is denied the losing team. This activity will be most effective if played in multiple rounds, so that no one team feels that it has been the victim of a single bad deal.
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VARIATIONS
DIAGRAM
NOTES
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The instructor may choose to divide the class into three or four equal teams. In the event of an odd number of teams, simply distribute cards evenly and retain the uneven remainder.
That Number Suits You CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Arithmetic
4th and 5th
45 min.
PREPARATION
Remove face cards from a standard deck. Divide the remaining 40 cards into two stacks of 20 cards. On the chalkboard, draw the four suits’ symbols, as in the diagram. To the right of each symbol, write an arithmetic operator and a small value, indicating an expression. For example, one line might read: ! + 4. For each suit, use a different operator and value.
ACTIVITY
Divide the class into two teams. Place both stacks of 20 cards face down in the midst of each team. Individual representatives from each team will take turns drawing the top card. Explain to students that they are to combine the value on the card with the expression indicated by the suit of the card, as per instructions on the chalkboard. For example, a student that draws the 2 of Spades, as indicated in the diagram, would take the value of the card, 2, and because it is of the Spades suit, subtract 1. The correct response, then, would be “1.” Have students take turns standing and informing their classmates of the card they drew and the resulting equation. If a student responds correctly, she may discard the card; else if the student responded incorrectly, she should replace the card at the bottom of the stack. Continue until one team has successfully discarded all of the cards from their stack.
OBJECTIVE
Students reinforce mental arithmetic abilities. Students contribute individually towards a collective goal, with some group dynamics at play.
TIPS
Some sort of progress tracking device, like a Cribbage board or a number line, can be used to provide visual feedback to students, tracking the number of correct answers. For subtraction, using “– 1” as the operand will always result in a nonnegative answer. For division, using simple halves, thirds, or fourths is recommended, and ask students to respond in mixed numbers, i.e. “One and one-fourth.” If the operators on the board become stale as the activity progresses, feel free to shuffle the suits on the board.
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VARIATIONS
DIAGRAM
NOTES
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Instructors may offer students a collective reward based on the total number of correct responses. For example, out of 40 possible correct answers, the instructor may offer a bonus point on a future exam for every 5 correct responses. In this case, incorrect answers should not be replaced in the deck but instead discarded in a separate pile. For younger students, all operators need not be used; multiplication and division can be substituted with more addition or subtraction expressions. Older students may be required to draw two cards, one at a time, in order to reinforce order of operations and increase the difficulty of mental math.
LOGIC GAMES
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A Lofty Figure CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Geometry
2nd and 3rd
5 min. per Puzzle
PREPARATION
Collect or design illustrations following these directions: (1) Choose a shape to review, e.g. the triangle, and draw it. (2) On the inside of the shape, draw lines that further dissect the shape into constituent parts reflecting generally the same shape as the outermost shape. For example, in Fig. 1 of the diagram, the outermost shape is a triangle, and on the inside are three smaller congruent triangles and a fourth upside-down triangle.
ACTIVITY
Ask students to collectively discuss how many shapes of a certain kind are visible in one of the illustrations. Allow students no more than 3 minutes to discuss with classmates, keeping classroom noise to a moderate level, and ultimately record their thoughts in a notebook. Take a poll of students’ responses, and ask a representative from each partition to elaborate on his or her findings. When finished, use differently colored chalk to identify all different iterations of the shape in the large figure, and congratulate the portion of the class that offered the correct answer.
OBJECTIVE
Students attempt to solve a puzzle with multiple interpretations and varying degrees of difficulty. Students further develop sight recognition of common shapes and their names.
TIPS
Try not to approach the activity as though there is exactly one correct answer; it is important to visibly welcome and treat with value any suitable contribution from students, even if they leave out one or more valid solutions.
VARIATIONS
For puzzles that may prove too difficult for students, as in Fig. 3 in the diagram, feel free to skip the polling step, and instead walk them through the breakdown of each part of the diagram.
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DIAGRAM
NOTES
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Moving Mountains CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Numeracy
3rd and 4th
15 min.
PREPARATION
Divide the chalkboard into three parts from left to right. Draw on the leftmost third of the chalkboard three boxes, or trapezoids, stacked in a column, each with a progressively larger base, such that the one with the largest base is at the bottom. Inside these boxes, write a two- or three-digit number that corresponds in magnitude to the dimensions of the box; that is, for the largest box, write the largest number, and for the smallest box, write the smallest number.
ACTIVITY
Explain to the students that the three boxes, stacked on top of each other, represents Mt. Liamuiga, and their objective is to move all three parts, one at a time, from the leftmost third of the chalkboard over to the rightmost third, following these rules: (1) a box may only be moved from one third of the chalkboard to either of the other two thirds, (2) only the topmost box on a stack may be moved at a time, (3) a box with a larger number may never be moved onto a box with a smaller number, and (4) students must say the number on the box to move it. Note: Students may move boxes from right to left, in addition to progressing them from left to right. Allow students to discuss among themselves the best course of action for solving the puzzle, and have a representative from the class relay the instructions. All the while, the instructor will erase and redraw the numbered boxes to their new positions. Continue in this manner until all three boxes have been successfully moved from the leftmost third of the board to the rightmost third.
OBJECTIVE
Students work together towards a collective goal. Students use reasoning and simple number recognition to break down a difficult task into smaller, more manageable pieces.
TIPS
Familiarizing oneself with the solution to the “Towers of Hanoi� puzzle, here, would benefit the instructor greatly. Do not hesitate to give subtle hints towards the solution if students become frustrated.
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VARIATIONS
DIAGRAM
NOTES
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For students who are older or previously familiar with the puzzle, simply adding a fourth box in the first stage of the puzzle increases the difficulty substantially. For very small classrooms, students may want to try to solve the problem themselves, one at a time. Keep track and reward the students who were able to solve the puzzle, and perhaps give a greater reward to the student who solved it in the fewest moves. This puzzle can also be transformed into an on-desk activity, using tiered blocks or manipulatives, with placement zones being denoted by pencils or squares of paper.
Figuring Out the Combination CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Numeracy
4th and 5th
10 min. per Game
PREPARATION
Write a 3-digit number in large print on a sheet of paper, and hide this paper from view. On the chalkboard, draw a standard H|T|O table, and to one side write each of the digits 0 to 9.
ACTIVITY
Explain to students that they are going to attempt to guess the hidden 3-digit number, but only with non-verbal hints. Select one student to guess first by first writing his 3-digit guess in the H|T|O table, and then saying aloud the name of the number. The instructor first scratches out the digits used in the student’s guess from the list of digits on the side, signifying that those digits have been guessed already. Then, any digits in the student’s guess that correspond exactly to the correct answer, the instructor will draw a square around them on the H|T|O table. Any digits in the student’s guess that are also included in the correct answer but are in the wrong column will be circled on the H|T|O table. Continue taking guesses from students in this manner until a student correctly guesses the hidden number.
OBJECTIVE
Students develop numeracy through constructing and reading large numbers. Students use logic and process of elimination to narrow down a search. Students contribute individually towards a collective goal.
TIPS
When beginning the activity, the instructor may choose to write the first number in front of the class, still hiding it from view, in order to attract attention at the outset. While in theory any 3-digit number can be used, it is often preferable to use numbers with three different digits, so as not to confuse students. It is at the discretion of the instructor whether or not to inform students of the nature of the hints before performing the activity.
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VARIATIONS
DIAGRAM
NOTES
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For younger students, starting with a 2-digit number in order to introduce the steps in the activity is encouraged. Many different clues can be instituted, like using letters adjacent each guess to signify correct digits, but with no indication of which digits they apply to. For example, a guess of 930 where the 9 matches and the 3 is in the wrong column would yield a result of “AB,” whereas a guess of 100 with no matches would yield a result of “C.”
A Sorted Affair CURRICULUM TOPIC
RECOMMENDED AGES
ANTICIPATED TIME
Numeracy
5th and 6th
10 min. per Diagram
PREPARATION
Collect a number of sheets of paper or large note cards equal to 2 more than the number of students in the class. On each sheet, write a 3-digit number in large print. On the chalkboard, draw a Venn diagram of two circles large enough to accommodate most of the numbered sheets.
ACTIVITY
Distribute the sheets of paper to students facedown on their desks, instructing them not to look at them or discuss their numbers with classmates. With the two numbers leftover, place one inside each circle, as in the example. Explain to students what purpose a Venn diagram serves, and ask students to, one at a time, to approach the chalkboard with their numbers in hand. There, a student should show the class her number, read aloud her number, choose a category for her number, explain to the class why she chose that category, and attach her number to the board in the appropriate location. The first student to add a number to a given circle will effectively be allowed to name the criterion for that circle, and the instructor should write it above that circle. In the event a student has no place to put his number, if he can identify a new common thread between all of the entries in one circle and his own, he may be allowed to name or rename the category, and the instructor may chalk in the new category above the corresponding circle. Ask the class to applaud the student’s contribution, and briefly and objectively discuss with the class the logic of the choice the student made. If the student’s logic is sound, continue the activity, or else if the student’s logic is flawed, explain to the class why and ask the student to adjust his categorization.
OBJECTIVE
Students learn the nature of Venn diagrams. Students develop numeracy through naming large numbers and recognizing discrete patterns. Students use reasoning to sort abstract objects in a largely unstructured environment. Students develop self-esteem and social cues through peer review of their contributions.
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TIPS
When choosing numbers for the students to categorize, the instructor may use discretion, selecting numbers based on a few obvious sorting rules. For example, of twenty different numbers, ten might start with the digit “1,” seven might start with the digit “3,” and only three might start with the digit “9.” When about 10 numbers have been placed on the board, or the categories start to become too unwieldy, the instructor may choose to start with a clean board for any students that have not yet added their numbers.
VARIATIONS
Instructors may choose to define the two categories in advance of the activity. For example, one circle may be marked “Even,” and the other circle marked “Divisible by 5.” Alternatively, one circle may be marked “Contains a 1” and the other circle marked “Larger than 500.”
DIAGRAM
NOTES
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