Ages 2-8; math songs: “One, two, buckle my shoe”, “One little, two little, three little Indians”; delay using electronic calculator until next book; don’t say things like: “here comes the tricky part” -> child will be less anxious to learn new concept; if you don’t have good memories with math, resist telling it to your child (eg “it’s ok, I was never very good at math either”); few minutes practice every day

1. QUANTITIES, NUMBERS, COUNTING: apply counting on simple things (food on plate, steps in staircase); difference between quantity (how many) and size (how much length etc) can be confusing; helpful visual aids: 1) number chart (1-100), 2) number line 1-10) -> useful to compare sizes and numbers (smaller/larger = farther to the left/right), 3) number strips (1-10) -> useful to learn addition/subtraction; playing games: Parcheesi, Sorry, Dominoes, Chutes and Ladders, Mancala (no counting needed); counting variations: start with 0, counting on (start from 2, and count from there), count backwards, count in groups; GAME: The Eating Triangle: Use 21 pieces of small food for each player. Arrange these in a triangle with one piece in the first row, two pieces in the second row, and so on, to make six rows. Roll a die during each person’s turn. If the number rolled is 3, then if the row with 3 things in it has not been removed, remove (and eat!) that row and roll again - otherwise, end that turn. The winner is the first one to have no rows left.; number reading: look for special numbers (eg 3) around the house, during traveling etc; number writing: use forgiving media (eg sand), cut out shapes from sandpaper, stick them on solid surface -> child can trace number shapes with fingers, or use sand on top of glue; number reversals: not a problem as long as it disappears before age 8, just ask the child to correct it; comparison: one-to-one matching, see which quantity is larger; number line: place it on the wall where your child can see it & play with it, make sure to start with 0 (becomes a familiar number, number = distance from 0); GAME: War: Each player gets half of a deck with the face cards removed. The players turn over one card at a time. The player with the higher card gets to keep both cards. In case of a tie, three more cards are turned over, and the fourth cards are compared-winner takes all. The first player to get all of the cards wins.; counting up to 20: same activities as before but extended to 20; calendar: at the start of each day count up to current day of month; connect-the-dots: you can make your own, challenge: do it backwards; counting backwards: helps prepare for addition & subtraction (eg. to “take away” 4 from 12 child needs to be comfortable counting backwards from 12 to 8); 10’s and 1’s columns: use physical objects (Legos, popsicle sticks) to practice breaking numbers into tens and ones, prearrange into groups of tens and ones; break down numbers into tens and ones verbally & written form; do not use dimes and pennies (too abstract for them at this point) -> use only pennies, stack them into piles of ten; counting up to 100: include step: multiply by 10, transition between levels of 10’s (number after 2 tens + 9 ones = 2 tens + 10 ones = 3 tens), emphasize difference between “-teen” and “-ty”, use counting table that starts with 0, use long number descriptions (eg 0 tens plus 7), count out objects, bundle them into tens, count backwards from as high as 100; comparing numbers up to 100: start with measuring lots of things, RULE: Compare two-digit numbers by comparing the tens digits first. If the tens digits are the same, then compare the ones digits., number line until 100: more spread but ordering is clearer; GAME: Rack-O: *This is a 2 to 4 player card game. It uses a deck of 60 cards, with the cards numbered from 1 to 60. Each player is dealt a hand of 10 cards which are placed in a rack. The play consists of taking turns picking cards and exchanging them for cards in the rack. The winner is the first person to get all 10 cards arranged in increasing order.”; symbols for comparing: “<” hungry alligator; groups of numbers (counting, natural, whole, negative, integers)
2. FINGER ADDING & SUBTRACTING: subtraction ~ “take away” or “difference” (both important); GAME: Hidden Objects: Start with any number of objects; for example, 6 coins. Take turns with your child removing some number of the 6 coins without letting the other person see. The other person is challenged to figure out how many coins were removed by looking at how many are remaining. A variation of this game is to let your child see how many coins are taken away and have your child figure out how many are remaining.; addition: illustrate with objects (eg cherry) or moving on the number line; adding-totals up to 5: use fingers on both hands; reversing order: addition is commutative but subtraction is not (learning the word “commutative” is not important); GAME: Flash Numbers: This is played by having the parent put up a number of fingers between 0 and 10, and having the child try to recognize how many fingers there are as quickly as possible. With practice, this can be done without counting the fingers. It is helpful when the number is 5 or more to put up all the fingers on one of the hands.; memorization is not needed: child needs to understand what adding means; adding with 0: can be confusing; subtracting-for 10 and under: using fingers or number line; subtracting with 0; subtracting a number from itself: illustrate with Cheerios; sums that are 10: use all fingers on both hands; easy way adding: eg 6+3 start with a closed fist, say 6, start counting 3 fingers: 7, 8, 9, better to start with the larger number, don’t memorize the answers; easy way subtracting: 1) take away method: eg 11-3, start with closed fist, say 11, start counting backwards 3 fingers: 10, 9, 8. 2) difference method: eg 7-3, start with closed fist, say 3, start counting until 7 -> how much do you need to add to reach the desired total: 7-3=? -> 3+?=7;
3. ADDING & SUBTRACTING: after some practice, sums & differences will be memorized (but it’s more than just memorization), practice steps that have been mastered frequently; make games out of the practice (Parcheesi, Sorry, Chutes and Ladders, Blackjack - without betting); GAME: Adding War or Difference War: Each player receives half of a card deck with the face cards removed. The cards are turned over two at a time. The two cards are added for Adding War, or their difference taken for Difference War. The player with the higher result gets to keep all of the cards. In case of a tie, three cards are turned over, and the next two cards are done again/winner takes all. The first player to get all of the cards wins.; fact families & reverse operations: eg 2+6=8, 8-2=6, 6+2=8, 8-6=2; makes child aware of direct connection between addition & subtraction; fact family card: triangle with two numbers on bottom (2 & 6) and sum on top (8), “-“ sign on left & right, “+” sign on bottom, demonstrate by dividing collection of 8 into two groups of 2 and 6; adding/subtracting with 1,2,3: start by counting backwards, after a while stop counting; adding/subtracting 10: add 10 to numbers 1-9, subtract 10 from 11-19; compensation: if you are adding two numbers, you can add the same thing to one number and subtract it from the other and the total won’t change (4+6=(4+1)+(6-1)=5+5); adding with 7,8,9: use compensation to turn them into easier problems (eg 6+9 -> 5+10); adding twins (adding number to itself): simply memorize if not covered earlier (eg 6+6); adding near twin: add/subtract from nearby twin problem; sums that are 10: practice fact families for sums that are 10: start with 1+9, use compensation to get other forms, use BLOCKOUT game (by Creative Teaching Associates); subtracting-numbers less than 10: subtracting 1,2,3 -> already covered, difference of 1,2,3: eg 9-7, “difference” problems rather than “take away” problems, use fact families if any cause trouble, all others: only three problems: 8-4, 9-4, 9-5 -> use fact families (4+4=8, 4+5=9); subtracting-numbers from 11 to 18: turn into simpler problems involving subtraction with 10, use 10 to create two differences: 15-8=(15-10)+(10-8)=5+2=7, or use constant difference: eg 15-8=(15+2)-(8+2)=17-10=7; breaking up larger numbers: optional method, addition: 5+6=(5+3)+3=8+3=11, subtraction: 11-7=(11-3)-4=8-4=4; memorizing and drill: can also be used if earlier methods don’t work
4. MULTIPLYING: do it as something fun, not something you expect to be hard, no need to wait until all multi-digit addition is mastered, multiplication if small numbers (up to 3, even 5) can start as early as addition, use quantities (eg 3x4: 3 piles of pennies, 4 pennies in each pile), arrange them in rectangular pattern, multiplying with 0,1,2,5,9,10,11 fairly easy, 4,6 can be reduced to 5, the rest (3,7,8) usually memorized, practice regularly, memorization is not a good idea, keep a close link between multiplication and division; multiplying by 2: same as adding twins, good time to introduce dividing by 2; multiplying by 3: eg 3x4 skip counting (4,8,12), or doubling plus one more (3x4=(2x4)+4=8+4=12); multiplying by 0 and 1: easy; reversing order: multiplication is commutative (2x3=3x2=6), illustrate by looking at the same rectangular from both sides; skip counting: eg 4,8,12,…,40, in the beginning count every number in-between but only softly, challenge child to skip count faster or backwards, note the patterns (5 -> ones alternate between 0 and 5, 8 -> ones digit decreases by 2, 9 -> ones digit decreases by 1, 11 -> ones digit increases by 1, start skip counting up/down at numbers other than 0/multiples; multiplying by 10: similar names, number chart to 100 useful; multiplying by 5: multiply by 10 & half the number (eg 4x5 -> 2x10, 5x5 -> 4x5+5 -> 2x10+5); multiplying numbers from 1 to 5: only 4x4 not covered -> skip count or memorize, create multiplication table; multiplying by 6 and 4: modify to 5, eg 6x8=(5x8)+8, 4x8=(5x8)-8, 4 can also be looked at doubling twice: 4x6=2x(2x6); multiplying by 9: two digits always add up to 9, symmetrical, eg 9x7 -> 1) subtract 1 from 7 -> 6 will be the number of tens, subtract this from 9 -> this will be the number of ones, or 2) 9x7=(10x7)-7, or 3) hold fingers on both hands, lower 7th finger: number on the left -> tens, number on the right -> ones; multiplying leftovers: memorization or use nearby numbers (eg 7x8 -> (7x7)+7 or (7x9)-7); multiplying by 6,7,8: there are alternative methods of previous techniques don’t work; multiplying by 11: easy & fun, boosts confidence; squres & cubes: child should learn & recognize squares from 1^2 to 10^2; near squares: alternative ways to multiply, eg 7x8=(7x7)+(7x1), numbers that are two apart: 6x8=7^2-1, numbers four apart: 5x9=7^2-2^2; powers and exponents: 2^3 shorthand writing: “multiply 2 by itself 3 times”; units, primes, composites: exactly 1 divisor, exactly 2 or more, prime numbers: building blocks for multiplication (prime factorization), number shapes: fun way to find out if number is prime or not, eg 6: give child 6 raisins, challenge to make rectangle out of them, or: make a triangle, child should know the first few primes (2,3,5,7); sieve of Eratosthenes: fun method for listing primes, place x below 1, repeat: mark first number without x, put x below all multiples, apply shortcuts if you like
5. DIVIDING: division is game children start can play almost when they start addition, ask child to put 9 marbles into 3 equal piles, fact family is good practice (eg triangle: 10 on top, 2 and 5 on bottom, “x” in middle low, “/” on sides), memorization not helpful (-> too many), emphasize that multiplication and division are reverse operations, you can think of division in two ways: eg 35:5 1) calculating how many groups of 5 are there in 35, 2) how big each group would be if you split 35 into 5 equal groups, both are important concepts; dividing by 2: gentle introduction, three approaches: 1) taking half: split into two equal groups 2) how many twos are there? 3) fact families; dividing by 1: easy but important; divides: ask child to divide objects into groups, natural time to introduce even & odd numbers, remainders can be introduced too; GAME: I’m thinking of a number: One person, “It,” says that he is thinking of a number between 1 and 10 (or whatever range the players are comfortable with). The other players get to ask questions of the form, “Does 2 (or 3 or …) divide your number?” After several such questions, the players can then ask questions like, “Is your number 6?”; dividing by 0, and into 0: important to learn that it is impossible (how many 0’s does it take to get 6? -> no single answer, how many 0’s are needed to get 0? -> no clear answer), dividing into 0: eg 0/6, always 0 (use fact families or ask how many 6’s does it take to get 0); dividing by 5,10: dividend multiples of 10 by 10 -> answer is digit in the tens place, dividing by 5: start by skip counting by 5, answer: twice the tens digit + 1 (eg 30:5=3x2=6, 35:5=(3x2)+1=7); dividing by 9: one more than the tens digit (63:9=6+1=7); dividing without remainders: 1) skip counting (24:6 -> say 6,12,18,24 while counting 1,2,3,4 on child’s fingers) 2) guessing: child encouraged to take a wild guess and see how close the answer is, usually easiest guesses are 5 times the number or 10 times the number (eg 24:6 -> guess: 5 -> 5x6=30 -> too high) 3) solid knowledge of multiplication (quickly scan to see which matches the division); dividing with remainders: this is harder, 1) use skip counting 2) use guessing, GAME: I’m thinking of a number: As before, one person, “It”, says that the number is between 1 and 10 (or whatever range the players are comfortable with). The other players get to ask questions of the form, “What is the remainder when your number is divided by 2 (or any other number less than 10)?” After several such questions the players can then ask questions like, “Is your number 6?”; checking division with multiplication: both with or without remainders; divisibility tests: dividing by 2 (when ones digit is 0,2,4,6,8), dividing by 4 (remainder same when using tens and ones only), dividing by 5 (when ones digit it 0,5), dividing by 10 (when ones digit is 0), dividing by 3,8 (same remainder as sum of digits, even after summing multiple times); prime factors: good practice: do prime factorization for numbers from 1 to 16, helps if child gets used to listing primes in increasing order, two approaches: 1) factor trees 2) repeating division by primes
6. FRACTIONS: basic addition & subtraction, when child can take half of things he is ready to play with fractions, first cut-up objects (eg. apples), then numbers, child wing treat it a big, difficult idea unless you make a big deal out of it, sharing is good practice (eg cookies), use “top” and “bottom” instead of “numerator” and “denominator”; fractions of an object: natural examples in kitchen, fractions larger than 1: be sure to include those too, multiple pieces per portion: twice as many pieces -> “equal portions”, fractions equal to 1; fraction strips: great way to visualize fractions, “1” should be at least a foot long -> 1/12 is one inch, get 2-3 sets so it’s easy to work with fractions >1, challenge child to find fractions to fit together to equal others; fractions of a number: start with breaking the number into equal pieces (3/5 of 10 -> 1) 1/5 of 10 2) 3/5 of 10), transition to multiplying: taking 5/3 of 6 = 5/3x6, use fractions greater than 1: be careful with your words (eg 5/4 of 8: first break 8 into 4 equal parts, than say you are taking “5 parts of that size” instead of “5 of those parts”; value and the number line: fractions are numbers with value, tie in to whole numbers: some fraction = whole number (when top part evenly divides bottom part, eg 8/4=2), use number line; adding & subtracting-same denominator: adding/subtracting apples to apples; two views of fractions: eg 3/5 1) breaking 1 whole thing into 5 equal pieces, taking 3 of them (3x1/5) 2) breaking 3 whole things into 5 equal pieces and taking one of them (1/5x3); fractions-special words: rational numbers: fractions with any integer divided by any non-zero integer, term “rational” is not very important now
7. EQUATIONS: playful approach: puzzles & mysteries that are fun to solve, try to avoid using variables too early; I’m thinking of a number: GAME: I’m Thinking of a Number: One person thinks of a number and says a mathematical clue concerning the number. For example, “When I add 5 to my number I get 9. What is my number?”, use reverse operations or fact families, switch roles with your child from time to time, play anywhere; the bag game: GAME: Bag Game: The game always starts off with “I have a bag and you have a bag.” This is followed by some information about how the two bags are related. For example, you might say, “Our bags have the same number of things, and together we have 10.” At the end always comes the question “How many are in my bag, and how many are in your bag?”, you can make it as tricky as your child can handle; using silly names: use a silly name instead of “the number I’m thinking of” (eg “I’m thinking of a number called Pluto. When I subtract 4 from Pluto I get 2. What is Pluto?”); using blank spaces: first practice with straightforward calculations: 3+4=q** -> then: **+3=9; letter substitution puzzles: digits replaced by letters: somewhat limited for single-digit arithmetic: a+a=c4; simple equations: 7+y=12, box/5=5
8. GEOMETRY: famous architect Frank Lloyd Wright played as a child with special set of blocks designed by Friedrich Froebel (-> Froebel blocks); start at young age by teaching names of shapes, make sure your child’s toys include wide variety of shapes (including shapes with more than 4 sides); designs & patterns: jigsaw puzzles, tiles & pattern blocks, Zillij: Moroccan art using ceramic tiles -> encourage child to draw simplified versions, Taprats: Java applet to make Islamic star patterns, tessellations (tiling): complete covering of a surface with geometric shapes -> Penrose Tilings (-> try to fit them together using different colors of stiff paper), drawings of M. C. Escher, Tangram, Pentominoes, Blokus, misc. designs: Oriental/Mideastern rugs, Celtic knot designs (Book of Kells), spiral designs, architecture (Taj Mahal, Alhambra Palace): look up on the internet, explore patterns with child; points, line, segment, ray, angle: pretty dry but will buy used to discuss interesting shapes later, line designs: draw lines on paper or connect nails with string, connect two points, keep moving both endpoints, can be curves too; taking directions: treasure hunt in yard: four kinds of directions: 1) go forward x steps/feet 2) go backward x steps/feet 3) turn right some number of degrees (start with 90/180 only) 4) turn left some number of degrees, more fun if you write down all directions in advance; plane figures: open/closed; GAME: Sprouts: You can play anywhere you have something to draw on. Invented by John Conway and Michael Paterson in 1967. Start by marking just a few spots anywhere on a piece of paper-usually 2, 3 or 4 dots are plenty. A move consists of adding a curve drawn between two spots, or a loop starting and ending at a single spot. A new spot must be added somewhere along this new curve or loop. The new curve or loop cannot cross or touch any earlier curves and loops. No spot can have more than three connections to it, where a loop counts as two connections. You win if your opponent has no legal move.; finding inside & outside: draw very complicated closed figure with lot of loops, take a point anywhere -> is it inside or outside? draw line to point outside of the figure, count how many times the line crosses the figure -> if even: outside, if odd: inside; circles & polygons: example: street signs, practice with tiling blocks (“please pass the yellow hexagon to me”); similar & congruent shapes; lines of symmetry: fun activities: folding paper shapes or use mirror to find symmetry lines; three dimensional shapes: 3x3x3 cube puzzle made up of 7 pieces, Klikko (by Kydko International): kit simplifying making 3D shapes, or use paper to make them
9. REASONING: three softwares useful for practicing patterns & logical reasoning: 1) “Mosaic Magic” (by Kinder Magic Software): good for small children, works with colored tiles, 2) “Pit Droids” (by Lucas Arts Entertainment): discover patterns & make them continue, 3) “Zoombinis” (by Broderbund): adventure involving fun puzzles; sorting & classifying: ask child to sort blocks by shape/color/size, practice everywhere & with everything, complicated characteristics (eg do not have certain characteristics or have both, or at least one), fun games: Quarto! & Set; start using term “set”: collection or group; patterns: create sequences, ask child to continue, ask his reasoning (eg waking, rhythm, nature), take turns creating; analogies: eg “girl is to mother as boy is to **”, “2 is to 6 as 4 is to **”, for younger kids start with pictures; logic: proposition (true/false statement), contrapositive, exclusion, puzzle books: Mind Benders, Sudoku puzzles: variants: KenKen puzzles
10. MEASUREMENTS: practice English (feet/inches) and metric measurements too, practice estimating, use abbreviations from time to time; length: string, pacing distance, car trips, explain where the names come from; area: use square units, measure rectangular areas, approximate irregular shapes by drawing inch grid; liquid volume: practice in kitchen, use educational cups (Measure Up! Cups by Discovery Toys), solve basic Math exercises; weight: use kitchen/bathroom scale, measure family members/pets; temperature: use outdoor thermometer, discuss body temperature, put big drawing of thermometer on the wall, mark some important temperatures for reference
11. TIME: make calendar together, fill with special days/upcoming events, teach hours when child can count to 12, add details when he can (skip) count to 60; time of day-talking and writing: start with hours only, AM/PM, write time in multiple forms, next step: half & quarter hours, finally: minutes; clock face reading: minute vs hour hand, use teaching clocks, read 1) exact hours 2) quarter/half hours 3) minutes multiples of five 4) all times; calendar: slow process, use knuckles & valleys on both hands to see how many days are in each month
12. PROBABILITY & GRAPHING: probability and chance: only after fractions, teach about chance when playing games (eg coin flips); graphing: age-appropriate graphs: bar & line graphs; bar graphs: use symbols (eg fruit) first -> then filled-in columns; line graphs: transition from bar graphs (make a dot/line at the top of the bar -> connect them), start left side with 0, then change to different number, check the differences, all questions (eg day with fewest/most children), combine daily activity with line graph (eg high/low temperatures)
13. MONEY: be careful with coins (choking hazard), give child chance to practice at the store, set up pretend store at home to practice; coins-learning and counting: money value is abstract, avoid using dimes and pennies as examples for 10’s and 1’s, start adding up group of coins with largest coin; making same amounts of money: start with simple exchanges (hand child nickel, ask to give back same values in pennies bac), more challenging requests (40 cents without any nickels), count number of ways to come up with a certain sum (organize counting by starting with the largest first); pretend store: pick favorite toys, put price tags on them, take turns being customer vs clerk
14. MANIPULATIVES: things that can be looked at, handled, moved around, many can be made at home easily; counting objects: should not be choking hazard (eg raisins, Cheerios), different colors helpful; number strips: each strip 1” wide, length = unit x 1” (eg Cuisenaire Rods), use different color for different length, make multiple copies (esp. number 10), make 10” by 10” square to represent number 100 with lines; fraction strips: 1 = 1 foot long; number lines: can be different sizes, attach to wall; counting chart: most common start at 1, but better if starts at 0; sorting containers: useful for grouping (eg empty egg cartons); number generators: dice with spots (you can buy dice with more than six sides), dominoes, playing cards, spinners; abacus: traditional vs Japanese (Soroban); number writing: pile of sand/ground coffee/rice (good for practice); number balance beam: practice multiplying using lever principle; two pan balance: compare quantities; volume measures: not heavy/breakable, Measure Up Cups by Discovery Toys; measuring devices: rulers, yardsticks, kitchen/bathroom scale, outdoor thermometer; geometry devices: ruler, protractor, compass (beware of sharp point); graph paper; geoboard: flat boards with pegs sticking up, use rubber bands to make interesting shapes; tiling blocks: pattern blocks, pentominoes, Tangram sets; 3D construction kits: Klikko (by Kydko International), Polydron, Zometool, D-Stix; clocks: Judy Clocks; calendars: you can make large ones by hand; money: use large plastic coins for young children
15. LEARNING GAMES & ACTIVITIES: small numbers: eating triangle (arrange 21 pieces of small food in triangle, roll dice, eat corresponding row), flash numbers (parent shows number on fingers, child says number as quick as possible), hidden objects (start with z coins, secretly remove some, child has to find out how many were removed by looking at remaining), number shapes with counting objects (ask child to make shapes using small objects, eg rectangles, squares, triangles), Mancala (six pits each side, same number in each pit); ordering games (cups with different number of raisins, ask child to put cups in order); logic/patterns: Set (symbol/color/number/shading, three cars with each feature all same/different), Quarto! (shape/color/height/solid, place 4 piece with at least 1 common characteristic), patterning & sequencing games (put several things down, ask child what the next one is), rush hour, towers of Hanoi; problem solving: math riddles (one friend gives you 3 apples, another gives 5, how many do you have?), I’m thinking of a number (comparing: child guesses, “too big/small”, math facts: it is the same as 2 plus 3, beginning equations: 8 is 2 less than my number, division: “what is the remainder when your divide by 3?”), bag game (I have a bag, you have a bag, you have twice as much, if I add 4 more to my bag, we have the same), book: Family Math for Young Children, splitting up groups of objects (eg 9 objects, ask child to split into two groups so first has 3 more than second), Nim (pick target number, start from 0, take turns to add 1, 2, or 3, whoever reaches target wins), ‘SMATH & Mixmath; Math facts (Math tic-tac-toe: choose a square, answer a question, gets a mark if the answer is correct, war card game: ordinary deck of cards, cards are turned over one at a time, player with higher card gets to keep both cards, extension: turn over two cards, one is the number in the tens place, second in the ones - remove 10’s and face cards, cards can be added/subtracted/multiplied, factor-multiple game: write down numbers from 1 to 30, pick one & cover it, players must choose either a factor of the current number, or a multiple of it which has not been covered yet, loser if the one who is forced to pick 1, factors: write down numbers from 1 to 30, choose one that has not been covered yet and at least one factor has not been covered yet, cover it, other player covers some/all of factors, player with larger total wins, playing cards used for math: practice operation, who is faster; flash cards: can be made at home, use for math facts, polygons, coins with names etc; fact family flash cards: triangle shaped, one number in each corner, cover one, ask child to calculate missing number; 100 bottles of pop on the wall: modify original lyrics, take down 3, add 1/4 more up etc, can go past zero if child is comfortable with negative numbers; numbo: bingo-like playing boards, make set of cards with math problems, pick randomly, cover solution in board; Rack-O: card game by Parker Brothers, cards with numbers 1-60, arrange cards in increasing order); geometry (views of block models: secretly build shape from sugar cubes, draw front & side views, other person draws missing view or builds block model; sprouts: mark few spots on paper, add curve between two spots or loop around single spot, add new spot on new curve, you win if other person cannot move; Tangram, Pentominoes, Blokus, cube puzzle); target numbers (24 game: by Suntex International, use 4 digits to produce 24; Number Jumbler: you can make your own version, similar to 24 but more variety; Blockout: you can make your own boards, can be played with cards; Make 7: by Pressman, similar to Connect 4 but with numbers); miscellaneous (Rami, the binary teacher; patterns on 100 counting boards: give tasks eg cover numbers who digit adds up to 6, check pattern; magic squares: numbers in every row/column/diagonal adds up to the same number); traditional commercial games (Sorry, Dominoes, Aggravation, Chutes and Ladders, Go Fish, Rummy, Solitaire, Parcheesi, Cribbage, Blackjack, Blackgammon)
16. ALTERNATIVE METHODS TO FINGERS: drilling: can be used to learn math facts, little emphasis on structure and relationships between numbers; touchmath: links symbol of number with quantity; abacus & Soroban; Chisanbop: two hands = first two columns in a Soroban abacus
17. RESOURCES: reading books with math: MathStart, Math Mysteries, The Greedy Triangle; books for parents & teachers; books for math games; workbook of exercises; software programs: Zoombinis, Pit Droids, Mosaic Magic, GeoGebra, Logo (https://el.media.mit.edu/logo-foundation/); educational supply companies; internet math resources: https://artofproblemsolving.com/; math curricula