Thinking math: Use Miquon Math for grades 1-3!!! Even if you have already started with something else, seriously consider re-starting with Miquon. Students advance much faster with a Miquon headstart, easily learning multiplication and division, fractions, even graphing rectangular coordinates with complete understanding (in 3rd grade!). They learn to think math, not just do math. Most students proceed directly from Miquon into Saxon 65 (6th grade) with no difficulty.
Facts List: Make hand-held reference cards for multiplication facts. When a student is learning their multiplication facts, write the tables vertically on an unlined 3×5″ card, using one card for each set of facts (1 times each number 0-10 or 12 on one card, 2 times each number on the next, etc.). Then punch a hole at the top of each card and hook them together with a split-ring keyring, making a tall, narrow flip-book. Have the student fill in the correct answer to each problem on the lists (using a chart or calculator if needed for accuracy), then refer to his cards whenever he is not sure of an answer when doing a math lesson. I would much rather have my student looking up the correct answer than guessing all day and never being sure. After seeing the correct answer often enough, it will become cemented in his memory, and the reference cards will no longer be required.
Calculator: Do not allow use of a calculator for schoolwork (except for experimenting and understanding how it works) until the student knows the math facts and can do problems easily by hand. The calculator is only a timesaving device for higher math and should not be used until algebra.
Fractions: We sailed through fractions by relating them to pies (circular units) or candy bars (such as segmented Hershey bars). Somehow always referring to food helped keep the students’ attention! Do not worry about drawing segment sizes exactly equal. Saying “pretend these are all the same size” is usually enough to aid students in understanding the concepts.
Draw fraction-pictures easily:
1/3’s — draw a broad “Y” in a circle
1/6’s — draw a broad “Y” in a circle, then extend each line to the opposite side
1/4’s — divide a candy bar in half, then divide each section in half
1/5’s — mark off approximately 1/5 of a candy bar, then divide the remainder into 1/4’s
1/10’s — do 1/5’s (using a candy bar shape), then divide entire shape in half the other direction
1/12’s — divide into 1/4’s, then each into 1/3’s (for a pie); or 1/4’s with vertical lines and 1/3’s with horizontal lines (for a candy bar)
Games: Play games using money, counting, dice, etc. Math can be done even with a game that ordinarily uses no math. Ask your students for ideas on how they could change a game to use math: math with CandyLand — choose a color, draw 10 cards, move the number of spaces that corresponds to how many of that color you drew in your 10 cards.
Math scavenger hunt: Make up a complex series of problems to be solved using numbers gleaned from your own supply of games (see Gee Whiz Quiz). This makes a great group activity, or “rainy day” exercise for when you need a change in routine.
“Warm up” problems:
— Simpler than gee Whiz Quiz, make a “running problem” — choose a number, add 3, multiply by 2, subtract 5…
— Put numbers and arithmetic symbols on dice (using stickers) to make a problem-solving game (1st number, operation symbol, 2nd number, = ). Increase difficulty with ability, such as using more dice for multiple digit numbers.
— Have a “prize box” with a sticker, piece of candy, stick of gum, etc. Student gets a tiny prize for each problem solved or a larger prize for completing a set of problems.
— Make tiny worksheets: several simple problems written on a 2×3 inch piece of paper. Increase the difficulty as student’s needs/abilities change.
— Have the students double or triple cookie recipes for practice in using fractions. Make the cookies to be sure the math was done correctly, and then eat your reward!
— Pour water into various measuring cups and milk jugs to see how much/how many.
— Compute measurements without using the “1-cup” — use the 1/4-cup 4 times, etc.
— Go shopping! Discuss comparison-shopping for differing prices and weights, etc. More advanced students can calculate price-per-ounce to compare brands.
Learn to use an abacus.
Change the numbers on dot-to-dot puzzles to use skip-counting by 2’s, 3’s, 7’s, etc.
Challenge your student to write the numbers or count backwards by 7’s from 1,001 (you could start with 1,000, but it won’t come out even!).
Learn and play various games of solitaire (with actual cards or on a computer) that require adding and other math concepts:
— “Pyramid” for learning which pairs of numbers add up to 13
— “15’s” (also “Cribbage” solitaire teaches adding to 15)
— “Royal Rendezvous” uses counting by 2’s with both odd and even numbers
— “Grandfather’s Clock” puts cards in numerical order around a clock face
FOR THE VISUAL LEARNER–
Seeing math facts: reference charts (wall charts, hand-held, etc.)
FOR THE AUDITORY LEARNER–
Hearing/saying math facts: counting aloud (see below), flashcards
FOR THE TACTILE/KINESTHETIC LEARNER–
— Writing math facts: Holey Cards, CalcuLadder, worksheets
— Moving around or standing instead of sitting at a table or desk
— Apply all of the “letter learning” hints to numbers (see Alternate Methods for Teaching Spelling)
Cut brownies into fractions, or use cups of yogurt or pudding and “draw” the fractions into the surface, then stir it together and do again.
Counting or Sorting:
— Dry beans
— Nails, screws, nuts bolts
— Empty thread spools
— Game pieces (dump them together, sort them out)
— The contents of your child’s bedroom/playroom floor/toybox
Counting aloud: Do “skip counting” together to count repetitions as the student swings, jumps rope, does chin-ups, etc. (may also use “skip counting” for counting small objects)
Hopscotch Math: Draw number blocks on the sidewalk and jump from block to block as you do a simple “running problem” with adding and subtracting, changing directions as needed (forward for adding, backwards for subtracting).
–or use masking tape to put numbers on your stairs or “draw” blocks on your carpeting
–or draw on freezer paper and roll up for re-use (be careful it doesn’t slide underfoot)
–or use the kitchen floor tiles
–be sure to make blocks an appropriate size for the student who will jump back and forth
Many more suggestions are available in our book Taking the Mystery Out of Learning Styles.