Posted by: katlea611 | March 22, 2008

28 Ways to Teach Beginning Math Without Textbooks

28 Ways to Teach Beginning Math Without Textbooks
All you need are ordinary items found in most homes
by Mary Ellen Carlise
Homeschooling Today Magazine – Volume 9 – Issue 1 – All Rights Reserved

Many parents fear math. A friend who recently began homeschooling called me to ask what curriculum I used when my son was a preschooler. When I told her I hadn’t used a formal curriculum until second grade, she was shocked. “How did you know what to do? Where did you start? How did you know if he was working at grade level?” These are the most common questions regarding an early non-textbook style math education. Learning math doesn’t have to come from a book to be successful.

Research shows that children in early grades learn math more effectively when they use physical objects (“hands-on” math) in lessons, but we don’t need research to tell us children love to play and do.

It is easy to put together a sound early elementary curriculum using homemade manipulatives, games, and toys. Your library has a number of books on fun things to do with preschoolers. Many publishers offer free scope and sequence listing objectives for each subject and grade level. Remember, various companies offer various ideas. Scope and sequences will help you know what your child’s peers are learning, and give you ideas on basic principles. Since even the most daring homeschoolers are usually using a formal textbook approach by the third grade, I’ve listed ideas only through the second grade. Depending on the interests of your child, grade level divisions may or may not be observed.


Counting: Count everything. Use pennies, marbles, beads, Legos™, etc. Move things from one pile to another. Master ones, then tens, and fives.

Matching: Match socks while folding laundry, match shoes while cleaning the closet. Play the memory game.

Categorizing/Sorting: Sort coins into denominations, toy cars, M&M’s™, or beads into like colors or sizes, or laundry into piles. Have your child put silverware into proper slots when putting away. Stack plastic bowls one inside the other. He can sort out screws, nuts, bolts, or nails into jars with dad in the workshop.

Sequencing: Arrange items into rows. Say “Long, short, long, short”, Red, blue, yellow, red”, “Apple, orange, apple, orange”, “What comes next?” Create a bead pattern on string, or a Lego™ tower in varying colors and have him copy it.

Number recognition: Point out and name numbers on everyday things. Read counting books and have him name the numbers. Play plenty of simple board games. Play card games that require counting and recognizing numbers concurrently, such as Crazy Eights, Go Fish, Dominoes, etc.

Geometry: Cut out felt shapes in many colors. To make a felt board, cover a heavy piece of cardboard with felt. Match or sequence the shapes. Name shapes of fruits, vegetables, everyday things. Cut out sponge shapes to play with in the tub, or to use to paint pictures on newspaper. Make your own wrapping paper with white butcher paper stamped with different color shapes.

Measurement: Learn basic concepts such as big/little, short/long, near/far, many/few, more/less, full/empty, etc. Use math words in conversation. Teach volume and weight by encouraging time for sand or water play using measuring cups, measuring spoons, graduated cups or bowls, sifters, plastic jugs, and pitchers. Purchase a scale with a variety of containers which can be filled with beans, rice, cotton balls, liquids, etc. Give the student a ruler, yardstick, and tape measure. Tell him to measure things and ask which are taller, longer, wider. Enjoy time in the kitchen with your child allowing him to assist in measuring and pouring ingredients.

Fractions: Cooking is the best way for preschoolers to begin conceptualizing fractions. Say, “This recipe calls for 1/4 cup of raisins and 1/4 cup of nuts. 1/4 and 1/4 equals 1/2.” Let him measure, sift, and pour. Talk about fractions when you cut pizza or cherry pie.

Time: Teach concepts like now/later, yesterday/today/tomorrow, morning/afternoon/evening, and day/night. Tell your child what time it is during the day. “Eight o’clock! My you were a sleepy-head this morning!” “Twelve-thirty, time for lunch.” “It’s four o’clock now. Dinner will be at five o’clock; one hour from now.”

Learn days/weeks/months: Use the calendar to mark special days with stickers. Associate events with months and seasons. Thanksgiving is in the fall. His birthday in May. It snows at Christmastime, in the winter.

Talk about time in unit
s: “We’re leaving in about five minutes. You have ten minutes to play.”

: Create a play box to use only during school time, when you need to work with your other children. Use a large plastic bin with a snap-on cover. Fill it with an assortment of manipulatives: large, colorful beads with string, Duplos™, sturdy puzzles, sorting and stacking toys, paint-with-water books, easy dot-to-dot books, plastic coins, cards with numbers printed on them, flannel pieces, scissors and paper, pencils and crayons, and assorted books about number concepts.


Kindergarten curriculum should be an extension of preschool curriculum. You will need to continue the fun, hands-on activities. If you’ve been excited about the manipulative approach to math, your child’s curiosity will soar. Don’t be anxious for the pencil and paper. Try another year using mostly games and manipulatives. Limit your paperwork to practicing numbers on unlined paper. Trying to form numbers and size them to tiny spaces is tedious work for a five-year-old.

Counting: Continue counting everything. Count small sets of marbles and Legos™, then put both sets together and count them again. Count the big beans, then count the small beans, then count them together. This is early addition. Count big numbers, 100 pennies, 300 beans. Learn to count by twos. Have him count while jumping rope or bouncing on the trampoline. Begin to use his number skills in practical ways. “Please count out twelve forks, twelve knives, and twelve spoons. We are having company for dinner.” “I’ll need twenty copies of this paper. You take them out of the machine and tell me when I have enough.” Count backwards from ten, then twenty.

Story Problems: Now is the time to begin using story problems. Do many simple story problems orally every day. Let him count on his fingers if he desires. This is his way of providing his own manipulatives. Let him ponder the problem a bit. If he seems to be having trouble, ask him if he has any questions.

Time: Make a paper plate clock. Mark the hour hand and all the numerals on the face in red. Mark the minute hand and all the minute lines in blue. Begin by learning the hour, then the half hour. Play “hours or minutes.” You ask, “Does this activity take hours or minutes? Visiting Grandma? Baking bread? Mowing the yard? Setting the table? Brushing your teeth?” Set the hands on the clock and have him tell you the time. Let him set the hands and tell you the time. Explain A.M. and P.M. Ask time questions to cement this concept. “It is four o’clock and everyone in our house is sleeping. Is it A.M. or P.M.?” “It is eight o’clock and we are getting ready for bed. Is it A.M. or P.M.?” You may want to purchase a clock fact stamp. Stamp many clocks on a blank paper and have him draw the hour and minute hands of the time you tell him.

Money: Learn penny, nickel, dime, and quarter. Start by placing piles of pennies in equivalent amounts next to each coin. Count a pile of nickels by fives, dimes by tens. Explain that 100 equals one dollar. Count like-coins until their value is understood, then mix coins and count. Playing store is one of the best ways to teach the value of money.

Calendar: Learn months of the year and days of the week. Have a large calendar with removable dates and months. Each day, say the day, date, month, and year. Learn the seasons. Count the days until certain events.

Geometry: Learn the names of shapes and continue with preschool geometry suggestions.

Measurement: Learn the terms inch and foot. Make an inch and a foot out of pieces of cardboard. Have him measure everything. Play “closer to” by asking, “Is the length of this closer to an inch or a foot?” substituting various things. Have him be a scale. Give him a bag of 500 cotton balls in one hand and a bag of five pounds of flour in the other. Ask which weighs more. Do this with many things. Continue to use your scales. Talk about pounds, ounces, cups, quarts, and gallons.

Games: Continue to play many games involving counting, numbers, and number concepts. Play with building toys to cement concepts such as patterning, sequencing, sorting, comparison, and matching. Start a collection of rocks, stamps, or something he enjoys to encourage a higher form of sorting or classifying.

First and second grade

I am combining first and second grade curriculum because second grade is an extension of first. Second grade is the time when previously taught concepts are more fully understood. Often, third graders move toward pencil and paper tasks in many textbooks.

Counting: Continue to count larger numbers, piles of pennies, beans, paper clips, and popcorn. Count to 500, then to 1000. Count everything by twos, fives, and tens. Play “before or after” with ones, tens and eventually hundreds. “Does twenty-five come before or after thirty-four?” Progress in difficulty. Begin estimating the number in piles of things. Using various sized piles, have him guess which has more and which has less, then count to see. Begin to learn to see things in groups — dominoes and dice games help. Use bundles of ten popsicle sticks banded together for manipulatives. This will help with the concept of place value later on.

Story Problems: Continue to use many oral story problems. Use addition and subtraction in your problems. Begin multiple step story problems. Use money in your story problems. Oral story problems help children to become thinkers and problem solvers. Even when your children are in the upper grades, practice oral story problems.

Writing: Tackle more pencil and paper tasks. If the core of your program has truly been manipulatives and games, you will be amazed at how quickly your children will progress in written problems from the simple to the difficult, and how much fun they think it is. Paperwork should be limited, a supplement to your core curriculum, not the entirety.

Using wide ruled paper, practice writing numbers. First practice ones through hundreds. When this is mastered, move on through the two digit numbers to the hundreds. Begin giving about twenty written one digit addition problems daily, with popsicle sticks to use as manipulatives. When this is understood, you might want to begin teaching addition facts with flashcards. First the ones, then the twos, and so on. Don’t overdo flashcards. Make a game out of learning facts. Time him and race with yesterday’s time. Start with simple subtraction, then subtraction facts. Move to twenty written two digit problems daily. Learn place value. Move to three digit addition if the previous concepts have been understood. Master addition and subtraction facts with great speed before moving on to multiplication facts.

Time: Continue to use the paper plate clock to learn the quarter hours and the five minute increments. Continue to play time games.

Money: Continue to play store, switching roles from checker to cashier. Have him plan a menu and purchase everything from the store. Have him give you the correct change. When he is the checker, have him make change, first for a dollar, then for an entire shopping cart of groceries. For more difficult challenges, have him calculate specials like three or five for a dollar. Use coupons. Use the newspaper food ads for more ideas.

Fractions: Learn 1/2, 1/4, 1/3, using felt shapes. Use a square cut in half, a circle cut in thirds, and a rectangle cut into fourths. Count piles of beans, pennies, marbles, then split them into halves, thirds, and fourths. Have him continue to help you bake.

Measurement: Continue to review inches, feet, and yards. Cut a one yard piece of string and have your child find things that are about a yard long. Use measuring cups: 1 cup, 1/2 cup, 1/4 cup, 1/3 cup. Use measuring spoons. Learn tablespoon and teaspoon. Learn gallon, quart, and pint. Use a thermometer to make candy. Use an outdoor thermometer to record the daily temperature. Use a thermometer to record the temperatures of different things: himself, the refrigerator, warm food, etc. Work on pounds and ounces.

Data Recording: Collect data and record it by learning to use simple graphs, charts, tables, and tallies.

Games: As previously mentioned, games are the most fun and motivating way to practice all the math concepts. Commercial board games, card games, building toys, and oral games all promote new thinking skills and reinforce skills already introduced.

Creating your own early elementary math curriculum isn’t difficult. All the concepts taught in textbooks can be taught with manipulatives and games you buy or make yourself. When you are ready to begin using a textbook, continue to have a math game day once a week to break the monotony of daily textbook use.

Bio: Mary Ellen and her husband, Tony, have five sons. They live and homeschool in Phoenix, Arizona


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