Teaching Arithmetic



Modes of Learning in Arithmetic

Manipulative Mode (Physical)

    Here’s where they use need to use objects in everyday life to perform arithmetic functions.

    Use objects such as spoons, marbles, beads, M&Ms, skiddles, pizzas, plastic bears or frogs, etc. to teach numbers and counting.

    Ask questions such as “How many apples do we need for our family?"

    Your child must become proficient in this mode before moving on to the concrete mode.

Concrete Mode (Mental)

    Children are ready for this when they freely give up the use of manipulatives because they find it quicker to do arithmetic without them.

    Most children use both the Manipulative mode and the Concrete Mode up to about age 12.

    In the Concrete Mode, they can work with images instead of real objects. The images can be in his/her head or on worksheets.

    When they don’t understand something in the concrete mode, take them back to the manipulative mode.

    Play games that use math (Monopoly, Dominos, Lotto games, Board games), talk about math when shopping (counting produce or cans, counting money), in the kitchen while cooking (reading numbers, measurements), in the garden (measuring rows, counting), driving (mileage, speed limits, street numbers, license plates), watching TV (read channel numbers, program listings), art projects (lines, patterns, shapes, geometric figures); baseball or coin collections (sorting, comparing, classifying)

Abstract Mode

    Children are generally able to think in the abstract mode at between ages 8 - 12.

    In the Abstract Mode, children can perform math without using real objects or images in their head.

    They use symbols such as 5 instead of having five items or seeing a picture of five items.

    Begin drilling your addition, subtraction, multiplication, & division facts in this stage.
    Practice is essential.

    At this stage, they can be introduced to simple Algebra.

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Fun Activities for Math Learning

Do some math activities instead of workbook pages all the time. You DO NOT have to finish the workbook! Here are some ideas:

Symbol fun: Choose some symbols that your child can easily draw such as a smiley face, a bow. Let face be equal to 5 and bow equal.

List some numbers and have your child draw the number using the symbols.

More or Less: First, decide who the winner will be the person with more or the person with less. Remove face cards from a deck of cards. Divide the deck between two players. Place the cards face down in front of each player. Each player turns over a card and compares. Is mine more or less? How many more? How many less?

Money Match. Need die, 10 of each coin, 6 quarters. Use only 2 different coins for 5-6 yr olds (pennies, nickels). The object of game is to be the first player to earn a set amount (10 or 20 cents for K). First player rolls die and gets the number of pennies shown on the die. Players take turns rolling die to collect additional coins. As each player accumulates 5 pennies or more, the 5 pennies are traded for a nickel, nickels for dimes, nickels and dimes for quarters, etc. The first player to reach the set amount wins.

In the News. Have your child look for numbers in the newspaper. Cut them out and glue them in order onto a large piece of paper. Have child say the number and practice counting.

Counting Book. Cut out pictures from magazines and paste into a booklet. page one will have one thing on it. page 2 will have 2 things, etc. Use for a counting book. My Number Book

Sorting & classifying. Sort and classify buttons, marbles, stamps, rocks, screws, sea shells, baseball cards, anything else that you can count. Sort according to color, size, texture, number of holes, etc.

Riding activity: Create a chart that lists the numbers from 1-50. Write down each number as family members locate that number on a car, sign, building, etc. Words too.

Patterning. Make a necklace out of colored macaroni. Alternate colors to make a pattern. Frogs

Plastic Pattern Blocks (Tangrams & Patterns)

Remember: The important thing is not so much that every child should be taught as that every child should be given the desire to learn. (John Lubbock)

Make the preschool and kindergarten years a time when you and your child bond, work together, play together, and explore God’s world together. Introduce formal learning only as they are ready and limit the time spent to short sessions that you both will enjoy. If you do this, you will nurture their desire to learn and put them years ahead of their peers.

Suggested Order of Introducing Math Concepts

Please note that this is just a suggestion! Kids are different in how they learn math. Some like you to give it to them all at once and textbooks work great. Others like it a step at a time in a logical order. This is one suggestion for those who like it a step at a time:

1. Use manipulatives to teach counting, adding, subtracting, etc. (this is ongoing)
2. Learn to count to 10
3. Recognize shapes - squares, etc.
4. Work on and sort by size (bigger, smaller, tallest, etc.), color, shape
5. Learn to count to 100
5. Count by 10's to 100 (practice until done)
6. Start simple adding - use manipulatives until child can write
7. Work on simple fractions - 1/2, 1/3, 1/4
7. Continue drilling counting by 2s, 3s, etc. Suggested order: 10s, 5s, 2s, 3s, 4s, 6s, 7s, 8s, 9s
8. Start simple subtracting - (by now your child should be able to write so you can use manipulatives and worksheets)
9. Take some time to teach measurements, weights, volumes, reading thermometer, counting money, and telling time.
The Checklist10. Once simple adding and subtracting has been mastered, work on carrying and borrowing.
11. At the same time, introduce simple multiplication (if your child has learned to count by 2's etc. this will be easy.
12. Then add simple division.
13. Now your child should be ready for harder adding, subtracting, multiplication, and division. 14. It's time to get a textbook! After this has all been accomplished, your child will be able to go into Saxon, Math U See or other Math, grade 6 or 7. You can skip all the rest.

Keep track of what you do in arithmetic with The Checklist.

See Math on the Internet and Math Reading for More Resources.

See Sample Curriculum Plan for a sample schedule.

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