of Learning in Arithmetic
where they use need to use objects in everyday life
to perform arithmetic functions.
objects such as spoons, marbles, beads, M&Ms,
skiddles, pizzas, plastic bears or frogs, etc.
to teach numbers and counting.
questions such as How many apples do we
need for our family?"
child must become proficient in this mode before moving
on to the concrete mode.
are ready for this when they freely give up the use
of manipulatives because they find it quicker to do
arithmetic without them.
children use both the Manipulative mode and the Concrete
Mode up to about age 12.
the Concrete Mode, they can work with images instead
of real objects. The images can be in his/her head or
they dont understand something in the concrete
mode, take them back to the manipulative mode.
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)
are generally able to think in the abstract mode at
between ages 8 - 12.
the Abstract Mode, children can perform math without using
real objects or images in their head.
use symbols such as 5 instead of having five items or
seeing a picture of five items.
drilling your addition, subtraction, multiplication, &
division facts in this stage.
Practice is essential.
this stage, they can be introduced to simple Algebra.
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
fun: Choose some symbols that your child can easily draw
such as a smiley face, a bow. Let face be equal to 5 and
some numbers and have your child draw the number using the
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?
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.
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.
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
& 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.
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.
Make a necklace out of colored macaroni. Alternate colors
to make a pattern. Frogs
Pattern Blocks (Tangrams & Patterns)
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)
the preschool and kindergarten years a time when you
and your child bond, work together, play together, and
explore Gods 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:
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
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.
10. 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
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.
track of what you do in arithmetic with The