skills are necessary life tools that children must learn.
adults, we use arithmetic daily. We add, subtract, multiply, or divide
when we balance our check-books, calculate tips in restaurants, figure
out how much wallpaper to buy, finance a car, keep score for games,
and so on. A person who can't do arithmetic is handicapped in many situations.
To help children
appreciate the importance of arithmetic, ask them to interview their
families about when they use arithmetic. The question they should ask
is: When do you have to add, subtract, multiply, or divide to find out
something you need to know? Record what children report on a class chart.
(For older children, sort the information into two groups: "at work"
and "at home.") Afterward, discuss how the chart shows that arithmetic
has many useful purposes.
should prepare children for real world math.
Most of the daily situations
that require arithmetic call for more than merely counting. For example,
we need to problem-solve in order to decide on the numbers to use or
which operation to choose.
Involve children in solving problems that relate to classroom routines,
- When taking
attendance, count children present, then ask the class to figure
out how many are absent.
- Ask children,
when lining up, to predict whether everyone will have a partner.
- When collecting
milk money, involve students in making change and figuring out how
much everyone spends on milk.
- Involve older
students in figuring out how much classroom supplies cost, such
as a year's supply of paper.
- For class
parties, have the students figure out how much refreshments will
to compute mentally is an essential skill.
We do many of our
daily arithmetic calculations mentally, such as when we keep track of
what we put in the supermarket cart so we don't go over the $20 we have,
when we divide a check at a restaurant, or when we double a recipe that
calls for 3/4 of a cup of broth. Usually we don't reach for paper and
pencil, but figure in our heads.
Ask children to do mental math on a regular basis. Call it "hands-on-the-table"
math and ask children not to reach for paper or pencil, but to reason
in their heads. Try this:
calculate efficiently, it's important to know basic facts.
- For younger
students: Have two children take a handful of beans or tiles and
count how many they have. Ask the class to figure out how many they
have together. To verify, count the objects. Or ask each student to
put two cubes in a jar and then have the class figure the total number
of cubes in the jar. To verify, count the cubes by 2s, 5s, and 10s.
(Not all young children know that you'll get the same result no matter
how you count.)
older students: Scoop
beans into a jar using a coffee scoop and have the students count
how many scoops it takes to fill the jar. Then give pairs of students
a scoop of beans to count, discuss with the class what might be the
average number of beans in a scoop, and then have students calculate
mentally how many beans are in the jar.
have math facts at their fingertips before they leave elementary school,
such as addition and subtraction combinations to 20, multiplication
tables to 12 x 12, and related division facts. Students learn some of
the facts easily, such as adding 1 to any number or doubling numbers.
Still, memorization is necessary to learn all of the facts. Classroom
strategies: While memorization is needed, it should follow, not precede,
understanding. Before they're expected to memorize addition combinations,
young children should have many experiences combining sets of objects
and learning to record addition sentences. And even when memorizing,
children should be encouraged to look for patterns and to reason. A
child who can't recall how much 8 x 4 is, for example, should be encouraged
first to think about something familiar, like 8 x 2 or 4 x 4, and then
use that information to figure out 8 x 4.
need to know when accuracy is essential and when estimates will suffice.
When we balance our checkbooks or make change, accuracy is important.
But in many situations, estimates will do, such as when we double the
amount of broth for a recipe or measure fertilizer for the lawn. Sometimes
estimates are the only answers possible, such as when contractors bid
for jobs, business owners figure margins of profit, or school districts
predict the next year's budget.
While knowing how to calculate accurate answers is important, students
also need experience estimating and learning when estimates are appropriate.
Have students review the list they compiled about when their families
do arithmetic. Then talk about when accurate answers or estimates are
needed. Also, provide opportunities for children to practice estimating.
For example, give prices for several items and have them figure out
the smallest bill they could use a $5, $10, or $20. Or ask students
to figure out about how much milk they drink in a week, a month, or
are basic tools that have their place in the classroom.
Practically everyone today has a calculator. We use them when numbers
are too complicated for us to do in our heads. Using a calculator is
easier than resorting to paper and pencil, and valuable when we want
to be sure we're correct. Calculators should not be viewed as arithmetic
crutches, but as useful tools.
Calculators can help children think and reason numerically. For example,
they're useful for introducing decimals. Third graders can explore equations
like 5 x __= 24 or 3x __= 40 with the help of a calculator, and learn
how decimals work.
are different ways to reason numerically.
Ask adults to double 38 in their heads, and you're sure to hear several
different methods. Some add 30 and 30 and then add on 16. Some double
40 and subtract 4. Some double 35 and add 6. Some think about multiplying,
not adding. There's no one best way.
Give students opportunities to discuss different ways to compute. With
young children, for example, have them think about all the different
ways they can add two numbers. Older students can talk about different
ways to add or multiply two-digit numbers. Have all students who volunteer
explain their reasoning aloud so students can learn from one another.