Credits
Source
U.S. Department of Education
Contents
Preface
Introduction
What Is Mathematics?
Activities for Your Day
Appendix
References
Acknowledgments
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What Is Mathematics?
The National Council of Teachers of Mathematics (NCTM), the world's
largest organization devoted to improving mathematics education, is developing a set
of mathematics concepts, or standards, that are important for teaching and
learning mathematics. There are two categories of standards:
thinking math standards
and content math standards. The thinking standards focus on the nature of
mathematical reasoning, while the content standards are specific math topics. Each of the
activities in this booklet touches one or more content areas and may touch all four
thinking math areas.
The four thinking math
standards are problem solving, communication,
reasoning, and
connections. The content math
standards are estimation, number sense,
geometry and spatial sense, measurement, statistics and probability, fractions and decimals,
and patterns and
relationships. We have described them and then provided
general strategies for how you as a parent can create your own activities that build skills
in each of these areas.
Problem solving is key in being able to do all other aspects of mathematics.
Through problem solving, children learn that there are many different ways to
solve a problem and that more than one answer is possible. It involves the ability
to explore, think through an issue, and reason logically to solve routine as
well as nonroutine problems. In addition to helping with mathematical thinking,
this activity builds language and social skills such as working together.
What parents can do:
 Children are naturally curious about everyday problems. Invite your children
to figure out solutions to everyday situations. You can do this by talking about
the problem, asking your children for ways to solve it, and then asking how
they came up with those solutions.
 Encourage your children to suggest problems and ask questions, too. Your
children will learn how to figure things out and will learn that many problems
can be solved several different ways.
Communication means talking with your children and listening to them. It means
finding ways to express ideas with words, diagrams, pictures, and symbols. When
children talk, either with you or with their friends, it helps them think about
what they are doing and makes their own thoughts clearer. As a bonus, talking
with children improves their vocabulary and helps develop literacy and early
reading skills as well.
What parents can do:
 Talk with your children and listen to what they have to say.
 Reading children's books that rhyme, repeat, or have numbers in
them (available at your local library) is a great way to communicate
using mathematics.
 All communication doesn't have to be in words. You can represent math
in ways other than talking. Your children can make diagrams or draw pictures
to solve problems or represent numbers. They can use concrete objects
like pieces of paper or even fingers to represent numbers.
Reasoning is used to think through a question and come up with a useful answer.
It is a major part of problem solving.
What parents can do:
 To promote reasoning, ask your children questions and give them time
to think about the answer. By simply asking questions and listening to
answers, you are helping your children learn to reason.
 Ask your children to figure out why something is the way it is and then
check out their ideas. Let them think for themselves, rather than try to figure
out what answer you want to hear.
Connections: Mathematics is not isolated skills and procedures. Mathematics is everywhere and most of
what we see is a combination of different concepts. A lot of mathematics relates
to other subjects like science, art, and music. Most importantly, math relates
to things we do in the real world every day. Connections make mathematics easier
for children to understand because they allow children to apply common rules
to many different things.
What parents can do:
 Ask children to think about and solve problems that arise in your everyday
activities. For example, ask children to help you put the groceries away. They
will practice sorting—the cereal boxes and the soup cans—and experiment with
relative size and shape and how the big boxes take up more room than the smaller
ones.
 Look for mathematics in your everyday life and don't worry about what
the particular aspect of mathematics might be. Something as simple as pouring
water into different sized cups and thinking about which cup will hold more is a
lowkey activity that actually involves estimation, measurement, and spatial sense.
Patterns and relationships: Patterns
are things that repeat; relationships are things that are connected by some
kind of reason. They are important because they help us understand the underlying
structure of things; they help us feel confident and capable of knowing what
will come next, even when we can't see it yet. Patterns and relationships are
found in music, art, and clothing, as well as in other aspects of math such
as counting and geometry. Understanding patterns and relationships means understanding
rhythm and repetition as well as ordering from shortest to longest, smallest
to largest, sorting, and categorizing.
What parents can do:
 Help your children find patterns in designs and pictures, as well as
in movement and in recurring events such as the days of the week or the
seasons of the year.
 For a handson activity try stringing wooden blocks or pasta necklaces into
a simple redblueredblue pattern. As children get older they can reproduce
and create more complex patterns.
Number sense and numeration: Number sense is much more than merely counting,
it involves the ability to think and work with numbers easily and to understand
their uses and relationships. Number sense is about understanding the different
uses for numbers (describe quantities and relationships, informational tools).
Number sense is the ability to count accurately and competently, to be able
to continue counting—or count on—from a specific number as well as to count backwards,
to see relationships between numbers, and to be able to take a specific number
apart and put it back together again. It is about counting, adding, and subtracting.
Counting and becoming familiar with numbers will help your children understand
all other aspects of math.
What parents can do:
 Count anything and everything! Count real things to help children use
their own experience with objects to better understand numbers. Therefore, one
of the best math activities you can do with your children is to have them
count real objects.
 To help children learn to count accurately and efficiently, up and down:
 Point out that counting lets them know how many things there are in a group.
 Point to the object as you recite each number name.
 Use fingers to count. Put
up a finger one at a time as you count it: fingers are tools you always have
with you.
 Help your children count without skipping numbers or counting something
twice.
 To help children learn that numbers are used to describe quantities and relationships,
encourage them to:
 Sort objects looking for similarities in either color, shape,
or size.
 Sort objects looking for differences, like which box is bigger.
 Talk to your children about what numbers are used for, such as keeping
score in a game, or finding an apartment or street address.
Geometry and spatial sense: Geometry is the area of mathematics that involves
shape, size, space, position, direction, and movement, and describes and classifies
the physical world in which we live. Young children can learn about angles, shapes,
and solids by looking at the physical world. Spatial sense gives children an awareness
of themselves in relation to the people and objects around them.
What parents can do:
 You can help your children learn geometry by helping them learn to
identify different angles, shapes, and threedimensional figures. Ask them to
identify and describe different shapes, to draw them in the air with their finger, to
trace over them with their fingers, and to draw them on paper.
 Children learn geometry best through handson experiences. Things they
can touch and manipulate are particularly helpful, like blocks, boxes or
containers, shape sorters, and puzzles. Even cutting the sandwiches they eat into
different shapes and letting them fit them together or rearrange them helps
children learn about geometry.
 Geometry and spatial sense help children with directions and finding their
way around. Let them climb in and out of boxes, on or around furniture, going
under, over, around, through, into, on top of, and out of different things to
experience themselves in space.
 As children get older, they play games to find "hidden" triangles, squares,
or rectangles that are turned in different ways or have odd shapes. Hidden
shapes are ones that do not have flat bases, but are turned in different directions.
Measurement: Measurement
is finding the length, height, and weight of an object using units like inches,
feet, and pounds. Time is measured using hours, seconds, and minutes. Measurement
is an important way for young children to look for relationships in the real
world. By practicing measurement your child will learn how big or little things
are and how to figure that out.
What parents can do:
 Standard measurements like inches, feet, and yards are only one way to measure.
Let children pick their own unit for measurement "Raymond is five cereal
boxes tall."
 Many daily activities involve measurement: cooking, gardening,
grocery shopping, sewing, and woodworking are only a few examples. Keep
your child involved in these chores by talking with them about what you are
doing, and by asking them to help you when possible.
 Young children won't understand the concept of time. However,
 They can learn
that some activities take longer than others. Compare one activity with another
to figure out what takes more time. Start by asking simple questions like "Who
can stand on one foot longer?"
 Set end of time limits. "You can only play for 5 more minutes, then we
have to go catch the bus." At first your children won't know what the minutes
mean, but gradually the children will understand the idea of time passing.
 You can relate units of time to counting by using a watch to time
events and counting the ticks on the second hand of the watch by saying,
"1 second, 2 seconds, 3 seconds" without timing the event. This
uses counting to help children develop a sense of the passing of time.
 Start time talk with ideas like "after lunch" or "after dinner" that
provide solid milestones for children. It is not until children are older that
they understand more abstract notions like yesterday, today, and tomorrow.
Fractions: Fractions represent parts of a whole. A very young child will see
something cut into three pieces and will believe that there is more after cutting it than before it was cut. This is typical and should not cause alarm in parents. It is one example
of how children and adults think differently!
To understand fractions, children need to think about:
 what the whole unit is,
 how many pieces are in the unit, and
 if the pieces are the same size.
What parents can do:
 Many sharing activities help children understand fractions by dividing
food, chores, or treats into equal portions. Cutting up pizzas or sharing a pan
of brownies are good ways to get children thinking about fractions.
Estimation: To estimate is to make an educated guess as to the amount or size
of something. To estimate accurately, numbers and size have to have meaning.
Very young children will not be able to estimate accurately, because they are still
learning these concepts. They first need to understand concepts like more, less, bigger,
and smaller. When children use estimation, they learn to make appropriate predictions,
to obtain reasonable results, and they learn math vocabulary such as "about,"
"more than," and "less than."
It is important for children to learn:
 how to use estimation,
 when the technique is appropriate, and
 when the solution is reasonable.
What parents can do:
 Regularly use words such as "about," "near," "approximately," "in
between," "around," "more than," and "fewer than."
 To practice estimation, use any daily activity like eating or going to the
store. Ask your child to make an estimate of how much, how long, or how
many. When you find the actual answer, compare it with the estimate you
originally made. This will help your child learn to make reasonable guesses.
 Estimation activities may sound complicated, but they don't have to be.
Just take a guess about something—like which one of his friends is the
tallest—and then check it out for accuracy.
 To help older children learn estimation, write down the estimate and then
the actual count. If you repeat the problem or give a similar problem,
children will eventually estimate closer to the real count. It isn't important to get
the "right" answer, but to see how close children can come. Help them
practice the technique to improve their estimation skills.
Statistics and probability: Using graphs and charts, people organize and
interpret information and see relationships. Graphing is another way to show and
see information mathematically. Charts, including calendars, can be used to
organize everyone's weekly activities. Even older children in elementary school may find
it hard to keep track of calendars, but, when adults use them with children,
calendars can be helpful tools to learning and understanding how we organize information.
Statistics, like batting averages in baseball, tell stories about our world. We
know which player is having the best season and which batter is most likely to hit a
home run. Probability tells the likelihood of something occurring.
What parents can do:
 Practically everything you do is "chartable." For example, you can take
the stickers from bananas, apples, or pears and place them in columns on a
piece of paper. At the end of the week you can count them up to see how many
of each type of fruit you ate. Graphs help some children reach a
greater understanding of numbers because they can see quantities displayed on
paper. This may help them understand math more than looking at numbers on paper.
 Use color forms or stickers to record any regular daily activity. Put a
color form next to the phone each time it rings, or have people put one next to
the front door to record the number of times someone enters.
Back to the Table of Contents
Credits
Early Childhood: Where Learning Begins June 1999
By Carol Sue Fromboluti and Natalie Rinck
Edited by Diane Magarity
Illustrations by Barbara Leonard Gibson
U.S. Department of Education
Office of Educational Research and Improvement
National Institute on Early Childhood Development and Education
[Introduction]
[Activities for Your Day (part 1 of 4)]
