Math All Around!
California After School Resource Center
Administered for the California Department of Education (C.D.E.)
Welcome to the Math All Around! training. This training was developed with funding
from the California Department of Education After School Division. It is designed for
school day and after school staff, and other educators who provide instruction to
build students’ mathematics skills. It will take about 30 minutes to complete, so let's
get started!
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Objectives
1. Obtain a basic overview of the various
uses of mathematics throughout history.
2. Become familiar with recommended
practices to support students with math.
3. Access high-quality math resources from
the California After School Resource
Center library.
By the end of this training, you will be able to:
1. Obtain a basic overview of the various uses of mathematics throughout
history.
2. Become familiar with recommended practices to support students with
math in after school programs.
3. Access high-quality mathematics resources from the California After School
Resource Center.
It is important to point out that this is a basic training intended to provide you with an
overview and resources to support students with math in after school. More in-depth
training addressing specific math content knowledge and teaching strategies may
be useful to you after you complete this module. We highly recommend that you
take the California After School Resource Center Making Sense of Math online
training to obtain information about balanced math instruction and to understand
how skills are organized for the teaching and learning of mathematics.
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Math is Everywhere!
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Patterns
Time
Sports
Locations
Buildings
Arts
Weather and
Climate
Look around you and you will surely find math in everyday things. From the
sequences and patterns in nature, to how we tell time and count the seasons, and
how we entertain ourselves through sports and the arts, math is everywhere.
Ancient civilizations infused geometric shapes into buildings, and we continue to do
so in modern architecture. We also use addresses to pin-point exact locations, and
we dial unique phone number sequences to communicate with one another. It is
through math that we often make sense of the physical world around us. Can you
imagine a world without math?
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How Did Math Originate?
What may have prompted humans to invent
things like numbers, shapes, angles, graphs,
symbols, measurements, and rules for how it
all works?
Before we delve into how to support students with foundational math skills, take a
moment to consider your thoughts or knowledge about how math began. What
prompted humans to invent things like numbers, shapes, angles, graphs,
measurements, and explanations for how it all works?
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The Origins of Math
Like most inventions, math originated due to necessity and natural human ingenuity.
Math involves natural patterns and sequences that our ancestors first noticed.
Daylight, night, animals, shapes in landscapes—these patterns prompted people to
create the early number and geometric foundations for math. For instance, the
Egyptians knew that the annual flooding of the Nile River signaled a change in
seasons. Because their civilization was dependent on water from the Nile, they
began recording the patterns of the seasons. They wrote number symbols on stone
and on papyrus paper. They based their system on tens. Indian mathematicians are
said to have invented both decimals and one of the first symbols to denote zero.
The Mayan civilization used a number system composed of three symbols: a shell
shape, representing zero; a dot representing one; and a bar representing five. And
who can forget the Greeks’ contributions to mathematics, like the Pythagorean
theorem and the Platonic solids? These are widely used in geometry.
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Amazing Math Feats
by Ancient Civilizations
How was math involved in the building of the
pyramids at Giza, the Great Wall of China,
and the Mayan calendar?
Take a moment to contemplate the accomplishments of early mathematicians. How
was math involved in the building of the pyramids at Giza, the Great Wall of China,
and the Mayan calendar? In order to build the famous Giza pyramids, the Egyptians
developed an in-depth understanding of shapes and angles. Similarly, the Chinese
employed elaborate calculations to measure distance, angles of elevation, and
materials needed to build the Great Wall of China. The Mayans created a calendar
that was based on the annual solar cycle rather than the lunar cycle. It helps to
predict eclipses, solstices, and other astronomical events with close precision. This
calendar became the basis for other calendars used by Central and North American
natives.
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Modern Uses
Today, math is used in a variety of forms throughout the world. From simple
machines to complex computers, from blueprints to fancy buildings, math is
connected with everyday life. If you become ill, your doctor may prescribe medicine
based on the precise dosage your body needs to recover. Recipes often involve
measuring the ingredients and having a basic understanding of fractions. Drivers
pay attention to the speedometer to stay within the speed limit. Math is involved in
all kinds of daily transactions, like sales and gambling; usually, math informs those
decisions and lets you know when the odds are against you. If you go abroad, you
may recognize the octagonal shape of a stop sign even if you can’t read the
message in a foreign language. You may need to be familiar with foreign currency
and different time zones. These are only a few examples. How do we help students
succeed in math, so they can make sound decisions, like becoming financially
responsible or choosing careers in math?
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Building Your Own Math Awareness
Through a Team Approach
• Be aware of your own math uses.
• Share ideas with colleagues.
• Look for ways to involve students.
To find math all around, be aware of your own math uses every day. Exchange
ideas with colleagues and look for ways to connect students to real-world math
applications. The educators on this slide are planning an expensive field trip. They
have estimated the costs and brainstormed fun fundraising ideas, some of which
will enlist students’ help. The talent show and art auction are estimated to raise
hefty amounts, and they are sure to draw community support. Most parents and
community members enjoy watching the students perform, or buying studentproduced artwork for a good cause. If this scenario were real, the field trip could be
a memorable experience for students, and one that staff helped to make possible
through teamwork.
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Case Scenario: Helping Students
Understand Why Math Matters
Based on what you have learned so far, what
information would you share with students
who may ask these questions:
• Who invented math?
• Why do I have to learn math?
• How am I ever going to use math in life?
Do any of these questions seem familiar to you:
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Why do I have to learn math?
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How am I ever going to use math in life?
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Who invented math?
If you work with students, you have probably heard these types of questions. That is
because students are naturally curious about the purpose for learning anything.
They want to make it meaningful, or connect it to the real world, which makes total
sense. After all, who would want to learn anything that takes so much practice
without having a purpose? It is important to provide thoughtful responses to these
questions. Before continuing to the next slide, take a moment to jot down some
possible responses based on what you have learned so far in this training. There is
no right or wrong answer. Just remember that students are impressionable, and
your reaction and answer may shape how they feel about math in general. Even if
math is not your or their favorite subject, it is important to encourage them to
consider how useful and relevant it is to everyone.
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Sample Response to Helping Students
Understand Why Math Matters
• Math is used in many ways by
professionals, such as doctors, business
people, and scientists.
• Without numbers, it would be difficult to tell
time, someone’s age, or which
supermarket aisle to visit.
• Shapes allow us to design homes,
buildings, transportation, etc.
Obviously, the answers to questions about why math matters vary. You may say
that math is used in many ways by professionals, such as doctors, business people,
and scientists. You may even provide some specific examples of how these
professionals apply math in their work. You may also say that without numbers, it
would be hard to tell time, someone’s age, or which supermarket aisle to visit. Give
examples of how ingrained numbers are in our society—from sports statistics to
coordinates on a map, and so on. You may even point out how geometric shapes
are used in the designs of homes, buildings, vehicles, and so forth. These are just a
few examples, but you can certainly draw from others presented in this training, or
invite students to think about their own examples so that they can begin connecting
math to the world around them. Sharing some of the mathematical contributions
made by ancient civilizations is also a great way to engage diverse students in the
learning of math. When they realize some of the math feats accomplished by their
ancestors, they realize that they can also be great mathematicians.
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Recommended Math Practices
1.
2.
3.
4.
Make math learning meaningful.
Make math learning collaborative.
Encourage problem solving.
Engage in writing and discussion based
on math.
For the rest of this training, we will explore the following research-based practices to
support the learning of math in after school programs:
1. Make math learning meaningful.
2. Make math learning collaborative.
3. Encourage problem solving.
4. Engage in writing and discussion based on math.
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Making Math Meaningful
1. Provide a brief history of math and
explain how math is used in everyday life.
2. Expose students to careers in math
through career awareness and guest
speakers.
3. Build financial literacy.
4. Provide math activities based on
students’ diverse cultures and interests
(sports, cooking, dance, etc.).
Let’s begin by looking at four ways to make math meaningful:
1. Provide a brief history of math and explain how math is used in everyday
life. The first part of this training is intended to help you do this.
2. Expose students to careers in math through career awareness and guest
speakers.
3. Build financial literacy.
4. Provide math activities based on students’ diverse cultures and interests
(sports, cooking, dance, etc.).
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Resources for Making Math Meaningful
Stash That Cash: Budgeting,
Saving, and Investing for
Teens #7933
The Story of Math #9438
Careers in Math: From
Architects to Astronauts #9089
There are a variety of resources available through the California After School
Resource Center library to help you make math meaningful in your after school
program. At the end of this training, you will be able to access these and other
resources, available for a four-week loan with free delivery anywhere in California.
Through The Story of Math DVD set, you can build your own understanding of the
history of math, learn more about the contributions of famous mathematicians over
time, and explore interesting math developments and concepts, such as why prime
numbers are fascinating.
If you need support helping students explore a future in math, you may use Careers
in Math: From Architects to Astronauts. In the video portion, teen hosts guide
viewers through an overview of career options that involve mathematics, from
cosmology to environmental engineering and computer game programming.
Interviews with professionals reveal how they use critical thinking, reasoning skills,
and other math-based skills on the job. This resource also contains activities for
students.
The Stash That Cash: Budgeting, Saving, and Investing for Teens resource offers a
video and activities to help teens learn money-management basics, including
budgeting, saving, investing, using credit responsibly, planning for retirement, and
more.
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Home Connections
You can also build home connections by encouraging parents to help students build
a better awareness of how math is used in everyday life. In the picture on the left of
the slide, a parent is encouraging his teens to consider ways to save money during
their shopping trip. This skill takes parental modeling, practice, and support. The
idea here is not to encourage consumerism, but to help families practice how to
make sound decisions about spending habits.
In the picture on the right of the slide, a son is helping his mother find the items on
the grocery list. This is a golden opportunity not only to build awareness of money
as a means for survival, but also to expand on specific math skills related to
fractions and measurements. Notice the grocery list looks like a recipe. It is possible
that the items on the shelves are not packaged to match the measurements on the
recipe. The two can work together to convert the measurements or estimate to
ensure they get the right amount of ingredients for the recipe. Measurement
conversion can be a challenging skill for young students, but opportunities like this
can help to make math concrete and useful.
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Make Math Learning Collaborative
1. Employ youth development practices,
build social skills, and set the behavior
expectations.
2. Prepare logistically and cognitively.
3. Build math centers.
4. Provide daily math games.
To make math learning collaborative means to enable students to work in groups.
To do this effectively, you may employ youth development practices, such as setting
goals, making good decisions, and building relationships with peers. Students will
need to practice social skills, such as using clear communication and self-control.
The educator sets the behavior expectations, models the desired behavior, and
applies appropriate consequences when students misbehave. At the end of this
training, you will be able to access materials to support students with behavior
management and group work, in addition to math.
For now, keep in mind that for collaborative learning to be effective, the educator
must prepare logistically and cognitively. Logistical preparation includes gathering
the required materials, handouts, and supplies needed for students to work in
groups successfully. Cognitive preparation refers to the act of being able to explain
a concept, provide examples, and support students as they carry out the activities.
By definition, collaborative learning involves interaction, discussion, movement, and
discovery. The educator must be prepared for organized chaos, or at least be open
to a certain level of noise and movement. It is still important to be in control, and to
observe the learning that is taking place.
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Math Centers
• Designated areas
• Based on students’
interests and skills
• Flexible
• Minimal
preparation
In an after school program, a math center can be a designated space where
students can choose from a variety of activities based on their interests and skill
levels. Small groups of students can gather in that area to use the computer to play
interactive math games, use a math board game, or simply work on skills. The
possibilities are endless, and the logistical and cognitive preparation is minimal, so
long as the students know the expectations and how to work together or
independently. On this slide, the students are at the Current Events Corner. Their
activity is to find examples of how math is used in different sections of the
newspaper, such as in the business, sports, or weather pages. They will read
stories of their choosing, and report on their findings to the whole class when they
debrief from today’s center activities. Here the logistical preparation includes
gathering current newspapers. The cognitive preparation may include skimming or
browsing the newspapers to help students with their presentations as needed.
Neither the educator nor the students need to be expert mathematicians to use this
center, which is a great way to help students practice reading and math skills, and
to connect math to the real world.
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Exploring Math in the Environment
• Find shapes.
• Make math art.
• Play musical math.
Another way to make math meaningful for students is to allow opportunities for them
to explore math in the environment. The image on this slide shows an educator
inviting students to find as many shapes as possible on the playground. Students
can be encouraged to look for shapes at home or in the classroom as an extension
activity. When doing this, it is always a good idea to help students understand the
difference between plane shapes, such as squares and circles, and their solid or
multidimensional counterparts, such as cubes and spheres. Properly identifying
shapes by their names and characteristics or attributes is a skill that will come in
handy as they learn more advanced geometry. To help reinforce this skill, students
can also practice making math art by learning to draw and combine the shapes, or
have a game of musical math, in which they identify the names of figures on the
floor as they dance around them in a circle. This reinforces the language of
geometry, and provides some physical activity for them.
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Tic-Tac-Toe Games
VARIABLE TIC-TAC-TOE
The Tic-Tac-Toe game lends itself to collaborative math practice. Research also
suggests that it helps students to become more strategic thinkers. It allows students
to practice math skills in a fun way, and only requires basic writing supplies and a
calculator for students to self-check their answers if needed. To play, the educator
can either create the problems for the Tic-Tac-Toe grids, or allow the students to
create their own problems. Then students compete to solve the problems with
partners. Whoever gets three Xs or Os in a row first wins. Tic-Tac-Toe can be an
open-ended activity, meaning that students can create their own problems and play
as long as they wish or as time allows once they understand the object of the game.
The level of complexity depends on their own skills and abilities.
In Variable Tic-Tac-Toe, shown on the left of the slide, tweens and teens solve
simple equations using single variables or unknown numbers. Here students are
reviewing and practicing various skills, including addition, subtraction, multiplication,
division, exponents, comparing numbers, and exploring number patterns. In
Regrouping Tic-Tac-Toe, shown on the right side, students as young as eight years
old can practice their regrouping skills using addition and subtraction. The
Regrouping Tic-Tac-Toe game shown on this slide is already solved. The student
who found three answers that involved regrouping in a row won.
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Encourage Problem Solving
1. Use real-world problems.
2. Teach problem-solving strategies (the
four-step plan, work backward, make
pictures, draw conclusions, etc.).
3. Allow students time to think, test their
solutions, and explain their rationale.
Problem solving is very important in mathematics. Unfortunately, it can be difficult to
teach and to understand. Because humans are unique by nature, students may
approach math problems differently and still arrive at the same answer. To practice
problem solving, they need ample opportunities to apply a variety of strategies or
techniques, and time to process how they are doing with the art of problem solving.
Using real-world problems, teaching them concrete methods to tackle them, and
allowing time to think, test their solutions, and explain their rationale are very
important.
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Problem-Solving Methods
1
The Four-Step Plan
Work Backward
Create Pictures/Models
Draw Conclusions
This slide shows four widely used problem-solving strategies:
1. The Four-Step Plan
2. Work Backward
3. Create Pictures
4. Draw Conclusions
You may access the Problem-Solving Method Handout available at the end of this
training for more detailed information about each of these methods.
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Engage in Writing and Discussion
Based on Math
• Provide ample time for students to keep a
math journal.
• Integrate math journal sharing time.
• Invite discussions about math.
Another important practice to bring math to life is to engage in writing and
discussion about math. Students can be encouraged to keep a math journal where
they write their reflections, questions, or observations about math. They can also
relate math to the real world, write or illustrate their own explanations for problem
solving, or wonder about concepts. Sharing their entries with a partner or in groups
is a great way to build a sense of community, and to expose everyone to diverse
ways of approaching mathematics. You may access the Math Journal and
Discussion Tips Handout available at the end of this training for more information on
this practice.
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Case Scenario
Much of the math practice students
encounter in traditional classrooms is
textbook- and workbook-based. What are
some fun ways to make math more
meaningful, collaborative, and enjoyable for
students?
Much of the math practice students encounter in traditional classrooms is textbookand workbook-based. What are some fun ways to make math more meaningful,
collaborative, and enjoyable for students? Take a moment to write down some
responses based on what you have learned in this training before going to the next
slide. Answers will vary.
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Sample Response
• Use math games, centers, and other interactive
activities.
• Teach problem-solving strategies using real-world
problems.
• Encourage students to keep a math journal and
share with their peers.
To help make math more enjoyable for students, you may use math games,
centers, and other interactive activities; teach problem-solving strategies using realworld problems; and encourage students to keep a math journal and share with their
peers.
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Wrap Up
Today you:
• Got a glimpse into the history and
presence of math in everyday life.
• Learned about four recommended
practices to support students with math:
1.
2.
3.
4.
Make math learning meaningful.
Make math learning collaborative.
Encourage problem solving.
Engage in writing and discussion based on
math.
In this training module, you got a glimpse into the history and presence of math in
everyday life, and learned about four recommended practices to support students
with math, which are:
1. Make math learning meaningful.
2. Make math learning collaborative.
3. Encourage problem solving.
4. Engage in writing and discussion based on math.
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Thank You
Congratulations! You have reached the end of the Math All Around training.
You will now have the opportunity to take a quiz to test the knowledge you have
acquired in this training. If you receive a passing score, a completion certificate will
be e-mailed to you at the e-mail address you provided. If you don’t receive a
passing score, you will have the opportunity to take the quiz again at any time.
Following the quiz, you will be asked to complete a brief feedback survey. After you
complete the survey, you will be able to access the accompanying handouts,
sample California After School Resource Center library resources, and additional
information about mathematics. You may start the quiz by selecting the quiz link.
Thank you for your participation!
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