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TURN HERE
PreK
ELEMENTARY SCHOOL
HIGH SCHOOL
MIDDLE SCHOOL
START
hmhco.com
2 31
Using your math skills to plan your future!
WHY MATH MATTERS
NUMERACY
2
UNEMPLOYMENT RATE (%)
ALL WORKERS 6.1%
You’ve probably had this conversation with yourself a million times, “When I grow up, I want to
be a ___________.” The answer has most likely changed many times over the years, but that
blank space is completely normal, especially considering some of the most popular jobs, like app
developer or social media programmer, didn’t even exist 15 years ago!
Plotting a Future in a Changing World
And things will continue to change— by the time you graduate high school and eventually enter the workforce:
Unemployment/Average Earning Power2
The average annual wage in
the U.S. will increase by 5%1
MEDIAN WEEKLY EARNINGS ($)
ALL WORKERS $827
Jobs will require a greater use
of computer- and technology-
based applications
More entry-level positions
will require a bachelor’s
degree or higher
Manual labor needs will drop
due to increased automation
2.2 1,623Doctoral Degree
2.3 1,714Professional Degree
3.4 1,329Master’s Degree
4.0 1,108Bachelor’s Degree
5.4 777Associate’s Degree
7.0 727Some College, No Degree
7.5 651High School Diploma
11.0 472Less than a High School Diploma
1 SOURCE: TRADINGECONOMICS.COM | U.S. BUREAU OF ECONOMIC ANALYSIS
2 SOURCE: UNITED STATES OF LABOR: BUREAU OF LABOR STATISTICS
DATA MINER PAGE 4
CHEF PAGE 8
PHYSICIAN PAGE 12
SOFTWARE DEVELOPER
PAGE 6
ANIMATOR PAGE 10
INTERIOR DESIGNER
PAGE 14
TABLE OF CONTENTS
8 of 20 6 of 20
85,000
Exciting Developments on the Horizon Most of you log into Facebook®, Twitter®,
and Instagram™ on a daily basis. Have you ever
considered how math—through technology—will
be changing your lives for the better?
Math awareness can play a key role in finding a
rewarding career in a competitive job market. Every
video game you play, website you visit, and app you
download are parts of industries that rely on young
adults to provide a creative and innovative spark—
and who are good with math skills!
Believe it or not, many of the job examples
that follow are based on things you’ve already
learned—or will learn in the next few years. Read on
to learn about how you can make math matter for
you…in the real world!
LinkedIn’s Most Promising Jobs of 2017 3 :
Number of careers in the high-tech industry
Number of careers in the medical field
Number of daily postings for ‘software engineer’
</>
3Source: Shapero, Daniel. LinkedIn Data Reveals the Most Promising Jobs of 2017. LinkedIn Corporation.
4
When shopping online, have you ever noticed that sidebar
with “suggested items” that are very similar to the ones you’ve
already viewed? That doesn’t happen by coincidence; it’s all part
of the job responsibilities of a market research data miner.
Market research companies hire analysts to review information
gathered from technology companies about people’s
shopping habits.
MATH COMES TO LIFE!Data miners use elements of algebra to discover patterns and
sales trends. They use statistics and data from surveys to build a
unique customer profile and provide solutions, like you will learn
to do in your high school math class, to chart and interpret data.
Companies use this data to get a better understanding of what
buyers are looking for and make those products available. So
both the company selling items and the person looking to buy
can get matched up more easily.
Careers in Math: Market Research Data Miner
6
Just about every part of your world is linked to technology in
some way. You use it to post on social media, buy a cool new set
of kicks, browse the latest news, and eventually to submit college
applications. And at the center of this technological revolution is
one all-important position: the software developer.
Software and app development are some of the most in-demand
positions for students looking to find a career with staying power.
Some of the biggest names in the history of the tech industry,
from Bill Gates to Mark Zuckerberg, are software developers.
MATH COMES TO LIFE!Software developers work in a virtual world, using various
programs to write detailed instruction that’s coded into the
program to tell the computer exactly what to do.
It’s the same concept that helps bring Minecraft® and other
popular video games to life. Each matrix simulates reality by using
equations and formulas to establish a particular set of rules that
allows the virtual world to take on a life of its own.
Careers in Math: Software Developer
MATRIX: A collection of numbers,
symbols, or expressions,
arranged in rows
and columns.
M =a + b a - b
a - b a + b
8
Believe it or not, good number sense can actually turn a good
cook . . . into a top chef! Does it really matter if you use an exact
measurement or not?
A ‘pinch’ of sugar or a ‘dash’ of salt could make or break your
culinary masterpiece. That’s why kitchen management depends
on several mathematical practices: measurement, percentage,
proportion, estimation, and time (not to be confused with the
leafy herb “thyme”) all factor into making the perfect dish.
MATH COMES TO LIFE!A chef uses the same math principles that you and your fellow
students first encountered in elementary school. Think about
it… in first grade you probably learned how to use a delicious-
sounding “pie” chart to section things off into halves, fourths, and
quarters. This is where fractions, speak louder than words.
In third grade, you most likely learned about standard units of
liquid measurement: teaspoons, cups, liters, gallons, etc. Eventually
your knowledge of fractions will grow to the point where you
can convert different-sized measurement units with ease—like
understanding that four quarts equals one gallon.
Careers in Math: Chef
Unit Conversions
3 teaspoons = 1 tablespoon
4 cups = 1 quart
4 quarts = 1 gallon
10
Ever wonder who dreams up the amazing visual effects you see
in movies, on TV, and in video games? Multimedia artists and
animators use 3D modeling techniques rooted in geometry to
create these effects.
MATH COMES TO LIFE!Multimedia artists and animators use geometry skills, particularly
their knowledge of shapes and patterns, as a base to make real-world
scenarios come to life on screen. In reality, it’s not much different
from what you will learn in your high school geometry class.
Animators work inside a two- or three-dimensional coordinate
plane. They use software that translates a shape’s position in space
and time into a set of numbers. Every animation, from people
walking to planets exploding, is a result of changing those numbers.
Multimedia animation is popular field that’s sure to keep growing.
Employment is projected to grow 6% from 2014 to 2024 due to
increased demand for animation effects in video games, movies,
and television.
Careers in Math: Animator
Play by the rules of proportion! Each character’s head, arms, legs, and body, all have their own
related rules for how they move in virtual space and time.
Animators need to pay close attention to proportion: not only
should body parts be proportional
to each other, but the entire
person in the foreground
should be proportional
to the background.
12
How does math come into play as doctors make their rounds
visiting patients? One important way is figuring out how much
medicine to give a patient.
If the weight of a patient is only known in pounds, doctors need
to convert that measurement to kilograms, then find the amount
of milligrams for the prescription. For patient safety, it is always
important to deliver medicine in correct and accurate amounts.
MATH COMES TO LIFE!Physicians use comparative reasoning to analyze data in order
to diagnose whether or not a patient is at a high, medium, or
lowrisk compared to an overall sample population. In real life
that could mean deciding whether heart or breathing rates are
within normal range.
Physicians must also have the ability to understand how
“mathematical theory” works in the real world. For instance, viewing
patient charts is like analyzing graphs and representations.
By spotting patterns of association in data they can figure out what’s
making someone ill.
Careers in Math: Physician
14
For interior designers, it’s not just about choosing fabrics or
different patterns: every minute of their work day is about
making sure that everything is to scale and in proportion.
MATH COMES TO LIFE!Before they even start working in an actual space, interior
designers use architectural blueprints to come up with an overall
plan for the space. They use basic math principles like adding,
subtracting, multiplying, and dividing in order to calculate
quantities like cost (for budget) and length (for materials).
For example, the total area of the floor plan must be measured
accurately so that the correct amount of carpet, tile, or laminate
can be purchased. Geometric representations of the finished
product are also created so designers—and clients—can get a
true sense of scale for the final design.
Once an interior designer is ready to add the finishing touches, a
mix of middle school algebra and geometry helps bring the room
to life. The Pythagorean Theorem is used to determine unknown
side lengths in right triangles, which really comes in handy when
hanging artwork or positioning furniture for maximum effect.
Careers in Math: Interior Designer
Total area
Pythagorean Theorem
length x width
a2 + b2 = c2
GOAL
Connect with us:
hmhco.com • 800.225.5425
Facebook® is a registered trademark of Facebook, Inc. Twitter® is a registered trademark of Twitter, Inc. Instagram and the Camera logos are trademarks of Instagram, LLC in the United States and elsewhere. Minecraft® is a registered trademark of Mojang Synergies AB Corporation. HMH® and Houghton Mifflin Harcourt® are registered trademarks of
Houghton Mifflin Harcourt. © Houghton Mifflin Harcourt. All rights reserved. 04/17 WF28444a
hmhco.com/numeracy-counts
NUMERACY
Teaching Companion
TURN HERE
PreK
ELEMENTARY SCHOOL
HIGH SCHOOL
MIDDLE SCHOOL
START
hmhco.com
2 31
Using your math skills to plan your future!
WHY MATH MATTERS
NUMERACY
2
Mathematical awareness is an important skill that is encountered in virtually every aspect of life.
The career outlook that your students will face upon entering the workforce may look completely
different from what it is now. Careers such as social media manager, cloud computing services, and
app developer barely existed ten years ago but are rapidly outpacing manual labor needs.
The Why Math Matters eBook is designed to provide your students with an overview of current
career trends that involve math and number sense, and hopefully encourage students who may be
struggling with math’s relevance to real life!
This Teaching Companion to the Student eBook includes expanded Math Comes to Life! sections
for more specifics on how math is used the in the different careers mentioned, and the grades
where the mathematical concepts are introduced. There’s also performance task activities to help
spark conversation about careers.
A Note to the Teacher
PHYSICIAN PAGE 7
ANIMATOR PAGE 6
INTERIOR DESIGNER
PAGE 8
TABLE OF CONTENTS
DATA MINER PAGE 3 SOFTWARE
DEVELOPER PAGE 4
</>
CHEF PAGE 5
At the most basic level, data mining involves the use of statistical data from surveys to build a
unique customer profile. Graphs, charts, tables, and other algorithms—although hidden from
consumer view—paint a complete picture that establishes patterns and correlations that enable
more effective marketing.
In addition to using statistics to predict behavior and future trends, a data miner uses elements
of algebra to discover hidden or overlooked patterns as well as sales trends, then uses that
information to provide solutions that will ultimately generate increased sales.
The mathematical processes used by a data miner are quite similar to what students encounter
in a high school math class to chart and interpret data. When data is analyzed from different
perspectives it can be summarized into useful information, providing consumers with additional
options that are predicted based on their existing preferences.
MATH COMES TO LIFE!
Data Miner
RELATED MATH INTRODUCED IN High School
SKILLS REQUIRED • Statistics and Probability
• Functions
• Algebra
4
Software developers work extensively in a virtual world, using various programs to create a
matrix algorithm, which is a detailed instruction that’s coded into the program to basically tell the
computer exactly what to do.
It’s the same concept that helps bring Minecraft® and other popular video games to life. Each
matrix simulates reality by using equations and formulas to establish a particular set of rules that
allows the virtual world to take on a life of its own.
Software development uses several principles introduced in eighth grade. Programmers use
mathematical functions such as graph plotting, binary coding, and algebraic expressions to assign
exactly one input to each output command.
MATH COMES TO LIFE!
Software Developer
RELATED MATH INTRODUCED IN • Grade 6
• Grade 7
• Grade 8
SKILLS REQUIRED • Compute fluently with multi-digit
decimals and integers
• Use variables to represent quantities
• Understand function as a rule
Elementary students begin to learn numerical and fractional concepts on a daily basis. First graders
already know how to partition whole shapes into halves, fourths, and quarters—perfect for slicing
and dicing a fruit medley.
In third grade, students can accurately measure and estimate liquid volumes using standard units of
measurement: teaspoons, cups, liters, gallons, etc. By fifth grade, students use fractions to convert
different-sized measurement units within a given measurement system, and use those conversions
in solving real-world problems.
MATH COMES TO LIFE!
Chef
RELATED MATH INTRODUCED IN • Grade 1
• Grade 3
• Grade 5
SKILLS REQUIRED • Partition whole shapes into halves, fourths, and
quarters
• Measure and estimate liquid volumes of objects
• Convert among different-sized measurement unitswithin a given measurement system and solverelated word problems
6
Multimedia artists and animators utilize the complete number system to find points on a two-
dimensional coordinate plane and interpret coordinate values of points in the context of that situation.
Beyond that, animators compose a variety of two- and three-dimensional figures to create a
composite shape. Ratios and proportions play a very important role here: for an animator, it is
critical that the characters in the foreground are in equal proportion with those in the background.
Multimedia animation is an established field that’s becoming ever more popular. Employment in this
sector is projected to grow 6% from 2014 to 2024. This growth will be due to increased demand for
animation effects in video games, movies, and television.
MATH COMES TO LIFE!
Animator
RELATED MATH INTRODUCED IN • Grades 1–2
• Grades 5–7
• Grades 9–12
SKILLS REQUIRED • Compose new shapes from composite shapes
• Interpret points on the coordinate plane
• Apply proportional reasoning in the context of asituation
Comparative reasoning, a skill generally learned in sixth grade, allows physicians to analyze data in
order to diagnose whether or not a patient is at a high, medium, or low risk compared to an overall
sample population. For example, identifying whether heart or breathing rates are within normal
range is just one of many tasks they routinely perform.
Much of their work requires intense research, and—for safety reasons—it’s often necessary to practice
their techniques via 3D modeling before moving on to an actual patient. Using geometric principles,
doctors can observe two-dimensional results that result from operating on three-dimensional figures.
Physicians must also have the ability to understand how mathematical theory works in the real
world. When viewing patient charts, patterns of association can be seen in data by analyzing graphs
and representations to help support a particular diagnosis.
MATH COMES TO LIFE!
Physician
RELATED MATH INTRODUCED IN • Grade 6
• Grade 7
• Grade 8
SKILLS REQUIRED • Use rate reasoning to solve real-world problems
• Describe two-dimensional plane sections that result fromslicing three-dimensional figures
• Construct a graph to understand patterns of association;use the equation of a model, or interpret a two-way table
8
Before ever setting foot into his or her design space an interior designer typically works from
architectural blueprints to come up with an overall plan of action. This draws directly from math
principles that you first encountered in sixth grade: Fluently adding, subtracting, multiplying, and dividing
multi-digit decimals in order to calculate quantities like cost (for budget) and length (for materials).
The total area of the floor plan must be measured accurately so that the correct amount of carpet, tile,
or laminate can be purchased. Computer modeling then fills in the gaps by providing scale drawings of
the overall floor plan, including geometric representations that offer true context and scale.
Once an interior designer is ready to add the finishing touches, a mix of middle school algebra and
geometry helps bring the room to life. The Pythagorean Theorem is used to determine unknown side
lengths in right triangles, which really comes in handy when hanging artwork or positioning furniture
for maximum effect.
MATH COMES TO LIFE!
Interior Designer
RELATED MATH INTRODUCED IN • Grade 6
• Grade 7
• Grade 8
SKILLS REQUIRED • Fluently add, subtract, multiply, and divide
multi-digit decimals
• Apply the Pythagorean Theorem to determineunknown side lengths in right triangles
Now that students have had a chance to see how math connects to so many fun and exciting careers, it’s time for them to put their skills to the test. We’ve included a short performance task that’s based on the information in they just reviewed in the Student eBook. Students will be playing the role of a Community Educator designing a career program guide for students like themselves.
PLAN A CAREER EDUCATION PROGRAMAppropriate for Grade 6
Students will: • Use proportional relationships to solve multistep percent problems
• Present numerical data in a graph and summarize the data using patterns,deviations, and measures of center
Directions 1. Pair up into small groups and review the information provided.
2. Design career programs for other teens by completing the table and creating agraph to interpret the data.
3. Explain the reasoning behind the work and reflect on which careers have themost potential.
4. Evaluate classmate(s) on how well they understood and completed the task.
Performance Activities
10
You are developing a program to educate teens about careers in the 21st century. Some increasingly popular jobs are given below. However, you must fill out the table and create a graph to interpret the data. Your manager thinks the percent increase should be used to decide which careers to educate teens about. What do you think?
Plan a Career Education Program Activity
Occupation Jobs in 2017
Jobs in 2018
Numeric Increase
Percent Increase
Data Miner 1,000 1,700 1,700-1000 = 700
700/1000 = 0.7 = 70%
Software Developer 3,000 4,650 1,650 55%
Chef 10,000 12,500 2,500 25%
Animator 300 327 27 9%
POPULAR 21 ST-CENTURY JOBS
Your Job: Community Educator
Your Task: Design career programs for teens
EXPLORE Use the information in the table to create a graph. For our example we use a bar graph.
Percent Increase80%
70%
60%
50%
40%
30%
20%
10%
0%Software
DeveloperChef AnimatorData Miner
Numeric Increase3000
2500
2000
1500
1000
500
0%Software
DeveloperChef AnimatorData Miner
ANALYZE What is more important, percent increase or numeric increase? Explain using the data.
EXPLAIN
REFLECT Which careers would your program focus on most?
WHY
EVALUATERate how well you and your partner understood and completed each part of the performance task.
Ranking ScaleNone [0] Limited [1] Partial [2] Thorough [3]
A: Accurately completed the table for projected occupations.
Me_____ Partner _____
B: Accurately completed the bar graphs to compare percent and numeric increases.
Me_____ Partner _____
C: Answered each question thoughtfully.
Me_____ Partner _____
EXTENDIf the number of jobs increases at a constant rate, in what year will the number of Chefs reach 13,300?
EXPLAIN
12
GOAL
BROWSE OUR LIBRARY OF MATH@WORK VIDEOS AND LESSON PLANS AT
hmhco.com/numeracycounts
Want to learn more?
Connect with us:
hmhco.com • 800.225.5425
Minecraft® is a registered trademark of Mojang Synergies AB Corporation. HMH® and Houghton Mifflin Harcourt® are registered trademarks of Houghton Mifflin Harcourt. © Houghton Mifflin Harcourt. All rights reserved. 04/17 WF28444b
hmhco.com/numeracy-counts
NUMERACY