You are now holding everything you need to
change your students' understanding of math forever.
TM9301
Get Your FREE Set
of Activity Sheets!
As our thank you for attending this TouchMath training, we have provided
you with a FREE set of downloadable TouchMath Activity Sheets.
Just go to www.touchmath.com/TTR
to confirm your attendance and
get your Activity Sheets now!
Use registration code: TM1021
Your FREE thank-you set includes 20 fun, engaging, and
reproducible Activity Sheets to get you started NOW! The skills
and topics cover the requisite Touching/Counting Patterns, plus
beginning TouchMath addition. `
© 2012 Innovative Learning Concepts Inc, 5445 Mark Dabling Blvd., Colorado Springs, CO 80918
1-800-888-9191 • www.touchmath.com
Get Your FREE Set
of Activity Sheets!
As our thank you for attending this TouchMath training, we have provided
you with a FREE set of downloadable TouchMath Activity Sheets.
Just go to www.touchmath.com/TTR
to confirm your attendance and
get your Activity Sheets now!
Use registration code: TM1021
Your FREE thank-you set includes 20 fun, engaging, and
reproducible Activity Sheets to get you started NOW! The skills
and topics cover the requisite Touching/Counting Patterns, plus
beginning TouchMath addition. `
© 2012 Innovative Learning Concepts Inc, 5445 Mark Dabling Blvd., Colorado Springs, CO 80918
1-800-888-9191 • www.touchmath.com
Print, cut, and distribute to training attendees.
Introducing TouchMath
Dear Colleague,
Welcome to the world of TouchMath! You are about to participate in our interactive TouchMath Teacher Training
Seminar that will guide you step-by-step through TouchMath computation and methodology. At each level, you
will have the opportunity to try the skill yourself. Your active involvement is essential to your success.
As you progress through the seminar and the following activity pages, you will discover why TouchMath has been
so popular with educators for over three decades. Our multisensory approach combines auditory, visual and
tactile/kinesthetic elements that enable students of all learning styles to be successful. TouchMath bridges the gap
between concrete experiences and abstract concepts, reinforces number values, eliminates guessing, dramatically
reduces student errors, and aids in memorization.
You will hear university educators explain why multisensory math is the best way to help all students learn math,
regardless of ability, background, learning style or language proficiency. TouchMath becomes a child’s internalized
“dictionary for the math facts.”
With TouchMath at your fingertips, you will overcome the most difficult teaching challenges with greater
confidence and speed.
This manual helps you practice and quickly master TouchMath counting, addition, subtraction, multiplication,
and division. It serves as a handy refresher and reference for later use. After you follow along with the video
workshop and complete the activities, you will be ready to teach your students this intuitive learning method.
If you have colleagues who would be interested in learning about TouchMath, it’s easy to organize your own
seminar. Just call us toll free at 1-800-888-9191 to request materials. We’ll send you a copy of the Teacher Training
DVD, a TouchMath Teacher Training Manual, and a TouchMath catalog for each attendee. When you arrange a
workshop for five or more teachers, you will receive a complimentary Student Number Card Set. After we receive
a copy of your workshop registration, we’ll also send each seminar participant a free 11” x 17” Memory Cue Poster.
We invite you to visit www.touchmath.com to sign up for our E-Flash which will keep you posted on new
developments, math teaching tips and exclusive sale items.
Please let me know if we can be of further assistance or answer any of your questions. Thank you for being a part of
the ever-growing TouchMath family.
Best regards,
Janet Bullock
Founder/CEO
TouchMath Teacher Training Manual © 2012
www.touchmath.com • 1-800-888-9191
1
TouchMath Touching/Counting Patterns
TouchMath TouchPoint Placement
1. Each TouchMath numeral has a corresponding number of TouchPoints™ placed upon the numeral. This
TouchPoint placement has been carefully researched. It is important to use the same pattern consistently.
Single TouchPoints are touched and counted once, while double TouchPoints are touched and counted twice.
2. Teach your students the correct patterns by having them count aloud following the Touching/Counting
Patterns shown below:
Zero has no TouchPoints and no value. Never touch and count
the zero. The zero is also used as a placeholder in place value.
This skill is presented in the TouchMath Pre-K, Kindergarten, First Grade, Second Grade and Upper Grades materials.
Free sample worksheets available online.
TouchMath TouchPoint Practice
2
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TouchMath Teacher Training Manual © 2012
TouchMath Addition
Beginning Addition Concept
1. For example A, count a group of 3 ladybugs: 1, 2, 3; then count a group of 5 ladybugs: 1, 2, 3, 4, 5.
2. For example B, combine the groups to make a set of 8 ladybugs: 1, 2, 3, 4, 5, 6, 7, 8.
3. For example C, the ladybugs are placed on the TouchPoints of the numerals. Count the ladybug
TouchPoints to get the answer to 3 + 5 = 8.*
4. You may use anything: bugs, buttons, checkers, etc. as TouchPoints on the TouchNumerals to show
students TouchPoints represent the same quantity with either TouchPoints or objects.
Example A
Example B
Example C
1
2
3
5
4
6
8
7
* Students frequently have difficulty making the transition from the concrete (ladybugs) to the
abstract (3 + 5). To help them make the transition, place the ladybugs in the correct Touching/
Counting Patterns on the numerals. Later, we replace the ladybugs with TouchPoints.
This skill is presented in the TouchMath Pre-K, Kindergarten, First Grade and Second Grade materials.
Free sample worksheets available online.
TouchMath Kids
"TouchMath makes me do math better than my sister.
It’s easier than her way so she does it with me."
Spencer, Second Grade
"Now I can add and subtract fast. It’s fun. I’m excited!"
Amanda, Third Grade
Hooper Bay School Children,
Alaska
TouchMath Teacher Training Manual © 2012
www.touchmath.com • 1-800-888-9191
3
TouchMath Addition
CONTINUED
Beginning Addition Practice
Example A
1. Teach the Beginning Addition Statement: “I
touch and count all the TouchPoints on the
numbers.” Touch the TouchPoints with a pencil
point and count aloud in the correct order.
Example B
2. For example A, begin counting with the top
number in the column, 5: “1, 2, 3, 4, 5.”
3. Continue counting on the 4: “6, 7, 8, 9.”
4. Record the answer: 9.
5. Reinforce the facts by repeating the problem and
the answer aloud.*
6. For a longer column of numbers, Example B,
repeat the first four steps and continue counting
on all of the numbers. Then write the answer.
* This step engages auditory learning and is key in helping students memorize number facts. It is very
effective for auditory learners.
This skill is presented in the TouchMath Pre-K, Kindergarten, First Grade, Second Grade and Upper Grades materials.
Free sample worksheets available online.
Transitioning from Concrete to
Symbolic Learning
Eminent learning theorists Jerome Bruner and
Jean Piaget concluded that there are three major
learning stages in early childhood development:
concrete, pictorial and symbolic. Children must
be in a state of readiness to absorb material on
each of these levels.
TouchMath is designed to help students
transition from concrete to symbolic learning.
Young students first learn to count using
familiar objects like apples, pencils, balloons,
etc. Then we place pictures of these objects on
the numerals. The objects are later replaced by
TouchPoints. Eventually, most students progress
to a symbolic understanding and leave the
TouchPoints behind.
TouchMath
combines the
concrete, pictorial,
and symbolic.
the numeral
that symbolizes
an amount
a piece of paper
with three dots
drawn on it
SYMBOLIC
Use of symbols,
such as letters
and numerals
PICTORIAL
Use of pictures
three dots cut
out of paper
CONCRETE
Use of hands-on
For research information, visit www.touchmath.com.
4
www.touchmath.com • 1-800-888-9191
TouchMath Teacher Training Manual © 2012
TouchMath Addition
CONTINUED
Addition With Counting On Practice
1. Teach the Addition Counting On Statement: “I
touch the greater(est) number, say its name, and
continue counting on the TouchPoints of the
other number(s).”
Example A
Example B
2. For example A, touch the greater number. Say its
name, “8.”
3. Continue counting on the TouchPoints of the 4:
“9, 10, 11, 12.”
4. Record the answer: 12.
5. Reinforce the addition facts by repeating the
problem and answer aloud.
6. For long columns of numbers (Example B), cross
out the greatest number as you say its name, and
continue counting from the top downward. Then
write the answer.*
* This step prevents students from counting a number twice.
This skill is presented in the TouchMath First Grade, Second Grade and Upper Grades materials.
Free sample worksheets available online.
Letters from Children
TouchMath Teacher Training Manual © 2012
www.touchmath.com • 1-800-888-9191
5
TouchMath Addition
CONTINUED
Addition Without Regrouping Practice
1. Teach the Arrow Statement. “I start on the side
with the arrow. The arrow is in the ones column
on the right side.”
Example A
Example B
2. For example A, say the greater number in the
ones column: “6,” and continue counting on the
TouchPoints of the 2: “7, 8.”
3. Record the answer: 8.
4. Repeat step 2 in the tens column: “4”, and
continue counting on the TouchPoints of the 3:
“5, 6, 7.”
5. Record the answer: 7.
6. Repeat the problem and answer aloud.*
7. For example B, start on the side with the arrow,
the ones (O) column. Then move to the tens (T)
column, and then the hundreds (H) column,
recording your answer for each column.
* This step reinforces the ability to read and recognize large numbers.
This skill is presented in the TouchMath First Grade, Second Grade and Upper Grades materials.
Free sample worksheets available online.
At-Risk Students Find Success
Dr. Poonam Dev first learned about TouchMath
while studying for her master's degree in 1991.
Later, with research partner Beverly Doyle,
she conducted a study of at-risk children in
kindergarten who scored below average in basic
mathematics. These children then received
TouchMath instruction for 25 to 55 minutes
every day through the first grade. After retesting
the following year, the at-risk students no longer
needed special help in math.
"TouchMath is a useful teaching tool. It has been
developed by former teachers, thus giving it a
lot of credibility. Providing kids with hands-on
learning opportunities is always helpful. It's a
huge help to have multisensory tools."
Dr. Poonam Dev
New York
For the complete story and research, visit www.touchmath.com.
6
www.touchmath.com • 1-800-888-9191
TouchMath Teacher Training Manual © 2012
TouchMath Addition
CONTINUED
Addition With Regrouping Practice
1. Teach the Addition Regrouping Statement: “I
must regroup if my answer is greater than 9.”
Example A
Example B
2. For example A, begin in the ones column below
the arrow. Say the name of the greater number
“8,” and continue counting on the 7: “9, 10, 11, 12,
13, 14, 15.”
3. Use the box to record the number of tens
regrouped to the tens column. Record the
number of tens, 1, in the box first. Then record
the number of ones, 5.*
4. Add the tens column starting at the top. You may
also start with the greatest number, cross it out, and
continue counting from the top: “1, 2, 3, 4, 5, 6.”
5. Record the answer: 6.
6. For long columns, Example B, repeat steps 1–5.
* This step is important to reduce number reversals. If students write the 5 before writing the regrouped 1 they
are writing the number 51 instead of 15.
This skill is presented in the TouchMath Second Grade and Upper Grades materials.
Free sample worksheets available online.
Above Grade Level:
An Administrator’s Dream Comes True
“My kindergarteners are above grade level in math. They are almost at
second grade level (average test score - first grade, ninth month). My first
graders are at about a third grade level (average test score - third grade, fifth
month). My second and third graders are currently doing fourth-grade math.
“I see TouchMath as a basic foundation. It’s like building a house; you start
from the very bottom and build up. With TouchMath, there are a lot of
hands-on activities with TouchPoints. The program is self-explanatory, and
children are able to learn at their own pace without constant direction.
“TouchMath helps us build a bridge between concrete and abstract thinking.
Children start out with TouchPoints, and eventually they understand
abstract concepts. You can see them thinking about the problems. They
don’t use their fingers anymore. They solve problems internally. It’s powerful
to see how they take something concrete and make it abstract. It becomes a
natural part of learning.”
Trinh Trinh
Founder & Principal
Monticello Academy
California
For the complete story, visit www.touchmath.com.
TouchMath Teacher Training Manual © 2012
www.touchmath.com • 1-800-888-9191
7
TouchMath Subtraction
Backward Counting Practice
Students will need to count backward from 18 and
every number below 18. Practice counting backward
from any number and stopping at any number. For
example, when counting backward from 6, stop at 5,
4, 3, 2, 1, or 0.
When teaching backward counting from the
numbers 6 to 18, add only one number in each
lesson and practice until students are proficient with
counting backward from that number.
Suggested activities:
1. For practice in backward counting, one activity
you can do is to say, “I’m thinking of the number
13. Count backward from 13 to 6.” Begin by using a
number line and progress to using no visual cues.
2. Physical activities such as walking backward,
bouncing a ball, tossing a beanbag, etc., while
counting backward may help reinforce the skill.
3. As children are leaving the classroom for lunch or
recess, begin with a number such as 15 and have
each child say a number, counting backward as
he or she exits. After they reach zero, assign a
new beginning number.
Note: In subtraction, you never have to count
backward from any number higher than 18. Look
at the examples. You can subtract any number
from 9; so in the problem 49 – 29, subtract 9 from 9
and get 0. 4 – 2 = 2. However, when the problem is
changed to 48 – 29, regrouping, or borrowing, must
occur. The 4 tens become 3, 8 becomes 18, and 9
is subtracted from 18, which is the largest number
from which we ever count backward for subtraction.
Example A
Example B
This skill is presented in the TouchMath Kindergarten, First Grade and Upper Grades materials.
Free sample worksheets available online.
8
www.touchmath.com • 1-800-888-9191
TouchMath Teacher Training Manual © 2012
TouchMath Subtraction
CONTINUED
Beginning Subtraction Practice
1. Teach the Beginning Subtraction Statement: “I
touch the first number, say its name, and count
backward on the TouchPoints of the other number.”
Example A
Example B
2. For example A, touch the top number and say its
name: “7.”
3. Count backward on the TouchPoints of the 5: “6,
5, 4, 3, 2.”
4. The answer is the last number spoken: “2.”
5. Record the answer: 2.
6. Reinforce the subtraction facts by repeating the
problem and the answer aloud.*
7. For example B, follow steps 1 through 6
counting backward from 14 while touching the
TouchPoints on the 6.
* This step engages auditory learning and is key in helping students begin to memorize number facts.
This skill is presented in the TouchMath Kindergarten, First Grade, Second Grade and Upper Grades materials.
Free sample worksheets available online.
A Visionary Plan for Los Angeles
Unified School District
Special education administrators in LAUSD had a clear
vision of how to close the gap in math proficiency between
general and special education students. They were looking
for a program that offered comprehensive teacher training,
research-based strategy, proven classroom track record and
age-appropriate materials.
They equipped 435 elementary schools with TouchMath
materials, trained 2,000 teachers and implemented a
district-wide intervention plan and Extended School Year
Program. Results from posttesting showed significant student
improvement across all grade levels.
Los Angeles
California
“TouchMath empowered our students not only to maintain
what they were able to do but also grow and show significant
progress,” said Meredith Adams, specialist in elementary
instruction. “It heartens me to no end that what we’ve chosen
to do for our students has had that kind of impact in such a
short period.”
TouchMath Teacher Training Manual © 2012
www.touchmath.com • 1-800-888-9191
9
TouchMath Subtraction
CONTINUED
Subtraction Without Regrouping Practice
Example A
1. Teach double-digit subtraction without
regrouping by starting with the Arrow Statement:
“I start on the side with the arrow. The arrow is in
the ones column on the right side.”
Example B
2. For example A, touch the top number, say its
name: “7.”
3. Count backward on the TouchPoints of the 4: “6,
5, 4, 3.”
4. The answer is the last number spoken: “3.”
5. Record the answer: 3.
6. Repeat the process in the tens column.
7. Introduce a three-digit problem (Example B) by
repeating the steps above, moving from the ones
(O) column to the tens (T) column, then to the
hundreds (H) column. Record the answer for
each column.
This skill is presented in the TouchMath First Grade, Second Grade and Upper Grades materials.
Free sample worksheets available online.
University of California Los Angeles
Los Angeles, California
e University
Athens Stat
a • June 2004
Athens, Alabam
Research Base
A Foundation
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for the TouchM
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Dr. Beth McCullo
Live
ivve O
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San
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B
Bernadino,
ernadino, Californ
ern
California
The Eff
ffec
ectiveness of the
TouchMath
ouchMa Curriculum to Teach
Addition
ddition and Subtraction to
Ele
ementa Aged Students
Elementary
Identifi
entifi
fied with Autism
Thee Effectiveness of the
Th
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F
Fourth
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Educa
E
du tion Students
TouchMath Intervention
n
vs. Traditional Intervention
Is There a Difference?
Effects of a Multisensory
Approach on Grade One
Mathematics Achievement
Dean Dulgarian, BA, MA, JD
Nora
ora D
D.. Green
Gree
Joanne M. Bedard
David Berry,
ry,, PhD
PhD
Bowling Gree
n State Univ
ersity
University of
Colorado
The TouchM
ath
it’s Effects on Program and
the Perform
ance
of First Grad
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Lyn Strand,
College of Rochester
a
Nazareth
N
University of Georgia
Rochester, NY
R
Roc
Special Education Department
Needn’t Stick:
L
Labels
k” First Graders Rescued
“At-Ris
“A
with Appropriate Intervention
w
Multisensory Mathematics for
or
Children with Disabilities
Kristin S. Scott
MA
reprinted from Exceptionality, 4(2), 97-111
Athens State
Universit
Athens, Alabam
a • February 2005 y
A Quantitative
and Qualitativ
e
Study of a High-P
erforming
Elementary Sch
ool in
Mathematics
C. Dev, Nazareth College of Rochester
Po
Poonam
Beverly A. Doyle, Creighton University
Be
District; Pittsford, New York
Barbara Valente, Pittsford Central School
B
Dr, Robert Michael
Dr. Beth McCullo Jarrett
ch Vinson
For research information, visit www.touchmath.com.
10
www.touchmath.com • 1-800-888-9191
TouchMath Teacher Training Manual © 2012
TouchMath Subtraction
CONTINUED
Subtraction With Regrouping Practice
1. Teach subtraction with regrouping using the
regrouping bar. Write the new number of tens on
the bar after regrouping.
Example A
Example B
2. Teach the Subtraction Regrouping Statement:
“If I cannot count all of the TouchPoints, I must
regroup.”
3. For example A, count backward in the ones
column from 3: “2, 1, 0.” Students will discover
they cannot count all the TouchPoints on the 6.
4. Regroup, or borrow, one ten from the tens
column. Cross out the top number in the tens
column, 8, and write the regrouped number, 7,
on the bar.
5. Write the regrouped ten in front of the 3 in the
ones column, making it as large as the 3. Then
count backward from the regrouped number, 13:
“12, 11, 10, 9, 8, 7.”
6. Record the answer: 7.
7. Subtract the tens column: “7, 6, 5, 4.”
8. Record the answer: 4.
9. Work Example B using the same steps as above.
This skill is presented in the TouchMath Second Grade and Upper Grades materials.
Free sample worksheets available online.
Pediatric Neurologist Agrees
with TouchMath's Sequential
Presentation of Concepts
“Treatment and educational programs produce
the best outcomes when they teach skills in a series
of simple, sequential steps; engage the child's
attention in structured activities; build on a child's
interests; and reinforce behavior.”
Dr. Brian Grabert
Pediatric Neurologist
Colorado
TouchMath Teacher Training Manual © 2012
www.touchmath.com • 1-800-888-9191
11
TouchMath Multiplication
Skip Counting Practice
Example A
Skip (or sequence) counting is a critical skill for
multiplication, division and higher mathematical
development. Students will need auditory stimulation,
visual patterning cues and tactile reinforcement to help
master this skill. Mastery of skip counting will lead to
an understanding of fractions and build a framework
for basic algebra.
Suggested activities:
1. Teach one sequence at a time. Start with the 2s
sequence: 2, 4, 6, ... to 20. Teach each sequence
for the 2s, 3s, ... through 9s.
2. In Example A, add the 5s in each row. Then say
the numbers in the boxes to skip count by 5.
3. In Example B, skip count by 7, shading each
square containing a number in the
7s sequence. Then draw a path through
the maze.
Example B
This skill is presented in the TouchMath Second Grade and Upper Grades materials.
Free sample worksheets available online.
12
www.touchmath.com • 1-800-888-9191
TouchMath Teacher Training Manual © 2012
TouchMath Multiplication
CONTINUED
Beginning Multiplication Practice
1. Teach the Multiplication Statement: “I skip count
by one number while touching the TouchPoints
on the other number.”
Example A
Example B
2. For example A, skip count by 2 while touching
the TouchPoints on the 6: “2, 4, 6, 8, 10, 12.”
3. Record the answer: 12.
4. Reinforce facts by repeating the problem and
answer aloud.*
5. In Example B, repeat the multiplication process
counting by 4 on the TouchPoints of the 5.
6. Multiplication problems without the TouchPoints
allow students to respond to a multiplication
problem in different ways. Students may
remember the fact and not use the TouchMath
strategy, or they may count by the number of
their choice on the other number. Often students
will learn to “touch” the points visually in order
to “figure out” a product.
* This step engages auditory learning and is key in helping students memorize number facts.
This skill is presented in the TouchMath Second Grade and Upper Grades materials.
Free sample worksheets available online.
TouchMath Worldwide
“Using TouchMath TouchPoints is far more achievable than
using manipulatives.”
Merell Liddle, Australia
“The children are all excited to be able to do math like
everyone else.”
Doreen Karni, Israel
“I brought TouchMath to this school. Many of the parents
have been asking about it because they are seeing the
improvement at home. TouchMath integrates visual with
tactile learning and makes it easier for students to learn
(math). It stays with them and that is the key.”
Elizabeth Mitchell, Canada
“When I saw your program, it was as though your
developers could read the way my mind works!”
Terrie Brown, Taiwan
“I have used TouchMath materials for the last eight years in
Warsaw, Poland, and they’ve been great!”
Kay Lynne Matheson, Poland
For stories and testimonials, visit www.touchmath.com.
TouchMath Teacher Training Manual © 2012
www.touchmath.com • 1-800-888-9191
13
TouchMath Multiplication
CONTINUED
Multiplication Without Regrouping Practice
1. Teaching multiplication without regrouping
by starting with the arrow statement: "I start
on the side with the arrow. The arrow is on the
right side." For example A, skip count by 3 while
touching the TouchPoints on the 2: “3, 6.”
Example A
Example B
2. Record the answer: 6.
3. Skip count by 3 while touching the TouchPoints
on the 3: “3, 6, 9.”
4. Record the answer: 9.
5. In Example B, multiply the ones (O) column and
the tens (T) column. Then move to the hundreds
(H) column.
Note: Repeating more difficult problems and
answers will ensure students learn to read and
recognize large numbers.
This skill is presented in the TouchMath Second Grade and Upper Grades materials.
Free sample worksheets available online.
TouchMath Made It Fun: Reflections
of a TouchMath Student
As a young student, Meghan Roussel hated math.
Today, she is a civil engineer. What transformed this
frustrated child into a confident woman pursuing
one of the most difficult quantitative professions?
She attributes her success to TouchMath.
“Even after years of theoretical and applied
mathematics, I sometimes return to TouchMath
as an old friend. I revert back sometimes in highstress situations when I need to take a deep breath
and get into my comfort zone. I return to sequence
counting and see the dots on numbers. They’re still
in the back of my mind, and they help.
“I remember bright colors and ‘friendly math.‘ I
remember TouchPoints, flashcards, repetition, and
solving problems until I got the hang of it.
“TouchMath gives children a solid basis for math.
It’s easier to understand because it’s visual. They
learn that math is fun. It’s extremely beneficial if
you get that idea clicking.”
For the complete story, visit www.touchmath.com.
14
www.touchmath.com • 1-800-888-9191
Meghan Roussel
Environmental Engineer
Texas
TouchMath Teacher Training Manual © 2012
TouchMath Multiplication
CONTINUED
Multiplication With Regrouping Practice
1. Begin teaching multiplication with regrouping
by teaching the regrouping statement: "I must
regroup if my answer is greater than 9." For
example A, skip count by 8 while touching the
TouchPoints of the 7: “8, 16, 24, 32, 40, 48, 56.”
Example A
Example B
2. Write the 5 tens in the box first. Then write the 6
ones in the ones column.
3. Count by 8 while touching the TouchPoints on
the 6: “8, 16, 24, 32, 40, 48.”
4. Add the tens in the box: 49, 50, 51, 52, 53.
5. Record the answer: 53.
6. In Example B, repeat the process as you multiply
by 5. Then move to the hundreds (H) and
thousands (TH) columns.
Note: When multiplying, the student may select
either the multiplier or multiplicand to skip count by.
However, it is best to begin teaching multiplication
with consistent usage of the multiplier.
This skill is presented in the TouchMath Upper Grades materials.
Free sample worksheets available online.
TouchMath is Based on Sound Research
College educator and author Dr. Beth McCulloch
Vinson has conducted extensive research in the field of
math education and has this to say about TouchMath:
“Effective instruction comes from appropriate portrayal
of the concept, modeling, guided practice, and plenty of
independent practice. TouchMath’s sequential learning
strategy provides a sense of numeration and then
progresses toward more complex skills and concepts.
“From the student’s perspective, one of the benefits of
TouchMath is that activity pages don’t have extraneous
images or symbols.
“When children develop effective skills through the
TouchMath Program, they are able to focus on reallife application.
“TouchMath is the best method available for making
mathematical symbols more understandable. It
bridges the gap between the concrete and pictorial
levels to the symbolic.”
TouchMath Teacher Training Manual © 2012
Dr. Beth McCulloch Vinson
Associate Professor of Education
Alabama
www.touchmath.com • 1-800-888-9191
15
TouchMath Division
Beginning Division Practice
1. Teach the division statement: “I skip count by the
divisor and get as close to the dividend as possible
without going over the dividend.”
Example A
Example B
2. For example A, skip count by 2: “2, 4, 6, 8.”
3. As each number is counted, make a tally mark in
the box above the division problem.
4. Count the tally marks.
5. Record the answer: 4.
6. In Example B, repeat the process as you skip
count by 6.
7. Multiply the answer (quotient) by the divisor
and write that answer below the dividend. Then
subtract to prepare students for long division.
Note: It is possible to teach multiplication and
division simultaneously. Once the students can
multiply by 6, they are able to divide by 6!
This skill is presented in the TouchMath Upper Grades materials.
Free sample worksheets available online.
Meeting Today's Rigorous Math Goals
When Dr. Germaine Taggart was asked about standards, she cited
five areas in which TouchMath helps meet today’s rigorous math
achievement goals:
1. TouchMath addresses the needs of visual, auditory and tactile/
kinesthetic learners.
2. It provides a unique approach to skip or sequence counting ... a plus
because it supplements rote memorization of multiplication facts.
3. TouchMath is another form of representation, an alternative way of
presenting numbers and mathematical operations.
4. A key component of today’s standards is the idea of “number
sense” and learning to play with numbers so concepts make sense;
TouchMath helps accomplish this.
5. TouchMath is a sequential learning process and helps students
reason through the process.
Dr. Germaine Taggert
Chair, Mathematics Department
Fort Hays State University
Kansas
For the complete story, visit www.touchmath.com.
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TouchMath Teacher Training Manual © 2012
TouchMath Division
CONTINUED
Division With Remainders Practice
1. Teach the division with remainders statement:
“I skip count by the divisor and get as close to
the dividend as possible without going over the
dividend. Then I continue counting by one up to
the dividend.”
Example A
Example B
2. For example A, skip count by 3.
3. As each number is counted, make a tally mark in
the box. Come as close to 23 as you can without
going over: “3, 6, 9, 12, 15, 18, 21.”
4. To find the remainder, continue counting forward
by ones. Put dots outside of the box for each
number counted: “22, 23.”
5. Count the tally marks, and record the answer
(quotient): 7. Count the dots. Record the
remainder: 2.
6. In Example B, repeat the division process
dividing by 5.
This skill is presented in the TouchMath Upper Grades materials.
Free sample worksheets available online.
"That's What's Great About TouchMath."
Like many of his peers across the country, Professer David Cihak teaches
TouchMath to his university students. Here's why:
“You can have the greatest strategy in the world, but if it's not teacherfriendly, teachers won't use it. Trying to come up with new and novel
ways to present math that are research-based and effective is very
challenging.
“TouchMath is an alternative approach – a bridge from manipulatives
to regular worksheets, as well as an efficient strategy compared to the
number line. The curriculum on the whole is laid out in a very teacherfriendly way that can be used in the general education classroom.
“It is sequenced in a very bottom-up curriculum style where skills are
building on each other. It mirrors standards very well, so it fits for a
teacher who is addressing both the state standards and alternative
standards.
“TouchMath is effective for helping kids raise test scores. More
importantly, students are learning basic computational skills and even
more advanced word problems and problem solving.”
TouchMath Teacher Training Manual © 2012
David Cihak, Ph.D.
Teaches Applied Behavioral Analysis and
Methods for Severe Multiple Disabilities
University of Tennessee, Knoxville
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17
TouchMath Division
CONTINUED
Long Division Practice
Example A
1. For example A, divide the 4 in the hundreds
column by 3, and record the answer.
2. Multiply 3 by 1, and record the answer below the 4.
3. Subtract 3 from 4, and record the answer.
4. Bring down the 6 in the tens column.
5. Divide 16 by 3, and record the answer.
6. Multiply 3 by 5, and record the answer.
7. Subtract 15 from 16, and record the answer.
8. Bring down the 0 in the ones column.
9. Divide 10 by 3, and record the answer.
10. Multiply 3 by 3, and record the answer.
11. Subtract 9 from 10, and record the answer, which
is the remainder.
This skill is presented in the TouchMath Second Grade and Upper Grades materials.
Free sample worksheets available online.
TouchMath – Prevention & Intervention
“I have a strong belief that all children can learn ... but
not in the same way. I encourage student teachers
to find out how each of their children learn and then
use the tools that work.
“The concept of TouchMath made sense for so many
of my students. They were unable to remember basic
facts, so they counted on their fingers, trying to add
large numbers. With TouchMath, they could use a
proven touching/counting method, and it was so
much easier and more effective. They made fewer
errors and quickly became proficient.
“TouchMath is based on research and on what we
know about how children learn in a variety of ways. It
has also stood the test of time.”
For research information visit www.touchmath.com.
18
www.touchmath.com • 1-800-888-9191
Mary Todd Allen, Ph.D.
Special Education Instructor
North Carolina
TouchMath Teacher Training Manual © 2012
TouchMath Division
CONTINUED
Short Division
1. For example A, divide the 4 in the hundreds
column by 3, and record the answer: 1.
Example A
Example B
2. Mentally subtract 3 from 4, and write the 1 in
front of the 6 in the tens column.
3. Divide 16 by 3. Write the answer: 5.
4. Mentally subtract 15 from 16. Write the 1 in front
of the 0 in the ones column.
5. Divide 10 by 3. Write the answer: 3. Then write
the remainder: 1.
6. For example B, repeat the process dividing by 8.
This skill is presented in the TouchMath Upper Grades materials.
Free sample worksheets available online.
TouchMath Teacher Training Manual © 2012
www.touchmath.com • 1-800-888-9191
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TouchMath Teacher Notes
20
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TouchMath Teacher Training Manual © 2012
TouchMath Teacher Notes
TouchMath Teacher Training Manual © 2012
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21
TouchMath Teacher Notes
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TouchMath Teacher Training Manual © 2012
This document certifies that
on this _______________ day of _______________ in the year _______________,
____________________________________________________________________________________________
has completed professional development lessons, discussions and activity pages on the following topic:
The TouchMath Program for Mathematics Instruction
to include ______ hours.
Instructor
SEE IT. SAY IT. HEAR IT. TOUCH
CH IT
IT. TTEACH IT.
Janet Bullock
Bu
ull
llock
Innovative Learning Concepts Inc.
President,
d
Innovative Learning Concepts Inc. • 6760 Corporate Drive • Colorado Springs, CO 80919-1999 • 800-888-9191 • www.touchmath.com
TouchMath® the Alphabet of Mathematics. Designed
for General Classrooms and Special Education.
Second Edition.
TouchMath materials were first published in 1975.
Innovative Learning Concepts Inc.’s publications
may not be reproduced or disseminated in any way,
or stored in any database or retrieval system, without
written permission of the publisher. However, limited
permission is granted to reproduce only the blackline
activity masters solely for noncommercial educational
use with students in a single classroom or a single
home, and for no other purpose.
TouchMath®, TouchNumerals®, and The Alphabet of
Mathematics® are registered trademarks of Innovative
Learning Concepts Inc., Touch2Learn™, TouchPoint™,
TouchShapes™, TouchStar™, TouchMath Tunes™,
TouchMath Tutor™, StepNumerals™ and Innovative
Learning Concepts™ are trademarks of Innovative
Learning Concepts Inc. of Colorado Springs, CO.
Copyright 2012 by Innovative Learning Concepts Inc.
All rights reserved.
Innovative Learning Concepts Inc.
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