First Grade
Unit 1
Program Overview
TouchMath SE First Grade Unit 1:
Numbers & Operations Level 1
The four units that make up the TouchMath SE First Grade
edition are as follows:
This is unit one of four that make up the TouchMath SE
First Grade 2022 Edition.
• Unit 1: Numbers & Operations Level 1
for continuing to build fluency with counting within 100,
reinforcing the TouchMath approach and the Touching/
Counting Patterns, reviewing and demonstrating
the concepts of addition and subtraction with 5,
incorporating TouchPoints as the primary strategy
in computation, and finding and applying sums and
differences within 9.
This edition is aligned with current, rigorous state
standards and follows current state ESSA plans that
mandate a culture of high expectations for all students
— from those who need remedial support, to students
benefiting from RtI and MTSS interventions, to Special
Education students with IEPs and students with disabilities.
TouchMath incorporates the Concrete–Representational–
Abstract (CRA) approach, allowing all students to access
a range of tools for building the foundational math skills
they must master if they are to succeed in operations and
algebraic thinking, geometry, other critical math domains,
and for career and college readiness.
The TouchMath SE First Grade edition covers grade 1
curriculum standards and can be used as a supplement
alongside other core programs, for example in
mainstreamed classrooms. TouchMath is both research
and evidence-based, and is effective across a range
of grade levels, even high school, because it follows
mathematical learning progressions that build upon critical
math concepts — and provides a scaffolded structure for
mastery of the foundations needed for career and college
readiness and success. TouchMath allows students who
were left behind or who thought they were not good at
math a chance to catch up.
• Unit 2: Numbers & Operations Level 2
for focusing on place value up to and including 20;
adding and subtracting within 13 and then 20 using
TouchPoints and strategies; and backward counting as a
subtraction strategy.
• Unit 3: Numbers & Operations Level 3
for extending place value to 100; continuing to apply
strategies to find solutions for addition and subtraction
equations; and demonstrating proficiency with mixed
operations within activities.
• Unit 4: Measurement, Geometry, and Data
for mastering telling time; identifying and using money
values; measuring length; interpreting and representing
data; defining 2-D and 3-D shapes by their attributes; and
partitioning shapes as foundational work for fractions.
View the TouchMath Implementation Guide
for classroom setup instructions.
www.touchmath.com/teacher-tools
Learn more about TouchMath research
and evidence basis:
www.touchmath.com/research
For additional information about TouchMath:
Visit www.touchmath.com
To speak with a TouchMath representative:
Email customerservice@touchmath.com
Call 1-800-888-9191
Teacher training and professional learning
opportunities are available:
www.touchmath.com/training
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Numbers & Operations Level 1
Unit 1
Program Overview
The TouchMath Approach
CRA-Continuum & Multisensory Instruction
The TouchMath program is grounded within the ConcreteRepresentational-Abstract (CRA) Continuum. The CRAContinuum is a sequence of multisensory instructional
practices and research-based best practices that move
from an instructional focus on concrete representations
(manipulative materials) and models, to semi-concrete
representations (drawings or pictures) and images, to
abstract (using only numerals, symbols (x), or mentally
solving problems). CRA corresponds to how our
brains take physical objects and learn that they can be
represented with abstract symbols and numerals.
We begin with concrete manipulations, using real-life
physical objects to explore a concept. This can be 1:1
correspondence, place value, and/or number bonds.
Using actual objects allows students to see and touch
something that is meant to become an abstract concept
and give them time to determine what they can do and
not do to make a concept, procedure, or algorithm work.
During the acquisition of number sense and base 10 the
TouchNumerals provide a much needed fading technique.
Try this with the numerals 2, 20, 102, 120, and 201 with
base 10 blocks and have students count each number
to explore the differences. See how many number bonds
there are in numerals such as 5, 10 and 12.
Students then move to the representational or semiconcrete step and use their drawings, other pictures, or
virtual manipulatives to represent the concrete materials
and do the math tasks. This enables them to manipulate
the concrete materials in a slightly more abstract manner.
For many students the TouchPoints provide an additional
intermediary step to enforce the understanding that each
object is equivalent to an image or drawing done by the
student. With older students and those with permanent
difficulties, finger tapping in its various forms can be a
continuing bridge.
The final step and goal is to have the student working in
the abstract with numerals and symbols taking the place
of objects and images. Finger tapping and adding dots
may continue as additional and needed support. The Build
It, Draw It, Write It template (page 9) is an additional tool
you should use to reinforce the CRA-Continuum.
The amount of time we spend in each of the three areas
depends upon the amount of time the student needs to
successfully perform the operation or master the concept.
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Multisensory teaching also includes adding multisensory
cuing, and providing structured language experiences.
Particularly where the teacher and student See It, Say It,
Hear It, Touch It, or Build It. The multiple sensory inputs
of sight, hearing, touch, and verbalization increase a
student’s engagement and aid memory of the concept or
procedure they are learning.
Concrete: TouchPoints
By providing students with TouchNumerals
and TouchPoints as a means of bridging physical
objects to their abstract counterpart — the numeral,
TouchMath makes it easier for students to move into
written representational or semi-concrete content and
then a solid understanding and mastery of abstract
mathematical concepts.
TouchMath uses each number as a manipulative, making
the learning experience real for students. Each numeral
from 1 through 9 has the same number of TouchPoints to
help students make physical connections with the semiconcrete images as well as the abstract numerals.
Numerals 1 through 5 have single TouchPoints. Numerals
6 through 9 have double TouchPoints (two concentric
circles), which means you touch and count each point
twice. Numerals 7 and 9 have both double and single
TouchPoints. Zero has no TouchPoints, so you never
touch or count zero.
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First Grade
Unit 1
Program Overview
The TouchMath Approach: CRA-Continuum & Multisensory Instruction continued
Students excel when they can see the numerals, touch
the TouchPoints, say the numbers, and hear the problem
— think multiple representations. Students should touch
and count the numbers in sequence as they learn the
Touching/Counting Patterns and the TouchPoints. First
graders need about a week to master the TouchPoints
and an average third grader can usually pick it up in one
lesson. Mastering these foundational patterns will set
students up for success with TouchMath.
Manipulative tips:
• Get to know the materials
• Organize the materials
• Thoughtfully introduce materials
• Make materials accessible
• Establish clear expectations
• Plan how manipulatives will expand
to models/drawing (representation)
Learn more about TouchMath’s line
of exclusive hands-on manipulatives:
www.touchmath.com/manipulatives
TouchMath Touching/Counting Patterns
video and printable instructions:
www.touchmath.com/numerals
Concrete: Finger Counting
Mathematics is considered one of the most
abstract domains of human cognition. Recent work on
the embodiment of mathematics has shown that we
make sense of mathematical concepts by using insights
and skills acquired through bodily activity. Fingers play
a significant role in many of these bodily interactions
and can be thought of as the first concrete manipulative.
Finger-based interactions provide preliminary access to
the beginning of mathematical thought processes, such
as number sense, one-to-one correspondence, and wholepart relations in early development. Children across a
variety of cultures use their fingers to count and do simple
arithmetic, and expand visual math concepts. There is
evidence for an association between children’s ability to
individuate fingers (finger gnosis) and mathematics ability
in elementary and middle school based on neuroscience
that shows clear evidence of parallel activation in
those areas of the motor cortex and parietal lobe. The
accumulating evidence for overlapping neural correlates
and functional associations between fingers and number
processing supports encouraging finger counting at all
ages as it can be a neural bridge between concrete math
processes and abstract concepts, both for children and
adults.
Concrete: Manipulatives
Students of all ages benefit from being able to
use manipulatives to model, solve problems, and explain
their thinking. Encourage all students to use tools and
materials and to explain how they use them. If used
only when someone is having difficulty, students can
get the mistaken idea that using manipulatives is a less
sophisticated and a less valued way of solving a problem
or modeling a solution. Therefore, they should see how
different people, including the teacher, use a variety of
materials to solve the same problem.
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TouchMath has the ability to bridge the gap between
concrete and representational mathematics. The program
takes into account students’ academic and cognitive
proficiencies and deficiencies while enriching both
the concept and the computation. The sequences that
TouchMath follows are built upon the work of Dr. Jean
Piaget and Dr. Lev Vygotsky. The work of both Piaget and
Vygotsky led to some of the most utilized constructivist
methodologies and developmental theories of our modern
educational systems.
Representational: Modeling & Drawing
TouchMath’s multimodality approach using
representations and manipulatives in the forms of
everyday numbers, aids in more advanced levels of math
concepts, particularly with modeling and representation.
There are ways to help support student’s positive beliefs
about math performance and help foster a mathematical
growth mindset:
• Praise effort over outcomes.
• Encourage students to embrace challenges.
• Give students time to engage in deep thinking and
conceptual thought.
• Celebrate mistakes as learning opportunities.
• Assist students with positive beliefs about themselves.
• Productive struggle through perseverance.
Representational: Number Lines
A number line is a very important modeling tool.
Number lines are a pictorial representation of numbers
— whole and rational, positive and negative, including
fractions — laid out evenly on a straight horizontal line.
It can be used to count or compare numbers, put them
in order, and perform operations such as addition and
subtraction. The number line is found across a number
of the state standards and, therefore, should be easily
accessible to the student, used frequently, and, where
appropriate, in conjunction with manipulatives.
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Numbers & Operations Level 1
Unit 1
Program Overview
The TouchMath Approach: CRA-Continuum & Multisensory Instruction continued
To start, have your number lines available and taped on
the student’s workspace or any way they can be held in
the horizontal or vertical position. For the student working
on number sense, a number line helps them visualize
number sequences. When needed, think CRA and pull
out those manipulatives with the number line. For the
student working on PK-2 skills, the TouchPoints provide
an additional visualization. Ask the student to touch
numbers on the number line and, where needed, use the
TouchPoints to identify the number.
While working with students in the upper elementary or
grades 3-6 — students working on multiplication — have
them use the number line for skip counting. Ask students
to count by 2s, or intervals of 2, along the number line.
Having the number line available also provides additional
visual memory support of where the numbers are in the
sequence. For students learning temperatures, make
a number line. Even when students determine which
fraction is more significant — they can use a number line.
The 2021 IES Practice guide states that “consistent use of
the number line can help students understand the number
system and improve their overall math performance
in several areas of mathematics.” Number lines can
be represented both vertically and horizontally. Using
concrete items within a number line makes multisensory
instructional practices more accessible. So number lines
are a research-proven, effective tool in teaching math.
They should be used when teaching number sense, base
ten, addition, subtraction, fractions, multiplication, etc.
Representational: Descriptive Modeling
Describing a Math Happening
Using real-world data to describe, represent, or analyze
a phenomenon.
• Encourage students for mathematical discourse.
Representational: Predictive Model
Making Predictions
Using trends and data analysis to predict an outcome.
• Encourage students to use mathematical modeling to
predict.
Representational: Optimizing Model
Finding the “Best”
Using data to find the “best” by optimizing or in some
cases minimizing some situations.
• Encourage students to find the “best” way to …
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Representational: Statistic & Probability
Models Use Data and Chance
Using data analysis and theoretic probability to determine
the chance of an event and trends to make decisions.
• Statistical and Probability models allow students to use
mathematics to determine the extent to which an event
is likely to occur.
Representational: Rating & Ranking Models
Making Decisions
Using criteria and mathematical measures as a way to
rate and rank options to make decisions.
Abstract: Concepts
Conceptual understanding is the comprehension
of mathematical concepts, operations, and relations.
TouchMath boosts conceptual understanding through
the reinforcement of visual manipulatives. Students
access multiple levels of conceptual understanding
using manipulatives and visuals to boost every student’s
performance in the categories of mathematical
proficiency. The goal for students is to access deeper
meanings of mathematical operations, relationships, and
concepts. The problem in a standard classroom is that
students have difficulty accessing the “comprehension” of
the concepts without a firm root in the visualization and
modeling with the concepts. (Boaler, 2018)
Abstract: Numbers
The multisensory approach of using TouchPoints
to an abstract item such as a number, helps students
conceptualize the total quantity of digits. When students
conceptualize quantities without degradation of their
working memory or executive processes, students gain
procedural and conceptual content at an increased rate.
Abstract: Operations
Mathematical Operations include Parenthesis,
Exponents, Multiplication, Division, Addition, and
Subtraction. Students use the order of operations to
understand the relationships between operations.
Operations are abstract in two layers, one being the
actual numbers and terms, the other layer being the
operational relationship between numbers and concepts.
To reinforce students’ understanding of operations,
making sense of problems through pattern recognition is
most important. We typically view a pattern as strings of
shapes or numbers. A pattern, in math, is much deeper
(and abstract) than that just that. Pattern recognition in
operations includes the order of operations. For example,
students need to identify the operation that comes first.
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5
First Grade
Unit 1
Program Overview
The TouchMath Approach: CRA-Continuum & Multisensory Instruction continued
In early elementary mathematics, PEMDAS is typically
taught. While this is an accurate depiction of the order
of operations, the M (multiplication) appears prior to
the D (division). Most students take this to mean that
multiplication comes first, then division. This is not
accurate, since division and multiplication are inverse
operations. For order of operations, MD stands for
multiplication OR division (first to appear from left to
right). This recognition is a form of abstract pattern
identification, which is extremely important for the
development of more complex mathematical equations.
Abstract: Calculator
Calculators in the elementary grades serve as aids
in advancing student understanding without replacing the
need for other calculation methods. Calculator use can
promote the higher-order thinking and reasoning needed
for problem-solving in our information- and technologybased society. Their use can also assist teachers
and students in increasing student understanding of
and fluency with arithmetic operations, algorithms,
and numerical relationships and enhancing student
motivation. Strategic calculator use can aid students
in recognizing and extending numeric, algebraic, and
geometric patterns and relationships.
Universal Design for Learning
The Universal Design for Learning (UDL) plays a pivotal
role in both the TouchMath Program and student
achievement for a wide range of learners: general
education, special education, intervention, remediation,
English Language Learners (ELL’s), and students
performing above or below grade level. In order for
students in the classroom to become active, motivated,
and successful learners, a deeper level of instructional
context must take place. The Universal Design for
Learning is derived from research-based best practices
in cognitive neuroscience and takes into account the
diversity of learners physiologically, psychologically, and
socio-emotionally. Neuroscience reveals tremendous
differences in how individuals learn even among those
who on the surface seem to have a lot in common — there
is a distinct variability not just from person to person, but
from within individuals. (CAST, 2013)
The Universal Design for Learning is based on three main
principles of learning: representation, action & expression,
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and engagement. These three learning principles are
connected to three corresponding neural networks, which
include respectively, the recognition, strategic, and affective
neurological networks of learning. TouchMath is deeply
grounded in scientifically-based practices that correspond
to the UDL framework. In practical applications, UDL and
TouchMath complement one another.
The Universal Design for Learning is a framework
for developing learners who are resourceful
and knowledgeable by providing multiple means of
representation. Representation activates the recognition
network of the brain, which is the “what” of learning. The
TouchMath program offers ways of customizing the
display of information, allowing students to benefit from
the perception of mathematics, thus maximizing the
transfer and generalization of key math concepts. The
language and symbols used in the TouchMath system
support the decoding of text, mathematical notions, and
symbols. Students gain cohesion within the math content
strands by activating background knowledge back to
the manipulation of a digit during this representation
frame. Teachers are able to highlight patterns, critical
features, big ideas, and relationships through the use
of a proven method of instruction through TouchPoints
for all operations, linking to the very fabric of the State
Standards and Response-to-Intervention frameworks.
The multiple means of action & expression
embedded within the TouchMath program develop
learners who are strategic and goal-oriented. Action and
expression activate the strategic network of the brain,
which is the “how” of learning. The TouchMath program
promotes varying methods for response and navigation,
which at its core are multisensory and grounded in
scientifically proven methods for intervention. Multiple
means of expression promote beneficial mathematical
discourse between teacher-to-student and even studentto-student interactions. This type of mathematical
discourse promotes fluency and offers graduated levels
of support for practice and performance. The “strategy”
of applying TouchPoints to numbers while accessing
higher-level math problems helps students with Executive
functions and also supports both planning and strategic
development. The following example is a math model
called a tape diagram. It is used to represent skip
counting by 3’s. Also shown is repeated addition, using
TouchPoints, to assist students in bridging the gap
between abstract numbers and representation.
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Numbers & Operations Level 1
Unit 1
Program Overview
The TouchMath Approach: Universal Design for Learning continued
division, and multiplication) to alleviate strain on working
memory and keep students focused on the task at hand.
Sustained rehearsal practice for fluency is very important.
TouchMath allows for students to practice fluency and
automaticity of math facts in a meaningful way.
3 3 3
3q3
3q3q3=d
3q3
3=d
The goal of the TouchMath Program is to develop
learners who are purposeful and motivated by
providing multiple means of engagement. Engagement
links to the Affective networks of neurology, which can
be defined as the “why” of learning. Recruiting interest by
minimizing distraction, sustaining effort and persistence
by varying demands, and developing strategies by
developing self-assessment are the pillars of strategies
behind the TouchMath program.
Reference: CAST (2018). Universal Design for Learning Guidelines version 2.2.
Retrieved from http://udlguidelines.cast.org
Standards of Mathematical Practice
The Standards of Mathematical Practice (SMP) are a series
of practices that effective mathematics educators use
at all levels and should seek within their students. These
standards focus on the key “processes and proficiencies”
successful math students exhibit when working through
complex problems, communicating results, and accessing
conceptual levels of understanding in key domain areas. It
is paramount that we recognize opportunities to emphasize
the Standards of Mathematical Practice during activities
that promote conceptual understanding. Conceptual
understanding in mathematics can take the form of:
•
•
•
•
Concrete and pictorial models
Real-world contexts
Conceptual questioning
Speaking and writing about understanding
Within the best practices, cross-grade coherence is
accessible through conceptual understanding which
improves students’ ability to not only learn math concepts
but to have those concepts stick along the learning
trajectory. (Illustrative Mathematics, 2014) The eight
Standards of Mathematical Practice are closely linked to
the TouchMath Program, and are represented as follows:
1
Make sense of problems and persevere
in solving them.
The TouchMath Program has embedded strategies
that enable students to access and persevere by using
TouchPoints for operations (addition, subtraction,
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2
Reason abstractly and quantitatively.
3
Construct viable arguments and critique
the reasoning of others.
With TouchMath, the visual strategies bridge
the gap between concrete manipulatives and the
representation of deeper levels of math domain areas.
The CRA-Continuum is used throughout the TouchMath
curriculum to boost reasoning in both abstract concepts
and quantitatively through procedural operations. The
result is increased proficiency in both quantitative and
abstract reasoning.
Students often struggle with the ability to not only create
mathematical justifications during application problems
but have difficulty critiquing the reasoning of their peers.
With metacognition being a key pillar for students’
retention of mathematical knowledge, many students
miss out on mathematical discourse. TouchMath can
assist students in organizing their mathematical thinking
to promote math discourse in the classroom by building
operational automaticity with gradual levels of support
and differentiation. We support rehearsal of metacognitive
strategies. These metacognitive strategies include finding
the larger number, saying it, counting on with the smaller
number, and many other strategies.
4
Model with mathematics.
5
Use appropriate tools strategically.
TouchMath combines researched-based
TouchPoint strategies with State Standards-aligned
modeling and the Build It, Draw It, Write It (BIDIWI) model
to help students understand complex concepts. The
outcome is successful students who can navigate the
conceptual levels of mathematics through multiple means
of representation, a key pillar of any successful math
student. See Teaching & Instructional Strategies to learn
more about the BIDIWI model.
Since TouchMath uses numerals as concrete
manipulatives and TouchPoints, students have a key tool
at their disposal whenever doing mathematics. This can
also aid in the proper use of strategy tools such as rulers,
calculators, and protractors. Math modeling tools include
number lines, part-part-whole modeling, array models,
tape diagrams, and much more. The appropriate use of
calculators is encouraged in TouchMath Upper Grades
Units 9 and 10.
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7
First Grade
Unit 1
Program Overview
The TouchMath Approach: Standards of Mathematical Practice continued
Calculator usage should be allowed, aside from when
the skill is computation. Calculator use for the late
elementary, and early middle school years is paramount
for utilizing mathematical tools correctly and allowing
students the opportunity to delve deeper into complex
math problems that will be found in the real world,
otherwise inaccessible without calculator usage.
Calculator usage should be balanced and not replace
efforts to develop fluency unless a student has shown
clear evidence of an ongoing inability to acquire math
facts.
6
Attend to precision.
7
Look for and make use of the structure.
TouchMath increases students’ ability to sustain
effort and positively influences their perseverance
throughout math problems. Precision and perseverance
are key pillars of State Standards and the Next Generation
Math Standards.
Mathematically proficient students look closely
to discern a pattern or structure. When students identify
and make use of structure they have not only a higher
probability of success but have a greater chance to access
higher levels of conceptual understanding. The use and
structure of patterns within the TouchMath numerals
assist students in seeking a deeper understanding of the
“structure” of the problem as opposed to finding the answer
without the justification of “why.”
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Look for and express regularity in
repeated reasoning.
Mathematically proficient students notice if calculations
are repeated, and look both for general methods and
shortcuts. Particularly when building skills from addition
to multiplication and skip counting, repeated reasoning
can be instrumental in successful learning acquisition.
TouchMath is a multisensory math program, and at its
essence trains students to look for repeated reasoning.
The program helps make math concepts easier and more
accessible for students with different learning styles or
learning difficulties. The approach uses auditory, visual,
and tactile strategies for understanding numbers and
operations.
The TouchMath Program allows students the accessibility
of conceptual understanding within deeper levels of
mathematical complexities. “Teachers teach more than
‘how to get the answer’ and instead support students’
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ability to access concepts from a number of perspectives
so that students are able to see math as more than a
set of mnemonics or discrete procedures. Students
demonstrate a deep conceptual understanding of core
math concepts by applying them to new situations as
well as writing and speaking about their understanding.”
TouchMath allows students to bridge gaps in
prerequisite knowledge necessary to activate conceptual
understanding and mathematical discourse.
Teaching & Instructional Strategies
Model, Lead, Test • I Do, We Do, You Do
Systematic or explicit instruction is a carefully planned
sequence of instruction that increases the likelihood for
students to master the concept. It involves modeling
and explicit explanations of new knowledge during direct
instruction, providing plenty of opportunities for the
student to respond, as well as guided and independent
practice. Guided practice is when students and teacher
work problems together, with students solving more
problems gradually. Independent practice has the student
working on their own or in small groups to practice the
skills that have been covered.
It assumes that the teacher is assessing prior knowledge
in order to build on prior learning and is a critical pre-step.
Students gain key concepts when there is foundational
knowledge that is present in the instructional approach.
The term “low floor high ceiling” applies here and means
that students can access the instructional materials
and instruction from a lower level than the topic is – but
with room for expansion through careful conceptual
questioning and open-ended inquiry.
Explicit or systematic instruction has been cited in the
2021 IES Practice Guide as an effective practice. What
does this look like in your TouchMath materials? Start
with direct instruction or modeling of the day’s goals.
This includes explicitly connecting previously and newly
learned material. Have them solve a few of the problems
they were successful at from the previous lessons. This
is a quick review and lets them start from a position of
success and shows them the evolution of the concept
or procedure. Systematic instruction also means use the
easiest numbers to start — teaching fractions, use 1/4
or 2/3 not 11/15 or 23/36. The goal is to guarantee an
easy entry point to the concept. Also start with a concrete
example of the concept, pull out those manipulatives.
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Numbers & Operations Level 1
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Program Overview
The TouchMath Approach: Teaching & Instructional Strategies continued
Then move to a more abstract representation of the
concept via having them draw the problem, then on to
working it with numerals or symbols. Use your Build It,
Draw It, Write It template during all 3 phases of the lesson
— direct, guided, and independent. During this first phase
the teacher is describing and demonstrating with ample
verbal descriptions of the daily work. Opportunities for
student response are frequent. Make sure to provide fully
worked, partially worked, and incorrectly worked examples
as appropriate.
The next step is to gradually release the lesson to the
student with guided practice. This can be sitting with
an individual or small group of students or the entire
class where you work problems together or have them
demonstrate or explain how to solve problems. The use
of partially worked problems is a good bridge to having
students solve problems.
Finally independent practice or sustained rehearsal. This
is a strong instructional strategy that is embedded within
the TouchMath curriculum, where the student works on
their own for a designated period of time. Having students
practice routine, computation, and step-by-step processes
with teacher feedback is paramount to student success.
This can be on the computer with MyTouchMath or
activity sheets, and can involve working alone, in pairs, or
in a group.
The modified Frayer Chart is a strong instructional
strategy that can focus on conceptual understanding
and learning with both vocabulary and computation. In
the middle of the Frayer Chart, a student would write the
keyword/concept. Teachers can also model the use of the
Frayer Chart when needed if it cannot be completed by the
student. The top left is designated for the definition of the
keyword. For example, “sum” is the answer to an addition
problem. The top right is where a student would create
an image or graphical representation of the concept/
keyword. In addition, drawing groups of items together
could represent a “sum.” The bottom left side of the Frayer
Chart is used for examples, such as 4 + 4 = 8; where 8
denotes the sum. For the non-example, this is similar to
error analysis, a student would have to think about how to
“break” the concept. With the concept of sum or addition,
the non-example could be subtraction problems. Students
gain value and much-needed reinforcement when dealing
with how to “break” an example, e.g. non-example. The
modified Frayer Chart can have several uses, particularly
when math journaling, vocabulary review, or concept
review. And think See It, Say It, Touch It, Hear It.
Download the modified Frayer Chart
model template:
www.touchmath.com/teacher-tools
Response to Intervention
Build It, Draw It, Write It Model
The Build it, Draw it, Write it model (BIDIWI) utilizes
a CRA-approach to helping students understand complex
concepts. This multisensory strategy is beneficial for
students struggling with mathematics or learning a new
concept. In the Build It phase, students use manipulatives
that they feel comfortable with, which can be counters
or any manipulative. In the Draw It phase, students draw
and interpret mathematical models to help with their
understanding. The Write It phase is focused around
interpreting the modeling and drawing phase using
numbers, symbols, or words to describe problems and
solutions. Looking carefully at the strategy, you can see
the relationship between CRA and BIDIWI, which follows
the research-based model of the CRA-Continuum.
Download the Build It, Draw It, Write It
(BIDIWI) model template:
www.touchmath.com/teacher-tools
SEF.1.TG
Modified Frayer Chart
Response to Intervention (RtI) is an early detection,
prevention, and support system that attempts to
identify and assist struggling students with appropriate
levels of intervention. The essential components for
implementing a successful RtI framework include
high-quality, scientifically based classroom instruction,
ongoing student assessment, and Tiered Instruction. The
TouchMath Program provides both a support system and
multi-level intervention system to assist students who fall
within the Tier 1, 2 and 3 levels of the federally mandated
Response-to-Intervention framework
Tier 1: Students learn at roughly grade level or above,
and are the least likely to fall behind or need intervention.
This type of intervention is typically done in a whole-class
setting.
Tier 2: Students lag well behind their peers, demonstrate
weak progress on screening and measures, and require
some form of intervention.
DO NOT REPRODUCE
©2022
9
First Grade
Unit 1
Program Overview
The TouchMath Approach: Response to Intervention continued
Tier 3: Students lag behind their peers by one or more
informal assessment is embedded assessment during
instruction which can save time and enable teachers to
make just-in-time adjustments to instruction.
Researchers advocate that students with learning
disabilities, particularly in math, require engagement
in learning with an application, plenty of feedback, and
teaching that correlates with personal learning style.
TouchMath provides these strategies with engagement,
feedback, and multisensory methods. The study shows
(Mays, 2008):
Stage 2: Planning
years, demonstrate very weak progress on screening
measures, and require intensive intervention.
• The use of the TouchMath strategy increases
computation skills and additionally promotes a
computation strategy that students use independently.
• 60% of the students met the goal of 100% improvement
on computation tasks.
• Decreasing errors as students learn the TouchMath
strategy and continued use of the program improves
student motivation and test scores.
• Knowledge of TouchPoints allows ease of use and
faster-timed scores.
TouchMath has been proven to be an effective RtI
intervention tool that will assist in helping students
access math curriculum.
TouchMath Instructional Cycle
Teachers enter the classroom, knowing what they
need students to know and be able to do every day. To
accomplish that they go through a 3-step cycle that
includes using what they know about their students to
plan appropriate and effective instructional activities that
will help students master content, implement those plans
with the right instructional materials, and supports and
assess progress allowing them to adjust instruction real
time or for the future. The three stages that comprise the
instructional cycle are:
Stage 1: Assessment
In this first stage, teachers conduct an initial assessment
to determine what knowledge and skills students are
bringing to the lesson. Assessments should include
ongoing formal (e.g., standardized tests) and informal
(e.g., teacher-made tests, portfolios) to determine
students’ entry point. An especially effective form of
10
©2022
The next stage in the instructional cycle begins with
identifying the standards and activities that need to
be presented during the time period selected. This
information will come from the state and local standards,
IEP’s, prior assessment data, etc. Teachers know what
they want students to know and be able to do, the
evidence-based strategies they will use for instruction,
and how they will measure progress. These are written as
measurable learning outcomes.
Stage 3: Teaching
The teaching stage recognizes the importance of using
strong research-based instructional practices with
the goal of a gradual release of responsibility from
teacher to student through a structured process such
as systematic instruction. This process includes prior
knowledge, presenting new materials and vocabulary, a
strong mathematical challenge, feedback, and repetition.
From the student’s brain’s perspective, learning — or the
storage of information and skills in long term memory
— is activated during the learning cycle, It also includes
using multisensory and other evidence-based strategies
to ensure that students master the content. The Teaching
Stage focuses on:
•
•
•
•
Prior Knowledge: Ensure there is something to connect to
Presentation: Initiate the pathway
Challenging Task: Activate the pathway
Feedback for Improvement: Check that it’s the
right pathway
• Spaced Repetition: Secure long-term connections
by re-using the pathway over a period of time
through practice
And finally, repeat the Assessment, Planning, and
Teaching cycle with a planned assessment; formal,
informal, or embedded to determine whether students
have met the goals of the teaching stage. This
assessment can occur at any time, not just at the end of
the teaching stage and the data collected can be used to
adjust instruction in real time or be used to plan the next
stages of the upcoming cycle of teaching.
DO NOT REPRODUCE
SEF.1.TG
Numbers & Operations Level 1
Unit 1
Program Overview
The TouchMath Approach: TouchMath Instructional Cycle continued
Response Modes & Standardized Tests
The TouchMath program has a variety of response modes
to provide students the opportunity to further understand
materials in a multitude of conceptual ways. This varying
response to problems increases critical thinking and
conceptual understanding. By providing students with
multiple ways of response, such as multiple-choice, multistep, visual, drawing, and written responses; standardized
tests and assessments become easier to complete
and help ensure that a student is not penalized for not
demonstrating mastery when it is the type of problem they
are being asked to solve that is the issue.
Unit Implementation
Module Instruction
Student Activity Sheets
The student activity sheets are carefully sequenced, clean,
and uncluttered. Artwork is included for instructional
purposes. The variety, quality, and quantity of the activities
make reinforcement immediately available on an asneeded basis. Frequent skill reviews offer practice before
testing. Tests and tracking materials are matched to
these skills, providing many opportunities for formative
assessment to guide the learning program of the
students. The program may be used in total or in part. It is
not necessary for every student to complete every activity
sheet since learners vary in skill level and the amount of
intervention support or reinforcement they need.
Print Edition: Use the box and included module tabs for
storage — the reproducible masters can also be three-hole
drilled if binder storage is preferred.
TouchMath Now Edition: Download/print the individual
activity sheets you need, when you need them, from any
Internet-connected computer or tablet device.
Each module begins with an overview and identifies
the content clusters — subsets of the featured skill.
The module overview explains the activities, presents
standards, specifies objectives, identifies basic
prerequisites, lists vocabulary words, and suggests
manipulatives and/or readily available materials.
The left column contains directions and suggested
dialogue for the teacher. The right column has color
answer key thumbnails and sample activities to be
modeled and/or discussed. Module pre- and post-tests
begin/end module instruction. Progress monitoring
records are included at the beginning of each module.
The module concludes with suggestions for differentiated
instruction, real world applications, and literature
connections.
Visual Features
Unit, Module, and Cluster Overview
Instruction for Guided Practice
Instruction for Assessment
Teacher’s Guide
The spiral bound teacher’s guide offers an introduction
to the TouchMath program with a comprehensive
overview of the research-backed strategies, suggestions
for implementation, and page-by-page activity sheet
instruction. The unit overview clearly defines the modules,
standards, objectives, vocabulary, and includes useful
links to access state curriculum standards, scope and
sequence, and additional teacher tools.
A comprehensive unit review and post-test follows
module 6 instruction with corresponding progress
monitoring records. English/Spanish parent/caregiver
communication letters and color answer keys are also
included in the guide.
SEF.1.TG
•
•
Performance Benchmarks
Materials Needed
Teacher Information
•
•
Students Collaborate in Pairs
•
Multisensory, Multi-step, Multi-level Directions
•
B
Suggested Dialogue
Monitor Students when Recommended
Vocabulary Words are Bolded
CRA (Concrete-Representational-Abstract)
UDL (Universal Design for Learning)
SMP (Standards of Mathematical Practice)
Instructional Strategies (BIDIWI, Frayer Chart)
DO NOT REPRODUCE
©2022
11
First Grade
Unit 1
Program Overview
Unit Implementation: Teacher’s Guide continued
Assessment
The lessons in each module begins with a pretest, which gives basic directions for completion. It is
recommended that you give little instruction related to
the skill before testing. A post-test follows the module
instruction at the end of each module. Refer to the module
instruction for directions for administering the post-test.
You can record results and compare them to the pre-test.
Pre- and post-assessment activity sheets are highlighted
in magenta throughout the teacher’s guide.
Ways to Get the Most Benefit from the
TouchMath Program
TouchMath Implementation Guide
The Implementation Guide will get you up and running
with comprehensive program overviews, classroom setup
instructions, and information for every manipulative,
digital resource, and TouchMath support we offer.
TouchMath Implementation Guide:
www.touchmath.com/teacher-tools
Answer Keys
Color answer keys are embedded in the module
instruction for a quick reference while planning or
presenting the lesson. The code found at the bottom left
corner (e.g., SEF.1.55) can be used to record activity sheet
scores in TouchMath Hub, our digital tool for student
information and reporting. Learn more about TouchMath
Hub at www.touchmath.com. A complete unit answer key
can also be found at the back of the teacher’s guide in the
appendix (see page A1).
Differentiated Instruction
To meet the varying needs of learners, each module
concludes with suggestions for remediation, additional
practice, and challenge. These will contribute to higher
achievement on the post-test if they are used throughout
the instructional process when the need for additional
support is evident. The real world applications are
examples of where students might come in contact with
the skill in their world and are included to ensure that
students see the relevance of what they are learning.
Literature connections include age-appropriate books,
short stories and poems that help support the lessons
within each module.
TouchMath Fidelity Checklist
We know from research that the level to which a program
is implemented as designed, the fidelity of implementation
matters. If you compare programs that are implemented
to programs that are not, the difference in the results can
be 2 to 3 times larger. (Durlak & DuPre, 2008).
A user of TouchMath should:
• Be adequately trained.
• Adhere to the instructional procedures of the practice
or program (e.g., follow the script, implement among
groups of the correct size).
• Implement the practice or program as frequently as
recommended (e.g., daily, three times per week).
• Implement the practice or program for the
recommended amount of time.
• Skillfully implement the instructional procedures.
Please use your TouchMath Fidelity of Implementation
Checklist as a “look for” list to ensure you are using all
of the components in the most effective way in order to
increase student success in mastering math.
Fidelity of Implementation Checklist:
www.touchmath.com/teacher-tools
Where to Start
•
•
•
•
•
•
•
•
•
•
•
Review the Fidelity of Implementation checklist.
Send home the parent/caregiver letter.
Ensure students know the Touching/Counting Patterns.
Gather the materials needed.
Administer the unit pre-test.
Record the results on the Progress Monitoring Record.
Determine placement in the unit based on the results.
Administer the module pre-test.
Record the results on the Progress Monitoring Record.
Begin instruction.
Assess regularly to ensure progress.
12
©2022
Parent/Caregiver Letter
Help engage parents/caregivers in their students math
activities by introducing them to the TouchMath program.
The letter is available in both English and Spanish and is
designed to be copied/printed on your school letterhead.
DO NOT REPRODUCE
Caregiver letters in English or Spanish:
www.touchmath.com/teacher-tools
SEF.1.TG
Numbers & Operations Level 1
Unit 1
Program Overview
Unit Implementation: Ways to Get the Most Benefit continued
TouchPoints
Provide explicit instruction to master the Touching/
Counting Patterns. Students will use them at the level that
supports their learning: kinesthetic, visual, or cues.
Touching/Counting Pattern instruction:
www.touchmath.com/numerals
Progress Monitoring
Record student scores for activity sheets and/or preand post-tests as an aid for a student’s IEP. Progress
Monitoring Records are included at the start of each
module within this guide. Digital versions (Excel format)
are also available on the TouchMath website.
Progress Monitoring Records:
www.touchmath.com/teacher-tools
Manipulatives
Integrate the use of concrete materials into the activities.
TouchMath hands-on manipulatives:
www.touchmath.com/manipulatives
Alternatively, TouchMath SE activity sheet scores can also
be recorded in TouchMath Hub, our digital tool for student
information and reporting. Learn more about registration
options at www.touchmath.com.
Alignments
Activity Sheets
Use only those that are needed to advance the learning of
individual students.
Use alignment documents to correlate TouchMath
lessons with state curriculum standards and/or to other
core math programs.
Practice
State and core math alignments:
www.touchmath.com/alignments
Use enough activity sheets to provide meaningful
repetition of the skill corresponding to the developmental
level of the students.
Scope and Sequence
Extra Support
Schedule a parent volunteer or paraprofessional to
work with small groups or individuals who need more
experience with the skill.
Use to chart the course for students in primary
classrooms in general education, in intervention
programs, and in IEPs for special education learners.
Vocabulary
Use the words in bold type in direct math instruction
and informal communication. Reinforce them in the
instructional strategies. Cue words are included in bold
type in the word problems.
TouchMath Scope and Sequence:
www.touchmath.com/teacher-tools
Equation Repetition
Repeat the problems and solutions orally to increase
fluency with the facts.
Pre- and Post-tests
Use pre-test results to determine placement in the
module. Use the post-test and differentiated instruction to
ensure mastery and/or application before proceeding to
the next module.
SEF.1.TG
DO NOT REPRODUCE
TouchMath Support
Customer Service
1-800-888-9191
customerservice@touchmath.com
Product and Sales
1-855-929-0880
sales@touchmath.com
©2022
13
First Grade
Unit 1
Unit Overview
Unit 1: Numbers & Operations Level 1
The goal of TouchMath SE First Grade Unit 1 is to review the concepts of addition and subtraction within 9. The
unit begins with extending the counting sequence to 120. These activities are scaffolded both in content (each
decade is presented separately) and in practice (recognizing, tracing, and writing). The scaffolding is integrated
to include counting on from any number, finding missing numbers, and saying the numbers in sequence. The
multi-sensory TouchMath approach is reinforced throughout the practice, ensuring that students see, say, touch,
and write the numerals. Once the rote learning of the sequence is mastered, association of number and numeral
using TouchPoints follows as a prerequisite strategy for addition and subtraction. Five ways to represent numbers
is modeled as students move through the concrete-representational-abstract sequence to build a foundation for
number sense. The Touching/Counting Patterns are repeated until they are an integral part of counting.
The addition and subtraction review begins with sums within 5, then differences within 5. The Touching/Counting
Patterns are the primary strategy in transitioning from objects to numerals. Understanding that addition is the
putting together of sets of objects and subtraction is the taking away a part from the set of objects is basis of
the operations. The review is scaffolded to addition and subtraction within 9, first separately and then together.
Backward counting is encouraged using the TouchPoints on the subtrahend. Again, a five-step process is used
to build the concept. The process begins with removing objects from a set, to backward counting from the whole
to the remaining part, to using TouchPoints. Solving for unknowns, comparisons, and word problems are included
throughout the guided practice. Vertical presentation of equations is introduced. Developing visual cues (e.g.,
highlighting the operation) is structured to implement the TouchMath philosophy of creating supports to ensure
understanding and success.
Teacher Practice: Counting • TouchPoints • Addition • Subtraction
Review the TouchMath Touching/Counting Patterns and approaches for Addition
& Subtraction with video lessons and our downloadable Teacher Practice Guide.
www.touchmath.com/video-training Access Code: touchpoint123
State and core math alignments:
www.touchmath.com/alignments
16
©2022
DO NOT REPRODUCE
TouchMath Scope and Sequence:
www.touchmath.com/teacher-tools
SEF.1.TG
Numbers & Operations Level 1
Unit 1
Unit Overview
Objectives
1.
Count orally to 120, forward and backward
13. Compare expressions with sums and differences
2.
Count on from any number
14. Solve word problems using rebus
3.
Identify missing numbers in sequence
15. Transfer understanding to everyday examples
4.
Use C-R-A to associate objects, pictures, and numbers
16. Relate addition and subtraction to counting
5.
Use TouchPoints and the Touching/Counting Patterns
to associate quantities
17. Apply TouchPoints on the lesser addend and the
subtrahend
6.
Compare numbers with different representations
7.
Demonstrate addition and subtraction in multiple ways
18. Use strategies and relationships to find sums and
differences
8.
Relate addition and subtraction
9.
Apply TouchPoints on both numerals in both operations
10. Use TouchPoints and visual cues as strategies
19. Solve for a missing addend as a strategy for finding an
unknown
20. Create stories and/or number sentences for equations
11. Solve for unknowns
12. Demonstrate and apply understanding of equality using
true/false
Vocabulary
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
add
addend
altogether
associate
clues
column
compare
comparisons
count backward
count on
diamond
difference
digits
domino
dominoes
double
SEF.1.TG
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
equal to (=)
equation
even
false
greater
greater than (>)
in all
left
lesser
location
maze
minus
missing numbers
number bonds
number family
odd
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
operation signs
pair
part
pattern
Pictorial TouchPoints
plus
quantities
relationship
remain
represent
representations
sequence
solution
solve
stacked
subtract
DO NOT REPRODUCE
•
•
•
•
•
•
•
•
•
•
•
•
sum
take away
total
Touching/Counting
Pattern
TouchPoints
trace
true
unknowns
vertical
whole
word problems
zero
©2022
17
Numbers & Operations Level 1
Unit 1
Unit Review & Post-test
Activity Sheets 158–165
ASSESSMENT
Numbers & Operations 1 Review
Name
121 122 123 124 125
Activity Sheet 158 Instruction
1.
158 146 147 148 149 150
2.
•
Rows 1–3:
179 180 181 182 183
3.
POINT to and SAY the number.
COUNT ON.
4.
SAY and WRITE the numbers.
Row 4:
SAY and TRACE the number names.
TOUCH and SAY the TouchPoints with pictures.
Use the Touching/Counting Pattern.
7
9
8
seven
eight
nine
SEF.1.158
DRAW a line to connect TouchPoints with pictures
to the number name.
©2022
SEF.1.158
*
&
(
Numbers & Operations Level 1 Review
158
TOUCH and SAY the TouchPoints.
Use the Touching/Counting Pattern.
DRAW a line to connect the number name to the
number with TouchPoints.
ASSESSMENT
Numbers & Operations 1 Review
Activity Sheet 159 Instruction
•
5.
159
Rows 5–9:
6.
Fill in the operation sign.
TOUCH, COUNT, and SAY the TouchPoints
on the first number.
SAY the operation.
7.
8.
TOUCH, COUNT On or COUNT backward the
TouchPoints on the second number.
9.
TOUCH the sign and SAY equals.
SAY and WRITE the solution.
@
!
#
@
#
SEF.1.159
©2022
READ the equation.
SEF.1.TG
$
#
%
#
$
Name
DO NOT REPRODUCE
SEF.1.159
2
4
2
5
1
Numbers & Operations Level 1 Review
©2022
159
163
First Grade
Unit 1
Unit Review & Post-test
Activity Sheets 158–165
ASSESSMENT
Numbers & Operations 1 Review
10.
Activity Sheet 160 Instruction
•
160
Rows 10–11:
SAY the greater number.
11.
@
5
Name
3
$
5
9
4
5
8
9
12.
0123456789
9
0
TOUCH the sign. SAY add.
COUNT ON. Use the TouchPoints
13.
TOUCH and SAY equals.
14.
SAY and WRITE the sum.
9
6
*
4
s
15.
Fill in the bubble that matches.
6
s in the
How many
Row 12:
SEF.1.160
SAY and TRACE the 9.
©2022
SEF.1.160
.
2
1
2
s on the
.
s are there altogether?
1
2
4
2
7
8
Numbers & Operations Level 1 Review
s
s
160
TRACE the arrow. COUNT backward.
WRITE the number.
TRACE the arrow. COUNT backward.
Complete the row.
Row 13:
TOUCH and SAY the first number.
TOUCH the sign and SAY subtract.
TOUCH and COUNT backward on the TouchPoints.
TOUCH and SAY equals.
SAY and WRITE the difference.
Fill in the bubble that matches.
Row 14:
TOUCH and SAY the first number.
TOUCH the sign and SAY subtract.
Find and WRITE the unknown.
TOUCH and SAY equals 2.
Fill in the bubble that matches the unknown.
Row 15:
READ and solve the word problem.
Fill in the bubble that matches.
164
©2022
DO NOT REPRODUCE
SEF.1.TG
Numbers & Operations Level 1
Unit 1
Unit Review & Post-test
Activity Sheets 158–165
ASSESSMENT
Numbers & Operations 1 Review
Activity Sheet 161 Instruction
•
16.
161
Rows 16–17:
17.
Solve. Use strategies.
WRITE the missing number.
18.
Fill in the bubble that matches.
19.
Rows 18–19:
Find the sum. Compare.
Name
7
@
9
8
9
9
s
4
5
5
4
6
!
7
8
0
9
20.
8
Fill in the bubble that matches.
s on a
How many
Row 20:
.
3
s fall off the
s are left on the
SEF.1.161
©2022
READ and solve the word problem.
SEF.1.161
.
?
4
5
Numbers & Operations Level 1 Review
s
s
161
Fill in the bubble that matches.
ASSESSMENT
Numbers & Operations 1 Post-test
Name
159 160 161 162 163
1.
Activity Sheet 162 Instruction
162 187 188 189 190 191
2.
•
Rows 1–3:
195 196 197 198 199
3.
POINT to and SAY the number.
COUNT ON.
4.
SAY and WRITE the numbers.
Row 4:
SAY and TRACE the number names.
TOUCH and SAY the TouchPoints with pictures.
Use the Touching/Counting Pattern.
DRAW a line to connect TouchPoints with pictures
to the number name.
6
8
9
nine
six
eight
SEF.1.162
©2022
SEF.1.162
*
(
^
Numbers & Operations Level 1 Post-test
162
TOUCH and SAY the TouchPoints.
Use the Touching/Counting Pattern.
DRAW a line to connect the number name to the
number with TouchPoints.
SEF.1.TG
DO NOT REPRODUCE
©2022
165
First Grade
Unit 1
Unit Review & Post-test
Activity Sheets 158–165
ASSESSMENT
Numbers & Operations 1 Post-test
Activity Sheet 163 Instruction
•
#
$
%
$
%
5.
163
Rows 5–9:
6.
Fill in the operation sign.
TOUCH, COUNT, and SAY the TouchPoints
on the first number.
7.
SAY the operation.
8.
TOUCH, COUNT On or COUNT backward the
TouchPoints on the second number.
9.
TOUCH the sign and SAY equals.
SAY and WRITE the solution.
@
!
@
@
!
SEF.1.163
©2022
READ the equation.
SEF.1.163
ASSESSMENT
Numbers & Operations 1 Post-test
10.
Activity Sheet 164 Instruction
•
Name
164
Rows 10–11:
SAY the greater number.
11.
4
@
5
3
3
2
4
Numbers & Operations Level 1 Post-test
163
Name
!
5
5
7
4
5
7
8
12.
0123456
6789
0
TOUCH the sign. SAY add.
COUNT ON. Use the TouchPoints
13.
TOUCH and SAY equals.
14.
SAY and WRITE the sum.
9
7
^
3
s
15.
Fill in the bubble that matches.
5
s in the
How many
Row 12:
SEF.1.164
©2022
SAY and TRACE the 9.
SEF.1.164
.
3
3
4
s in the
3
4
3
4
.
s are there altogether?
2
8
Numbers & Operations Level 1 Post-test
s
s
164
TRACE the arrow. COUNT backward.
WRITE the number.
TRACE the arrow. COUNT backward.
Complete the row.
Row 13:
TOUCH and SAY the first number.
TOUCH the sign and SAY subtract.
TOUCH and COUNT backward on the TouchPoints.
TOUCH and SAY equals.
SAY and WRITE the difference.
Fill in the bubble that matches.
166
©2022
DO NOT REPRODUCE
SEF.1.TG
Numbers & Operations Level 1
Unit 1
Unit Review & Post-test
Activity Sheets 158–165
Row 14:
TOUCH and SAY the first number.
TOUCH the sign and SAY subtract.
Find and WRITE the unknown.
TOUCH and SAY equals 2.
Fill in the bubble that matches the unknown.
Row 15:
READ and solve the word problem.
Fill in the bubble that matches.
ASSESSMENT
Numbers & Operations 1 Post-test
Activity Sheet 165 Instruction
•
16.
165
Rows 16–17:
17.
Solve. Use strategies.
WRITE the missing number.
18.
Fill in the bubble that matches.
19.
Rows 18–19:
Find the sum. Compare.
Name
6
#
9
8
9
8
s
4
4
3
4
7
@
8
5
0
5
20.
6
Fill in the bubble that matches.
s on the
How many
Row 20:
.
2
s go into a
s are left on the
SEF.1.165
©2022
READ and solve the word problem.
SEF.1.165
?
.
8
4
Numbers & Operations Level 1 Post-test
s
s
165
Fill in the bubble that matches.
SEF.1.TG
DO NOT REPRODUCE
©2022
167