Grade 1 Mathematics, Quarter 3, Unit 3.1
Counting and Comparing Numbers to 100
(formerly Unit 1.3.3)
Overview
Number of Instructional Days:
10
(1 day = 45–60 minutes)
Content to be Learned

Read and write numerals to 100.

Represent a number of objects with a written
numeral.

Compare two 2-digit numbers 10–99 and
record the results of comparisons using correct
mathematical symbols (<, >, =).

Add a two-digit number and one-digit number
within 100 using concrete models or drawings
and strategies based on place value.

Add a two-digit number and a multiple of 10
using concrete models or drawings and
strategies based on place value.

Mentally find 10 more or 10 less than a twodigit number without having to count, and
explain the reasoning used.
Mathematical Practices to Be Integrated
3 – Construct viable arguments and critique the
reasoning of others.
 Justify their conclusions using objects, drawing,
diagrams and actions.
 Communicate their conclusions and justifications
and respond to the arguments of others.
6 – Attend to precision.
 Communicate precisely using appropriate
mathematical vocabulary.
 State the meaning of symbols they choose,
including the equal sign consistently and
appropriately.
 Express numerical answers with a degree of
precision appropriate for the context.
7 - Look for and make use of structure.
 Look closely to discern a pattern or structure.
8 - Look for and express regularity in repeated
reasoning.
 Look for general methods and shortcuts.
 Continually evaluate the reasonableness of
intermediate results.
Essential Questions

What number would you write to represent this
____ ? (amount up to 100)

What number represents this group of objects? How
do you write that number?

What is this number? (Teacher shows numeral up to 100.)

How can you use a symbol (<, >, =) to make these
statements true. (e.g., 61 ___ 50 + 40;
25 ___ 2 tens and 5 ones; 98 ___89)

Add these two numbers (e.g., 48 + 7; any two-digit
plus one-digit combination). What strategy did you
use? Explain your thinking. (Within 100, using
concrete models or drawings and strategies based on
place value)


Add these two numbers (e.g., 48 + 30; any twodigit number plus a multiple of 10). What
strategy did you use? Explain your thinking.
(Within 100, using concrete models or
drawings and strategies based on place value)
What is 10 more than ____? What is 10 less
than ____? Explain how you know. What
pattern do you notice? (Mental strategies only)
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of
Texas at Austin
Revised 2013-2014
Grade 1 Mathematics, Quarter 3, Unit 3.1
Counting and Comparing Numbers to 100 (10 days)
Written Curriculum
Common Core State Standards for Mathematical Content
Number and Operations in Base Ten
1.NBT
Extend the counting sequence.
1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and
represent a number of objects with a written numeral.
Understand place value.
1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the
results of comparisons with the symbols >, =, and <.
Use place value understanding and properties of operations to add and subtract.
1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a
two-digit number and a multiple of 10, using concrete models or drawings and strategies based
on place value, properties of operations, and/or the relationship between addition and
subtraction; relate the strategy to a written method and explain the reasoning used. Understand
that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is
necessary to compose a ten.
1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having
to count; explain the reasoning used.
Common Core Standards for Mathematical Practice
3
Construct viable arguments and critique the reasoning of others.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established
results in constructing arguments. They make conjectures and build a logical progression of statements to explore
the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and
use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of
others. They reason inductively about data, making plausible arguments that take into account the context from
which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible
arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—
explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings,
diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made
formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all
grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to
clarify or improve the arguments.
6
Attend to precision.
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in
discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including
using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling
axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express
numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students
give carefully formulated explanations to each other. By the time they reach high school they have learned to
examine claims and make explicit use of definitions.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of
Texas at Austin
Revised 2013-2014
Grade 1 Mathematics, Quarter 3, Unit 3.1
Counting and Comparing Numbers to 100 (10 days)
7
Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might
notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes
according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 ×
3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see
the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can
use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift
perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being
composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square
and use that to realize that its value cannot be more than 5 for any real numbers x and y.
8
Look for and express regularity in repeated reasoning.
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for
shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations
over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they
repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the
equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 +
x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they
work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the
details. They continually evaluate the reasonableness of their intermediate results.
Clarifying the Standards
Prior Learning
In kindergarten, students counted to 100 by ones and tens. They began at any given number within a
known sequence. Students wrote and represented numbers 0–20 and represented the number of objects
with a written numeral 1–20.
Current Learning
This is a critical area in grade 1.
Reading and writing numerals 0–60 and the concept of equality are taught at the reinforcement level.
Skills taught at the developmental level are as follows:

Students read and write numbers 61–100 and use the symbols for greater than and less than to
compare numbers up to 100.

Students add within 100, including adding a two-digit number and a one-digit number and a twodigit number and a multiple of 10 (using open number lines, 10 frames, number grid, bundles).
They should relate their strategies to a written method and explain the reasoning used.

Students mentally find 10 more or 10 less without counting, given a two-digit number, and
explain the reasoning used.
Future Learning
In grade 2, students will understand that the digits of a three-digit number represent hundreds, tens, and
ones. They will count, read, and write numbers up to 1,000 using base-10 numerals and expanded form.
Students will compare three-digit numbers using the symbols for greater than, less than, or equal.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of
Texas at Austin
Revised 2013-2014
Grade 1 Mathematics, Quarter 3, Unit 3.1
Counting and Comparing Numbers to 100 (10 days)
Students will add and subtract within 100 using strategies based on place value and properties of
operations and/or relationships between addition and subtraction. In addition, they will mentally add and
subtract 10 or 100 to a given number 100–900.
Additional Findings
According to K–5, Number and Operations in Base Ten Learning Progressions, “Grade 1 students use
their base-ten work to help them recognize that the digit in the tens place is more important for
determining the size of a two-digit number. They use this understanding to compare two two-digit
numbers, indicating the result with the symbols <, =, and >. Correctly placing the < and > symbols is a
challenge for early learners. Accuracy can improve if students think of putting the wide part of the symbol
next to the larger number.” (p. 6)
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of
Texas at Austin
Revised 2013-2014
Grade 1 Mathematics, Quarter 3, Unit 3.1
Counting and Comparing Numbers to 100 (10 days)
According to Fostering Children’s Mathematical Power (Baroody),
“Children with a counting-based concept of numbers do not think in terms of grouped items (larger
units like tens, hundreds, and so for the) and single items (units). Thus, they view 24 for instance, as a
collection of twenty-four units not as two groups of 10 and four ones. To understand. … multi-digit
arithmetic procedures—particularly those involving renaming (carrying and borrowing) —children
must discover the importance of grouping quantities into larger and larger units. … They must
transcend their informal counting-based concept of number and construct a new understanding of
number—based on a grouping concept (e.g., view 24 as two groups of 10 and four single items).”
(p. 6-3)
“Children initially do not realize that a digit’s position is crucial to its value. They view a numeral
such as 12 either as two distinct single-digit numbers (“one and two”) or as an inseparable whole
(‘twelve units”). Children need to learn that each place increases in value by a factor of 10 as we
move from right to left, because items are repeatedly grouped by 10 (e.g., 10 units are grouped to
make a hundred, 10 hundreds are grouped to make a thousand, and so forth). … These are foreign
and relatively abstract ideas for children.” (p. 6-3)
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of
Texas at Austin
Revised 2013-2014