Grade 1 Mathematics, Quarter 2, Unit 2.1
Ordering and Comparing Whole Numbers to 30
Overview
Number of instructional days:
10
(1 day = 45–60 minutes)
Content to be learned
Mathematical practices to be integrated
•
Order whole numbers from 0 to 30.
Look for and make use of structure.
•
Connect number words to numerals (0–20).
•
•
Connect a numeral to a quantity.
Use appropriate tools strategically.
•
Connect a numeral to a number line, a
hundreds chart, and/or a given representation.
Evaluate and shift perspective when needed.
•
Consider tools that are available, and choose
appropriately.
•
Use tools to assist in visualizing and
deepening understanding of number concepts.
Essential questions
Routines
•
What numeral comes before or after a given
numeral?
•
Estimate the number of objects in a set (up to
30).
•
How can you show the number ____ in a
different way (e.g., models, illustrations,
manipulatives)?
•
Count part of a set and revise estimate.
•
What are the missing numbers in a given set
(13, __, __, 16)?
•
Which group has more (or less)? How do you
know?
•
What is the sequence of these numbers from
greatest to least? From least to greatest?
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-19
Grade 1 Mathematics, Quarter 2, Unit 2.1
Final, July 2011
Ordering and Comparing Whole Numbers to 30 (10 days)
Written Curriculum
Grade-Level Expectations
M(N&O)–1–2 Demonstrates understanding of the relative magnitude of numbers from 0 to 100 by
ordering whole numbers; by comparing whole numbers to each other or to benchmark whole numbers (5,
10, 25, 50, 75, 100); by demonstrating an understanding of the relation of inequality when comparing
whole numbers by using “1 more”, “1 less”, “5 more”, “5 less”, “10 more”, “10 less”; and by connecting
number words (from 0 to 20) and numerals (from 0 to 100) to the quantities and positions that they
represent using investigations, models, representations, or number lines. (Local)
Routines
M(N&O)–1–7 Makes estimates of the number of objects in a set (up to 30 ) and revises estimates as
objects are counted (e.g., A student estimates the number of pennies in a jar as 28. Then the student
counts the first 10 and makes another estimate based on those that have been counted and those that
remain in the jar.). (Local)
(IMPORTANT: Estimation should be imbedded instructionally throughout all strands.)
Clarifying the Standards
Prior Learning
In kindergarten, students learned the relative magnitude of numbers from 0 to 20. Students also learned
the names and values of coins (pennies, nickels, and dimes) and made estimates of objects in a set (up to
20).
Current Learning
In grade 1, students demonstrate understanding of the relative magnitude of numbers by connecting
numerals (0–20) to corresponding number words. In addition, students order and compare whole numbers
(0–30) to each other and to the quantities and positions that these numbers represent using investigations,
models, representations, or number lines. The grade 1 benchmark of 0–100 will be met by the end of the
year.
Future Learning
In grade 2, students will expand their knowledge of relative magnitude of numbers from 0 to 199 using
models, number lines, or explanations. Students will demonstrate understanding of monetary value by
adding coins together.
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-20
Grade 1 Mathematics, Quarter 2, Unit 2.1
Final, July 2011
Ordering and Comparing Whole Numbers to 30 (10 days)
Additional Research Findings
According to the mathematical inquiry cluster of mathematical models in The Atlas of Science Literacy,
numbers can be used to count things, place them in order, or name them (pp. 26–27).
Additionally, Principles and Standards for School Mathematics states that first-grade students should
understand numbers, ways of representing numbers, relationships among numbers, and number systems,
and should be able to make reasonable estimates. Representing numbers with various physical materials
should be a major part of mathematics instruction in elementary grades (pp. 32–33).
Notes About Resources and Materials
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-21
Grade 1 Mathematics, Quarter 2, Unit 2.1
Final, July 2011
Ordering and Comparing Whole Numbers to 30 (10 days)
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-22
Grade 1 Mathematics, Quarter 2, Unit 2.2
Adding Numbers to 30 Without Regrouping
Overview
Number of instructional days:
10
(1 day = 45 minutes)
Content to be learned
Mathematical Practices to be integrated
•
Use appropriate tools strategically.
•
Demonstrate conceptual understanding of
addition by adding whole numbers to 30.
Identify different strategies to add more than
two one-digit whole numbers.
•
Mentally add whole numbers by naming the
number that is one or two more than the
original number.
•
Mentally add whole number facts to 10.
•
•
Use manipulatives, diagrams, and calculators
to solve problems.
•
Select appropriate tools.
Make sense of problems and persevere in solving
them.
•
Identify the missing information needed to find
the solution to a given story problem.
Use composition and decomposition strategies
to solve addition problems.
•
Explain conclusions, thought processes, and
strategies in problem-solving situations.
•
Apply field properties (identity: x + 0 = x, and
commutative: x + y = y + x) to solve problems
or simplify computations.
•
Formulate and solve multi-step problems from
everyday and mathematical situations.
•
Apply understanding of odd/even to solve
addition problems.
Essential questions
Routines
•
What are different ways a number can be
composed?
•
Use estimation to plan your solution.
•
•
Revise estimates when necessary.
What strategies do you use to add 2 numbers?
More than 2 numbers?
•
What is your strategy for mental addition?
•
How can known facts help you solve facts you
don’t know?
•
What happens when you add zero to a number?
•
How is 2 + 3 related to 3 + 2?
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-23
Grade 1 Mathematics, Quarter 2, Unit 2.2
Final, July 2011
Adding Numbers to 30 Without Regrouping (10 days)
Written Curriculum
Grade-Level Expectations
M(N&O)–1–3 Demonstrates conceptual understanding of mathematical operations involving
addition and subtraction of whole numbers (from 0 to 30) by solving problems involving joining actions,
separating actions, part-part whole relationships, and comparison situations; and addition of multiple onedigit whole numbers. (Local)
(See Appendix A.)
M(N&O)–1–8 Applies properties of numbers (odd, even, composition, and decomposition [e.g., 5 is the
same as 2 + 3]) and field properties (commutative and identity for addition) to solve problems and to
simplify computations involving whole numbers. (Local)
M(N&O)–1–6 Mentally adds and subtracts whole numbers by naming the number that is one or two
more or less than the original number; and adds and subtracts whole number facts to ten (e.g., 5 + 3 = 8; 8
– 5 = 3). (Local)
(IMPORTANT: The intent of this GLE is to embed mental arithmetic throughout the instructional
program, not to teach it as a separate unit.)
Routines
M(N&O)–1–7 Makes estimates of the number of objects in a set (up to 30 ) and revises estimates as
objects are counted(e.g., A student estimates the number of pennies in a jar as 28.Then the student counts
the first 10 and makes another estimate based on those that have been counted and those that remain in
the jar.). (Local)
(IMPORTANT: Estimation should be imbedded instructionally throughout all strands.)
Clarifying the Standards
Prior Learning
In kindergarten, students added and subtracted whole numbers 0 to 10 by solving problems with joining
actions, separating actions, part-part-whole relationships, and comparison situations. They also added
multiple one-digit whole numbers.
Current Learning
In grade 1, students add whole numbers (0 to 30) by solving problems involving joining actions, partpart-whole relationships, and addition of multiple one-digit numbers. First-grade students also mentally
add whole numbers by naming the number that is one or two more than the original number.
According to Bloom’s taxonomy, students’ responses should reflect knowledge, analysis, synthesis, and
comprehension levels. First-graders may be assessed at the local level.
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-24
Grade 1 Mathematics, Quarter 2, Unit 2.2
Final, July 2011
Adding Numbers to 30 Without Regrouping (10 days)
Future Learning
Second-grade students will continue adding and will begin to mentally add whole-number facts to a sum
of 20, name numbers that are 10 more than the original number, and add 2-digit numbers in multiples of
10.
Additional Research Findings
According to The Principles and Standards for School Mathematics, teachers should guide students to
recognize that solving one problem relates to solving another problem. Teachers should provide
opportunities for students to repeatedly encounter situations where the same numbers appear in different
ways. This allows students to become flexible in using problem-solving strategies (p. 83).
Notes About Resources and Materials
Resources will vary by district (i.e., Everyday Mathematics, Investigations, Pearson Scott Foresman, etc.).
Suggested materials:
•
Hundreds charts
•
Manipulatives
•
Number lines
•
Teacher-created worksheets if necessary
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-25
Grade 1 Mathematics, Quarter 2, Unit 2.2
Final, July 2011
Adding Numbers to 30 Without Regrouping (10 days)
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-26
Grade 1 Mathematics, Quarter 2, Unit 2.3
Subtracting Numbers to 30 Without Regrouping
Overview
Number of instructional days:
10
(1 day = 45 minutes)
Content to be learned
Mathematical Practice to be integrated
•
Demonstrate conceptual understanding of
subtraction involving situations with whole
numbers 0–30.
Make sense of problems and persevere in solving
them.
Solve problems using a variety of strategies.
•
•
Apply properties of numbers (odd/even).
•
•
Decompose whole numbers up to 30 in order to
solve subtraction problems.
Formulate and solve multistep problems from
everyday and mathematical situations.
•
Mentally subtract numbers by naming the
number that is one or two less than the original
number.
•
Construct viable arguments and critique the
reasoning of others.
• Explain conclusions, thought processes, and
strategies in problem-solving situations.
Mentally subtract whole number facts from 10.
Essential questions
Routines
•
What strategy could you use to solve this
problem?
•
Mentally add whole number facts from 10.
•
How many ways are there to decompose this
number_____? (0–10)
•
Mentally add one or two more to a given
number.
•
What are two ways you can solve this
problem?
•
What is your strategy for subtracting mentally?
•
How can you tell if a number is odd or even?
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-27
Grade 1 Mathematics, Quarter 2, Unit 2.3
2010-2011
Subtracting Numbers to 30 Without Regrouping (10 days)
Written Curriculum
Grade-Level Expectations
M(N&O)–1–3 Demonstrates conceptual understanding of mathematical operations involving
addition and subtraction of whole numbers (from 0 to 30) by solving problems involving joining actions,
separating actions, part-part whole relationships, and comparison situations; and addition of multiple onedigit whole numbers. (Local)
(See Appendix A.)
M(N&O)–1–8 Applies properties of numbers (odd, even, composition, and decomposition [e.g., 5 is the
same as 2 + 3]) and field properties (commutative and identity for addition) to solve problems and to
simplify computations involving whole numbers. (Local)
M(N&O)–1–6 Mentally adds and subtracts whole numbers by naming the number that is one or two
more or less than the original number; and adds and subtracts whole number facts to ten (e.g., 5 + 3 = 8; 8
– 5 = 3). (Local)
(IMPORTANT: The intent of this GLE is to embed mental arithmetic throughout the instructional
program, not to teach it as a separate unit.)
Routines
M(N&O)–1–7 Makes estimates of the number of objects in a set (up to 30 ) and revises estimates as
objects are counted(e.g., A student estimates the number of pennies in a jar as 28.Then the student counts
the first 10 and makes another estimate based on those that have been counted and those that remain in
the jar.). (Local)
(IMPORTANT: Estimation should be imbedded instructionally throughout all strands.)
M(N&O)–1–6 Mentally adds and subtracts whole numbers by naming the number that is one or two
more or less than the original number; and adds and subtracts whole number facts to ten (e.g., 5 + 3 = 8; 8
– 5 = 3). (Local)
(IMPORTANT: The intent of this GLE is to embed mental arithmetic throughout the instructional
program, not to teach it as a separate unit.)
Clarifying the Standards
Prior Learning
In kindergarten, students performed addition and subtraction to 10. Students mentally added and
subtracted whole numbers by naming the number that is one more or one less than the original number.
Current Learning
Students solve problems involving separating actions, part-part-whole relationships, and comparison
situations. Students begin to mentally subtract whole numbers up to 10 using one less or two less than the
original number.
C-28
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
Subtracting Numbers to 30 Without Regrouping (10 days)
Grade 1 Mathematics, Quarter 2, Unit 2.3
2010-2011
Future Learning
Second-grade students will continue to gain conceptual understanding of addition and subtraction with
larger numbers. Students will mentally subtract whole-number facts to a sum of 20. They will name the
number that is 10 less than the original number and will mentally subtract two-digit number problems
using multiples of 10.
Additional Research Findings
According to The Atlas of Science Literacy, the mathematical processes map shows explicit and extensive
connections to maps on mathematic topics. “Mathematical Inquiry: Mathematical Models” shows that
choices have to be made about which operation will give the best results. Results should always be judged
by whether they make sense and are useful. Students will readily give the sums and differences of singledigit numbers in familiar contexts with the operation that makes sense to them, and they will judge the
reasonableness of the answer (pp. 28–29).
According to Principles and Standards for School Mathematics, first-grade students should understand
numbers and operations, develop number sense, and gain fluency in arithmetic computations—the core of
mathematic education for the elementary grades. Students should attain a rich understanding of numbers,
including what they are; how they are represented with objects, numerals, or on number lines; how they
are related to one another; how numbers are embedded in systems that have structures and properties; and
how to use numbers to solve problems (pp. 32–34).
Notes About Resources and Materials
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-29
Grade 1 Mathematics, Quarter 2, Unit 2.3
2010-2011
C-30
Subtracting Numbers to 30 Without Regrouping (10 days)
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
Grade 1 Mathematics, Quarter 2, Unit 2.4
Using Addition and Subtraction
Strategies for Facts Using Equality
Overview
Number of instructional days:
10
(1 day = 45 minutes)
Content to be learned
Mathematical practices to be integrated
•
Demonstrate conceptual understanding of
addition and subtraction involving situations
with numbers from 0 to 30.
Look for and express regularity in repeated
reasoning.
•
Demonstrate conceptual understanding of
addition of multiple one-digit whole numbers.
Attend to precision.
•
Estimate a number of objects and revise when
appropriate.
•
•
Use number fact families to solve problems.
•
Apply accurate and efficient calculations.
•
Communicate strategies precisely.
Explore the concept of equality by finding the
missing number to make an equation true.
Essential questions
Routines
•
What strategies do you use to add or subtract
whole numbers from 0 to 30?
•
•
How can you add multiple one-digit numbers?
Mentally add/subtract numbers by naming the
number that is one or two more/less than the
original number.
•
How many objects do you estimate are in the
jar? How can you find out if you are correct?
•
Mentally add/subtract numbers to 10.
•
Make and revise estimates.
•
When would you revise your estimate?
•
How can you find the missing number in the
equation?
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-31
Grade 1 Mathematics, Quarter 2, Unit 2.4
Final, July 2011
Using Addition and Subtraction
Strategies for Facts (10 days)
Written Curriculum
Grade-Level Expectations
M(N&O)–1–3 Demonstrates conceptual understanding of mathematical operations involving
addition and subtraction of whole numbers (from 0 to 30) by solving problems involving joining actions,
separating actions, part-part whole relationships, and comparison situations; and addition of multiple one
digit whole numbers. (Local)
(See Appendix A.)
M(F&A)–1–4 Demonstrates conceptual understanding of equality by finding the value that will make
an open sentence true (e.g., 2 + W = 7 ) using models, verbal explanations, or written equations. (limited to
one operation and limited to use addition or subtraction) (Local)
Routines
M(N&O)–1–6 Mentally adds and subtracts whole numbers by naming the number that is one or two
more or less than the original number; and adds and subtracts whole number facts to ten (e.g., 5 + 3 = 8; 8
– 5 = 3). (Local)
(IMPORTANT: The intent of this GLE is to embed mental arithmetic throughout the instructional
program, not to teach it as a separate unit.)
M(N&O)–1–7 Makes estimates of the number of objects in a set (up to 30 ) and revises estimates as
objects are counted (e.g., A student estimates the number of pennies in a jar as 28. Then the student
counts the first 10 and makes another estimate based on those that have been counted and those that
remain in the jar.). (Local)
(IMPORTANT: Estimation should be imbedded instructionally throughout all strands.)
Clarifying the Standards
Prior Learning
In kindergarten, students worked on addition and subtraction with numbers up to ten. Students began
learning how to add multiple one-digit numbers.
Current Learning
In grade 1, students build upon their knowledge of addition and subtraction with numbers from 0 to 30.
Students practice how to add multiple one-digit numbers using strategies such as doubles, counting on,
and combinations of ten (7 + 3, 8 + 2, etc.).
According to Bloom’s taxonomy, student responses are at the knowledge (identify, label), analysis
(classify, compare), and synthesis (organize, plan) levels. Students are tested locally.
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-32
Grade 1 Mathematics, Quarter 2, Unit 2.4
Final, July 2011
Using Addition and Subtraction
Strategies for Facts (10 days)
Future Learning
In grade 2, students will continue to build upon their knowledge of addition and subtraction with
numbers. In grade 3, students will be introduced to the concept of regrouping. In future grades, students
will learn and demonstrate the relationship between repeated addition and multiplication, use multiple
representations, and investigate the relationship between repeated subtraction and division. This can be
tested at the state level.
Additional Research Findings
According to Principles and Standards for School Mathematics:
An understanding of addition and subtraction can be generated when young students solve joining
and take away problem by directly modeling the situation or by using counting strategies such as
counting on and counting back. In developing the meaning of addition and subtraction of whole
numbers students should also encounter the properties of operations (commutative and associative).
In pre-k through grade 2 students should also begin to develop an understanding of the concepts of
multiplication and division (pp. 83–84).
Notes About Resources and Materials
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-33
Grade 1 Mathematics, Quarter 2, Unit 2.4
Final, July 2011
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
Using Addition and Subtraction
Strategies for Facts (10 days)
C-34