Grade 1 Mathematics, Quarter 3, Unit 3.1
Using Benchmark Numbers of 5, 10, 25,
50, 75, 100
Overview
Number of instructional days:
10
(1 day = 45–60 minutes)
Content to be learned
Mathematical practices to be integrated
•
Order numbers by comparing them to
benchmark numbers of 5, 10, 25, 50, 75, 100.
Look for and make use of structure.
Make connection or relationships-patterns
•
•
Compare whole numbers using more or less
and benchmark numbers of 5, 10, 25, 50, 75,
100.
•
Use prior knowledge (i.e., this pattern reminds
me of …).
•
Use benchmark numbers to analyze patterns,
trends, or distributions in a variety of contexts
using the ideas of more, less, or equal.
Model with mathematics.
•
Make predictions and estimations realizing
changes can be made if necessary.
•
Ask, “Does it make sense?”
Essential questions
Routines
•
•
Describe numbers as odd or even.
•
Name different ways to state a number.
•
Compose and decompose numbers.
How can you use a number line or grid to
identify numbers that are before, after, or in
between benchmark numbers?
•
How can benchmark numbers help you to order
numbers?
•
How can you compare the relationship between
two numbers using 1, 5, 10, or more/less?
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-35
Grade 1 Mathematics, Quarter 3, Unit 3.1
Final, July 2011
Using Benchmark Numbers of 5, 10, 25, 50, 75, 100 (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)
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)–1–8 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)
Clarifying the Standards
Prior Learning
In kindergarten, students learned the relative magnitude of numbers from 0 to 20 through investigations
of numbers. They compared numbers to benchmark numbers using 1 more and 1 less. Kindergarteners
also learned the names and values of coins including pennies, nickels, and dimes. Through routines, they
made estimates of objects in a set up to 20.
Current Learning
In grade 1, students order and compare whole numbers to each other using benchmark numbers. Students
analyze patterns and trends to explain the ideas of more, less, or equal as they relate to benchmark
numbers. According to Bloom’s taxonomy, student responses should reflect knowledge and a higher level
of comprehension.
By the end of grade 1, students know the value and name of a quarter. They add collections of like coins
up to a sum no greater than a dollar. Students also use benchmark numbers of 50, 75, and 100. Using
investigations, models, representations, or number lines, students connect number words (0–20) and
numerals (0–100) to the quantities and positions that these words and numerals represent.
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-36
Grade 1 Mathematics, Quarter 3, Unit 3.1
Final, July 2011
Using Benchmark Numbers of 5, 10, 25, 50, 75, 100 (10 days)
Future Learning
In grade 2, students will expand their relative understanding of numbers from 0 to 199 using benchmark
numbers of 10, 25, 50, 75, 100, 125, 150, or 175. They will compare whole numbers by using 1
more/less, 10 more/less, and 100 more/less. Through routines, they will demonstrate understanding of
monetary value by adding like coins to a sum no greater than $1.99 and will represent results using dollar
notation. Grade 2 students will recognize equivalent coin representations of the same value and will make
change from a dollar or less.
Additional Research Findings
Principles and Standards for School Mathematics states that instructional programs from pre-K through
12 should enable students to understand numbers, represent numbers, and show relationships between
numbers and number systems (pp. 32–33). Additionally, estimation is an important tool in self-checking
computations (p. 155).
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-37
Grade 1 Mathematics, Quarter 3, Unit 3.1
Final, July 2011
Using Benchmark Numbers of 5, 10, 25, 50, 75, 100 (10 days)
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-38
Grade 1 Mathematics, Quarter 3, Unit 3.2
Identifying, Extending, and Applying
Non-Numeric and Numeric Patterns
Overview
Number of instructional days:
7
(1 day = 45 minutes)
Content to be learned
Mathematical practices to be integrated
•
Identify and extend numeric and non-numeric
patterns to the next one, two, or three elements.
Look for and make use of structure.
•
Find a missing element in a repeating pattern.
•
Identify and/or extend a growing pattern.
•
Make connections or relationships (i.e.,
patterns).
•
Use prior learning to apply to current learning,
(i.e., This pattern reminds me of…).
Model with mathematics.
•
Draw pictures to illustrate a pattern.
•
Use words to explain the pattern.
Essential questions
Routines
•
What comes next in this pattern (numeric or
non-numeric)?
•
Mentally add/subtract using benchmark
numbers.
•
How can you show this pattern in a different
way? (sound, body movements, manipulatives)
•
Describe 1 more/less, 5 more/less, 10 more/less
of a number.
•
What is missing from the pattern (numeric or
non-numeric)? How do you know?
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-39
Grade 1 Mathematics, Quarter 3, Unit 3.2
Final, July 2011
Identifying, Extending, and Applying
Non-Numeric and Numeric Patterns (7 days)
Written Curriculum
Grade-Level Expectations
M(F&A)–1–1 Identifies and extends to specific cases a variety of patterns (repeating and growing
[numeric and non-numeric]) represented in models, tables, or sequences by extending the pattern to the
next one, two, or three elements, by finding a missing element (e.g., 2, 4, 6, ___, 10), or by translating
repeating patterns across formats (e.g., an abb pattern can be represented as snap, clap, clap; or red,
yellow, yellow; or 1,2,2). (Local)
Routines
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)
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 used sequences of shapes, sounds, movement, colors, and letters to extend
repeating patterns to the next one, two, or three elements across formats.
Current Learning
In grade 1, students use sequences of shapes, sounds, movement, colors, letters, and numbers to extend
repeating and growing patterns to the next one, two, or three elements. Numeric patterns are new in this
unit. Students continue to translate patterns across formats. According to Bloom’s taxonomy, student
responses will be at the synthesis (compose, construct, create), comprehension (tell), and application
(show) levels.
Future Learning
In grade 2, students will work with a variety of patterns—including linear, nonlinear, numeric and nonnumeric—represented in models, tables, or sequences.
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-40
Grade 1 Mathematics, Quarter 3, Unit 3.2
Final, July 2011
Identifying, Extending, and Applying
Non-Numeric and Numeric Patterns (7 days)
Additional Research Findings
According to the Atlas of Science Literacy, Volume 1, (Mathematical Representations), simple graphs can
help students describe their observations. Tables and graphs can show values of one quantity related to
values of another. Mathematical ideas can be represented concretely, graphically, or symbolically as a
mathematical process.
Science for all Americans states that science provides mathematics with interesting problems to
investigate, and mathematics provides science with powerful tools to use in analyzing data. Often abstract
patterns that have been studied for their own sake by mathematicians have turned out much later to be
very useful in science. Both science and mathematics are working to discover general patterns and
relationships. In this sense, these disciplines are parts of the same endeavor.
Notes About Resources and Materials
Resources will vary by district (i.e., Everyday Mathematics, Investigations, Pearson Scott Foresman, etc.).
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-41
Grade 1 Mathematics, Quarter 3, Unit 3.2
Final, July 2011
Identifying, Extending, and Applying
Non-Numeric and Numeric Patterns (7 days)
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-42
Grade 1 Mathematics, Quarter 3, Unit 3.3
Adding Like Coins
Overview
Number of instructional days:
5
(1 day = 45–60 minutes)
Content to be learned
Mathematical practices to be integrated
•
Look for and make use of structure.
•
Recognize and name coins and their respective
values (penny, nickel, dime, and quarter).
Add collections of like coins to sums no
greater than $1.00.
•
Make connections of relationships (i.e.,
patterns in counting coins).
•
Use coins to count days on the calendar.
Use appropriate tools strategically.
•
Select appropriate tools (i.e., coins, pictures,
drawings, etc.).
•
Visualize patterns when adding like coins.
Essential questions
Routines
•
Which of these coins is a (penny, nickel, dime,
quarter)?
•
•
What is the value of a (penny, nickel, dime,
quarter)?
Make estimates of a number of objects in a set
up to 30; revise estimates as objects are
counted.
•
•
What is the sum of this like coin set? [No
greater than $1.00.]
Add and subtract whole numbers mentally by
naming the number that is one or two more/less
than the original number.
•
How would you organize a set of like coins to
show this value? [After this is done] Show this
value with a different set of like coins.
•
Use pennies to add one more, nickels to add
five more, dimes to add 10 more.
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-43
Grade 1 Mathematics, Quarter 3, Unit 3.3
Final, July 2011
Adding Like Coins (5 days)
Written Curriculum
Grade-Level Expectations
M(N&O)–1–5 Demonstrates understanding of monetary value by knowing the names and values for
coins (penny, nickel, dime, and quarter); and by adding collections of like coins together to a sum no
greater than $1.00. (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.)
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)–1–2 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)
Clarifying the Standards
Prior Learning
In kindergarten, students learned the names and values of pennies, nickels, and dimes.
Current Learning
In grade 1, students demonstrate knowledge of the names and monetary values of pennies, nickels, dimes,
and quarters. They also add collections of like coins together to a sum no greater than $1.00.
According to Bloom’s taxonomy, student responses are at the knowledge (identify, label), analysis
(classify, compare), and synthesis (organize, plan) levels.
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-44
Grade 1 Mathematics, Quarter 3, Unit 3.3
Final, July 2011
Adding Like Coins (5 days)
Future Learning
As part of a routine established in quarter 1 of grade 2, students will begin to add coins together. Later,
the routine will expand to include adding coins to a value no greater than $1.99 and representing the
results in dollar notation. Students will make change from a dollar or less; they will also recognize
equivalent coin representations of the same value.
In grade 5, students will mentally calculate change back from $1.00, $5.00, and $10.00.
Additional Research Findings
Benchmarks for Science Literacy states that students at this level should recognize that money can buy
things that people need or want. People earn money by working at a job making or growing things, selling
things, or doing things to help other people.
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-45
Grade 1 Mathematics, Quarter 3, Unit 3.3
Final, July 2011
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
Adding Like Coins (5 days)
C-46
Grade 1 Mathematics, Quarter 3, Unit 3.4
Comparing and Ordering Whole Numbers to 100
Overview
Number of instructional days:
8
(1 day = 45–60 minutes)
Content to be learned
Mathematical practices to be integrated
•
Order and compare numbers (0–100) using
place value.
Construct viable arguments and critiques the
reasoning of others.
•
Demonstrate an understanding of inequality
when comparing whole numbers (one more,
one less, etc.).
•
•
Use benchmark numbers to compare whole
numbers up to 100.
•
Explain the meaning of symbols to represent
relationships.
•
Order whole numbers by comparing them to
each other.
•
Use manipulatives to measure and compare
quantities as precisely as possible.
•
Use models, explanations, and other
representations to show equivalency in
composing and decomposing numbers (0–100)
using expanded notation.
Reason abstractly and quantitatively.
•
Support arguments using objects, drawings,
diagrams and actions.
Attend to precision.
•
Attend to the meaning of quantities.
•
Make sense of quantities in problem situations.
Use mathematical symbols to represent
relationships of numbers.
Essential questions
Routines
•
What is your strategy for comparing numbers?
•
•
How can you use place value to order/compare
numbers?
Continue to practice mental addition and
subtraction as related to benchmark numbers.
•
Reinforce the properties of odd/even.
•
How can you use benchmark numbers to
order/compare numbers?
•
How can you use expanded notation to
compare/order numbers?
•
How does a number line help you
compare/order numbers?
•
How do mathematical symbols help you show
and record relationships of numbers?
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-47
Grade 1 Mathematics, Quarter 3, Unit 3.4
Final, July 2011
Comparing and Ordering Whole Numbers to 100 (8 days)
Written Curriculum
Grade-Level Expectations
M(N&O)–1–1 Demonstrates conceptual understanding of rational numbers with respect to: whole
numbers from 0 to 100 using place value, by applying the concepts of equivalency in composing or
decomposing numbers; and in expanded notation using models, explanations, or other representations;
and positive fractional numbers (benchmark fractions: a/2, a/3, or a/4, where a is a whole number
greater than 0 and less than or equal to the denominator) as a part to whole relationship in area
models where the denominator is equal to the number of parts in the whole using models,
explanations, or other representations. (Local)
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)–1–6 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)–1–8 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)
Clarifying the Standards
Prior Learning
In kindergarten, students used models, explanations, and other representations to investigate the concepts
of equivalency in decomposing and composing numbers whole numbers (0–12). They investigated the
concept of “fair share” and positive fractional numbers.
Current Learning
In grade 1, students use models, explanations, and other representations to develop the concept of
equivalency in decomposing and composing whole numbers (0–100). Students begin to use expanded
notation as another way to represent numbers (0–100). They use additional benchmark numbers of 50, 75,
and 100 to order and compare numbers, and they express the relationship of numbers in terms of
inequality (more or less). Students begin to use mathematical symbols <, >, or = to create number models
that show relationships among numbers from 0 to 100. These concepts may be tested 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-48
Grade 1 Mathematics, Quarter 3, Unit 3.4
Final, July 2011
Comparing and Ordering Whole Numbers to 100 (8 days)
Future Learning
In grade 2, students will continue to expand their understanding of the relationships among numbers 0–
199. They will also begin to use positive fractional numbers as part-to-whole numbers. They will be
tested at the state level.
Additional Research Findings
According to Principles and Standards for School Mathematics, it is absolutely essential that, by the end
of second grade, students develop the notion of the base-10 numeration system and place-value concepts.
They need to understand how numbers are written. Additionally, 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, 81).
Notes About Resources and Materials
Resources will vary by district (i.e., Everyday Mathematics, Investigations, Pearson Scott Foresman, etc.).
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-49
Grade 1 Mathematics, Quarter 3, Unit 3.4
Final, July 2011
Comparing and Ordering Whole Numbers to 100 (8 days)
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-50
Grade 1 Mathematics, Quarter 3, Unit 3.5
Investigating 2-D Geometrical Shapes
Overview
Number of instructional days:
5
(1 day = 45–60 minutes)
Content to be learned
Mathematical practices to be integrated
•
Model with mathematics.
Use properties/attributes to sort/classify
polygons and objects (triangles, squares,
rectangles, rhombi, trapezoids, hexagons) by a
combination of two non-measurable or
measurable attributes.
•
Draw objects in the environment that are
polygons and/or circles.
•
Use line symmetry and mirror images to show
congruency.
•
Draw pictures and use objects to illustrate
mathematical concepts.
•
Use words to describe shapes.
Make sense of problems and persevere in solving
them.
•
Give verbal descriptions of attributes of
shapes.
•
Consider similar problems to gain insight into
a problem solution.
Construct viable arguments and critique the
reasoning of others.
•
Justify argruments using objects, drawings,
diagrams, and actions.
•
Listen to another’s argument and decide if it
makes sense, asking questions to clarify and
improve the argument.
Essential questions
Routines
•
What are the attributes of this polygon
(triangle, square, rectangle, rhombi, trapezoid,
hexagon)?
•
•
How can you compare these different shapes
by at least two attributes?
Order whole numbers from 0–100 by
comparing whole numbers to each other or to
benchmark whole numbers (5, 10, 25, 50, 75,
100).
•
•
Where are all of the (trapezoids, triangles,
squares, rectangles, rhombi, hexagons) in this
set of polygons?
Demonstrate understanding of the relationship
of an inequality when comparing whole
numbers by using 1 more, 1 less, 5 more, 5
less, 10 more, and 10 less.
•
What are some real objects that are
polygons/circles?
•
•
How can you prove that two shapes are the
same shape and size (congruent)?
Connect number words (0–20) and numerals
(0–100) to the quantities and positions that they
represent using investigations, models,
representations, or number lines.
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-51
Grade 1 Mathematics, Quarter 3, Unit 3.5
Final, July 2011
Investigating 2-D Geometrical Shapes (8 days)
Written Curriculum
Grade-Level Expectations
M(G&M)–1–1 Uses properties, attributes, composition, or decomposition to sort or classify
polygons (triangles, squares, rectangles, rhombi, trapezoids, and hexagons) or objects by a combination
of two non-measurable or measurable attributes; and recognizes, names, builds, and draws polygons and
circles in the environment. (Local)
M(G&M)–1–4 Demonstrates conceptual understanding of congruency by making mirror images and
creating shapes that have line symmetry. (Local)
Routines
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)
Clarifying the Standards
Prior Learning
In kindergarten, students used properties and attributes to sort or classify polygons (triangles, squares,
rectangles) by using one non-measurable or measurable attribute. Students also recognized, named, and
built polygons and circles in their environment.
Current Learning
In grade 1, students use properties and attributes to sort or classify polygons (triangles, squares,
rectangles, rhombi, trapezoids, hexagons) by using two non-measurable or measurable attributes. They
continue to explore shapes by drawing objects in the environment that are polygons and circles. This GLE
can be tested at the local level. Students in grade 1 make mirror-images and create shapes that have line
symmetry to demonstrate conceptual understanding of congruency.
According to Bloom’s taxonomy, student responses are at the knowledge (describe, identify, label),
analysis (classify, distinguish, compare), and synthesis (organize, create) levels.
Future Learning
In grade 2, students will consider properties and a combination of two or more non-measurable or
measurable attributes to sort or classify polygons (triangles, squares, rectangles, rhombi, trapezoids,
hexagons). This GLE will be tested in grade 2 at the state level. In grades 3–5, students will begin to
incorporate angles as a property by which shapes can be distinguished from one another.
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-52
Grade 1 Mathematics, Quarter 3, Unit 3.5
Final, July 2011
Investigating 2-D Geometrical Shapes (8 days)
Additional Research Findings
The Atlas of Science Literacy, Volume 2 (The Mathematical World cluster; Shapes map), states, “to make
sense of the world, the human mind relies heavily on its perception of shapes and patterns. The artifacts
around us and the familiar forms we see in nature can often be characterized in terms of geometric
shapes” (p. 66).
According to Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics, children
compose and decompose plain and solid figures, thus building an understanding of part-whole
relationships as well as the properties of the original and composite shapes. As they combine figures, they
recognize them from different perspectives and orientations, describe their geometric attributes and
properties, and determine how they are alike and different, in the process developing a background for
measurement and initial understanding of such properties as congruence and symmetry.
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-53
Grade 1 Mathematics, Quarter 3, Unit 3.5
Final, July 2011
Investigating 2-D Geometrical Shapes (8 days)
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-54
Grade 1 Mathematics, Quarter 3, Unit 3.6
Investigating 3-D Geometrical Shapes
Overview
Number of instructional days:
5
(1 day = 45–60 minutes)
Content to be learned
Mathematical practices to be integrated
•
Model with mathematics.
•
Recognize 3-D shapes and structures in the
environment (rectangular prisms, cylinders,
spheres).
Recognize 3-D shapes in different perspectives
(drawings vs. real objects).
•
Draw pictures and use objects to illustrate
mathematical concepts.
•
Use words to describe 3-D shapes.
Make sense of problems and persevere in solving
them.
•
Give verbal descriptions of 3-D shapes.
•
Consider similar problems to gain insight into
a problem solution.
Construct viable arguments and critique the
reasoning of others.
•
Make and test own conjectures using objects,
drawings, diagrams, and actions.
•
Listen to another’s argument and decide if it
makes sense, asking questions to clarify and
improve the argument.
Essential questions
Routines
•
How can you describe this shape?
•
•
How is this object different from other shapes?
•
Where can you find examples of this shape in
the environment?
Order whole numbers from 0–100 by
comparing whole numbers to each other or to
benchmark whole numbers (5, 10, 25, 50, 75,
100).
•
Demonstrate understanding of the relationships
of inequality when comparing whole numbers
by using 1 more, 1 less, 5 more, 5 less, 10
more, and 10 less.
•
Connect number words (0–20) and numerals
(0–100) to the quantities and positions that they
represent using investigations, models,
representations, or number lines.
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-55
Grade 1 Mathematics, Quarter 3, Unit 3.6
Final, July 2011
Investigating 3-D Geometrical Shapes (5 days)
Written Curriculum
Grade-Level Expectations
M(G&M)–1–3 Given an example of a three-dimensional geometric shape (rectangular prisms,
cylinders, or spheres)finds examples of objects in the environment that are of the same geometric shape
(e.g., show a wooden cylinder and students identify common objects of the same shape). (Local)
Routines
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)
Clarifying the Standards
Prior Learning
In kindergarten, students began interpreting the physical world through geometrical ideas; they identified,
named, and described a variety of shapes in a variety of ways. Kindergarteners also began to use their
knowledge of shapes to construct more complex shapes that modeled objects in their environment.
Current Learning
Grade 1 students investigate two-dimensional polygons such as trapezoids, hexagons, triangles, squares,
rhombi, and rectangles using measurable and non-measurable attributes. Students connect objects in their
environment to three-dimensional shapes. These skills may be assessed at the local level.
Future Learning
In grade 2, students will use geometric knowledge and spatial reasoning to develop foundations for area
fractions and proportion.
In grade 4, students will use properties or attributes (shape of bases or number of lateral faces) to identify,
compare, or describe three-dimensional shapes (rectangular, prisms, triangular prisms, cylinders, or
spheres).
In grade 5, students will use properties or attributes (shape of bases, number of lateral faces or number of
bases) to identify, compare, or describe three-dimensional shapes (rectangular prisms, triangular prisms,
cylinders, spheres, pyramids, or cones).
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-56
Grade 1 Mathematics, Quarter 3, Unit 3.6
Final, July 2011
Investigating 3-D Geometrical Shapes (5 days)
Additional Research Findings
According to Principles and Standards for School Mathematics, the knowledge of geometry and spatial
relationships that children bring to school should be expanded through explorations, investigations, and
discussions of shapes and structures in the classroom. Students use their notions of geometry to become
more proficient in describing, representing, and navigating their environment and they should explore
shapes by decomposing and creating new ones (p. 97).
Geometry lays the foundation for other topics in math, art, science, and social studies. Some students are
stronger in geometry than in number skills, therefore teachers should use this strength to foster
enthusiasm for mathematics.
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-57
Grade 1 Mathematics, Quarter 3, Unit 3.6
Final, July 2011
Investigating 3-D Geometrical Shapes (5 days)
Cumberland, Lincoln, and Woonsocket Public Schools
in collaboration with the Charles A. Dana Center at the University of Texas at Austin
C-58