Grade 1 Mathematics, Quarter 1, Unit 1.1
Distinguishing Between Shapes and Attributes
Overview
Number of Instructional Days:
5
(1 day = 45 minutes)
Content to Be Learned
Mathematical Practices to Be Integrated
•
Understand defining attributes (e.g., triangles
are closed and three-sided).
Construct viable arguments and critique the
reasoning of others.
•
Understand non-defining attributes (e.g., color,
orientation, overall size).
•
Reason with shapes and their attributes.
•
Distinguish between defining and non-defining
attributes.
•
Make conjectures and build a logical
progression of statements.
•
Build shapes to understand defining attributes.
•
Critique the reasoning of others.
•
Draw shapes to understand defining attributes.
Look for and make use of structure.
•
Discern a pattern or structure.
•
How can you draw a _____________ (square,
triangle, rectangle, hexagon, circle, trapezoid)?
Show me.
•
How can you build a _____________ (square,
triangle, rectangle, hexagon, circle, trapezoid)?
Show me.
•
How do you know the shape you drew/built is a
___________?
Essential Questions
•
What is this shape and how do you know?
•
What attributes did you use to sort these
shapes?
•
Why did you choose those attributes to sort
these objects?
•
How can you sort these shapes in another way?
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 1 Grade 1 Mathematics, Quarter 1, Unit 1.1
Distinguishing Between Shapes and Attributes (5 days)
Written Curriculum
Common Core State Standards for Mathematical Content
Geometry
1.G
Reason with shapes and their attributes.
1.G.1
Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus nondefining attributes (e.g., color, orientation, overall size); build and draw shapes to possess
defining attributes.
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.
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.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 2 Grade 1 Mathematics, Quarter 1, Unit 1.1
Distinguishing Between Shapes and Attributes (5 days)
Clarifying the Standards
Prior Learning
Students named objects in the environment using names of shapes. They also named shapes correctly
regardless of orientation. Students analyzed and compared two- and three-dimensional shapes describing
their similarities and differences using informal language. Students built and drew shapes as well as
composing simple shapes to form larger ones.
Current Learning
In this unit, students distinguish between defining (number of sides, number of vertices) and non-defining
(color, size, orientation) attributes and use this formal language to describe shapes. They expand
knowledge of two-dimensional shapes (square, circle, triangle, hexagon, rectangle, and trapezoid) using
defining attributes and they draw and build shapes to distinguish defining attributes (draw/build closed
shape with four equal sides). This is being taught at the developmental level.
Later in the year (unit 2.3), students will compose two-dimensional and three-dimensional shapes to make
composite shapes.
Future Learning
In second grade, students will use their knowledge of attributes to recognize and draw shapes having
specified attributes (number of angles or faces).
Additional Findings
According to Principles and Standards for School Mathematics, “Teachers must ensure that students see
collections of triangles in different positions and with different sizes of angles and shapes that have a
resemblance to triangles but are not triangles.” (p. 98)
See A Research Companion to Principles and Standards for School Mathematics for information on
theories on geometric thinking learning and teaching geometry. (p. 152)
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 3 Grade 1 Mathematics, Quarter 1, Unit 1.1
Distinguishing Between Shapes and Attributes (5 days)
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 4 Grade 1 Mathematics, Quarter 1, Unit 1.2
Ordering Objects and Interpreting Data
Overview
Number of Instructional Days:
5
(1 day = 45 minutes)
Content to Be Learned
Mathematical Practices to Be Integrated
•
Order three objects by length.
Model with mathematics.
•
Interpret data with up to three categories.
•
Apply mathematics known to everyday life.
•
Answer questions about the total number of
data points.
•
Use tools to identify important quantities in
practical situations.
•
Tell how many data points are in each
category.
•
Analyze and interpret data mathematically to
draw conclusions.
Attend to precision.
•
Communicate precisely to others.
•
Specify units of measure to clarify the
quantity.
•
Calculate/count accurately.
•
What is the total number of data points in each
category? What is the total number of data
points in all?
Essential Questions
•
How would you put these objects in order?
Explain.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 5 Grade 1 Mathematics, Quarter 1, Unit 1.2
Ordering Objects and Interpreting Data (5 days)
Written Curriculum
Common Core State Standards for Mathematical Content
Measurement and Data
1.MD
Measure lengths indirectly and by iterating length units.
1.MD.1.
Order three objects by length; compare the lengths of two objects indirectly by using a third
object.
Represent and interpret data.
1.MD.4.
Organize, represent, and interpret data with up to three categories; ask and answer questions
about the total number of data points, how many in each category, and how many more or less
are in one category than in another.
Common Core Standards for Mathematical Practice
4
Model with mathematics.
Mathematically proficient students can apply the mathematics they know to solve problems arising in
everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition
equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a
school event or analyze a problem in the community. By high school, a student might use geometry to
solve a design problem or use a function to describe how one quantity of interest depends on another.
Mathematically proficient students who can apply what they know are comfortable making assumptions
and approximations to simplify a complicated situation, realizing that these may need revision later. They
are able to identify important quantities in a practical situation and map their relationships using such
tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships
mathematically to draw conclusions. They routinely interpret their mathematical results in the context of
the situation and reflect on whether the results make sense, possibly improving the model if it has not
served its purpose.
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 6 Grade 1 Mathematics, Quarter 1, Unit 1.2
Ordering Objects and Interpreting Data (5 days)
Clarifying the Standards
Prior Learning
Students used the attribute of length to describe objects. They compared two objects by direct comparison
of length to find which object is taller/shorter, longer/shorter, etc.
Current Learning
In this unit, students order three objects by length. They interpret data with up to three categories.
Students ask and answer questions about the total number of data points. This is taught at the
developmental level.
Later in the year (Unit 2.2), students compare the length of two objects indirectly by using a third object.
Students organize and represent data with up to three categories (Unit 3.2). They ask and answer
questions about the total number of data points, how many in each category, and how many more or less
are in one category than in another.
Future Learning
In second grade, students will use and select appropriate tools to measure objects using standard units.
Students will generate data by measuring line plots. They will draw a picture graph and a bar graph to
represent data with up to four categories. They will solve word problems using information presented in a
bar graph.
Additional Findings
Representing measurements and discrete data in picture and bar graphs involves counting and
comparisons that provide another meaningful connection to number relationships (Curriculum Focal
Points, p. 18).
Students in grade 1 can ask and answer questions about categorical data based on a representation of the
data (Mathematical Progressions, K–3, Categorical Data; Grades 2–5, Measurement Data p.5–6).
Students struggle to see the data as a whole versus individual categories. Teachers need to help students
make the conceptual leap to move from seeing data as disaggregate pieces to a comprehensive whole as
referenced from A Research Companion to Principles and Standards for School Mathematics, p. 202.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 7 Grade 1 Mathematics, Quarter 1, Unit 1.2
Ordering Objects and Interpreting Data (5 days)
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 8 Grade 1 Mathematics, Quarter 1, Unit 1.3
Introduction to Place Value and Comparing to 30
Overview
Number of Instructional Days:
15
(1 day = 45 minutes)
Content to Be Learned
Mathematical Practices to Be Integrated
•
Count to 120, starting at any number less than
120.
Make sense of problems and persevere in solving
them.
•
Read and write numerals to 30.
•
•
Represent number of objects with written
numerals.
Continually ask themselves, “Does this make
sense?”
•
Understand that the two digits of a two-digit
number are made up of tens and ones.
Use concrete objects or pictures to help
conceptualize and solve problems.
•
Understand the approaches of others.
•
•
Understand that 10 is a bundle of 10 ones
called a “ten.”
•
Understand that the numbers 11–19 are
composed of a ten and ones.
•
Understand that the decade numbers (10, 20,
30, 40 …) refer to 1, 2, 3, 4 tens and zero ones.
•
Compare two 2-digit numbers using various
strategies including place value.
Look for and make use of structure.
•
Recognize the structure of two-digit numbers
(understand two-digit numbers as composed of
tens and ones).
•
Detect the pattern in a counting sequence.
•
Detect patterns in word names and their
numeral representations.
Essential Questions
•
Starting at ______, how far can you count?
What patterns do you notice?
•
How can you use tens and ones to describe the
number ____? (11–19 and 10, 20, 30?)
•
What is this number (shown by this amount of
objects)?
•
Which number is more? Which number is
fewer? How do you know?
•
How many ____ (objects) do you see? How do
you write this number?
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 9 Grade 1 Mathematics, Quarter 1, Unit 1.3
Introduction to Place Value and Comparing to 30 (15 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.2
1.NBT.3
Understand that the two digits of a two-digit number represent amounts of tens and ones.
Understand the following as special cases:
a.
10 can be thought of as a bundle of ten ones — called a “ten.”
b.
The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six,
seven, eight, or nine ones.
c.
The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six,
seven, eight, or nine tens (and 0 ones).
Compare two two-digit numbers based on meanings of the tens and ones digits, recording the
results of comparisons with the symbols >, =, and <.
Common Core Standards for Mathematical Practice
1
Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem and
looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They
make conjectures about the form and meaning of the solution and plan a solution pathway rather than
simply jumping into a solution attempt. They consider analogous problems, and try special cases and
simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate
their progress and change course if necessary. Older students might, depending on the context of the
problem, transform algebraic expressions or change the viewing window on their graphing calculator to
get the information they need. Mathematically proficient students can explain correspondences between
equations, verbal descriptions, tables, and graphs or draw diagrams of important features and
relationships, graph data, and search for regularity or trends. Younger students might rely on using
concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students
check their answers to problems using a different method, and they continually ask themselves, “Does
this make sense?” They can understand the approaches of others to solving complex problems and
identify correspondences between different approaches.
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
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 10 Grade 1 Mathematics, Quarter 1, Unit 1.3
Introduction to Place Value and Comparing to 30 (15 days)
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.
Clarifying the Standards
Prior Learning
In kindergarten, students counted to 100 by 1s and 10s. They began at any given number within the
known sequence. Students also wrote numbers 0–20 and represented a number of objects with a written
numeral 0–20. Students began to build the foundation for place value by composing and decomposing
numbers from 11–19 into ten ones and some further ones by using objects or drawings or equations.
Students compared the number of objects in one group to the number of objects in another group.
Students also compared two numbers between 1 and 10 presented as a written numeral.
Current Learning
This is a critical area of learning in Grade 1.
In first grade, students generalize their understanding by counting to 120 starting from any number less
than 120. In this unit, students read and write numerals and represent a number of objects with a written
numeral up to 30. By the end of the year, students represent, read, write, and compare numbers to 120.
This is taught at the reinforcement level for numbers 0–20 and the developmental level for numbers
21–30.
Place value is a critical area of instruction in first grade. Students understand that the two digits of a 2digit number represent bundles of tens and some ones. This is taught at the developmental level. They
understand that 10 is a bundle of ten ones called a “ten.” Students understand the teen numbers (11–19)
are composed of a ten and additional ones, and the decades (10, 20, 30, etc.) refer to a number of tens and
no additional ones. This is taught at the reinforcement level. Students compare two 2-digit numbers. This
is taught at the developmental level. At this time of year, students need to develop this understanding by
using bundles, such as snap cubes and linking chains, that are easy to count and separate into ones.
Students are at the discrete stage of development and solid place-value rods may promote confusion. As
students gain experience with countable bundles, they may be able to transition to place-value rods and
other more abstract visuals and models.
Later in the year, students record the results of these comparisons using <, >, and =, and increase the
number range to 120. Students will use their understanding of place value to compute sums within 100.
(1.NBT.4)
Future Learning
In second grade, students will learn that 100 is a bundle of ten 10s. The numbers (100, 200, 300, etc.)
refer to the number of hundreds (and 0 tens and 0 ones). They will count within 1,000. Students will skip
count by 5s, 10s, and 100s. Students will read and write numbers to 1,000 using base-ten numerals,
number names, and expanded form. They will compare 2- and 3-digit numbers and use symbols <, >, and
= to record results.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 11 Grade 1 Mathematics, Quarter 1, Unit 1.3
Introduction to Place Value and Comparing to 30 (15 days)
Additional Findings
Learning Progression K–5, Number and Operations in Base Ten (pp. 5–6): See the number-bond
diagram, 5 and 10 frames, place value cards, numeral list, and visual supports as teacher resources to
highlight the base-ten structure of numbers.
“The number words continue to require attention at first grade because of their irregularities. The decade
words, “twenty,” “thirty,” “forty,” etc., must be understood as indicating 2 tens, 3 tens, 4 tens, etc. Many
decade number words sound much like teen number works. For example, “fourteen” and “forty” sound
very similar…” (p. 6)
Principles and Standards for School Mathematics, students should recognize that the word ten may
represent a single entity (1 ten), and, at the same time, ten separate units (10 ones) and that these
representations are interchangeable. (p. 81)
A Research Companion to Principles and Standards for School Mathematics, “As with the ‘teens’ words,
the English number words between twenty and one-hundred complicate the teaching and learning
processes for multidigit addition and subtraction.”(p. 78)
“Children view numbers as single digits side by side: 827 is functionally ‘eight two seven’ and not 8
groups of one hundred, 2 groups of ten, and 7 single ones.”(p. 79)
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 12 Grade 1 Mathematics, Quarter 1, Unit 1.4
Understanding, Representing, and Solving
Addition Within 20
Overview
Number of Instructional Days:
15
(1 day = 45 minutes)
Content to Be Learned
Mathematical Practices to Be Integrated
•
Add within 20 to solve word problems (adding
to, putting together).
Reason abstractly and quantitatively.
•
Relate counting to addition.
•
•
Represent a situation symbolically using
objects, drawings, and equations.
Add within 20 using counting on, making 10,
and decomposing strategies.
•
Given a symbolic representation, identify or
create a situation.
•
Understand the meaning of equals sign (=)
involving addition.
Look for and make use of structure.
•
Apply the commutative property as a strategy
to solve addition problems.
•
Represent an addition problem with an
equation using symbols to represent the
unknown number.
•
When solving and representing addition
problems, understand that the sum is composed
of several objects (addends).
•
Detect the structure of the commutative
property of addition (3 + 7 = 10, 7 + 3 = 10).
•
Recognize the structure of the distributive
property to use the “make 10” strategy to add
(8 + 6 = 8 + 2 + 4 = 10 + 4 = 14).
•
Use decomposing numbers by place value as a
strategy for solving addition problems
involving two-digit numbers.
Essential Questions
•
How would you solve this word problem?
•
•
How would you represent this word problem
with an equation?
When counting on to add these two numbers,
how do you decide which number to start with?
•
What does “=” mean in this equation?
•
How would you represent this problem using a
model or drawing?
•
How can counting help you find the total
amount?
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 13 Grade 1 Mathematics, Quarter 1, Unit 1.4
Understanding, Representing, and Solving
Addition Within 20 (15 days)
Written Curriculum
Common Core State Standards for Mathematical Content
Operations and Algebraic Thinking
1.OA
Represent and solve problems involving addition and subtraction.
1.OA.1
Use addition and subtraction within 20 to solve word problems involving situations of adding
to, taking from, putting together, taking apart, and comparing, with unknowns in all positions,
e.g., by using objects, drawings, and equations with a symbol for the unknown number to
represent the problem.2
2
See Glossary, Table 1.
Understand and apply properties of operations and the relationship between addition and
subtraction.
1.OA.3
Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is
known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4,
the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative
property of addition.)
3
Students need not use formal terms for these properties.
Add and subtract within 20.
1.OA.5
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
1.OA.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use
strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14);
decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the
relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8
= 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the
known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Work with addition and subtraction equations.
1.OA.7
Understand the meaning of the equal sign, and determine if equations involving addition and
subtraction are true or false. For example, which of the following equations are true and which
are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 14 Grade 1 Mathematics, Quarter 1, Unit 1.4
Understanding, Representing, and Solving
Addition Within 20 (15 days)
Common Core Standards for Mathematical Practice
2
Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem situations.
They bring two complementary abilities to bear on problems involving quantitative relationships: the
ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the
representing symbols as if they have a life of their own, without necessarily attending to their referents—
and the ability to contextualize, to pause as needed during the manipulation process in order to probe into
the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent
representation of the problem at hand; considering the units involved; attending to the meaning of
quantities, not just how to compute them; and knowing and flexibly using different properties of
operations and objects.
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.
Clarifying the Standards
Prior Learning
In kindergarten, students solved addition word problems within 10 using objects, fingers, mental images,
simple drawings, sounds, acting out, verbal explanations, or equations. Students used drawings or
equations to decompose numbers less than or equal to 10 (5 = 2 + 3; 5 = 4 + 1). For any number 1–9,
students found the number that made 10 when added to a given number by using objects or drawing and
recorded answers with an equation or drawing. Students became fluent adding and subtracting within 5.
Kindergarten students were exposed to equations and the equals sign symbol (=), and were encouraged to
write equations, but writing equations was not required.
Current Learning
This is a critical area of learning in Grade 1.
In this unit, students relate counting to addition to solve word problems within 20 using strategies
involving adding to and putting together using objects, drawings, and equations with a symbol for the
unknown number. Working with the commutative property of addition (8 + 3 = 11; 3 + 8 = 11)
encourages students to use counting on strategies when combining quantities. Students add within 20 by
counting on, making a ten, and creating equivalent, but easier known sums. They develop understanding
of the meaning of the equals sign (=). This is taught at the developmental level.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 15 Grade 1 Mathematics, Quarter 1, Unit 1.4
Understanding, Representing, and Solving
Addition Within 20 (15 days)
Later this year, students apply their understanding of counting and decomposing a number leading to a ten
to subtract within 20. Students use this understanding to solve word problems by taking from, taking
apart, and comparing with unknowns in all positions, solving all problem types listed in CCSS glossary
table 1 (p. 88). Students use strategies based the relationship between addition and subtraction to solve
problems involving unknown addends. They will determine if equations involving addition and
subtraction are true or false.
Future Learning
In second grade, students will develop understanding of odd and even within 20 and will fluently add
within 20 using mental strategies. Students will add and subtract within 1,000 using concrete models,
drawings, and strategies based on the properties of operations, place value, and the relationship between
addition and subtraction; they will fluently add and subtract within 100 using these strategies. Third grade
students will generalize these strategies to larger numbers, and in fourth grade students will be expected
to fluently apply the standard algorithm for addition and subtraction.
Additional Findings
Kindergarten, Counting and Cardinality; K–5, Operations and Algebraic Thinking Learning
Progressions gives more information on representing and solving subtypes for all unknowns in all three
positions. Students will need level 2 and 3 strategies to extend addition problem solving beyond 10 (pp.
14–16).
“Linking equations to concrete materials, drawings, and other representations of problem situations afford
deep and flexible understandings of these building blocks of algebra” (p. 13).
According to A Research Companion to Principles and Standards for School Mathematics, “Teachers
should not just focus on keywords in word problems, but rather build a complete mental model of the
problem. (p. 68) Children move through an experiential progression of single-digit addition methods.
Helping children progress through methods can lead all first graders to methods that are efficient enough
to use for all later multidigit calculations (p. 73). A major step is that children notice that they can count
on. Children in time learn to chunk (doubles, make 10). Ten frames enable children to see sums of 10.”
(p. 74)
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 16