Grade 2 Mathematics, Quarter 1, Unit 1.1
Representing and Solving Problems Using
Addition
Overview
Number of Instructional Days:
15
(1 day = 45 minutes)
Content to Be Learned
Mathematical Practices to Be Integrated
•
Add within 100.
Model with mathematics.
•
Solve one-step addition word problems with
unknowns in all positions (result unknown,
change unknown, start unknown).
•
Apply mathematics to solve problems in
everyday life.
•
Write an addition equation to describe a
situation.
•
Mentally add 10 or 100 to a number 100–900.
•
Represent whole numbers as equally spaced
units on a number line.
•
Use tools such as drawings and equations.
Analyze relationships to draw conclusions.
•
•
Represent whole number sums on a number
line.
•
Reflect on whether the results make sense.
•
Use drawings and equations with a symbol for
the unknown number to represent the problem.
•
Revise work as needed.
Attend to precision.
•
Give explanations to others using clear
definitions in discussion and reasoning.
•
Explain symbols.
•
Specify units of measurement.
•
Calculate accurately and efficiently.
•
What is your strategy for locating a given
number on a partially labeled number line?
•
What addition strategy would you use to solve
this word problem: You have 15 crayons and
10 break. How many crayons are not broken?
Why did you choose this strategy?
Essential Questions
•
How would you use place value to add
___+___ mentally? How do you know you are
accurate? Explain your thinking.
•
In what ways would you use a number line to
demonstrate addition? Explain which of your
strategies is most efficient.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 1 Grade 2 Mathematics, Quarter 1, Unit 1.1
Representing and Solving Problems Using Addition (15 days)
Written Curriculum
Common Core State Standards for Mathematical Content
Operations and Algebraic Thinking
2.OA
Represent and solve problems involving addition and subtraction.
2.OA.1
Use addition and subtraction within 100 to solve one- and two-step word problems involving
situations of adding to, taking from, putting together, taking apart, and comparing, with
unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.1
1
See Glossary, Table 1.
Number and Operations in Base Ten
2.NBT
Use place value understanding and properties of operations to add and subtract.
2.NBT.8
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a
given number 100–900.
Measurement and Data
2.MD
Relate addition and subtraction to length.
2.MD.6
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced
points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and
differences within 100 on a number line diagram.
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.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 2 Grade 2 Mathematics, Quarter 1, Unit 1.1
6
Representing and Solving Problems Using Addition (15 days)
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.
Clarifying the Standards
Prior Learning
In grade 1, students used addition and subtraction within 20 to solve one-step word problems. They
utilized objects, drawings, and equations to solve these problems. They understood the mathematical
language and concepts of adding to, taking from, putting together, taking apart, and comparing. Students
found the missing number, in any position, when the unknown number was represented by a symbol.
Also, students are fluent in addition and subtraction facts to 10. They practiced addition and subtraction to
20. Students added and subtracted 10 to/from a two-digit number without having to count. They used
concrete models or drawings to support their thinking. Students started at any number and counted up to
120. They also read and wrote numerals up to 120. They represented a number of objects with a written
numeral.
Students measure lengths using objects, and iterate length units, which is a precursor to developing
understanding of a number line.
Current Learning
In grade 2, students build on their knowledge of addition by expanding the number range to 100. They
continue to develop their skills to represent and solve various one-step addition problems with unknowns
in all positions. Students use drawings and equations, rather than concrete objects, to represent the
problem. Students mentally add 10 or 100 to a given number from 100–900. Students represent whole
numbers as lengths and whole number sums within 100 on a number line diagram.
Later in grade 2, students will solve two-step problems incorporating subtraction and will mentally
subtract 10 or 100 from a given number using place value strategies. They will also represent whole
number differences within 100 on a number line diagram.
See CCSS Glossary p. 88 Table 1, Common Addition and Subtraction problem types and language. A
challenge this year is transitioning from the concrete direct modeling to abstract and mental calculations.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 3 Grade 2 Mathematics, Quarter 1, Unit 1.1
Representing and Solving Problems Using Addition (15 days)
Future Learning
In grade 3, students will build on their knowledge of solving addition and subtraction two-step word
problems to develop their multiplication and division skills. They will continue to represent these
problems using equations with a letter standing for the unknown quantity. Students will add and subtract
within 1,000 and will multiply and divide within 100 fluently. Students continue to develop fluency with
addition and subtraction using a variety of strategies and algorithms. By the end of grade 4, students will
be expected to fluently apply the standard algorithms for addition and subtraction.
Third grade students will use place value understanding to round whole numbers to the nearest 10 or 100.
Students will move from adding multiples of 10 to multiplying by 10 in the range of 10–90.
Additional Findings
According to Principles and Standards for School Mathematics, in second grade, “students develop the
ability to deal with numbers mentally and to think about numbers without having a physical model”
(p. 80)
Teachers need to “engage students in mathematical thinking and reasoning, which builds their
understanding of numbers and relationships among numbers” (p. 80); and “teachers should ask students to
reflect on, explain, and justify their answers so that problem solving both leads to and confirms students’
understanding of mathematical concepts” (p. 121).
“It is absolutely essential that students develop a solid understanding of the base-ten numeration system
and place value concepts by the end of grade 2” (p. 81).
For specific examples, see K–5, Number and Operations in Base Ten (p. 8) and Operations in Algebraic
Thinking (p. 18) (K–12 Learning Progressions).
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 4 Grade 2 Mathematics, Quarter 1, Unit 1.2
Understanding and Using Place
Value Within 1,000
Overview
Number of Instructional Days:
15
(1 day = 45 minutes)
Content to Be Learned
Mathematical Practices to Be Integrated
•
Understand a three-digit number represents
amounts of hundreds, tens, and ones.
Model with mathematics.
•
Understand a “hundred” is a bundle of ten tens.
•
•
•
Apply mathematics to solve problems in
everyday life.
Use place value strategies to add within 100.
•
Add within 1,000 using concrete models or
drawings.
Write an addition equation to describe a
situation.
•
Use tools such as drawings and equations.
•
Relate models and drawings to a written
method.
•
Analyze relationships to draw conclusions.
•
Explain why addition strategies work using
place value.
•
Reflect on whether the results make sense.
•
Revise work as needed.
•
Use place value strategies to compose and
decompose three-digit numbers.
Attend to precision.
•
Give explanations to others using clear
definitions in discussion and reasoning.
•
Explain symbols.
•
Calculate accurately and efficiently.
•
How can understanding place value help you
add these amounts?
•
Which drawings or models would you use to
represent your understanding of adding two or
more three-digit numbers? Why?
Essential Questions
•
How can you use drawings or materials to
represent your understanding of a three-digit
number? Explain your thinking using symbols,
numbers and words.
•
What is the sum of _____+_____?
•
How do you know your strategy is accurate?
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 5 Grade 2 Mathematics, Quarter 1, Unit 1.2
Understanding and Using Place Value Within 1,000 (15 days)
Written Curriculum
Common Core State Standards for Mathematical Content
Number and Operations in Base Ten
2.NBT
Understand place value.
2.NBT.1
Understand that the three digits of a three-digit number represent amounts of hundreds, tens,
and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special
cases:
a.
100 can be thought of as a bundle of ten tens — called a “hundred.”
b.
The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four,
five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
Use place value understanding and properties of operations to add and subtract.
2.NBT.5
Fluently add and subtract within 100 using strategies based on place value, properties of
operations, and/or the relationship between addition and subtraction.
2.NBT.7
Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit
numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and
sometimes it is necessary to compose or decompose tens or hundreds.
2.NBT.9
Explain why addition and subtraction strategies work, using place value and the properties of
operations.3
3
Explanations may be supported by drawings or objects.
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.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 6 Grade 2 Mathematics, Quarter 1, Unit 1.2
6
Understanding and Using Place Value Within 1,000 (15 days)
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.
Clarifying the Standards
Prior Learning
In grade 1, students counted, read, and wrote numbers to 120. Given a two-digit number, they mentally
found 10 more or 10 less. Students explained their reasoning and they developed understanding of place
value as a bundle of ten ones and some more ones (e.g., 14 is a bundle of ten ones and four more ones).
Current Learning
In this unit, students learn that the three digits of a three-digit number represent amounts of hundreds,
tens, and ones.
With strong emphasis on place value, this unit is a critical focus area for second grade students. This unit
focuses on understanding and applying place value strategies for adding within 1,000. Students add twodigit numbers within 100 based on place value strategies, and add within 1,000 using concrete drawings
and models. They relate their strategy to a written method and explain why their strategy works.
Later in the year, students apply strategies based on place value, properties of operations, and the
relationship between addition and subtraction to add and subtract fluently within 100. Students solve
problems within 1,000 and add up to four two-digit numbers using strategies and concrete models or
drawings. Students are expected to explain why their addition and subtraction strategies work.
Future Learning
In grade 3, students will use place value understanding to round whole numbers to the nearest 10 or 100.
By the end of grade 3, students will use strategies and algorithms based on place value, properties of
operations, and the relationship between addition and subtraction to fluently add and subtract within
1,000. By the end of grade 4, students will round numbers to any place, and will fluently add and subtract
using the standard algorithm.
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 7 Grade 2 Mathematics, Quarter 1, Unit 1.2
Understanding and Using Place Value Within 1,000 (15 days)
Additional Findings
According to Principles and Standards for School Mathematics, the expectation of second graders is
to…“develop the sense of whole numbers and represent and use them in flexible ways, including relating,
composing, and decomposing numbers” (p. 78).
Additionally, “It is absolutely essential that students develop a solid understanding of the base ten
numeration system and place value concepts by the end of grade 2” (p. 81).
The most challenging concept for students and teachers is the extra layer of complexity in composing and
decomposing numbers. For additional information, see K–5 Number and Operations in Base Ten
Learning Progressions (p. 9).
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 8 Grade 2 Mathematics, Quarter 1, Unit 1.3
Measuring, Estimating, and Representing
Data in Standard Units
Overview
Number of Instructional Days:
10
(1 day = 45 minutes)
Content to Be Learned
Mathematical Practices to Be Integrated
•
Use rulers, yardsticks, meter sticks, and
measuring tapes to measure the length of an
object.
Model with mathematics.
•
Apply mathematics to solve problems in
everyday life.
•
Draw a picture graph to represent a data set up
to four categories.
•
Use tools such as drawings, picture graphs, and
bar graphs.
•
Draw a bar graph with single-unit scale to
represent a data set up to four categories.
•
Use appropriate tools such as rulers,
yardsticks, meter sticks, and measuring tapes.
•
Solve simple put together problems using
information presented in a bar graph.
•
•
Analyze data presented in a graph to draw
conclusions.
Solve simple compare problems using
information presented in a bar graph.
•
Reflect on whether the results make sense.
•
Make improvements to the model if it does not
represent what was intended.
Attend to precision.
•
Communicate understanding precisely.
•
Use clear definitions when discussing and
reasoning with others.
•
Explain models they use to represent their
work.
•
Carefully specify units of measurement.
•
Calculate accurately and efficiently.
•
What are three things you notice about the data
in your graph? Explain your observations.
Essential Questions

How would you use a ruler (yardstick, meter
stick, measuring tape) to accurately measure
this object? How long is the object? What unit
label would you use?

How could you represent this data on a picture
graph? On a bar graph?
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 9 Grade 2 Mathematics, Quarter 1, Unit 1.3
Measuring, Estimating, and Representing Data
in Standard Units (10 days)
Written Curriculum
Common Core State Standards for Mathematical Content
Measurement and Data
2.MD
Measure and estimate lengths in standard units.
2.MD.1
Measure the length of an object by selecting and using appropriate tools such as rulers,
yardsticks, meter sticks, and measuring tapes.
Represent and interpret data.
2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to
four categories. Solve simple put-together, take-apart, and compare problems4 using
information presented in a bar graph.
4
See Glossary, Table 1.
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 10 Grade 2 Mathematics, Quarter 1, Unit 1.3
Measuring, Estimating, and Representing Data
in Standard Units (10 days)
Clarifying the Standards
Prior Learning
In grade 1, students measured accurately using non-standard units and tools. Students understood the
length of an object is measured by using the same-size length units that span the object with no gaps or
overlaps. They have ordered three objects by length and compared the length of two objects by using a
third object. Students expressed length in whole number units. Also in grade 1, students organized,
represented, and interpreted data with up to three categories. They asked and answered questions about
the total number of data points, how many in each category, and how many more or less are in one
category than another.
Current Learning
In grade 2, students measure using standard units of length (rulers, yardsticks, meter sticks, and
measuring tapes). They draw a picture graph and a bar graph with a single-unit scale to represent the data
set with up to four categories. They solve simple compare and put together problems using information
presented in a bar graph. Compare problems are further explained in CCSS Glossary, Table 1 Common
Addition and Subtraction Situations (p. 88).
Later in grade 2, students select the appropriate tools (rulers, yardsticks, meter sticks, and measuring
tapes) to measure an object. They will also solve simple take-apart problems using information presented
in a bar graph.
Measurement and data is a critical area for students to solidify an understanding of how to accurately
measure, represent, and interpret data in a variety of ways.
The concepts in this unit should be taught at the instructional level as measuring with rulers, yardsticks,
meter sticks, and measuring tapes is new to grade 2 students.
Future Learning
In grade 3, students will draw a scaled picture graph and scaled bar graph to represent a data set with
several categories. They will solve one and two-step “how many more” and “how many less” problems
based on the data in their bar graphs. They will measure lengths using rulers marked with halves and
fourths of an inch. They will also measure areas by counting unit squares (square cm, square m, square
in., square ft. and improvised units). Grade 3 students will solve problems involving measurement and
estimation of intervals of time, liquid volumes, and masses of objects.
Additional Findings
According to Principles and Standards for School Mathematics, “A foundation in measurement concepts
that enables students to use measurement systems, tools, and techniques should be established through
direct experiences with comparing objects, counting units, and making connections between spatial
concepts and number” (p. 103).
The book also states, “Using tools accurately and questioning when measurements may not be accurate
require concepts and skills that develop over extended periods through many varied experiences” and …
“estimating measurements contributes to students’ development of spatial sense, number concepts, and
skills” (p. 106).
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 11 Grade 2 Mathematics, Quarter 1, Unit 1.3
Measuring, Estimating, and Representing Data
in Standard Units (10 days)
According to Progressions: K–3 Categorical Data; 2–5 Measurement Data Learning, students are familiar
with graphs and data sets; they may face the challenge of differentiating between categories and
measurement data (p. 9). A challenge for teachers may be selecting appropriate tools and formats to build
graphs. For example, grid paper may not be as useful for line plots as it is for bar graphs. (p. 10)
Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin 12