Collegium Charter School
Grade 2 Math
Scope & Sequence
Global Vision
We Use Math in Our Everyday Lives
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nd
Standards of Mathematical Practice (Habits of Mind) in 2 Grade:
Make sense of problems and persevere in solving them.
Realize that doing mathematics involves solving problems and discussing
how they solved them.
Explain to themselves the meaning of a problem and look for ways to
solve it.
Use concrete objects or pictures to help them conceptualize and solve
problems.
Check their thinking by asking themselves, “Does this make sense?”
Make conjectures about the solution and plan out a problem solving
approach.
Reason abstractly and quantitatively.
Recognize that a number represents a specific quantity.
Connect the quantity to written symbols.
Create a representation of a problem while attending to the meanings of
the quantities (quantitative reasoning).
Begin to know and use different properties of operations and objects.
Construct viable arguments and critique the reasoning of others.
Construct arguments using concrete referents, such as objects, pictures,
drawings, and actions.
Practice their mathematical communication skills as they participate in
mathematical discussions involving questions like “How did you get
that?” “Explain your thinking,” and “Why is that true?”
Explain their own thinking, but listen to others’ explanations.
Decide if the explanations make sense and ask appropriate questions.
Model with mathematics.
Experiment with representing problem situations in multiple ways
including numbers, words (mathematical language), drawing pictures,
using objects, acting out, making a chart or list, creating equations, etc.
Connect the different representations and explain the connections.
Use all of these representations as needed.
Use appropriate tools strategically.
Consider the available tools (including estimation) when solving a
mathematical problem.
Decide when certain tools might be better suited.
Decide to solve a problem by drawing a picture rather than writing an
equation.
Attend to precision.
Develop their mathematical communication skills.
Use clear and precise language in their discussions with others and when
they explain their own reasoning.
Look for and make use of structure.
Look for patterns. For instance, they adopt mental math strategies based
on patterns (making ten, fact families, doubles).
Look for and express regularity in repeated reasoning.
Look for patterns. For instance, they adopt mental math strategies based
on patterns (making ten, fact families, doubles).
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CMQ Task Rubric
Students complete a task or investigation at any time during the CM unit that addresses Big Ideas of this unit. Standards of Mathematical Practice
in this task are evaluated by the problem solving rubric. Tasks may be differentiated according to student interest, ability level, etc.
Grade 2 critical areas:
Extending understanding of base-ten notation; Building fluency with addition and subtraction; Using standard units of measure; and Describing and analyzing shapes.
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CMQ1 How do we use operations and algebraic thinking in our everyday lives?
Big Ideas:
Essential Questions:
EQUIVALENCE: Any number, numerical expression or equation can be
 How can we represent what we don’t know in a mathematical
represented in an infinite number of ways that have the same value
problem?
 How can verbal statements be changed into number sentences?
OPERATION MEANINGS & RELATIONSHIPS: There are many ways to
 How is addition used to represent parts of a whole?
show addition & subtraction. Each operation is related.
 How do you use the information from a real world problem and
determine what is the correct method to solve the problem?
 How are addition & subtraction related?
 How is subtraction used to compare numbers?
 What are some ways to compose and decompose a number?
Concepts:
Students use their understanding of addition to develop fluency with
addition and subtraction within 100.
Competencies:
Represent and solve problems involving addition and subtraction.
Add and subtract within 20.
Work with equal groups of objects to gain foundations for
multiplication.
CM1 Operations and Algebraic Thinking Assessments
CM1 Vocabulary FK: Teacher-created assessment. Each word is worth one point. Teacher may differentiate method of assessment. May be more
than one test.
Add
Compose
Equal addend
Making ten
Regroup
Subtrahend
Addend
Count back/count down
Equation
Number
Related facts
Sum
Algebra
Count on/count up
Even number
Odd number
Repeated addition
Symbol (for an
Array
Decompose
Expression
Operations
Row
unknown number)
Bar model
Difference
Fact family
Pair
Subtract
Ten frame
Column
Doubles
Pattern
Whole number
Compensation
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CMQ1 How do we use operations and algebraic thinking in our everyday lives?
CM1FK1 Sums & Differences to 10
Fluently add and subtract within 10 using mental strategies.
Ten frames, number bonds, bar models, part-whole
CM1FK2 Sums & Differences to 20
Fluently add and subtract within 20 using mental strategies.
By end of Grade 2, know from memory all sums of two one-digit numbers.
Strategies may include the following:
 Sums to 11 & 20
 Fact families/related facts(8 + 5 = 13 is the same as 13 - 8 = 5)

 Making tens (9 + 7 = 10 + 6)




Doubles
Doubles + 1 (7 + 8 = 7 + 7 + 1)
Counting on
Decomposing a number leading to a ten (14 – 6 = 14 – 4 – 2 = 10 – 2 = 8
CM1FK3 Sums to 100 Place Value Foundations
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.
CM1FK4 Foundations for Multiplication.
Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an
equation to express an even number as a sum of two equal addends.
Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express
the total as a sum of equal addends.
Operations and Algebraic Thinking Assessment CMQ1 Task
Student completes task or investigation at any time during the CM unit that addresses Big Ideas of this Unit. Standards of Mathematical Practice in
this task are evaluated by the problem solving rubric. Tasks may be differentiated according to student interest, ability level, etc.
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CMQ2 How do we use base ten place value in our everyday lives?
Big Ideas:
BASE TEN NUMBER SYSTEM: The base-ten number system is a way to
organize, represent, and compare numbers using digits 0-0, groups of ten
and place value.
EQUIVALENCE: Any number, numerical expression or equation can be
represented in an infinite number of ways that have the same value.
Essential Questions:
 What patterns do you find in the base-ten place-value system?
 What strategies & models help us to understand how to solve
addition or subtraction problems with number or money?
 Why do we add or subtract?
 How are adding and subtracting related?
PROPERTIES: For a given set of numbers and operations, there are rules
that are always true called properties. These are the rules that govern
arithmetic & algebra.
Concepts:
Students understand multi-digit numbers (up to 1000) written in base-ten
notation, recognizing that the digits in each place represent amounts of
thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3
ones).
This includes ideas of counting in fives, tens, and multiples of hundreds,
tens, and ones, as well as number relationships involving these units,
including comparing.
Competencies:
Solve problems within 1000 by applying their understanding of models
for addition and subtraction.
Develop, discuss, and use efficient, accurate, and generalizable
methods to compute sums and differences of whole numbers in baseten notation, using their understanding of place value and the
properties of operations.
CM2 Base Ten Place Value
CM2 Vocabulary FK: Teacher-created assessment. Each word is worth one point. Teacher may differentiate method of assessment. May be more than one test.
Base ten numeral form
Compare
Digits
Equal
Equal to
Expanded form
Greater than
Greater than, more than
Hundreds
Less than
Less than, fewer than
Making ten
Number names (word form)
Ones
Place value
Properties
 Additive property of 0
(zero)
 Associative property of
addition
 Commutative property
of addition.
Skip count
Standard form
Tens
Thousands
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CMQ2 How do we use base ten place value in our everyday lives?
CM2 FK1 Understand place value. CC.2.1.2.B.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… refer to one, two, three, four…hundreds (and 0 tens and 0 ones).
 Count within 1000; skip-count by 5s, 10s, and 100s.
 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of
comparisons.
CM2FK2 Use place value understanding and properties of operations to add and subtract.
CC.2.1.2.B.2
 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition
and subtraction.
 Add up to four two-digit numbers using strategies based on place value and properties of operations.
 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900
 Explain why addition and subtraction strategies work, using place value and the properties of operations.
Explanations may be supported by drawings or objects.
Number and Operations in Base Ten Assessment: CMQ2 Task
Student completes task or investigation at any time during the CM unit that addresses Big Ideas of this Unit. Standards of Mathematical Practice in
this task are evaluated by the problem solving rubric. Tasks may be differentiated according to student interest, ability level, etc.
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CM3 How do we use measurement & time in our everyday lives?
Big Ideas:
Essential Questions:
MEASUREMENT: Some attributes of objects are measureable, e.g., length,
and can be quantified using unit amounts. Standard units of measurement
provide common language for communicating and solving problems.
Context helps us decide the appropriate degree of accuracy in
measurement.
What types of things can be measured?
Why do we use standard units of measurement?
Why do measures need both numbers and units?
What types of problems are solved with measurements?
How do we decide the best measurement to use?
How can there be more than one way to measure something?
How do measurements help us compare objects?
ESTIMATION: Numerical quantities and calculations can be estimated by
using numbers that are close to the actual values, but easier to compute.
Estimations produce approximate results & are useful for judging the
reasonableness of an answer.
Concepts:
Students recognize the need for standard units of measure (centimeter and
inch) and they recognize that the smaller the unit, more repetition of the
unit is needed to cover a given length.
Competencies:
Use rulers and other measurement tools and describe how the units
that were used to measure are related to the object, or attribute
being measured.
CM3 Measurement & Time FK Assessments
CM3 Vocabulary FK: Teacher-created assessment. Each word is worth one point. Teacher may differentiate method of assessment. May be more than one test.
Measurement
Unit
Estimate Ruler
Length
Measuring tape
Customary
System
Inch
Foot
Yard
Yard stick
Metric System
Meter
Meter stick
Centimeter
a.m. / p.m.
Analogue clock
Digital clock
Half-past
Hour
Hour hand
Midnight
Minute
Minute hand
Noon
Quarter after/past
Second
Second hand
Time
Cent
Cent sign(¢)
Dime
Decimal point
Dollar
Dollar sign($)
Money
Nickel
Penny
Quarter
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CM3 How do we use measurement & time in our everyday lives?
CM3FK1
Measure and estimate lengths in standard units.
 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements
relate to the size of the unit chosen.
 Estimate lengths using units of inches, feet, centimeters, and meters.
 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

CM3FK2
Relate addition and subtraction to length.
 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such
as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
 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.
CM3FK3
Time
Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
CM3FK4
Money
Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2
dimes and 3 pennies, how many cents do you have?
Measurement & Time Assessment: CMQ3 Task
Student completes task or investigation at any time during the CM unit that addresses Big Ideas of this Unit. Standards of Mathematical Practice in
this task are evaluated by the problem solving rubric. Tasks may be differentiated according to student interest, ability level, etc.
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CMQ4 How do we use base ten place value to 1,000 in our everyday lives?
Big Ideas:
BASE TEN NUMBER SYSTEM: The base-ten number system is a way to
Essential Questions:
organize, represent, and compare numbers using digits 0-0, groups of
 What patterns do you find in the base-ten place-value system?
ten and place value.
 What strategies & models help us to understand how to solve
EQUIVALENCE: Any number, numerical expression or equation can be
addition or subtraction problems with number or money?
represented in an infinite number of ways that have the same value.
 Why do we add or subtract?
PROPERTIES: For a given set of numbers and operations, there are rules
 How are adding and subtracting related?
that are always true called properties. These are the rules that govern
arithmetic & algebra.
Concepts:
Competencies:
Students understand multi-digit numbers (up to 1000) written in baseSolve problems within 1000 by applying their understanding of models
ten notation, recognizing that the digits in each place represent
for addition and subtraction.
amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds
Develop, discuss, and use efficient, accurate, and generalizable methods
+ 5 tens + 3 ones).
to compute sums and differences of whole numbers in base-ten
This includes ideas of counting in fives, tens, and multiples of hundreds, notation, using their understanding of place value and the properties of
tens, and ones, as well as number relationships involving these units,
operations.
including comparing
CM4
Use place value understanding and properties of operations to add and subtract to 1,000. CC.2.1.2.B.3
CM5 Vocabulary FK: Teacher-created assessment. Each word is worth one point. Teacher may differentiate method of assessment. May be more than one test.
Base ten numeral form
Making ten
Place value
Tens Place
Thousands Place
Digits
Making one hundred
Ones Place
Hundreds place
Expanded form
CM4FK1
 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
 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900
 Explain why addition and subtraction strategies work, using place value and the properties of operations.
Explanations may be supported by drawings or objects
Base Ten to 1,000 CMQ4 Task
Student completes task or investigation at any time during the CM unit that addresses Big Ideas of this Unit. Standards of Mathematical Practice in
this task are evaluated by the problem solving rubric. Tasks may be differentiated according to student interest, ability level, etc.
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CMQ5 How do we use data in our everyday lives?
Big Ideas:
DATA COLLECTION: Some questions can be answered by collecting and
analyzing data, and the question to be answered determines the data
that needs to be collected and how best to collect it.
Essential Questions:
 How does the type of data we collect influence the type of graph
we create?
 How can using graphs help us to solve problems and display data
we collect?
DATA REPRESENTATION: Graphs and charts are visual representations of
functions and numerical relationships. The type of data determines the
best choice of visual representation.
MEASUREMENT: Some attributes of objects are measureable, e.g.,
length, and can be quantified using unit amounts & ordered on a
number line.
Concepts:
Developing understanding of how data can be organized in graphs &
ordered on a number line.
Competencies:
Represent and interpret data by drawing simple bar graphs and line
plots.
CM5 Data FK Assessments
CM4 Vocabulary FK: Teacher-created assessment. Each word is worth one point. Teacher may differentiate method of assessment. May be more than one test.
bar graph
Horizontal bar graph
Nearest whole
Survey
Tally mark
data
Key
number line
symbol
Vertical bar graph
data table
line plot
pictograph (picture graph)
tally chart
CM5FK1 Represent and Interpret Data –line plots
 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the
same object.
 Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
CM5FK2 Represent and Interpret Data – Bar Graphs
 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 problems1 using information presented in a bar graph.
Data Assessment: CMQ5 Task
Student completes task or investigation at any time during the CM unit that addresses Big Ideas of this Unit. Standards of Mathematical Practice in
this task are evaluated by the problem solving rubric. Tasks may be differentiated according to student interest, ability level, etc.
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CMQ6 How do we use geometry in our everyday lives?
Big Ideas:
SHAPES & SOLIDS: Two- dimensional objects can be described, classified,
and analyzed by their attributes. Quadrilaterals can be described,
categorized and named based on the relative lengths of their sides and
the size of their angles
FRACTIONS: Shapes can be combined to make new shapes
Wholes can be partitioned into equal parts.
Concepts:
Through building, drawing, and analyzing two- and three-dimensional
shapes, students develop a foundation for understanding area, volume,
congruence, similarity, and symmetry in later grades.
Essential Questions:
 How can we describe two-dimensional and three-dimensional
shapes?
 How does putting shapes together and taking them apart help us
understand them?
Competencies:
Students describe and analyze shapes by examining their sides and
angles.
Students investigate, describe, and reason about decomposing and
combining shapes to make other shapes.
CM6 Geometry FK Assessments
CM6 Vocabulary FK: Teacher-created assessment. Each word is worth one point. Teacher may differentiate method of assessment. May be more than one test.
Angles
Circle
Rhombus
Cone
Columns
Half of
Attribute
Closed shape
Square
Cube
Equal groups
Halves
Category
Hexagon
Trapezoid
Cylinder
Equal parts
Partition
Line
Open Shape
Triangle
Edge
Equal shares
Rows
Sides
Pentagon
Two dimensional shape
Rectangular prism
Fourth of, quarter of
Third of
Sort
Quadrilateral
Three-dimensional shape
Sphere
Fourths
Thirds
Vertex
Rectangles
Solid Shape
Half
CM6FK1 Geometry
 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.
 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
CM6FK2 Geometry & Fractions
 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third
of, etc., and describe the whole as two halves, three thirds, four fourths.
 Recognize that equal shares of identical wholes need not have the same shape.
Geometry Assessment: CMQ6 Task
Student completes task or investigation at any time during the CM unit that addresses Big Ideas of this Unit. Standards of Mathematical Practice in
this task are evaluated by the problem solving rubric. Tasks may be differentiated according to student interest, ability level, etc.
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