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District OverviewThe mathematics curriculum provides sequential and comprehensive K-12 instruction in a collaborative, student-centered learning environment that fosters critical thinking, creativity, skillful problem-solving, and effective communication in order to enable all students to adapt to an ever-changing, global society and increase college and career readiness. An emphasis has been placed on conceptual understanding, higher-order thinking, and problem solving skills to prepare students for 21st century careers. This is further embedded through the integrated use of technology into daily lessons. Instruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with content as they build and expand their knowledge and understanding of mathematics. Students will experience mathematics as a coherent and useful subject within the context of real-life situations. In all, the curriculum aims to reach high standards while encouraging curiosity and building confidence in a collaborative atmosphere.

Grade 2 DescriptionIn grade 2, instructional time should focus on these mathematical core content areas:

Operations and algebraic thinking Number and operations in base ten Measurement and data Geometry

In grade 2, instructional time should focus on these mathematical practices: Make sense of problems and persevere in solving them (MP. 1) Reason abstractly and quantitatively (MP. 2) Construct viable arguments and critique the reasoning of others (MP. 3) Model with mathematics (MP. 4) Use appropriate tools strategically (MP. 5) Attend to precision (MP. 6) Look for and make sense of structure (MP. 7) Look for and express regularity in repeated reasoning (MP. 8)

Grade 2 Topics: Topic 1: Fluently Add and Subtract Within 20 Topic 2: Work with Equal Groups Topic 3: Add Within 100 Using Strategies Topic 4: Fluently Add Within 100 Topic 5: Subtract Within 100 Using Strategies Topic 6: Fluently Subtract Within 100 Topic 7: More Solving Problems Involving Addition and Subtraction Topic 8: Work with Time and Money Topic 9: Numbers to 1,000

Topic 10: Add Within 1,000 Using Models and Strategies Topic 11: Subtract Within 1,000 Using Models and Strategies Topic 12: Measuring Length Topic 13: More Addition, Subtraction, and Length Topic 14: Graphs and Data Topic 15: Shapes and Their Attributes

Subject: Mathematics

Grade:2

Suggested Timeline: 10 days

Topic 1: Fluently Add and Subtract Within 20

Topic 1 Overview/Essential Understanding: Counting on is a strategy to find sums. Near doubles can be found using a related doubles fact. Some addition facts can be found by changing to an equivalent fact with 10. Patterns in 0-10 additional facts tables are useful for adding numbers, developing mental math strategies, and number sense. A number line is a tool to count on and back to add and subtract. Addition and subtraction have an inverse relationship and every subtraction fact has a related addition fact. Some subtraction facts can be simplified by making use of the numbers’ relationships to 10. The addends determine efficient strategies. Objects, diagrams, and equations can help you solve different types of word problems. Good math thinkers use math to explain why they are right.

Topic 1 Objectives: At the end of Topic 1, students will be able to independently use their learning to:

count on to find sums use doubles and near doubles to add quickly make 10 to add and subtract quickly and accurately use number patterns on addition fact tables count on and back on a number line understand the inverse relationship of addition and subtraction use mental math strategies to add and subtract quickly and accurately use addition and subtraction to solve word problems use words, pictures, numbers, and symbols to construct viable math arguments

Focus Standards Addressed in this Topic:

CC.2.2.2.A.1 – Represent and solve problems involving addition and subtraction within 100 CC.2.2.2.A.2 – Use mental strategies to add and subtract within 20

Important Standards Addressed in this Topic:

CC.1.2.2.J – Acquire and use grade-appropriate conversational, general academic, and domain specific words and phrases CC.1.5.2.A – Participate in collaborative conversations with peers and adults in small and larger groups CC.1.5.2.G – Demonstrate command of the conventions of standard English when speaking, based on grade 2 level and content CC.1.4.2.F – Demonstrate a grade appropriate command of the conventions of standard English grammar, usage, capitalization,

punctuation, and spelling

Misconceptions: Keeping track of second addend when making 10 to add Total number of counters doesn’t change in a 10 frame, just their positions Keeping track of how many spaces have been counted up and back on a number line Finding the missing subtrahend Writing an equation to solve a word problem

Concepts/Content: Addition and subtraction Properties of operations

Competencies/Skills: Add and subtract within 20 using

strategies and mental math Apply properties of operations as

strategies to add and subtract

Description of Activities: Whole group direct instruction Small group work with peers Small group work with teacher Technology and center games

Assessments: Topic 1 Assessment Addition/Subtraction fluency quizzes

Interdisciplinary Connections:N/A

Additional Resources: http://www.abcya.com (Math games) http://sumdog.com http://xtramath.com Pearson, enVisionmath2.0

Subject: Grade: Suggested Timeline:

http://xtramath.com/

http://sumdog.com/

http://www.abcya.com/

Mathematics 2 5 daysTopic 2: Work with Equal Groups

Topic 2 Overview/Essential Understanding: Numbers can be classified as even or odd by showing numbers as two equal parts. A group of objects can be classified as even or odd by analyzing skip counting patterns. An array shows equal groups and you can use repeated addition to find the total number of objects in an array. Good math thinkers use math they know to show and solve problems.


tell if a group of objects is even or odd find the total number of objects in a set of rows and columns make arrays with equal rows or equal columns to solve addition problems model problems using equations, drawings, arrays, and bar diagrams


CC.2.2.2.A.1 – Represent and solve problems involving addition and subtraction within 100 CC.2.2.2.A.2 – Use mental strategies to add and subtract within 20 CC.2.2.2.A.3 – Work with equal groups of objects to gain foundations for multiplication

Important Standards Addressed in this Topic: CC.1.2.2.J – Acquire and use grade-appropriate conversational, general academic, and domain specific words and phrases CC.1.5.2.A – Participate in collaborative conversations with peers and adults in small and larger groups CC.1.5.2.G – Demonstrate command of the conventions of standard English when speaking, based on grade 2 level and content CC.1.4.2.F – Demonstrate a grade appropriate command of the conventions of standard English grammar, usage, capitalization,


Misconceptions: Looking at the ones digit determines even or odd Drawing an array – understanding rows vs. columns Writing an equation based on an array

Concepts/Content: Addition and subtraction Properties of operations Equal groups of objects



strategies to add and subtract Determine if a group of objects

has an odd or even number Use addition to find the total

number of objects in rectangular arrays

Write an equation to express the total of an array



Interdisciplinary Connections:Connecting arrays to real world situations (shelves in stores, parking lots, donuts in a box, windows in buildings, etc).



Grade:2



http://sumdog.com/


Topic 3: Add Within 100 Using Strategies

Topic 3 Overview/Essential Understanding: Patterns on a hundred chart can be used to add numbers and to develop mental math strategies and number sense. Two-digit numbers can be broken apart into tens and ones and added in different ways. When adding two-digit numbers, you can add an amount to one addend and subtract the same amount from another addend to make

addition easier. Some problems can be solved in one step, while others need to be solved in two steps. Good math thinkers know how to pick the right tools to solve math problems.


add within 100 using place value strategies and a hundred chart add tens and ones to two-digit numbers using an open number line within 100 break apart numbers into tens and ones to find their sum break apart addends and combine them in different ways to add mentally choose appropriate tools and strategies to add two-digit numbers use drawings and equations to solve one and two-step problems


CC.2.2.2.A.1 – Represent and solve problems involving addition and subtraction within 100 CC.2.1.2.B.3 – Use place value understanding and properties of operations to add and subtract within 1,000


punctuation, and spellingMisconceptions:

Difference between moving down a row and moving to the right one column on a hundred chart Counting on by groups of ten and labeling work on an open number line Isolating tens and ones when using the break apart strategy

Deciding which strategy would be best to use Determining where to place numbers on a comparison bar diagram

Concepts/Content: Addition and subtraction









Grade:2


Topic 4:


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Fluently Add Within 100

Topic 4 Overview/Essential Understanding: Partial sums addition provides a bridge between mental addition and the standard algorithm. Two-digit numbers can be broken apart into tens and ones and added in different ways. Addition algorithms and addition strategies can be used to add more than two 2-digit numbers. Some problems can be solved in one step, while others need to be solved in two steps. Good math thinkers use math they know to show and solve problems.


add using place value and partial sums use models to add 2-digit numbers and then explain the work add three or four 2-digit numbers use mental math strategies and models to add more than two numbers use drawings, models, and equations to solve one and two-step problems






Misconceptions: Regrouping ones into the tens column Not all strategies will work for each problem

Concepts/Content: Competencies/Skills: Description of Activities:

Addition and subtraction Add and subtract within 100 using strategies and mental math

Apply properties of operations as strategies to add and subtract

Whole group direct instruction Small group work with peers Small group work with teacher Technology and center games





Grade:2


Topic 5: Subtract Within 100 Using Strategies


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Topic 5 Overview/Essential Understanding: Patterns on a hundred chart can be used to subtract numbers and develop mental math strategies and number sense. Two-digit numbers can be broken apart using tens and ones to subtract in different ways. One and two-digit numbers can be broken apart to make it easier to subtract mentally. When subtracting two-digit numbers, you can add or subtract the same amount to or from both numbers in the problem. You can use bar diagrams, equations, and the relationship between addition and subtraction to solve one and two-step problems. Good math thinkers use math to explain why they are right.


use a hundred chart to subtract tens and ones use an open number line to subtract tens and ones add up to subtract on an open number line break apart one and two-digit numbers to make it easier to subtract solve one and two-step problems using addition and subtraction critique the thinking of others by using what is known about addition and subtraction






Keeping track of the numbers when working backward on a hundred chart to subtract Deciding what amount to add or subtract when using compensation strategy



Description of Activities: Whole group direct instruction



Small group work with peers Small group work with teacher Technology and center games





Grade:2


Topic 6: Fluently Subtract Within 100

Topic 6 Overview/Essential Understanding: Sometimes it is necessary to regroup when subtracting.


http://sumdog.com/


The standard subtraction algorithm can be used to break the calculation into simpler steps, starting with the ones and moving to the tens.

The inverse relationship between addition and subtraction can be used to solve and check subtraction. Bar diagrams, equations, and objects can be helpful when solving one and two-step word problems. Good math thinkers know how to think about words and numbers to solve problems.


exchange 1 ten for 10 ones use place value, regrouping, and models to subtract 1 and 2-digit numbers add to check subtraction use models and equations to solve word problems reason about word problems and use bar diagrams and equations to solve them






Misconceptions: Regrouping 1’s and 10’s on a place value chart Checking subtraction with addition and getting the correct answer


Competencies/Skills: Add and subtract within 100 to

solve one and two-step word problems using drawings and

Description of Activities: Whole group direct instruction Small group work with peers Small group work with teacher

equations with a (?) for the unknown number

Understand subtraction as an unknown-addend problem.

Apply properties of operations as strategies to add and subtract

Technology and center games

Assessments:Topic 6 AssessmentAddition/Subtraction fluency quizzes




Grade:2


Topic 7: More Solving Problems Involving Addition and Subtraction

Topic 7 Overview/Essential Understanding: You can write equations to model and solve word problems using a (?) to represent the unknown. You can use drawings and equations to make sense of words in a word problem.


http://sumdog.com/


Sometimes a problem has a hidden or unstated question that needs to be answered before you can find the final answer. Good math thinkers know how to think about words and numbers to solve problems.


model problems using equations with unknowns in any position using drawings and equations to make sense of word problems use different ways to solve two-step problems use reasoning to write and solve number stories


CC.2.2.2.A.1 – Represent and solve problems involving addition and subtraction within 100




Misconceptions: Deciding on an equation to represent a word problem Deciding when to add and when to subtract Approaching a two-step word problem and solving the second step


Competencies/Skills: Add and subtract within 100 to

solve one and two-step word problems using drawings and equations with a (?) for the unknown number


Assessments: Topic 7 Assessment

Addition/Subtraction fluency quizzes




Grade:2


Topic 8: Work with Time and Money

Topic 8 Overview/Essential Understanding: Each coin and bill has a specific value. Money is measurable and can be quantified using dollar and cent amounts.


http://sumdog.com/


Word problems about money can be solved by adding and subtracting. Good math thinkers know how to think about words and numbers to solve problems. Time can be told to the nearest five minutes. Time can be described before and after the hour, as well as a.m. and p.m.


solve problems with coins and bills reason about values of coins and bills and find different ways to make the same total value tell time to the nearest five minutes say the time in different ways


CC.2.2.2.A.1 – Represent and solve problems involving addition and subtraction within 100 CC.2.1.2.B.2 – Count within 1,000; skip count by 5’s, 10’s, and 100’s CC.2.1.2.B.3 – Use place value understanding and properties of operations to add and subtract within 1,000 CC.2.4.2.A.2 – Tell and write time to the nearest five minutes using both analog and digital clocks CC.2.4.2.A.3 – Solve problems using coins and paper currency with appropriate symbols




Size of coins determines value Differentiating between silver coins Counting on with money and transitioning to counting by 1’s, 5’s, 10’s, 20’s Differentiating between hour and minute hands on analog clock Finding time before and after the hour (quarter to or 5 minutes until; half past; quarter past)


Competencies/Skills: Add and subtract within 1,000

Description of Activities: Whole group direct instruction

Place value Time and money Represent and interpret data

Count within 1,000; skip-count by 5’s, 10’s, and 100’s

Tell and write time from analog and digital clocks to the nearest five minutes

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies

Small group work with peers Small group work with teacher Technology and center games


Interdisciplinary Connections:Social Studies Unit – People in the Marketplace (Economics)Presidents Day



Grade:2


Topic 9: Numbers to 1,000

Topic 9 Overview/Essential Understanding: Number system is based on groups of ten. Place value blocks and drawings can be used to model and write three-digit numbers. The position of a digit tells its value. There are three common ways to write numbers: standard form, expanded form, and word form. Place value patterns and number lines can help you skip count by 5’s, 10’s, and 100’s.


http://sumdog.com/


The symbols <, >, and = can be used to compare numbers. Number lines go on forever in both directions. Good math thinkers look for patterns in math to help solve problems.


understand place value and count by hundreds to 1,000 use place value blocks and drawings to model and write 3-digit numbers tell the value of a digit by where it is placed in a number read and write 3-digit numbers in standard, expanded, and word form use place value patterns to mentally count by 1’s and 10’s from a given number skip count by 5’s, 10’s, and 100’s on a number line compare numbers using place value and symbols look for patterns to help when solving problems


CC.2.1.2.B.1 – Use place value concepts to represent amounts of tens and ones and to compare 3-digit numbers CC.2.1.2.B.2 – Use place value concepts to read, write, and skip count to 1,000 CC.2.1.2.B.3 – Use place value understanding and properties of operations to add and subtract within 1,000




Values of digits in place value chart (ex. 8 in tens place equals 80, not 8) Spelling word form correctly Breaking apart a 3-digit number into hundreds, tens, and ones does not change the value of the number Writing missing numbers into a segment of a number chart when not all numbers are represented Skip counting when 2 or more consecutive numbers are missing on a number line

Differentiating between < and >Concepts/Content:

Place value Addition and subtraction

Competencies/Skills: Understand that the three digits

of a 3-digit number represent hundreds, tens, and ones

Count within 1,000; skip-count by 5’s, 10’s, and 100’s

Compare two 3-digit numbers using <, >, and =.

Read and write numbers to 1,000 using base-ten numerals, number names, and expanded form.

Add and subtract within 1,000






Grade:2


Topic 10: Add Within 1,000 Using Models and Strategies

Topic 10 Overview/Essential Understanding: Place value patterns and basic facts can be used to mentally add 10 or 100 to 3-digit numbers. Three-digit numbers can be broken apart into hundreds, tens, and ones and added in different ways. Partial sums addition provides a bridge between mental addition and the standard algorithm. Addition sums are the same no matter which strategy is used. Good math thinkers look for things that repeat in a problem, and apply what they learned from one problem to solve another.

Topic 10 Objectives:


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At the end of Topic 10, students will be able to independently use their learning to: add 10 or 100 mentally to any 3-digit number use an open number line, partial sums, and models to add 3-digit numbers use different addition strategies and explain why they work think about and check work while solving a problem

Focus Standards Addressed in this Topic: CC.2.1.2.B.3 – Use place value understanding and properties of operations to add and subtract within 1,000




Misconceptions: Regroup whenever the sum of the digits is greater than 9; each place only holds one digit Keeping track of the jumps on an open number line

Concepts/Content: Place value Addition and subtraction



Explain why addition and subtraction strategies work, using place value and properties of operations.





Additional Resources: http://www.abcya.com (Math games) http://sumdog.com

http://sumdog.com/


http://xtramath.com Pearson, enVisionmath2.0


Grade:2


Topic 11: Subtract Within 1,000 Using Models and Strategies

Topic 11 Overview/Essential Understanding: Place value patterns and basic facts can be used to mentally subtract 10 or 100 from 3-digit numbers. Three-digit numbers can be broken apart into hundreds, tens, and ones and subtracted in different ways. Open number lines can be used to represent how to break apart and subtract numbers. The standard subtraction algorithm for 3-digit numbers breaks the calculation into simpler calculations using place value; the difference

is the same no matter which strategy is used. Good math thinkers know what the problem is about, have a plan to solve it, and keep trying if they get stuck.

Topic 11 Objectives:


At the end of Topic 11, students will be able to independently use their learning to: subtract 10 or 100 mentally to any 3-digit number use an open number line, mental math, and models to subtract 3-digit numbers use different subtraction strategies and explain why they work solve problems that take more than one step

Focus Standards Addressed in this Topic: CC.2.1.2.B.3 – Use place value understanding and properties of operations to add and subtract within 1,000




Keeping track of the jumps on an open number line Mentally subtracting 10 and 100 Understanding and explaining why strategies work

Concepts/Content: Place value Addition and subtraction



Explain why addition and subtraction strategies work, using place value and properties of operations.





Additional Resources: http://www.abcya.com (Math games) http://sumdog.com

http://sumdog.com/


http://xtramath.com Pearson, enVisionmath2.0


Grade:2


Topic 12: Measuring Length

Topic 12 Overview/Essential Understanding: The length of a known object can be used to estimate the length of another object to the nearest inch, foot, or yard. Length and height are measureable in inches, feet, and yards. When measuring length, the longer the chosen unit, the fewer units are needed; the shorter the unit, the more units are needed. Length and height are measureable in centimeters and meters. The length of two objects can be compared by subtracting the difference. Good math thinkers are careful about what they write and say, so their ideas about math are clear.



estimate the length of an object by relating the length of the object to a known measurement estimate measures and use tools to measure length and height to the nearest inch, foot, and yard estimate measures and use tools to measure length and height to the nearest centimeter and meter measure the length and height of objects using different metric units tell how much longer one object is than another choose tools, units, and methods for precise measurement


CC.2.4.2.A.1 – Measure and estimate lengths in standard units using appropriate tools




Estimating in yards can be difficult (“How many baseball bats long?”) Using correct end of the ruler Finding correct start and end points for measuring an object’s height Understanding metric units Determining if the work of another is precise in measurement

Concepts/Content: Measurement

Competencies/Skills: Measure the length of an object

by selecting and using appropriate tools

Measure the same length with different-sized units and discuss the measurement made with smaller units vs. larger units

Estimate lengths using inches, feet, yards, centimeters, and


meters Compare lengths of objects


Interdisciplinary Connections:Science – Unit 1 – Tools Scientists UseSTEM Social Studies – Map skills



Grade:2


Topic 13: Measuring Length

Topic 13 Overview/Essential Understanding: Measurements in the same unit can be added or subtracted the same way as adding and subtracting whole numbers. Pictures and equations can be used to solve word problems involving measurements. A sum can be represented as the total length of two line segments on a number line. Good math thinkers know how to pick the right tools to solve math problems.


solve problems by adding or subtracting length measurements add or subtract to solve measurement problems by using drawings and equations add or subtract on a number line choose the best tool to use to solve problems


http://sumdog.com/


Focus Standards Addressed in this Topic: CC.2.2.2.A.1 – Represent and solve problems involving addition and subtraction within 100 CC.2.4.2.A.6 – Extend the concepts of addition and subtraction to problems involving length



Estimating in yards can be difficult (“How many baseball bats long?”) Using correct end of the ruler Finding correct start and end points for measuring an object’s height Understanding metric units Determining if the work of another is precise in measurement

Concepts/Content: Addition and subtraction Measurement

Competencies/Skills: Use addition and subtraction

within 100 to solve word problems involving lengths that are given in the same units by using drawings 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


Assessments: Topic 13 Assessment

Addition/Subtraction fluency quizzesInterdisciplinary Connections:Science – Unit 1 – Tools Scientists UseSTEM Social Studies – Map skills



Grade:2


Topic 14: Graphs and Data

Topic 14 Overview/Essential Understanding: The lengths of objects can be organized in different ways. Different types of data can be displayed on a line plot. Bar graphs can be used to organize and display data. Picture graphs use a single symbol to show data. Picture graphs and bar graphs are useful tools for comparing data and drawing conclusions. Good math thinkers know how to think about words and numbers to solve problems.


measure the length of objects and make a line plot to organize the data draw bar diagrams and picture graphs and use them to solve problems draw conclusions from graphs


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reason about data in bar and picture graphs to write and solve problems

Focus Standards Addressed in this Topic: CC.2.4.2.A.1 – Measure and estimate lengths in standard units using appropriate tools CC.2.4.2.A.4 – Represent and interpret data using line plots, picture graphs, and bar graphs




Misconceptions: Keeping track of dots on a line plot Transferring data from table to bar graph Aligning the number and axis on bar graphs (use ruler or edge of paper) Interpreting graph to solve a problem

Concepts/Content: Represent and interpret data Measurement

Competencies/Skills: Make a line plot to show

measurement data of the lengths of several objects to the nearest whole-number unit

Draw a picture graph and a bar graph to represent a data set with up to four categories. Solve simple problems using information from a graph



Interdisciplinary Connections: Additional Resources:

ScienceSTEM Social Studies – Map skills

http://www.abcya.com (Math games) http://sumdog.com http://xtramath.com Pearson, enVisionmath2.0


Grade:2


Topic 15: Shapes and Their Attributes

Topic 15 Overview/Essential Understanding: Two-dimensional shapes can be classified, sorted, defined, and differentiated based on their attributes. Polygons can be described by their number of sides and angles Cubes can be described by their faces, edges, and vertices. A rectangle can be divided into rows and columns of squares that are the same size. A whole can have equal shares called halves, thirds, and fourths. A whole can be divided into equal shares in different ways. Good math thinkers look for things that repeat in a problem and apply what they know from one problem to solve another.


recognize and describe shapes by how they look


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draw polygon shapes draw cubes and describe how they look divide rectangles into equal squares divide circles and rectangles into halves, thirds, and fourths make equal shares that do not have the same shape use repeated reasoning to divide rectangles into rows and columns and create designs with equal shares

Focus Standards Addressed in this Topic: CC.2.3.2.A.1 – Analyze and draw two and three-dimensional shapes having specified attributes CC.2.3.2.A.2 – Use the understanding of fractions to partition shapes into halves, quarters, and thirds CC.2.2.2.A.3 – Work with equal groups of objects to gain foundations for multiplication



A circle is not a polygon A polygon is a two-dimensional (flat) closed shape that has straight sides (not curved) Recognizing all faces of a cube when drawn on paper and being unable to see other faces because drawing is 2D Understanding difference between shares that have the same shape and equal shares

Concepts/Content: Equal groups of objects Shapes Attributes Fractions

Competencies/Skills: Determine whether a group of

objects has an odd or even number of members and write an equation to express an even number as a sum of two equal addends

Recognize and draw shapes having specific attributes. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes

Partition circles and rectangles


into two, three, or four equal shares, recognize that equal shares of identical wholes need not have the same shape


Interdisciplinary Connections:Science tools



http://sumdog.com/


€¦ · web viewwriting an equation to solve a word problem. concepts ... reason about word...

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