Evidence Outcomes:

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: (CCSS: 2.NBT.A.1)

   • 100 can be thought of as a bundle of ten tens &mash; called a “hundred.” (CCSS: 2.NBT.A.1.a)

   • 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 tons and 0 ones). (CCSS: 2.NBT.A.1.b)

2. Count within 1000; skip-count by 5s, 10s, and 100s. (CCSS: 2.NBT.A.2)

3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. (CCSS: 2.NBT.A.3)

4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. (CCSS: 2.NBT.A.4)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

How place value is structured and follows a pattern within the base ten number system

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Patterns of the base ten number system (10 ones = 1 ten, 10 tens = 1 hundred, 10 hundreds = 1 thousand)

• The value of each digit in a number based on its place value

• Compose, decompose, and compare three-digit numbers according to their place value

• Numbers written in different forms represent the same value

In order to meet these essential understandings, students must know...

Academic vocabulary: Place value (value of digit based on its place in a number), Ones, tens, hundreds, thousand, Skip count, Compare, Less than <, Greater than >, Equal to =, Standard form (348), Base-ten model (348 = □□□ llll ……..), Expanded form (348 = 300+40+8), Word form (348 = three hundred forty-eight), Unit form (348 = 3 hundreds, 4 tens, 8 ones)

• A three-digit number consists of ones, tens, and hundreds and each digit has a specific value based on its place in the number

• Bundling is used to understand place value:

  • 10 ones can be bundled into 1 ten

  • 10 tens can be bundled into 1 hundred

  • 10 hundreds can be bundles into 1 thousand

  • How base ten models/manipulatives can represent and help with the understanding of place value

• 100-900 consist of 1-9 hundreds and 0 tens and 0 ones

• Flexibly skip count within 1,000 by 5s, 10s, and 100s (ex. Count from 68 to 280 flexibly with ones, fives, tens, and hundreds)

• Numbers can be written in different forms: standard/number form, base-ten numerals, word form, unit form, expanded form

• What it means to compare numbers

• Less than <, greater than >, equal to =

• Compare three-digit numbers based on their place value

In order to meet these essential understandings, students must be able to...

• Explain place value and its purpose

• Decompose numbers and identify numbers as ones, tens and hundred

• Construct base-10 models of numbers as ones tens and hundreds

• Demonstrate understanding of grouping 10 ones into 1 ten

• Demonstrate understanding of grouping 10 tens into 1 hundred

• Recognize that 0 is a placeholder (Ex: 700 is 7 hundreds 0 tens and 0 ones)

• Describe a number based on its place value- hundreds, tens, and ones

• Explain skip counting and its purpose

• Fluently and flexibly skip count by 5s, 10s, and 100s interchangeably to count within 1,000 (ex. Count from 68 to 280 flexibly with ones, fives, tens, and hundreds)

• Recognize and generate numbers within 1,000 using various forms (standard/number form, base-ten numerals, word form, unit form, and expanded form)

• Explain the purpose of comparing number

• Compare three-digit numbers based on their place value (hundreds, tens, and ones) using the less than < , greater than >, and equal to = symbols accurately

• Justify and reason with academic vocabulary to explain thinking

Evidence Outcomes:

1. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and

subtraction. (CCSS: 2.NBT.B.5)

2. Add up to four two-digit numbers using strategies based on place value and properties of operations. (CCSS: 2.NBT.B.6)

3. 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. (CCSS: 2.NBT.B.7)

4. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. (CCSS: 2.NBT.B.8)

5. Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.) (CCSS: 2.NBT.B.9)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

Examine and apply a variety of strategies to accurately and effectively solve problems

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes tudents must understand are...

• the relationship between addition and subtraction

• there are concrete and abstract strategies based on place value to solve addition and subtraction problems

• Operations can be used to solve problems

In order to meet these essential understandings, students must know...

Academic Vocabulary: Mental math, Sum, Difference, Addend, Equation, Fact family, Fluency in addition and subtraction, Compose, Decompose, Regroup, Break apart method, Open number line, Base ten blocks and base ten model, Evidence, Strategy, Make a ten

• fact families (turn around facts)

• addition & subtraction strategies based on place value

  • base ten blocks

  • break apart method (decompose into unit or expanded form)

  • open number line

  • hundreds chart

• It is possible to add more than two numbers at one time (apply grade 1 skills making a ten, skip counting, etc)

• In adding or subtracting three-digit numbers one adds or subtracts ones and ones, tens and tens, hundreds and hundreds

• compose and decompose tens and hundreds

• How and when to regroup

• Mental math strategies (make a ten/hundred, skip count)

• 10 more/less and 100 more/less of a given number 100-900

• Why do we show evidence of our thinking in math

In order to meet these essential understandings, students must be able to...

• Apply schema (background knowledge) to solve fact families in addition and subtraction

• Fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

• Apply strategies to add up to 4 two-digit numbers using 2 different strategies

• Add and subtract within 1000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

• Create evidence of solving addition & subtraction equations using 2 different strategies

• Monitor for meaning to determine if regrouping is necessary in addition and subtraction within 1000

• Use mental math to add/subtract 10 or 100 to/from a given number

• Integrate drawings, objects, equations, and writing to explain why addition and subtraction strategies work

• Justify and reason with academic vocabulary to explain thinking

Evidence Outcomes:

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. (see Appendix, Table 1) (CCSS: 2.OA.A.1)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• The ability to make sense of problems and persevere in solving them

• Examine and apply a variety of strategy to accurately and effectively solve problems

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Students understand there are concrete and abstract strategies to solve various situations of addition and subtraction problems

In order to meet these essential understandings, students must know...

Academic Vocabulary: Word problem, Adding to, Taking from, Putting together, Taking apart, Comparing, Part part whole model (number bond), Unknown, Position

• How to generate meaning of a problem and determine the unknown information

• addition & subtraction strategies based on place value

  • base ten blocks

  • break apart method (decompose into unit or expanded form)

  • open number line

  • hundreds chart

• Addition/subtraction situations: (see Appendix table 1)

  • Adding to

  • Taking from

  • Putting together

  • Taking apart

  • Comparing

• Part part whole model (number bond)

• The unknown or missing information can be in all positions of the various situations

• Some words have different meanings in word problems (more does not always mean add more)

In order to meet these essential understandings, students must be able to...

• Mathematicians represent situations in word problems using drawings and equations with symbols for unknown numbers

• Determine importance and monitor for meaning to comprehend a mathematical word problem

• Fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

• Create evidence of solving addition & subtraction equations using 2 different strategies

• Identify the situation represented by a word problem:

  • Adding to

  • Taking from

  • Putting together

  • Taking apart

  • Comparing

• Use the part part whole model to identify the known and unknown in a word problem

• Justify and reason with academic vocabulary to explain thinking

Evidence Outcomes:

1. Fluently add and subtract within 20 using mental strategies. (See 1.OA.C.6 for a list of strategies.) By end of Grade 2, know from memory all sums of two one-digit

numbers. (CCSS: 2.OA.B.2)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

The ability to solve addition and subtraction problems with automaticity

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• The importance of and strategies for mental math

• Apply 0-20 facts in addition and subtraction within 1000

In order to meet these essential understandings, students must know...

• Mental math strategies

  • Making a ten

  • Counting on

  • Decompose a number leading to a 10

  • Fact Families

  • Doubles

  • Near Doubles

• Fluency in math

• 0-20 fact fluency with automaticity

In order to meet these essential understandings, students must be able to...

• Apply mental math strategies to fluently add and subtract within 20

• Recall from memory all sums and differences in numbers 0-20

• Evaluate the problem and determine impotence to choose the most efficient strategy

• Justify and reason academic vocabulary to explain thinking

Evidence Outcomes:

1. 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. (CCSS: 2.OA.C.3)

2. 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. (CCSS: 2.OA.C.4)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Examine and apply a variety of strategies to accurately and effectively solve problems

• Organizing objects into equal groups allows us to solve complex problems

Essential Understandings: In order to meet these transfer goals, the essential ideas and core process students must understand are...

• Understand the relationship between arrays, repeated addition, equal groups, and multiplication

• Explore the arrangement of objects and how some arrangement afford mathematical power to solve problems

In order to meet these essential understandings, students must know...

Academic Vocabulary: Odd, Even, Skip count, Repeated addition, Array, Row, Column , Equal groups

• What is an odd number

• What is an even number

• Skip count by 2’s

• Even numbers have relationships to doubles facts

• What is repeated addition

• How to write a repeated addition equation

• Strategies to solve repeated addition

• How to create a rectangular array of rows and columns (up to 5 rows and up to 5 columns)

• How to use strategies to solve higher level repeated addition equations

**expose to multiplication but not expected to master the use of the equation structure of multiplication (gaining a foundation for multiplication by understanding equal groups and arrays)

In order to meet these essential understandings, students must be able to...

• Determine whether a group of objects has an odd or even number of members

• Pair objects or skip count by 2s to determine odd or even

• Construct an equation to express an even number as a doubles fact

• Use repeated addition to find the total number of objects arranged in rectangular arrays (5+5+5 =15; is the same as 3 rows of 5)

• Create arrays of rows and columns (up to 5 rows and up to 5 columns)

• Apply skip counting to solve arrays

• Demonstrate how to place objects into equal groups

• Use mental math and concrete addition strategies to solve higher level repeated addition equations

• Apply mental math strategies

  • Making a ten

  • Counting on

  • Decompose a number learning to a 10

  • Fact Families

  • Doubles

  • Near Doubles

• Justify and reason with academic vocabulary to explain thinking

Evidence Outcomes:

1. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. (CCSS: 2.MD.A.1)

2. 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. (CCSS: 2.MD.A.2)

3. Estimate lengths using units of inches, feet, centimeters, and meters. (CCSS: 2.MD.A.3)

4. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. (CCSS: 2.MD.A.4)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

Rely on spatial awareness to use appropriate tools to deepen understanding of mathematical concepts

Essential Understandings: In order to meet these transfer goals, the essential ideas and core process students must understand are...

• Choose the most efficient unit of measurement and tool for measuring an object depending on its size

• Estimations are not precise but are a way of using background knowledge and reasoning to gauge an object's length

• addition and subtraction strategies can aid in comparing lengths of objects

In order to meet these essential understandings, students must know...

Academic Vocabulary: Measure, Unit of measure- inch, foot, centimeter, meter, Measurement tool: ruler, yardstick, meter stick, measuring tape, Estimate, Benchmark measurement, Accurate, Precise, Compare

• How to generate meaning of a word problem to determine the unknown information and the operation needed to solve

• addition & subtraction strategies based on place value

  • base ten blocks

  • break apart method

  • open number line

  • hundreds chart

• Part part whole model

• The unknown or missing information can be in all positions of the various situations

• Some words have different meanings in word problems (more does not always mean add more)

• Relationship between a ruler and a number line

• Understand the impact of the beginning and ending points when measuring an object

In order to meet these essential understandings, students must be able to...

• Determine importance and monitor for meaning to generate meaning and identify the operation needed to solve a problem

• Fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

• Create evidence of solving addition & subtraction equations using 2 different strategies

• Use the part part whole model to identify the known and unknown in a word problem

• Make connections between the relationship of a ruler and number line (equally spaced 0,1,2,3)

• Model object length in pictorial form on a ruler and number line diagram

• Create a number line diagram to model the sum or difference of two or more objects

• Justify and reason with academic vocabulary to explain thinking

Evidence Outcomes:

1. 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. (CCSS: 2.MD.B.5)

2. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, \lots, and represent whole-number sums and differences within 100 on a number line diagram. (CCSS: 2.MD.B.6)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• The ability to make sense of problems and persevere in solving them

Essential Understandings: In order to meet these transfer goals, the essential ideas and core process students must understand are...

• Students understand there are concrete and abstract strategies to solve various situations of addition and subtraction problems

In order to meet these essential understandings, students must know...

Academic Vocabulary: Word problem , Part part whole model, Tape diagram, Sum, Difference, Units of measurement

• How to generate meaning of a word problem to determine the unknown information and the operation needed to solve

• addition & subtraction strategies based on place value

  • base ten blocks

  • break apart method

  • open number line

  • hundreds chart

• Part part whole model

• The unknown or missing information can be in all positions of the various situations

• Some words have different meanings in word problems (more does not always mean add more)

• Relationship between a ruler and a number line

• Understand the impact of the beginning and ending points when measuring an object

In order to meet these essential understandings, students must be able to...

• Determine importance and monitor for meaning to generate meaning and identify the operation needed to solve a problem

• Fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

• Create evidence of solving addition & subtraction equations using 2 different strategies

• Use the part part whole model to identify the known and unknown in a word problem

• Make connections between the relationship of a ruler and number line (equally spaced 0,1,2,3)

• Model object length in pictorial form on a ruler and number line diagram

• Create a number line diagram to model the sum or difference of two or more objects

• Justify and reason with academic vocabulary to explain thinking

Evidence Outcomes:

1. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. (CCSS: 2.MD.C.7)

2. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using and ¢ symbols appropriately. Example: If you have two dimes and three pennies, how many cents do you have? (CCSS: 2.MD.C.8)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Tell and manage time to be both personally responsible and responsible for the needs of others

• Recognize that some real-world word problems can be solved using quantities of money

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Recognize that time is a quantity that can be measured with different degrees of precision

• Money can relate to other mathematical operations, skip counting, place value, addition, and subtraction

• Money is related to economics

In order to meet these essential understandings, students must know...

Academic Vocabulary: Analog clock, Digital clock, Hour, Minute, Second, Hour hand, Minute hand, AM and PM, O’clock, half past, quarter till, quarter after, Money: Coins: penny, nickel, dime, quarter, Bills: 1, 5, 10, 20, 50, 100, Money symbols: $ ₵

Time:

• What is the purpose of time

• Minute hand

• Hour hand

• Seconds in a minute

• Minutes in an hour

• Hours in a day

• AM (midnight to noon) and PM (noon to midnight)

• Numbers on clock face- Skip counting by 5’s

• O’clock, half past, quarter till, quarter after

• Analog and digital time

Money:

• Purpose and use of money (Connect to SS-Economics)

• Names and values of money units

• How/when to use symbols in money $ ₵

• Strategies to add and subtract money quantities

In order to meet these essential understandings, students must be able to...

Time:

• Demonstrate understanding that one minute = 60 seconds and that one hour = 60 minutes

• Write the time shown on an analog clock to the nearest 5 minutes using the hour and minute hand accurately

• Accurately place the hands on an analog clock for a given time to the nearest 5 minute

• Classify and define a time as AM or PM using context clues

• Recognize that each number on a clock face beginning at 1 represents a multiple of 5 minutes (the 12 on the clock face represents 0 minutes and resets the hour)

• use the appropriate phrase to describe the time within an hour (o’clock, half past, quarter till, quarter after)

Money:

• Explain the purpose of money and how it has changed over time- economics

• Identify and recall the names and values of money units

• Demonstrate understanding of symbols used with money and when used accurately

• Determine importance to select the appropriate symbol to represent the monetary amount

• Use skip counting and counting to count coins

• Use addition and subtraction strategies to solve word problems involving money and time

Evidence Outcomes:

1. 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. (CCSS: 2.MD.D.9)

2. Draw a picture graph and a bar graph (with a single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems (see Appendix, Table 1) using information presented in a bar graph. (CCSS: 2.MD.D.10)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

Organize, represent and interpret data to make connections to real-world situations

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Objects/concepts can be categorized to deepen our understanding of them

• Graphs serve as a tool to represent data in a visual format

In order to meet these essential understandings, students must know...

Academic Vocabulary: Data, Line plot, Bar graph, Picture graph, Category and categorize, Scale, Tally, table/chart

• Gather, represent, and interpret data on a line plot, bar graph, and picture graph (pictograph) with up to 4 categories

• Skills to compare different categories and data sets

In order to meet these essential understandings, students must be able to...

• Explain the purpose of gathering and representing data

• Interpret data shown on a line plot

• Collect and organize data to create a line plot to shows how frequent objects occur on a number line

• Collect and organize data to create a picture graph and bar graph to represent a set of data (up to 4 categories, single-unit scale)

• Reflect and respond to solve put together, take apart, and comparison problems using information presented in a graph

• Justify and reason with academic vocabulary to explain thinking

Evidence Outcomes:

1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. (CCSS: 2.G.A.1)

2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. (CCSS: 2.G.A.2)

3. 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. (CCSS: 2.G.A.3)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Demonstrate flexibility, imagination, and inventiveness in composing shapes

• Spatial awareness is essential in identifying equal parts

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Shapes have attributes that are defining and non-defining

• Shapes can be partitioned into equal parts

In order to meet these essential understandings, students must know...

Academic Vocabulary: Angle, Face, Side, Vertice, Triangle, Quadrilateral, Pentagon, Hexagon, Cube, Partition, Equal share, Rows, Columns, Halves (half of), Thirds (a third of), Fourths (a fourth of)

• What are attributes (angles, faces, sides, vertices)

• Shapes can be classified as two- or three-dimensional

• Various shapes

  • Triangle

  • Quadrilaterals

  • Pentagon

  • Hexagon

  • Cube

• How to make observations to compare sizes without measuring

• What it means to partition into same-size squares (divide equally by drawing lines)

• The difference between rows (horizontal) and columns (vertical)

• Two, three, and four equal shares are known as halves, thirds, and fourths respectively

• A whole is known as two halves, three thirds, and four fourths

• Equal shares of identical wholes need not have the same shape

In order to meet these essential understandings, students must be able to...

• Identify and create visual representations to show understanding of attributes of shapes

• Partition a rectangle into rows and columns of same-sized squares to find the total number of them

• Recognize the size of the shape by counting squares within boundaries

• Partition a circle or rectangle into two, three, or four equal shares

• Describe, model and create to show equal shares as halves, thirds, or fourths

• Recognize that one whole is equal to two halves, three thirds, and four fourths

• Recognize that equal shares of identical wholes need not have the same shape (example: square can be partitioned into halves vertically, horizontally, and diagonally)

• Students recognize and generate meaning from content vocabulary

• Students apply content vocabulary in student discourse and in explaining their thinking