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Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
1
Unit: Operations and Algebraic Thinking
Topic: Fluent Computation to Add and Subtract
Enduring Understandings:
Addition and subtraction can be represented on various models.
Numbers are composed of other numbers.
Mental strategies help in solving problems quickly and accurately.
Essential Questions:
What are some ways to think about addition and subtraction?
What are strategies for finding addition and subtraction facts?
How can sums and differences be found mentally?
Why do we have to know how to add and subtract quickly without mistakes?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
Illustrate the mental strategy used in adding and subtracting numbers greater than 20.
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0
The student will:
fluently add and subtract within 20 using mental strategies. (2.OA.2) Add and subtract using accuracy (correct answer), efficiency (within 4-5 seconds), and flexibility (using strategies such as making 10 or breaking apart numbers). Research indicates that teachers’ can best support students’ memorization of sums and differences through varied experiences making 10, breaking numbers apart and working on mental strategies, rather than repetitive timed tests.
Addition Strategies Subtraction Strategies
Zero/ones properties Zero/ones properties
Counting on Counting up
Make a ten Counting back
Doubles Subtract 10
Doubles +1/+2 Subtract half
Fast 9/Fast 10 Inverse relationship to addition
Commutative Add to check
mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. (2.NBT.8)
The student exhibits no major errors or gaps in the learning goal (complex ideas and processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
accurately add and subtract within 20 using mental strategies.
recognize or recall specific terminology:
o addends o doubles
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.
Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
2
Unit: Operations and Algebraic Thinking
Topic: Represent and Solve Problems
Enduring Understanding:
There are different problem solving structures which can be used to solve problems in multiple ways.
Essential Questions:
How do composing and decomposing numbers lead to understanding word problems?
How can numbers be put together and taken apart to solve problems?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
make a diagram/chart using addition and subtraction within 100 to solve multiple 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. Sometimes it is necessary to compose or decompose tens or hundreds.
given a word problem involving length, identify the error and justify your answer.
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0
The student will:
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. Sometimes it is necessary to compose or decompose tens or hundreds. (2.OA.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. (2.MD.5)
The student exhibits no major errors or gaps in the learning goal (complex ideas and processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
solve simple one/two digit addition/subtraction problems.
recognize or recall specific terminology: o regrouping
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.
Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
3
Unit: Operations and Algebraic Thinking
Topic: Arithmetic Patterns
Enduring Understandings:
Flexible methods of computation involve grouping numbers in strategic ways.
Even numbered objects can be modeled using pairs or rectangular arrays.
Number patterns repeat predictably and can be generalized and applied.
Essential Questions:
What is the relationship between arrays and repeated addition?
What are efficient methods for finding sums and differences using even and odd properties of numbers?
How can you use a number pattern to solve problems?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
describe the relationship between odd and even numbers.
make a rectangular array with greater than 5 rows and 5 columns. Write multiple equations and describe the relationship between addition and multiplication.
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0
The student will:
determine whether a group of objects is odd or even, 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 (doubles addition facts). (2.OA.3)
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. (2.OA.4)
The student exhibits no major errors or gaps in the learning goal (complex ideas and processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
name whether a group of objects is odd or even and tell why.
recognize a rectangular array that represents an addition sentence.
recognize or recall specific terminology: o array o odd number o even number o patterns o column o row
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.
Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
4
Unit: Numbers and Operations- Base 10
Topic: Place Value
Enduring Understandings:
Numbers are composed of other numbers.
Place value is based on groups of ten.
Numbers can represent quantity, position, location and relationships.
Place value can be used to understand and model properties of operations.
Essential Questions:
How can numbers to 100 be shown and compared?
What number patterns are helpful in reading and writing numbers to 1,000?
How does the position of a digit in a number affect its value?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
determine the best way to compare two 4 digit numbers and explain your thinking.
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0
The student will:
understand that a three digit number represents the amounts of hundreds, tens, and ones; e.g., one hundred can be thought of ten tens. (2.NBT.1, 2.NBT.1a)
understand 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). (2.NBT.1b)
read and write numbers to 1000 using base-ten numerals, number names, and expanded form. (2.NBT.3)
compare two three-digit numbers based on the value of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. (2.NBT.4)
The student exhibits no major errors or gaps in the learning goal (complex ideas and processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
read, write, and compare whole numbers less than 1000.
recognize or recall specific terminology: o place value o hundreds
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.
Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
5
Unit: Numbers and Operations- Base 10
Topic: Extend the Counting Sequence
Enduring Understandings:
Flexible methods of computation involve grouping numbers in strategic ways.
Number patterns repeat predictable and can be generalized and applied.
Essential Questions:
What number patterns are helpful in reading and writing numbers to 1,000?
How do predictable patterns help me understand how numbers work?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
explain the rule used when skip-counting by 3s and 4s within 1000.
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0
The student will:
count within 1000; skip-count by 2s, 5s, 10s, and 100s. (2.NBT.2) Such as find, identify, and apply number patterns to numbers on a 100s chart.
The student exhibits no major errors or gaps in the learning goal (complex ideas and processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
count within 100; skip-count by 2s, 5s, 10s, and 100s.
recognize or recall specific terminology: o skip count
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.
Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
6
Unit: Numbers and Operations- Base 10
Topic: Place Value Strategies to Add and Subtract
Enduring Understandings:
Numbers are composed of other numbers.
Numbers can represent quantity, position, location and relationships.
Essential Questions:
What is the standard procedure for adding two-digit numbers?
What is the standard procedure for subtracting two-digit numbers?
How does the position of a digit in a number affect its value?
What are efficient methods for finding sums and differences?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
fluently add and subtract within 1,000 using strategies based on place value, properties of operations, and /or the relationship between addition and subtraction.
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
3.0 The student will:
fluently add and subtract within 100 using strategies based on place value and properties of operations, and/or the relationship between addition and subtraction. (2.NBT.5)
add up to four two-digit numbers using strategies based on place value and properties of operations. (2.NBT.6) Explain why addition and subtraction strategies work, using place value and the properties of commutative and associative operations.
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. (2.MD.6)
The student exhibits no major errors or gaps in the learning goal (complex ideas and
processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
add up to four two-digit numbers using strategies based on place value..
show the inverse relationship between addition and subtraction, e.g., fact families using manipulatives.
recognize or recall specific terminology: o regrouping
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.
Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
7
Unit: Numbers and Operations- Base 10
Topic: Add and Subtract with Regrouping
Enduring Understandings:
Numbers can represent quantity, position, location and relationships.
Place value is based on groups of ten.
Essential Questions:
What are the ways to add and subtract three-digit numbers?
How does the position of the digit in a number affect its value?
In what ways can numbers be composed or decomposed?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
given a multi digit addition/subtraction problem, explain how you would overcome not having enough ones, tens, or hundreds to solve the problem.
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
Score
3.0
The student will:
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. (2.NBT.7)
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.7)
explain why addition and subtraction strategies work, using place value and the properties of operations. (2.NBT.9)
The student exhibits no major errors or gaps in the learning goal (complex ideas and processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
add/subtract 2 three-digit numbers using manipulatives.
recognize or recall specific terminology: o regrouping
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.
Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
8
Unit: Geometry
Topic: Shapes and Attributes
Enduring Understandings:
Objects can be described and compared using their geometric attributes.
The area of a shape can be found by counting units.
Essential Questions:
How can shapes and solids be described, compared, and used to make other shapes?
How can you find the area of a given shape using units?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
compare and contrast the relationships of certain attributes of 2 and 3 dimensional shapes that make them part of one category and not of another.
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0
The student will:
recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify 2-dimensional shapes, e.g, triangles, circles, squares. (2.G.1)
recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces and 3-dimensional shapes, e.g., rectangular prism, cone, cubes. (2.G.1)
partition a rectangle into rows and columns of same-size squares and count to find the total number. (2.G.2)
The student exhibits no major errors or gaps in the learning goal (complex ideas and processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
identify which rectangle is evenly divided into rows and columns of same-size squares and count to find the total number.
recognize shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify 2-dimensional shapes, e.g., triangles, circles, squares.
recognize shapes having specified attributes, such as a given number of angles or a given number of equal faces and 3-dimensional shapes, e.g., rectangular prism, cone, cubes.
recognize or recall specific terminology: o angles o faces o edges o vertex
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.
Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
9
Unit: Geometry
Topic: Fractions of Shapes
Enduring Understanding:
Fractions represent equal parts of a whole or a group.
Essential Question:
How do fractions help me describe shapes and groups?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
develop a way to partition a shape into fifths 2 different ways..
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0
The student will:
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. (2.G.3)
recognize that equal shares of identical wholes need not have the same shape. (2.G.3)
The student exhibits no major errors or gaps in the learning goal (complex ideas and processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
identify which shapes are divided into halves, thirds, and fourths.
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.
Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
10
Unit: Measurement and Data
Topic: Time
Enduring Understandings:
Time can be measured.
Standard units provide common language for communicating time.
Equivalent periods of units are used to measure time.
Essential Questions:
How can clocks be used to show data and answer questions?
How do units within a system relate to each other?
How are various representations of time related?
How do we tell time to 5 minutes?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
solve word problems involving addition and subtraction of time intervals in minutes.
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0
The student will:
tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. (2.MD.7)
The student exhibits no major errors or gaps in the learning goal (complex ideas and processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
identify time from analog and digital clocks to the nearest five minutes.
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.
Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
11
Unit: Measurement and Data
Topic: Money
Enduring Understanding:
Coins have different values and are counted according to their values.
Essential Questions:
What strategies can be used to count money?
How can sums and differences be estimated?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
solve word problems involving up to $5, which requires students to make change.
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0
The student will:
solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. (2.MD.8)
The student exhibits no major errors or gaps in the learning goal (complex ideas and processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
count a given set of coins using dollar bills, quarters, dimes, nickels, and pennies.
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.
Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
12
Unit: Measurement and Data
Topic: Linear Measurement
Enduring Understandings:
A specific process is used to measure attributes of unit length.
There is a relationship between estimation and measurement.
Essential Questions:
What is the process for measuring length?
When should you estimate and when do you need an exact answer?
How do we measure (unit, tool, and process)?
How can accurate measurements help to solve problems and make sense of our world?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
tell how measuring with a ruler (inches) is different than measuring with a yardstick (feet).
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0
The student will:
measure the length of an object twice, using units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. (2.MD.2)
estimate lengths using units of inches, feet, centimeters, and meters. (2.MD.3)
measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. (2.MD.4)
The student exhibits no major errors or gaps in the learning goal (complex ideas and processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
estimate lengths using units of inches, feet, centimeters, and meters given a list of four choices.
measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. (2.MD.1)
measure the length of an object twice, using units of different lengths for the two measurements.
tell how much longer one object is than another.
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.
Content Area: Mathematics- 2nd Grade
May 2014 –CCSS Bolded standards are critical areas per Common Core
13
Unit: Measurement and Data
Topic: Represent and Interpret Data
Enduring Understanding:
Data can be collected, classified, and sorted in various ways.
Essential Question:
How can bar graphs and pictographs be used to show data and answer questions?
Score 4.0
In addition to Score 3.0, in-depth inferences or applications that go beyond level 3.0. For example, the student may:
design an investigation (survey) where multiple data sets are represented in either a bar or line graph.
3.5 In addition to 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0
The student will:
generate measurement data by measuring lengths of several objects to the nearest 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. (2.MD.9)
draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. (2.MD.10)
solve simple put-together, take-apart, and compare problems using information presented in a bar graph. (2.MD.10)
The student exhibits no major errors or gaps in the learning goal (complex ideas and processes).
2.5 No major errors or gaps in 2.0 content and partial knowledge in 3.0 content.
Score 2.0
The student will:
given a picture graph, solve simple addition and subtraction problems.
given measurement data, complete a line plot.
recognize or recall specific terminology: o bar graph
The student exhibits no major errors or gaps in the simpler details and processes.
1.5 Partial understanding of the 2.0 content with major errors or gaps in 3.0 content.
Score 1.0
With help, a partial understanding of the 2.0 content and some of the 3.0 content.
0.5 With help, a partial understanding of the 2.0 content and none of the 3.0 content.
Score 0.0
Even with help, no understanding or skill demonstrated.