Sampler

COMMON CORE State Standards

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THIRD GRADEARTS MATHEMATICS

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ELA-Literacy

Critical Focus — These are the items relevant to each grade teachers need to be focused on. It includes the most important Learner Outcomes for that grade in that anchor standard.

Big Idea(s): These are statements summarizing important ideas and core processes that are central to the anchor standard. They have lasting value beyond the classroom with real-world connections. They synthesize what students should understand — not just know or do — as a result. They articulate what students should “revisit” one the course of their life tines in relationship to the content area.

They transfer to other fields and provide a conceptual foundation for studying the content area. Many times they can be used to write “enduring understandings” and/or rewritten as an overarching essential question.

Academic Vocabulary — These are the vocabulary words for that anchor standard that require direct, explicit instruction and should be used in oral discussions and written responses.

R E L P M A

Essential Questions — These are important questions that are at the heart of the matter, or the essence of a standard. They help create genuine and relevant inquiry. The ones we have written for the standards are primarily considered Topic Essential Questions.

Learning Progressions — The standard from the grade prior to the featured grade and the standard from the grade after the featured grade is noted for easy reference.

Depth of Knowledge Range Target for Instruction & Assessment — The range of the DOK for that standard is noted so everyone is aware of the DOK ceiling.

Learning Expectations — These are our Instructional Targets of Know (Concepts/Skills), Think and Do. Here is where we show the deconstruction of the standard.

Key Strategies — We highlight a few key instructional strategies that are critical for teaching that standard and may want to be considered as additions to unit/lesson plans.

Math

Domain & Cluster: These are noted and include a brief description of the focus of that cluster for the featured grade.

Key Changes: The key concepts that are new to the featured grade, have moved from the featured grade and the Critical Areas of

Focus are highlighted to guide teachers on how to set priorities and look at changes that may need to be made in their curriculum.

Big Idea: These are statements summarizing important ideas and core processes that are central to the math cluster. They have lasting value beyond the classroom with real-world connections. They synthesize what students should understand — not just know or do — as a result. They articulate what students should “revisit” one the course of their life tines in relationship to the content area. They transfer to other fields and provide a conceptual foundation for studying the content area. Many times they can be used to write “enduring understandings” and/or rewritten as an overarching essential question.

Academic Vocabulary: These are the vocabulary words for that cluster that require direct, explicit instruction and should be used in

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oral discussions and written explanations.

Cluster Learning Progressions: In math, the learning progressions are done by clusters. Research from the University of Arizona was used to write these progressions that include content focus statements. The featured grade is bookended with the prior and the following grades.

Essential Question(s): These are important questions that are at the heart of the matter, or the essence of a standard. They help create genuine and relevant inquiry. The ones we have written for the standards are primarily considered Topic Essential Questions.

Mathematical Practice(s); The Mathematical Practice(s) that align to the standard are noted.

Depth of Knowledge Range Target for Instruction & Assessment: The range of the DOK for that standard is noted so everyone is aware of the DOK ceiling.

Assessment Types: This information comes from the PARCC information on the types of assessments that align best to the instructional targets of the standard.

Explanations & Examples: This is a brief summary of what instruction of this standard includes and sometimes includes visuals in the description.

Please note that each grade level will have an individual booklet. Here is the how they break down: ELA/Literacy — K, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 6-8 Literacy Hist/SoSt/Sci/Technical Subjects, 9-12 Literacy Hist/SoSt/Sci/Technical Subjects Math — K, 1, 2, 3, 4, 5, 6, 7, 8, HS: Number and Quantity, HS: Algebra, HS: Functions, HS: Modeling, HS: Geometry, HS: Statistics & Probability

COMMON CORE State Standards

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3 S

THIRD GRADEARTS MATHEMATICS

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THIRD Grade lexile gRAde level bAnds: 520l TO 820l Domain:

Operations and Algebraic Thinking (OA)

Cluster:

Represent and solve problems involving multiplication and division.

Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal - sized group situations, division can require finding the unknown number of groups or the unknown group size.

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Key Changes: NEw TO THIRD GRaDE mOvED fROm THIRD GRaDE

CRITICal aREaS Of fOCUS

Area and perimeter

Permutation and combinations Rectangular Coordinate system Circle graphs

1. developing understanding of multiplication and division and strategies for multiplication and division within 100.

Use activities and problems involving equal-sized groups, arrays, and area models to build understanding of the meanings of multiplication and division Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies of properties to solve multiplication and division problems involving single-digit factors.

Students learn the relationship between multiplication and division.

2. developing understanding of fractions, especially unit fractions (fractions with numerator 1).

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Students develop an understanding of fractions, beginning with unit fractions.

Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole.

Students understand that the size of a fractional part is relative to the size of the whole.

Students are able to use fractions to represent numbers equal to, less than, and greater than one.

They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators

3. developing understanding of the structure of rectangular arrays and of area.

Students recognize area as an attribute of two-dimensional regions.

They measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area.

Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle.

4. describing and analyzing two-dimensional shapes.

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Students describe, analyze, and compare properties of two-dimensional shapes.

They compare and classify shapes by their sides and angles, and connect these with definitions of shapes.

Students relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole.

Common Core State StandardS deConStrUCted for CLaSSroom ImPaCt

MathEMatICS Big iDea: aCaDemiC VoCaBulary:

multiplication and division are related operations.

The terms students should learn to use with increasing precision with this cluster are: products, groups of, quotients, partitioned equally, multiplication, division, equal groups, group size, arrays, equations, unknown.

Cluster learning Progressions

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2ND GRaDE

3RD GRaDE

S 3RD GRaDE

Represent and solve situational problems, which involve addition and subtraction within 100. Represent and solve two-step situational problems.

2.0a.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.

2.0a.2

Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Common types of multiplication and division situations.

3.0a.1

Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7.

3.0a.2

Interpret whole-number quotients of whole numbers, e.g. interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

3.0a.3

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

3.0a.4

determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = ? ÷ 3, 6 x 6 = ?.

3.oa.5

apply properties of operations as strategies to multiply and divide. examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication). 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (associative property of multiplication). Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (distributive property).

3.oa.6

Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

3.oa.7

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Using a letter for the unknown quantity, the order of operations, and two-step word problems with all four operations.

3.oa.8

Solve two-step word problems using the four operations. represent these problems using equations with a letter standing for the unknown quantity. assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Common Core STaTe STandardS deConSTrUCTed For CLaSSroom ImPaCT

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THIRD Grade lexile gRAde level bAnds: 520l TO 820l Cluster learning Progressions 4TH GRaDE

4TH GRaDE

Multiplication compare.

4.0a.1

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. represent verbal statements of multiplicative comparisons as multiplication equations.

4.0a.2

multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

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Remainders

4.oa.3

4TH GRaDE

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. represent these problems using equations with a letter standing for the unknown quantity. assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Factors, multiples, and prime and composite numbers.

4.oa.4

Find all factor pairs for a whole number in the range 1–100. recognize that a whole number is a multiple of each of its factors. determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. determine whether a given whole number in the range 1–100 is prime or composite.

4.0a.5

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. explain informally why the numbers will continue to alternate in this way.

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stanDarD 3.Oa.1.

ESSENTIal QUESTION(S) maTHEmaTICal pRaCTICE(S)

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interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

How can i find the total number of objects in equal groups?

3.MP.1. Make sense of problems and persevere in solving them.

3.MP.4. Model with mathematics.

3.MP.7. look for and make use of structure.

Common Core State StandardS deConStrUCted for CLaSSroom ImPaCt

MathEMatICS DeConstruCtion: DOK Range Target for Instruction & Assessment

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1

T

2

3

o

o

4

Learning Expectations:

Know: Concepts/Skills

Think

Students should be able to:

Find the product of multiple groups of objects.

Interpret products of whole numbers as a total number of objects in a number of groups.

Tasks assessing concepts, skills and procedures

Tasks assessing expressing mathematical reasoning

Do

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Assessment Types

Tasks assessing modeling / applications

eXPlanations anD eXamPles:

Students recognize multiplication as a means to determine the total number of objects when there are a specific number of groups with the same number of objects in each group. multiplication requires students to think in terms of groups of things rather than individual things. Students learn that the multiplication symbol ‘x’ means “groups of” and problems such as 5 x 7 refer to 5 groups of 7.

To further develop this understanding, students interpret a problem situation requiring multiplication using pictures, objects, words, numbers, and equations. Then, given a multiplication expression (e.g., 5 x 6) students interpret the expression using a multiplication context. (See Table 2) They should begin to use the terms, factor and product, as they describe multiplication.

S 3.Oa.2.

ESSENTIal QUESTION(S) maTHEmaTICal pRaCTICE(S)

interpret whole-number quotients of whole numbers, e.g. interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

When you divide what do you find?

3.MP.1. Make sense of problems and persevere in solving them.

3.MP.4. Model with mathematics.

3.MP.7. look for and make use of structure.

Common Core STaTe STandardS deConSTrUCTed For CLaSSroom ImPaCT

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THIRD Grade lexile gRAde level bAnds: 520l TO 820l DOK Range Target for Instruction & Assessment Learning Expectations:

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1

T

2

o

3

Know: Concepts/Skills

Students should be able to:

Know what the numbers in a division problem represent

o

4

Think

Do

explain what division means and how it relates to equal shares

R E L P M A Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally

Assessment Types:

eXPlanations anD eXamPles:

Tasks assessing concepts, skills and procedures

Tasks assessing expressing mathematical reasoning

Tasks assessing modeling / applications

This standard focuses on two distinct models of division: partition models and measurement (repeated subtraction) models. Partition models provide students with a total number and the number of groups.

These models focus on the question, “How many objects are in each group so that the groups are equal?” a context for partition models would be: There are 12 cookies on the counter. If you are sharing the cookies equally among three bags, how many cookies will go in each bag? measurement (repeated subtraction) models provide students with a total number and the number of objects in each group. These models focus on the question, “How many equal groups can you make?” a context for measurement models would be: There are 12 cookies on the counter. If you put 3 cookies in each bag, how many bags will you fill?

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(continues to the next standards in the cluster)

Common Core State StandardS deConStrUCted for CLaSSroom ImPaCt

COMMON CORE State Standards

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7 S

SEVENTH gRadE

ENglish laNguagE aRts —

litERaCy iN histORy/sOCial studiEs, sCiENCE & tEChNiCal subjECts

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SEVENTH Grade lexile grade level bands: 970l to 1120l

Key ideas and details aNCHor readiNg staNdard:

7.ri.1. read closely to determine what the text says explicitly and to make logical inferences from it: cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

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CritiCal FoCus:

informational textliterary nonfiction and Historical, scientific and technical texts learner outcomes

Includes biographies and autobiographies; books about history, social studies, science, and the arts; technical texts, including directions, forms and information displayed in graphs, charts or maps; and digital sources on a range of topics.

Seventh grade students develop the ability to gather more than one piece of evidence to support their thinking about the informational texts they read. They need to be able to find pieces of relevant evidence that not only support their thinking, but are linked together to a common idea or conclusion. In order to do so, students at this level need practice locating, evaluating, and categorizing evidence and linking this evidence to conclusions or claims they have made about the text.

At this level, seventh grade students must be able to locate and describe the central ideas presented in a text. They understand how the central ideas are related to the details and examples that support them. Students pay attention to how the central ideas are developed throughout the text and they observe how the details and examples work together to uphold the central idea.

Students in seventh grade should be able to summarize what they have read, free from their own opinions and bias.

S Big idea:

aCademiC VoCaBulary:

2

Students in seventh grade need to be able to read closely to analyze relationships between individuals, events, and ideas in a text. For example, in an informational history book, they may reflect on how historical figures influenced ideas or events of the time period and vice versa. In order to do so, students will need wide and deep exposure to informational texts. They may also need tools for recording the relationships they observe, such as a graphic organizer or structured note-taking.

We read to develop as people and citizens in our global society.

We make interpretations and draw conclusions both from what we read and experience in life.

The terms students should learn to use with increasing precision with this anchor standard are: relevant, credible, reliable, opinion, substantiate, unsubstantiated, infer, summarize, synthesize, critique, thesis, organizational pattern, controlling idea, transitional words and phrases, context, denotative meaning, connotative meaning, inductive reasoning, deductive reasoning, drawing conclusions, subtle inference, procedural text.

Common Core State StandardS deConStrUCted for CLaSSroom ImPaCt

English languagE arts deCoNstruCtioN: Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

7.RI.1.

ESSENTIal QUESTION(S)

How can I provide proof of what I have learned from different kinds of text?

R E L P M A

lEaRNINg pROgRESSIONS

Cite strong and thorough evidence to support analysis of what the text says explicitly as

grade 6 well as inferences drawn from the text. grade 7

Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Cite the textual evidence that most strongly supports an analysis of what the text says

grade 8 explicitly as well as inferences drawn from the text.

DOK Range Target for Instruction & Assessment

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Learning Expectations:

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2

T

3

o

Know: Concepts/Skills

Students should be able to:

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1

Identify inferences from a text

Identify explicit information from a text

recognize credible resources/sources

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Think

Do

Analyze several pieces of text to determine what they each explicitly say Formulate inferences from textual material

Key strategies:

Assimilating prior knowledge rereading to clarify information – close reading techniques Text-based questions Seeking meaning of unknown vocabulary making and revising predictions Using critical and divergent thinking and assimilating prior knowledge to draw conclusions making connections and responding to text

Common Core STATe STAndArdS deConSTrUCTed For CLASSroom ImPACT

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