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Goddard: Third Grade Common Core State Standards (CCSS) Mathematics

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Number and Operations—Fractions16

(16 Grade 3 expectations in this domain are limited to fractions with denominators 2,3,4,6, and 8Code: 3.NF.1

Cluster: Develop understanding of fractions as numbers.Standard: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒

Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐Know (nouns) Definition

List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Fractions – part of a whole

Numbers –a word or symbol used in counting Equal parts – same size or amount Partitioned – divided or separated

Be Able to Do (Verbs) Level I Level II Level III Level IV Level V

List the verbs that are key learning targets, then determine the cognitive demand level (Bloom’s/SEC) with verbs in context by placing a checkmark in the appropriate square:

Knowledge/ Remembering

Memorize facts, definitions, &

formulas

Comprehension/ Understanding

Perform Procedures

ApplicationDemonstrate

understanding of math

AnalysisConjecture,

Generalize, Prove

Synthesis/Evaluate/ Create; Solve non-routine problems; make connections

Develop understanding –bring out the capabilities of, elaborate or expand

☒ ☒ ☐ ☐ ☐

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

The student will understand that fractions are numbers. The students will understand that the whole has been divided into equal parts. The student will understand that the numerator is one equal part of the whole (denominator).

Essential Questions:

Can I identify a fraction when given different examples of numbers? Can I explain that a fraction is part of a whole number? Can I identify when a whole is cut into equal pieces? Can I label a fraction when shown a pictures of a whole cut into parts?

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What learning progressions are needed to master this standard? Give specific, measurable skill statements.

Learning Sequence Prior skill(s) needed Check Level of Rigor/Cognitive Demand(Depth of Knowledge

There are different ways to represent numbers other than whole numbers, i.e. fractions. I ☐ II ☐ III ☐ IV ☐ V ☐ Fractional parts must be equal size. I ☐ II ☐ III ☐ IV ☐ V ☐ The number of equal parts tells how many make a whole. I ☐ II ☐ III ☐ IV ☐ V ☐ Know how to understand and use a number line. I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)

Instructional Resources/Tools:

Study Island, www.visualfractions.com, http://www.aaamath.com/fra.html, http://www.softschools.com/math/fractions/games/, http://teacher.scholastic.com/activities/studyjams/fractions/,

Assessment Item Type: Selected Response ☒ Extended Constructed Response ☒ Technology Enhanced ☒ Performance Task ☒ Oral Response ☐ Eligible as summative item ☒Example: Provide possible instructional learning example/formative assessment item(s) for this standard:

Example 1: Example 2: Example 3:

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http://teacher.scholastic.com/activities/studyjams/fractions/

http://www.softschools.com/math/fractions/games/

http://www.aaamath.com/fra.html

http://www.visualfractions.com/



Cluster: Develop understanding of fractions as numbers.Standard: Understand a fraction as a number on the number line; represent fractions on a number line diagram.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Number line – a straight line with corresponding points of real numbers Fraction – parts of a whole number – a word or number used in counting





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Understand - bring out the capabilities of, elaborate or expand

☐ ☒ ☐ ☐ ☐

Represent – to present image of, symbolize ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

The student will understand that fractions can be represented on a number line. The student will be able to correctly label fractions on a number line.Essential Questions:

Can I identify fractions on a number line? Can I label fractions on a number line? Can I organize fractions on a number line? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

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Read a whole line number line. I ☐ II ☐ III ☐ IV ☐ V ☐ Use fraction bar to represent fractions, ex. fold into half or fourths I ☐ II ☐ III ☐ IV ☐ V ☐ Label fractions on a number line. I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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(16 Grade 3 expectations in this domain are limited to fractions with denominators 2,3,4,6, and 8Code: 3.NF.2a

Cluster: Develop understanding of fractions as numbers.Standard: Represent a fraction 1/ b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part

has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒

Level 3: Strategic Thinking ☒ Level 4: Extended Thinking ☐Know (nouns) Definition

List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Fraction - parts of a whole number line - a straight line with corresponding points of real numbers interval – distance or gap in between Partitioning – divide or separate endpoint – the point on each side of an interval





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


recognize - identify ☐ ☒ ☐ ☐ ☐ define – state the meaning of, give description ☒ ☐ ☐ ☐ ☐ represent - to present image of, symbolize ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

The student will define intervals from 0 to 1 into equal parts. The student will recognize that each part is the same size. The student will use their endpoints to identify fractions on the number line.


Can I identify equal intervals? Can I identify equal intervals on a number line?

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6


(16 Grade 3 expectations in this domain are limited to fractions with denominators 2,3,4,6, and 8Code: 3.NF.2b

Cluster: Develop understanding of fractions as numbers.Standard: Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint

locates the number a/b on the number line.Depth of Knowledge: Level 1: Recall ☐ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Fraction – parts of a whole Number line – a straight line with corresponding points of real numbers interval – distance or gap in between endpoint – the point on each side of an interval lengths – measure of distance





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Represent – to present image of, symbolize ☐ ☐ ☒ ☐ ☐ Recognize - identify ☐ ☒ ☐ ☐ ☐ Marking- a visible impression or mark identifying

something, label, point☐ ☐ ☒ ☐ ☐

Locates – to find or pinpoint ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

The student will mark off the fractional lengths from 0 on a number line using tick or hash marks(eg. 1/3, ¼). The student will recognize that the first segment represents one part of the whole (second segment represents 2 parts of the whole.)


Can I mark off fractional lengths from 0 to 1? Can I use the endpoint of zero to locate the fraction?

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Assessment Item Type: Selected Response ☐ Extended Constructed Response ☐ Technology Enhanced ☐ Performance Task ☐ Oral Response ☐ Eligible as summative item ☐Example: Provide possible instructional learning example/formative assessment item(s) for this standard:


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Cluster: Develop understanding of fractions as numbers.Standard: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.Depth of Knowledge: Level 1: Recall ☐ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Equivalent – sameness, similarities Fraction – parts of a whole





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Explain – make clear, give a reason for ☐ ☒ ☐ ☐ ☐ compare – examine similarities ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

The student will compare fractions by looking at the size of the parts and the number of parts. The student will use visual fraction models to compare fractions and determine equivalence.


By using visual models can I compare fractions and identify equivalent fractions? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


Understand fractions are part of a whole I ☐ II ☐ III ☐ IV ☐ V ☐

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Numerator represents the number or parts being used. I ☐ II ☐ III ☐ IV ☐ V ☐ Denominator represents the total parts. I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)



Example 1: 1/8 is smaller than ½ because when 1 whole is cut into 8 pieces the pieces are much smaller than when it is cut into 2 pieces.Example 2: Example 3:

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(16 Grade 3 expectations in this domain are limited to fractions with denominators 2,3,4,6, and 8Code: 3.NF.3a

Cluster: Develop understanding of fractions as numbers.Standard: Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.Depth of Knowledge: Level 1: Recall ☐ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Fraction – parts of a whole Equivalent (equal)– sameness, similarities Number line – a straight line with corresponding points of real numbers Point – the mark





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Understand - bring out the capabilities of, elaborate or expand

☐ ☒ ☐ ☐ ☐

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

The student will use visual models and a number line to show equivalent fractions. The students will begin reasoning about the size of pieces (eg. The larger the denominator the smaller the pieces.)


Can I identify 2 equivalent fractions using visual models or a number line? Can I explain why 1/3 is larger than ¼? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

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Understand fractions are part of a whole I ☐ II ☐ III ☐ IV ☐ V ☐ Numerator represents the number or parts being used. I ☐ II ☐ III ☐ IV ☐ V ☐ Denominator represents the total parts. I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




12


(16 Grade 3 expectations in this domain are limited to fractions with denominators 2,3,4,6, and 8Code: 3.NF.3b

Cluster: Develop understanding of fractions as numbers.Standard: Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.Depth of Knowledge: Level 1: Recall ☐ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. fraction model – representation of a fraction Fraction – parts of a whole Equivalent fractions– fractions that are the same





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


recognize - identify ☐ ☒ ☐ ☐ ☐ generate – produce or create ☐ ☐ ☐ ☐ ☒ explain – make clear, give a reason for ☐ ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

The student will recognize simple equivalent fractions (1/2 = 2/4). The student will generate simple equivalent fractions (4/6 = 2/3). The student will use a visual fraction model to explain why fractions are equal.


Given 2 fractions, can I identify whether they are equivalent of not? Given 1 fraction, can I create an equivalent fraction using a visual model? Can I visually model a set of equivalent fractions? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

Learning Sequence Prior skill(s) needed Check Level of Rigor/Cognitive Demand

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(Depth of Knowledge Understand that fractions can be equivalent even if they don’t look exactly the same. I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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(16 Grade 3 expectations in this domain are limited to fractions with denominators 2,3,4,6, and 8Code: 3.NF.3c

Cluster: Develop understanding of fractions as numbers.Standard: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.Depth of Knowledge: Level 1: Recall ☐ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Fraction – parts of a whole Whole numbers – positive integers including 0, counting numbers





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Express - give, show ☐ ☐ ☐ ☐ ☒ recognize - identify ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

The student will recognize that fractions are equivalent to whole numbers (eg. 6/1 = 6, 4/4 =1). The student will express whole numbers as fractions. The students can locate 4/4 and 1 at the same point on the number line.


Can I recognize that fractions are equivalent to whole numbers? Can I express whole numbers as fractions? Can I locate 4/4 and 1 at the same point on the number line? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


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I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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(16 Grade 3 expectations in this domain are limited to fractions with denominators 2,3,4,6, and 8Code: 3.NF.3d

Cluster: Develop understanding of fractions as numbers.Standard: Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two

fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.Depth of Knowledge: Level 1: Recall ☐ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Fraction – parts of a whole Numerator – the number of equal parts that are being used Denominator – number of equal parts the whole is divided into comparisons – how 2 or more are the same symbols – an image used to represent something (<, >, =)





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


compare – find similarities ☐ ☐ ☐ ☒ ☐ recognize - identify ☐ ☒ ☐ ☐ ☐ record – keep track of data ☒ ☐ ☐ ☐ ☐ justify – give reason for ☐ ☐ ☐ ☒ ☒ reasoning – the process of forming conclusions, analysis ☐ ☐ ☐ ☒ ☐This standard means a student will know and be able to do…(use your own words)

The student will compare fractions with the same numerator or the same denominator. The student will compare fractions with the same numerators by reasoning about their size and justify their answer using visual models. The student will compare fractions with the same denominator by reasoning about their size and justify their answer using visual models. The student will compare fractions using the symbols <, > = and justify using visual models. The students will recognize that comparisons are only valid if the whole numbers are identical (ex. ½ of a large pizza is different than ½ of a small pizza.)


Can I compare fractions with the same numerator or same denominator? Can I use visual models to justify a comparison of fractions with the same numerator? Can I use visual models to justify a comparison of fractions with the same denominator? Can I use visual models to justify a comparison of fractions using the symbols <, >, =?

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I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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