Mathematics | Grade 3 Standards for Mathematical …...Mathematics | Grade 3 In Grade 3, student...
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Page 87 2018 Wyoming Mathemacs Standards hp://edu.wyoming.gov/educators/standards Mathemacs | Grade 3 In Grade 3, student learning is focused on four crical areas: (1) develop understanding of mulplicaon and division including strategies for mulplicaon and division within 100; (2) develop understanding of fracons, especially unit fracons (fracons with numerator 1); (3)develop understanding of the structure of rectangular arrays and of area; (4) describe and analyze two- dimensional shapes. (1) Students develop an understanding of the meanings of mulplicaon and division of whole numbers through acvies and problems involving equal-sized groups, arrays, and area models; mulplicaon is finding an unknown product, and division is finding an unknown factor in these situaons. For equal-sized group situaons, division can require finding the unknown number of groups or the unknown group size. Students use properes of operaons to calculate products of whole numbers, using increasingly sophiscated strategies based on these properes to solve mulplicaon and division problems involving single-digit factors. By comparing a variety of soluon strategies, students learn the relaonship between mulplicaon and division. (2) Students develop an understanding of fracons, beginning with unit fracons. Students view fracons in general as being built out of unit fracons, they use fracons along with visual fracon models to represent parts of a whole. Students understand that the size of a fraconal part is relave to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fracons to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fracons by using visual fracon models and strategies based on nocing equal numerators or denominators. (3) Students recognize area as an aribute 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 idencal rows or into idencal columns. By decomposing rectangles into rectangular arrays of squares, students connect area to mulplicaon, and jusfy using mulplicaon to determine the area of a rectangle. (4) Students describe, analyze, and compare properes of two- dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definions of shapes. Students also relate their fracon work to geometry by expressing the area of part of a shape as a unit fracon of the whole. Standards for Mathemacal Pracce at Grade Level 1. Make sense of problems and persevere in solving them. In third grade, students know that doing mathemacs involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Third grade students may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense? “They listen to the strategies of others and will try different approaches. They oſten will use another method to check their answers. 2. Reason abstractly and quantavely. Students recognize that a number represents a specific quanty. They connect the quanty to wrien symbols and create a logical representaon of the problem at hand, considering both the appropriate units involved and the meaning of quanes. 3. Construct viable arguments and crique the reasoning of others. Students may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathemacal communicaon skills as they parcipate in mathemacal discussions involving quesons such as, “How did you get that? and “Why is that true?” They explain their thinking to others and respond to others’ thinking. 4. Model with mathemacs. Students experiment with represenng problem situaons in mulple ways including numbers, words (mathemacal language), drawing pictures, using objects, acng out, making a chart, list, or graph, creang equaons, etc. Students need opportunies to connect the different representaons and explain the connecons. They should be able to use all of these representaons as needed. Students should evaluate their results in the context of the situaon and reflect on whether the results make sense. 5. Use appropriate tools strategically. Students consider the available tools (including esmaon) when solving a mathemacal problem and decide when certain tools might be helpful. For instance, they may use graph paper to find all the possible rectangles that have a given perimeter. They compile the possibilies into an organized list or a table, and determine whether they have all the possible rectangles. 6. Aend to precision. As students develop their mathemacal communicaon skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the area of a rectangle they record their answers in square units. 7. Look for and make use of structure. Students look closely to discover a paern or structure. For example, students use properes of operaons as strategies to mulply and divide (commutave and distribuve properes). 8. Look for and express regularity in repeated reasoning. Students noce repeve acons in computaon and look for shortcut methods. For example, students may use the distribuve property as a strategy for using products they know to solve products that they don’t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 then mulply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56. In addion, third graders connually evaluate their work by asking themselves, “Does this make sense?”
Transcript of Mathematics | Grade 3 Standards for Mathematical …...Mathematics | Grade 3 In Grade 3, student...
Page 87 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
Mathematics | Grade 3 In Grade 3, student learning is focused on four critical areas: (1) develop understanding of multiplication and division including strategies for multiplication and division within 100; (2) develop understanding of fractions, especially unit fractions (fractions with numerator 1); (3)develop understanding of the structure of rectangular arrays and of area; (4) describe and analyze two-dimensional shapes. (1) 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. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division. (2) Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, 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. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. 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) 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) 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 also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole.
Standards for Mathematical Practice at Grade Level 1. Make sense of problems and persevere in solving them.
In third grade, students know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Third grade students may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense? “They listen to the strategies of others and will try different approaches. They often will use another method to check their answers.
2. Reason abstractly and quantitatively.
Students recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities.
3. Construct viable arguments and critique the reasoning of others.
Students may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they participate in mathematical discussions involving questions such as, “How did you get that? and “Why is that true?” They explain their thinking to others and respond to others’ thinking.
4. Model with mathematics.
Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Students should evaluate their results in the context of the situation and reflect on whether the results make sense.
5. Use appropriate tools strategically.
Students consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper to find all the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table, and determine whether they have all the possible rectangles.
6. Attend to precision.
As students develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the area of a rectangle they record their answers in square units.
7. Look for and make use of structure.
Students look closely to discover a pattern or structure. For example, students use properties of operations as strategies to multiply and divide (commutative and distributive properties).
8. Look for and express regularity in repeated reasoning.
Students notice repetitive actions in computation and look for shortcut methods. For example, students may use the distributive property as a strategy for using products they know to solve products that they don’t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 then multiply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56. In addition, third graders continually evaluate their work by asking themselves, “Does this make sense?”
Page 88 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.OA.A Represent and
solve problems involving multiplication and division.
Mathematical Practices
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3.OA.A.1 Represent the concept of multiplication of whole numbers using models including, but not limited to, equal-sized groups ("groups of"), arrays, area models, repeated addition, and equal "jumps" on a number line.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
ELA
L.3.4 Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3 reading
and content, choosing flexibly from a range of strategies.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 89 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.OA.A Represent and
solve problems involving multiplication and division.
Mathematical Practices
Op
erati
on
s and
Alge
braic Th
inkin
g
3.OA.A.2 Represent the concept of division of whole numbers (resulting in whole number quotients) using models including, but not limited to, partitioning, repeated subtraction, sharing, and inverse of multiplication.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
CVE
CV5.3.1 Students identify and define
real-world problems and meaningful
questions for investigation.
CV5.3.2 Students plan and manage
activities to develop a solution or
complete a project.
ELA
L.3.4 Determine or clarify the meaning of unknown and multiple-meaning
word and phrases based on grade 3 reading and content, choosing flexibly
from a range of strategies.
L.3.6 Acquire and use accurately grade-appropriate conversational, general
academic, and domain specific words and phrases, including those that
signal spatial and temporal relationships.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 90 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.OA.A Represent and
solve problems involving multiplication and division.
Mathematical Practices
Op
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Alge
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3.OA.A.3 Solve multiplication and division word problems within 100 using appropriate modeling strategies and equations.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
CVE
CV5.3.1 Students identify and define real-world problems and meaningful questions for investigation.
CV5.3.2 Students plan and manage activities to develop a solution or complete a project.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 91 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.OA.A Represent and
solve problems involving multiplication and division.
Mathematical Practices
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3.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient. (Students need not know formal terms.)
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
ELA
L.3.4 Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3
reading and content, choosing flexibly from a range of strategies.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 92 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.OA.B Understand properties of
multiplication and the relationship between
multiplication and division.
Mathematical Practices
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3.OA.B.5 Apply properties of multiplication as strategies to multiply and divide. (Students need not use formal terms for these properties.)
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 93 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.OA.B Understand properties of
multiplication and the relationship between
multiplication and division.
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3.OA.B.6 Understand division as an unknown-factor problem.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 94 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.OA.C Multiply and divide
within 100. Mathematical
Practices
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3.OA.C.7 Fluently multiply and divide with factors 1 - 10 using mental strategies. By end of Grade 3, know automatically all products of one-digit factors based on strategies.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
ELA
L.3.4 Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3
reading and content, choosing flexibly from a range of strategies.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 95 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.OA.D Solve problems involving the four
operations, and identify and explain patterns in
arithmetic.
Mathematical Practices
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3.OA.D.8 Solve two-step word problems (limited to the whole number system) using the four basic operations. Students should apply the Order of Operations when there are no parentheses to specify a particular order. A. Represent these problems
using equations with a symbol standing for the unknown quantity.
B. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
ELA
L.3.4 Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3
reading and content, choosing flexibly from a range of strategies.
L.3.6 Acquire and use accurately grade-appropriate conversational, general academic, and domain specific words and
phrases, including those that signal spatial and temporal relationships.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
3c,d Knowledge Constructor
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 96 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.OA.D Solve problems involving the four
operations, and identify and explain patterns in
arithmetic.
Mathematical Practices
Op
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Alge
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3.OA.D.9 Identify arithmetic patterns and explain the relationships using properties of operations.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Example:
Source: https://www.engageny.org/file/34966/download/math-g3-m3-topic-d-lesson-12.pdf?token=Vir-k0Ou
Wyoming Cross-Disciplinary Connections
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 97 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.NBT.E Use place value understanding and
properties of operations to perform multi-digit
arithmetic (a range of algorithms may be used).
Mathematical Practices
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Ten
3.NBT.E.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 98 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.NBT.E Use place value understanding and
properties of operations to perform multi-digit
arithmetic (a range of algorithms may be used).
Mathematical Practices
Nu
mb
er an
d O
pe
ratio
ns in
Base
Ten
3.NBT.E.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of addition, and/or the relationship between addition and subtraction.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 99 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.NBT.E Use place value understanding and
properties of operations to perform multi-digit
arithmetic (a range of algorithms may be used).
Mathematical Practices
Nu
mb
er an
d O
pe
ratio
ns in
Base
Ten
3.NBT.E.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of multiplication.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 100 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.NF.F Develop understanding of fractions
as numbers. (Limited to denominators 2, 3, 4, 6, and 8) *use horizontal
fractions
Mathematical Practices
Nu
mb
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3.NF.F.1 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.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 101 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.NF.F Develop understanding of fractions as
numbers. (Limited to denominators 2, 3, 4, 6, and 8) *use horizontal fractions
Mathematical Practices
Nu
mb
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ratio
ns –Fracti
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3.NF.F.2 Understand and represent fractions on a number line diagram. A. 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.
B. 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.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
ELA
L.3.4 Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3
reading and content, choosing flexibly from a range of strategies.
L.3.6 Acquire and use accurately grade-appropriate conversational, general academic, and domain specific words
and phrases, including those that signal spatial and temporal relationships.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 102 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.NF.F Develop understanding of fractions as numbers. (Limited to
denominators 2, 3, 4, 6, and 8) *use horizontal fractions
Mathematical Practices
Nu
mb
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d O
pe
ratio
ns –Fracti
on
s
3.NF.F.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
A. Understand two fractions as equivalent if they are the same size, or the same point on a number line.
B. Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent.
C. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
D. Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
CVE
CV5.3.1 Students identify and define
real-world problems and meaningful
questions for investigation.
CV5.3.2 Students plan and manage
activities to develop a solution or
complete a project.
ELA
L.3.4 Determine or clarify the meaning of unknown and multiple
-meaning word and phrases based on grade 3 reading and
content, choosing flexibly from a range of strategies.
L.3.5 Demonstrate understanding of word relationships and
nuances in word meanings.
L.3.6 Acquire and use accurately grade-appropriate
conversational, general academic, and domain specific words
and phrases, including those that signal spatial and temporal
relationships.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 103 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.MD.G Solve problems involving measurement and estimation of intervals of time, liquid volumes,
and masses of objects.
Mathematical Practices
Me
asure
men
t and
Data
3.MD.G.1 Use analog clocks to tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 104 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.MD.G Solve problems involving measurement and estimation of intervals of time, liquid volumes,
and masses of objects.
Mathematical Practices
Me
asure
men
t and
Data
3.MD.G.2 Measure and estimate liquid volumes and masses of objects using grams (g), kilograms (kg), and liters (L). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units. (Excludes multiplicative comparison problems involving notions of “times as much.”)
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
CVE
CV5.3.1 Students identify and define real-world problems and meaningful questions for investigation.
CV5.3.2 Students plan and manage activities to develop a solution or complete a project.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 105 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.MD.H Represent and
interpret data. Mathematical
Practices
Me
asure
men
t and
Data
3.MD.H.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled graphs.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
Science
3-ESS2-1 Represent data in tables and graphical displays
to describe typical weather conditions expected during a
particular season.
PE
PE 5.2.1 Students assess current levels of personal
health-related fitness.
CVE
CV5.3.1 Students identify and define real-world problems
and meaningful questions for investigation.
CV5.3.2 Students plan and manage activities to develop a
solution or complete a project.
Health
HE 4.4.7 Set a measurable short-term personal health
goal and monitor progress on achieving the goal (e.g.,
brush teeth two times per day, walk 10,000 steps every
day). PA, NUT, IP/S
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
5b Computational Thinker
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 106 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.MD.H Represent and
interpret data. Mathematical
Practices
Me
asure
men
t and
Data
3.MD.H.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Use the data to create a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
CVE
CV5.4.4 Students interpret information presented
visually, orally, or quantitatively (e.g., in charts, graphs,
diagrams, time lines, animations, or interactive elements
on Web pages) and explain how the information
contributes to an understanding of the text in which it
appears. (*Adapted from CCSS RI.4.7)
CV5.3.2 Students plan and manage activities to develop a
solution or complete a project.
ELA
L.3.4 Determine or clarify the meaning of unknown and
multiple-meaning word and phrases based on grade 3
reading and content, choosing flexibly from a range of
strategies.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
5b Computational Thinker
Computer Science
1B-DA-06 Organize and present
collected data visually to highlight
relationships and support a claim.
Computational Thinking
Financial Literacy
3rd
Page 107 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.MD.I Geometric measurement: understand concepts of area and relate area to multiplication and
to addition.
Mathematical Practices
Me
asure
men
t and
Data
3.MD.I.5 Understand area as an attribute of plane figures and understand concepts of area measurement, such as square units without gaps or overlaps.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 108 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.MD.I Geometric measurement: understand concepts of area and relate area to multiplication and
to addition.
Mathematical Practices
Me
asure
men
t and
Data
3.MD.I.6 Measure areas by counting unit squares (square cm, square m, square in., square ft, and improvised units).
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
ELA
L.3.4 Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3
reading and content, choosing flexibly from a range of strategies.
L.3.6 Acquire and use accurately grade-appropriate conversational, general academic, and domain specific words and
phrases, including those that signal spatial and temporal relationships.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 109 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.MD.I Geometric measurement: understand concepts of area and relate area to multiplication and
to addition.
Mathematical Practices
Me
asure
men
t and
Data
3.MD.I.7 Relate area to the operations of multiplication and addition. A. Find the area of a rectangle with
whole-number side lengths (dimensions) by multiplying them. Show that this area is the same as when counting unit squares.
B. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
C. Use area models to represent the distributive property in mathematical reasoning. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
ELA
L.3.4 Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade
3 reading and content, choosing flexibly from a range of strategies.
L.3.6 Acquire and use accurately grade-appropriate conversational, general academic, and domain specific
words and phrases, including those that signal spatial and temporal relationships.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 110 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.MD.J Geometric measurement: recognize perimeter as an
attribute of plane figures and distinguish between linear and
area measures.
Mathematical Practices
Me
asure
me
nt an
d D
ata
3.MD.J.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different area or with the same area and different perimeter.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
ELA
L.3.4 Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade
3 reading and content, choosing flexibly from a range of strategies.
L.3.6 Acquire and use accurately grade-appropriate conversational, general academic, and domain specific
words and phrases, including those that signal spatial and temporal relationships.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 111 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.G.K Reason with shapes
and their attributes. Mathematical
Practices
Ge
om
etry
3.G.K.1 Use attributes of quadrilaterals to classify rhombuses, rectangles, and squares. Understand that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
ELA
SL.3.1 Engage effectively in a range of
collaborative discussions (one-on-one,
in groups, and teacher-led) with diverse
partners on grade 3 topics and texts,
building on others' ideas and expressing
their own clearly.
L.3.6 Acquire and use accurately grade
-appropriate conversational, general
academic, and domain specific words
and phrases, including those that signal
spatial and temporal relationships.
CVE
CV5.3.1 Students identify and define
real-world problems and meaningful
questions for investigation.
CV5.3.2 Students plan and manage
activities to develop a solution or
complete a project.
FPA
FPA 4.1.A.3 Students apply the
elements and principles of design to
their artwork.
FPA 4.4.A.1 Students identify
connections between the visual arts
and other disciplines in the
curriculum.
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 112 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
3.G.K Reason with shapes
and their attributes. Mathematical
Practices
Ge
om
etry
3.G.K.2 Partition rectangles, regular polygons, and circles into parts with equal areas. Express the area of each part as a unit fraction of the whole.
MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Example
Wyoming Cross-Disciplinary Connections
Wyoming 2018 Mathematics Content and Performance Standards
Cross-Disciplinary Connections
ISTE
Computer Science
Computational Thinking
Financial Literacy
3rd
Page 113 2018 Wyoming Mathematics Standards http://edu.wyoming.gov/educators/standards
Grade 3 Resources
Standard/Page Number Resource/Link
3.OA.D.9 on page 96. https://www.engageny.org/file/34966/download/math-g3-m3-topic-d-lesson-12.pdf?token=Vir-k0Ou
Grade Level Math Practices on page 87. Source: www.k12.wa.us/corestandards/pubdocs/mpbygradelevel.pdf
Adapted from Arizona Department of Education Mathematics Standards—2010
CSTA Standards https://www.csteachers.org/page/standards
ISTE Standards https://www.iste.org/standards/for-educators
