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 Numbers, Number Sense, and Computation
Nevada English Language Arts Standards Content Standard 5.0 Students write a variety of texts using the writing process. All indicators are based on grade-appropriate text and skills. At a minimum, students will maintain previously-learned skills and attain the followin...
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Nevada English Language Arts Standards Content Standard 5.0 Students write a variety of texts using the writing process. All indicators are based on grade-appropriate text and skills. At a minimum, students will maintain previously-learned skills and attain the following: K 1 2 3 4 5.0 Effective Writing 41 Revising 5.K.3 I/L With assistance, revise drafts for • ideas • voice • audience 5.1.3 I/L With
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http://www.doe.nv.gov/Standards/EngLang/ELA_Standards_Final.pdf#page=50
www.doe.nv.gov/Standards/EngLang/ELA_Standards_Final.pdf#page=50
Nevada English Language Arts Standards Content Standard 5.0 Students write <span class="highlight">a</span> variety of texts <span class="highlight">using</span> the writing process. All indicators are <span class="highlight">based</span> on grade-appropriate text and skills. At <span class="highlight">a</span> minimum, students will maintain previously-learned skills and attain the following: K 1 2 3 4 5.0 Effective Writing 41 Revising 5.K.3 I/L With assistance, revise drafts <span class="highlight">for</span> • ideas • <span class="highlight">voice</span> • audience 5.1.3 I/L With
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http://www.doe.nv.gov/Standards/EngLang/ELA_Standards_Final.pdf#page=51
www.doe.nv.gov/Standards/EngLang/ELA_Standards_Final.pdf#page=51
Nevada English Language Arts Standards Content Standard 5.0 Students write <span class="highlight">a</span> variety of texts <span class="highlight">using</span> the writing process. All indicators are <span class="highlight">based</span> on grade-appropriate text and skills. At <span class="highlight">a</span> minimum, students will maintain previously-learned skills and attain the following: 5 6 7 8 9-12 5.0 Effective Writing 5.5.3 E/I/S Revise drafts <span class="highlight">for</span> • <span class="highlight">voice</span> • organization • focused ideas • audience • purpose • relevant details • word choice • sentence fluency
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http://www.doe.nv.gov/Standards/EngLang/ELA_Standards_Final.pdf#page=85
www.doe.nv.gov/Standards/EngLang/ELA_Standards_Final.pdf#page=85
Nevada English Language Arts Standards Content Standard 8.0 Students speak <span class="highlight">using</span> organization, style, tone, <span class="highlight">voice</span>, and media aids appropriate to audience and purpose. Students participate in discussions to offer information, clarify ideas, and support <span class="highlight">a</span> position. All indicators are <span class="highlight">based</span> on grade-appropriate skills. At <span class="highlight">a</span> minimum, students will maintain previously-learned skills and attain the following: 5 6 7 8 9-12 Phonology 8.0 Speaking 76
Microsoft Word - 2007 MS Math Framework Competencies and Objectives 9-18-07.doc
2007 Mississippi Mathematics Framework Revised 66 PRE-CALCULUS CONTENT STRANDS: Number and Operations Algebra Geometry Data Analysis & Probability Competencies and Objectives: NUMBER AND OPERATIONS 1. Explore and illustrate the characteristics and operations connecting sequences and ser...
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2007 Mississippi Mathematics Framework Revised 66 PRE-CALCULUS CONTENT STRANDS: Number and Operations Algebra Geometry Data Analysis & Probability Competencies and Objectives: NUMBER AND OPERATIONS 1. Explore and illustrate the characteristics and operations connecting sequences and series. a. Express sequences and series using recursive and explicit formulas. (DOK 2) b. Evaluate and apply formulas for arithmetic and geometric sequences and series. (DOK 2) c. Calculate
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http://www.mde.k12.ms.us/acad/id/curriculum/math/2007_framework/2007%20MS%20Math%20Framework%20Competencies%20and%20Objectives%209-18-07.pdf#page=67
www.mde.k12.ms.us/acad/id/curriculum/math/2007_framework/2007%20MS%20Math...
2007 Mississippi Mathematics Framework Revised 66 PRE-CALCULUS CONTENT STRANDS: Number and Operations Algebra Geometry Data Analysis & Probability Competencies and Objectives: NUMBER AND OPERATIONS 1. Explore and illustrate the characteristics and operations connecting sequences and series. <span class="highlight">a</span>. Express sequences and series <span class="highlight">using</span> recursive and explicit formulas. (DOK 2) b. Evaluate and apply formulas <span class="highlight">for</span> arithmetic and geometric sequences and series. (DOK 2) c. Calculate
GRADE 8
Explanations and Examples Students are expected to: Estimation strategies for calculations with fractions and decimals extend from students’ work with whole number operations. Estimation strategies include, but are not limited to: • front-end estimation with adjusting (using...
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Explanations and Examples Students are expected to: Estimation strategies for calculations with fractions and decimals extend from students’ work with whole number operations. Estimation strategies include, but are not limited to: • front-end estimation with adjusting (using the highest place value and estimating from the front end making adjustments to the estimate by taking into account the remaining amounts), • clustering around an average (when the values are close together an average value is
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade8.pdf#page=6
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Explanations and Examples Students are expected to: Estimation strategies <span class="highlight">for</span> calculations with fractions and decimals extend from students’ work with whole number operations. Estimation strategies include, but are not limited to: • front-end estimation with adjusting (<span class="highlight">using</span> the highest place value and estimating from the front end making adjustments to the estimate by taking into account the remaining amounts), • <span class="highlight">clustering</span> around an average (when the values are close together an average value is
Microsoft Word - mathstdglossary2004.docmathstdglossary2004.pdf
Kansas Curricular Standards for Mathematics January 2004 6 E ellipse – a closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points is a constant empirical results – results based on exper...
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Kansas Curricular Standards for Mathematics January 2004 6 E ellipse – a closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points is a constant empirical results – results based on experiments equation – a mathematical sentence that states that two expressions are equal; 2 + 3 = 1 + 4 equilateral – all sides congruent equivalent – numbers or variable expressions that have the same value (5 is equivalent to 2 + 3) estimation
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http://www.ksde.org/LinkClick.aspx?fileticket=T526GF1N0EM%3d&tabid=141&mid=8017&forcedownload=true#page=6
www.ksde.org/LinkClick.aspx?fileticket=T526GF1N0EM%3d&tabid=141&mid=8017&...
Kansas Curricular Standards <span class="highlight">for</span> Mathematics January 2004 6 E ellipse – <span class="highlight">a</span> closed plane curve generated by <span class="highlight">a</span> point moving in such <span class="highlight">a</span> way that the sums of its distances from two fixed points is <span class="highlight">a</span> constant empirical results – results <span class="highlight">based</span> on experiments equation – <span class="highlight">a</span> mathematical sentence that states that two expressions are equal; 2 + 3 = 1 + 4 equilateral – all sides congruent equivalent – numbers or variable expressions that have the same value (5 is equivalent to 2 + 3) estimation
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http://www.ksde.org/LinkClick.aspx?fileticket=T526GF1N0EM%3d&tabid=141&mid=8017&forcedownload=true#page=7
www.ksde.org/LinkClick.aspx?fileticket=T526GF1N0EM%3d&tabid=141&mid=8017&...
Kansas Curricular Standards <span class="highlight">for</span> Mathematics January 2004 7 <span class="highlight">Clustering</span> can be used as an estimation strategy when you have <span class="highlight">a</span> group of numbers that cluster around <span class="highlight">a</span> common value. 7225 6734 This set of numbers clusters around 7,000. 6829 <span class="highlight">A</span> good estimate would be 7000 x 6 or 42,000. 7295 7101 + 6642 Compatible “nice” Numbers Compatible (nice) numbers are numbers that can easily “fit together” and are easy to manipulate mentally. Take <span class="highlight">a</span> global look at all
Microsoft Word - mathstdrev0703.docmathstdrev0703.pdf
Kansas Curricular Standards for Mathematics January 2004 333 E ellipse – a closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points is a constant empirical results – results based on exp...
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Kansas Curricular Standards for Mathematics January 2004 333 E ellipse – a closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points is a constant empirical results – results based on experiments equation – a mathematical sentence that states that two expressions are equal; 2 + 3 = 1 + 4 equilateral – all sides congruent equivalent – numbers or variable expressions that have the same value (5 is equivalent to 2 + 3) estimation
1
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http://www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=8017&forcedownload=true#page=94
www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=801...
? <span class="highlight">Using</span> the language of estimation is important, so students begin to realize that <span class="highlight">a</span> variety of estimates (answers) are possible. In addition, when students are taught specific estimation strategies, they develop mental math and estimation skills easier. Estimation strategies include front-end with adjustment, compatible “nice” numbers, <span class="highlight">clustering</span>, or special numbers. Mathematical models such as concrete objects, pictures, diagrams, number lines, unifix cubes, hundred charts, or base ten blocks are
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http://www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=8017&forcedownload=true#page=128
www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=801...
Mathematics, NCTM, 2000). Mental math and estimation are distinct but related mathematical skills. Proficiency in mental math contributes to increased skill in estimation. In order <span class="highlight">for</span> students to become more familiar with estimation, teachers should introduce estimation with examples where rounded or estimated numbers are used. Emphasis should be placed on real-world examples where only estimation is required, e.g., About how many hours do you sleep <span class="highlight">a</span> night? <span class="highlight">Using</span> the language of estimation is important, so
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http://www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=8017&forcedownload=true#page=159
www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=801...
“nice” numbers, <span class="highlight">clustering</span>, or special numbers. Mathematical models such as concrete objects, pictures, diagrams, Venn diagrams, number lines, hundred charts, base ten blocks, or factor trees are necessary <span class="highlight">for</span> conceptual understanding and should be used to explain computational procedures. If <span class="highlight">a</span> mathematical model can be used to represent the concept, the indicator in the Models benchmark is identified in the parentheses. <span class="highlight">For</span> example, (2.4.K1a) refers to Standard 2 (Algebra), Benchmark 4 (Models), and
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http://www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=8017&forcedownload=true#page=194
www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=801...
? <span class="highlight">Using</span> the language of estimation is important, so students begin to realize that <span class="highlight">a</span> variety of estimates (answers) are possible. In addition, when students are taught specific estimation strategies, they develop mental math and estimation skills easier. Estimation strategies include front-end with adjustment, compatible “nice” (friendly) numbers, <span class="highlight">clustering</span>, special numbers, or truncation. Mathematical models such as concrete objects, pictures, diagrams, Venn diagrams, number lines, hundred charts
5
0
http://www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=8017&forcedownload=true#page=229
www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=801...
? <span class="highlight">Using</span> the language of estimation is important, so students begin to realize that <span class="highlight">a</span> variety of estimates (answers) are possible. In addition, when students are taught specific estimation strategies, they develop mental math and estimation skills easier. Estimation strategies include front-end with adjustment, compatible “nice” numbers, <span class="highlight">clustering</span>, special numbers, or truncation. Mathematical models such as concrete objects, pictures, diagrams, Venn diagrams, number lines, hundred charts, base ten
6
0
http://www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=8017&forcedownload=true#page=270
www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=801...
? <span class="highlight">Using</span> the language of estimation is important, so students begin to realize that <span class="highlight">a</span> variety of estimates (answers) are possible. In addition, when students are taught specific estimation strategies, they develop mental math and estimation skills easier. Estimation strategies include front-end with adjustment, compatible “nice” numbers, <span class="highlight">clustering</span>, special numbers, or truncation. Mathematical models such as concrete objects, pictures, diagrams, Venn diagrams, number lines, hundred charts, base ten
7
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http://www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=8017&forcedownload=true#page=303
www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=801...
Mathematics, NCTM, 2000) Mental math and estimation are distinct but related mathematical skills. Proficiency in mental math contributes to increased skill in estimation. In order <span class="highlight">for</span> students to become more familiar with estimation, teachers should introduce estimation with examples where rounded or estimated numbers are used. Emphasis should be placed on real-world examples where only estimation is required, e.g., About how many hours do you sleep <span class="highlight">a</span> night? <span class="highlight">Using</span> the language of estimation is important, so
8
0
http://www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=8017&forcedownload=true#page=334
www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=801...
Kansas Curricular Standards <span class="highlight">for</span> Mathematics January 2004 333 E ellipse – <span class="highlight">a</span> closed plane curve generated by <span class="highlight">a</span> point moving in such <span class="highlight">a</span> way that the sums of its distances from two fixed points is <span class="highlight">a</span> constant empirical results – results <span class="highlight">based</span> on experiments equation – <span class="highlight">a</span> mathematical sentence that states that two expressions are equal; 2 + 3 = 1 + 4 equilateral – all sides congruent equivalent – numbers or variable expressions that have the same value (5 is equivalent to 2 + 3) estimation
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http://www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=8017&forcedownload=true#page=335
www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=801...
Kansas Curricular Standards <span class="highlight">for</span> Mathematics January 2004 334 <span class="highlight">Clustering</span> can be used as an estimation strategy when you have <span class="highlight">a</span> group of numbers that cluster around <span class="highlight">a</span> common value. 7225 6734 This set of numbers clusters around 7,000. 6829 <span class="highlight">A</span> good estimate would be 7000 x 6 or 42,000. 7295 7101 + 6642 Compatible “nice” Numbers Compatible (nice) numbers are numbers that can easily “fit together” and are easy to manipulate mentally. Take <span class="highlight">a</span> global look at all
GRADE 3
mathematically correct, and answers the question. Estimation strategies include, but are not limited to: • front-end estimation with adjusting (using the highest place value and estimating from the front end making adjustments to the estimate by taking into account the remaining amounts...
1
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mathematically correct, and answers the question. Estimation strategies include, but are not limited to: • front-end estimation with adjusting (using the highest place value and estimating from the front end making adjustments to the estimate by taking into account the remaining amounts), • clustering around an average (when the values are close together an average value is selected and multiplied by the number of values to determine an estimate), • rounding and adjusting (students
14
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade3.pdf#page=14
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
mathematically correct, and answers the question. Estimation strategies include, but are not limited to: • front-end estimation with adjusting (<span class="highlight">using</span> the highest place value and estimating from the front end making adjustments to the estimate by taking into account the remaining amounts), • <span class="highlight">clustering</span> around an average (when the values are close together an average value is selected and multiplied by the number of values to determine an estimate), • rounding and adjusting (students
Microsoft Word - Front Cover Page
number gives the same result as multiplying each addend by the number and then adding the products together. (a(b + c) = a ● b + a ● c) Divisible: A number n is divisible by a number m if there is no remainder when n is divided by m. Domain: Th...
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number gives the same result as multiplying each addend by the number and then adding the products together. (a(b + c) = a ● b + a ● c) Divisible: A number n is divisible by a number m if there is no remainder when n is divided by m. Domain: The set of all possible input values for a function or relation. Draw: To create a figure in a set form without the use of a construction tool. Edge: The line segment formed when two faces of a three-dimensional figure intersect. Elapsed Time: The
50
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http://www.doe.nv.gov/Standards/Mathematics/New_Nevada_Math_Standards_Complete_Document_6.29.06_PDF.pdf#page=50
www.doe.nv.gov/Standards/Mathematics/New_Nevada_Math_Standards_Complete_D...
number gives the same result as multiplying each addend by the number and then adding the products together. (<span class="highlight">a</span>(b + c) = <span class="highlight">a</span> ● b + <span class="highlight">a</span> ● c) Divisible: <span class="highlight">A</span> number n is divisible by <span class="highlight">a</span> number m if there is no remainder when n is divided by m. <span class="highlight">Domain</span>: The set of all possible input values <span class="highlight">for</span> <span class="highlight">a</span> function or relation. Draw: To create <span class="highlight">a</span> figure in <span class="highlight">a</span> set form without the use of <span class="highlight">a</span> construction tool. Edge: The line segment formed when two faces of <span class="highlight">a</span> three-dimensional figure intersect. Elapsed Time: The
Microsoft Word - 5thgrindrev.docmathstd20035g.pdf
” numbers, clustering, or special numbers. Mathematical models such as concrete objects, pictures, diagrams, Venn diagrams, number lines, hundred charts, base ten blocks, or factor trees are necessary for conceptual understanding and should be used to explain computational proce...
1
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” numbers, clustering, or special numbers. Mathematical models such as concrete objects, pictures, diagrams, Venn diagrams, number lines, hundred charts, base ten blocks, or factor trees are necessary for conceptual understanding and should be used to explain computational procedures. If a mathematical model can be used to represent the concept, the indicator in the Models benchmark is identified in the parentheses. For example, (2.4.K1a) refers to Standard 2 (Algebra), Benchmark 4 (Models), and Knowledge
1
0
http://www.ksde.org/LinkClick.aspx?fileticket=ikzxQJ%2bltWY%3d&tabid=141&mid=8017&forcedownload=true#page=8
www.ksde.org/LinkClick.aspx?fileticket=ikzxQJ%2bltWY%3d&tabid=141&mid=801...
” numbers, <span class="highlight">clustering</span>, or special numbers. Mathematical models such as concrete objects, pictures, diagrams, Venn diagrams, number lines, hundred charts, base ten blocks, or factor trees are necessary <span class="highlight">for</span> conceptual understanding and should be used to explain computational procedures. If <span class="highlight">a</span> mathematical model can be used to represent the concept, the indicator in the Models benchmark is identified in the parentheses. <span class="highlight">For</span> example, (2.4.K1a) refers to Standard 2 (Algebra), Benchmark 4 (Models), and Knowledge
Microsoft Word - mathstd20038g.docmathstd20038g.pdf
(Principles and Standards for School Mathematics, NCTM, 2000) Mental math and estimation are distinct but related mathematical skills. Proficiency in mental math contributes to increased skill in estimation. In order for students to become more familiar with estimation, teachers shou...
1
0
(Principles and Standards for School Mathematics, NCTM, 2000) Mental math and estimation are distinct but related mathematical skills. Proficiency in mental math contributes to increased skill in estimation. In order for students to become more familiar with estimation, teachers should introduce estimation with examples where rounded or estimated numbers are used. Emphasis should be placed on real-world examples where only estimation is required, e.g., About how many hours do you sleep a night? Using the
1
0
http://www.ksde.org/LinkClick.aspx?fileticket=VJee7vha%2bsQ%3d&tabid=141&mid=8017&forcedownload=true#page=7
www.ksde.org/LinkClick.aspx?fileticket=VJee7vha%2bsQ%3d&tabid=141&mid=801...
(Principles and Standards <span class="highlight">for</span> School Mathematics, NCTM, 2000) Mental math and estimation are distinct but related mathematical skills. Proficiency in mental math contributes to increased skill in estimation. In order <span class="highlight">for</span> students to become more familiar with estimation, teachers should introduce estimation with examples where rounded or estimated numbers are used. Emphasis should be placed on real-world examples where only estimation is required, e.g., About how many hours do you sleep <span class="highlight">a</span> night? <span class="highlight">Using</span> the
Microsoft Word - 9th10thgrindrev.docmathstd20039g10g.pdf
9/10-6 January 31, 2004 ▲ – Assessed Indicator ■ – Assessed Indicator on the Optional Response Assessment N – Noncalculator ($) – Financial Literacy THESE STANDARDS ARE ALIGNED ONLY TO THE ASSESSMENTS THAT WILL BEGIN DURING THE 2005-06 SCHOOL YEAR. Teacher Not...
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9/10-6 January 31, 2004 ▲ – Assessed Indicator ■ – Assessed Indicator on the Optional Response Assessment N – Noncalculator ($) – Financial Literacy THESE STANDARDS ARE ALIGNED ONLY TO THE ASSESSMENTS THAT WILL BEGIN DURING THE 2005-06 SCHOOL YEAR. Teacher Notes: Estimate, as a verb, means to make an educated guess based on information in a problem or to give an answer close to the exact number. Estimation is used when an exact answer is not needed, as in many real-life situations for
1
0
http://www.ksde.org/LinkClick.aspx?fileticket=CU7hwnZRxUA%3d&tabid=141&mid=8017&forcedownload=true#page=6
www.ksde.org/LinkClick.aspx?fileticket=CU7hwnZRxUA%3d&tabid=141&mid=8017&...
9/10-6 January 31, 2004 ▲ – Assessed Indicator ■ – Assessed Indicator on the Optional Response Assessment N – Noncalculator ($) – Financial Literacy THESE STANDARDS ARE ALIGNED ONLY TO THE ASSESSMENTS THAT WILL BEGIN DURING THE 2005-06 SCHOOL YEAR. Teacher Notes: Estimate, as <span class="highlight">a</span> verb, means to make an educated guess <span class="highlight">based</span> on information in <span class="highlight">a</span> problem or to give an answer close to the exact number. Estimation is used when an exact answer is not needed, as in many real-life situations <span class="highlight">for</span>
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