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 STATE BOARD OF EDUCATION
people when each one feels he or she is better off after the trade (e.g., if you sell your old exercise bike for cash, you gain because you would rather have the cash than the bike, but the other person gains because he or she would rather have the...
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people when each one feels he or she is better off after the trade (e.g., if you sell your old exercise bike for cash, you gain because you would rather have the cash than the bike, but the other person gains because he or she would rather have the bike than the cash) Warsaw Pact an agreement among Eastern Block countries… watershed the entire area drained by a river and its tributaries
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http://www.ade.state.az.us/standards/sstudies/articulated/SSStandard-full-05-22-06.pdf#page=172
www.ade.state.az.us/standards/sstudies/articulated/SSStandard-full-05-22-...
interest rates to influence economic activity monoculture <span class="highlight">the</span> practice <span class="highlight">of</span> growing a <span class="highlight">cash</span> crop <span class="highlight">for</span> export to one or more countries; a plantation economy monopoly <span class="highlight">the</span> exclusive control <span class="highlight">of</span> a service or product by one individual or company monotheism <span class="highlight">the</span> doctrine or belief that there is only one god mutual fund a fund <span class="highlight">of</span> securities owned jointly by investors who have purchased shares <span class="highlight">of</span> it national security condition <span class="highlight">of</span> a nation's safety from threats, especially threats from external sources
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http://www.ade.state.az.us/standards/sstudies/articulated/SSStandard-full-05-22-06.pdf#page=177
www.ade.state.az.us/standards/sstudies/articulated/SSStandard-full-05-22-...
people when each one feels he or she is better off after <span class="highlight">the</span> trade (e.g., if you sell your old exercise bike <span class="highlight">for</span> <span class="highlight">cash</span>, you gain because you would rather have <span class="highlight">the</span> <span class="highlight">cash</span> than <span class="highlight">the</span> bike, but <span class="highlight">the</span> other person gains because he or she would rather have <span class="highlight">the</span> bike than <span class="highlight">the</span> <span class="highlight">cash</span>) Warsaw Pact an agreement among Eastern Block countries… watershed <span class="highlight">the</span> entire area drained by a river and its tributaries
GRADE 4
Students develop a sense of what numbers are, i.e., to use numbers and number relationships to acquire basic facts, to solve a wide variety of real-world problems, and to estimate to determine the reasonableness of results. Concept 1: Number Sense Understand and...
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Students develop a sense of what numbers are, i.e., to use numbers and number relationships to acquire basic facts, to solve a wide variety of real-world problems, and to estimate to determine the reasonableness of results. Concept 1: Number Sense Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems. In Grade 4, students build on their prior knowledge of whole numbers, fractions, and decimals, making connections with percents. They
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade4.pdf#page=1
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Students develop a sense <span class="highlight">of</span> what numbers are, i.e., to <span class="highlight">use</span> numbers and number relationships to acquire basic facts, to solve a wide variety <span class="highlight">of</span> real-world problems, and to estimate to determine <span class="highlight">the</span> reasonableness <span class="highlight">of</span> results. Concept 1: Number Sense Understand and apply numbers, ways <span class="highlight">of</span> representing numbers, and <span class="highlight">the</span> relationships among numbers and different number systems. In Grade 4, students build <span class="highlight">on</span> their prior knowledge <span class="highlight">of</span> whole numbers, <span class="highlight">fractions</span>, and decimals, making connections with percents. They
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade4.pdf#page=3
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Process Integration Explanations and Examples Students are expected to: PO 3. Express <span class="highlight">fractions</span> as fair sharing, parts <span class="highlight">of</span> a whole, parts <span class="highlight">of</span> a set, and locations <span class="highlight">on</span> a real number line. Connections: M04-S1C1-01, M04-S1C1- 05 M04-S5C2-05. Represent a problem situation using any combination <span class="highlight">of</span> words, numbers, pictures, physical objects, or symbols. Fair sharing - Pictures work better <span class="highlight">for</span> representing fair sharing problems since students often need to represent fractional parts. Examples
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade4.pdf#page=5
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
expected to: PO 1. Add and subtract decimals through hundredths including money to $1000.00 and <span class="highlight">fractions</span> with like denominators. Connections: M04-S1C1-01, M04-S1C2- 06, M04-S1C3-02, M04-S5C1-01, SS04- S5C1-01 M04-S5C2-04. Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies <span class="highlight">for</span> solving <span class="highlight">the</span> problem. M04-S5C2-05. Represent a problem situation using any combination <span class="highlight">of</span> words, numbers, pictures, physical objects, or symbols. M04
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade4.pdf#page=9
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Operations Concept 3: Estimation <span class="highlight">Use</span> estimation strategies reasonably and fluently while integrating content from each <span class="highlight">of</span> <span class="highlight">the</span> other strands. In Grade 4, students apply benchmarks in estimation <span class="highlight">of</span> whole numbers, decimals, and <span class="highlight">fractions</span>. Performance Objectives Process Integration Explanations and Examples Students are expected to: PO 1. <span class="highlight">Use</span> benchmarks as meaningful points <span class="highlight">of</span> comparison <span class="highlight">for</span> whole numbers, decimals, and <span class="highlight">fractions</span>. Connections: M04-S1C1-01, M04-S1C1- 04, M04-S1C3-02, M04-S2C2-01
GRADE 3
Arizona Mathematics Standard Articulated by Grade Level The bulleted items within a performance objective indicate the specific content to be taught. Explanations and Examples Updated 1.19.09 Grade 3 Arizona Department of Education: Standards and Assessment Division 5 Approv...
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Arizona Mathematics Standard Articulated by Grade Level The bulleted items within a performance objective indicate the specific content to be taught. Explanations and Examples Updated 1.19.09 Grade 3 Arizona Department of Education: Standards and Assessment Division 5 Approved 6.24.08 Performance Objectives Process Integration Explanations and Examples Students are expected to: PO 6. Compare and order benchmark fractions. Connections: M03-S1C1-05, M03
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade3.pdf#page=1
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Arizona Mathematics Standard Articulated by Grade Level he bulleted items within a performance objective indicate <span class="highlight">the</span> specific content to be taught. Explanations and Examples Updated 1.19.09 Grade 3 Arizona Department <span class="highlight">of</span> Education: Standards and Assessment Division 1 Approved 6.24.08 T GRADE 3 Every student should understand and <span class="highlight">use</span> all concepts and skills from <span class="highlight">the</span> previous grade levels. <span class="highlight">The</span> standard is designed so that new learning builds <span class="highlight">on</span> preceding skills
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade3.pdf#page=5
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Arizona Mathematics Standard Articulated by Grade Level <span class="highlight">The</span> bulleted items within a performance objective indicate <span class="highlight">the</span> specific content to be taught. Explanations and Examples Updated 1.19.09 Grade 3 Arizona Department <span class="highlight">of</span> Education: Standards and Assessment Division 5 Approved 6.24.08 Performance Objectives Process Integration Explanations and Examples Students are expected to: PO 6. Compare and order benchmark <span class="highlight">fractions</span>. Connections: M03-S1C1-05, M03
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade3.pdf#page=13
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Select and <span class="highlight">use</span> one or more strategies to efficiently solve <span class="highlight">the</span> problem and justify <span class="highlight">the</span> selection. M03-S5C2-04. Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies <span class="highlight">for</span> solving <span class="highlight">the</span> problem. Students estimate using all four operations with whole numbers. Students will also <span class="highlight">use</span> estimation to compare <span class="highlight">fractions</span> using benchmark <span class="highlight">fractions</span>. Estimation strategies <span class="highlight">for</span> comparing <span class="highlight">fractions</span> extend from students’ work with whole numbers
GRADE 5
the question. Students use models, pictures, symbols and spoken and written words. Benchmark fractions include common fractions between 0 and 1 such as halves, thirds, fourths, fifths, sixths, eighths, and tenths. Continued on next page...
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the question. Students use models, pictures, symbols and spoken and written words. Benchmark fractions include common fractions between 0 and 1 such as halves, thirds, fourths, fifths, sixths, eighths, and tenths. Continued on next page
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade5.pdf#page=1
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
<span class="highlight">the</span> question. Students <span class="highlight">use</span> models, pictures, symbols and spoken and written words. Benchmark <span class="highlight">fractions</span> include common <span class="highlight">fractions</span> between 0 and 1 such as halves, thirds, fourths, fifths, sixths, eighths, and tenths. <span class="highlight">Continued</span> <span class="highlight">on</span> next page
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade5.pdf#page=3
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers <span class="highlight">the</span> question. A ratio is a comparison <span class="highlight">of</span> two quantities which can be written as a to b, b a , or a:b. A rate is a ratio that compares different types <span class="highlight">of</span> measures. A unit rate compares a quantity in terms <span class="highlight">of</span> one unit <span class="highlight">of</span> another quantity. Students need many opportunities to <span class="highlight">use</span> models to demonstrate <span class="highlight">the</span> relationships between quantities before they are expected to work with rates numerically. <span class="highlight">Continued</span> <span class="highlight">on</span>
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade5.pdf#page=7
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
students <span class="highlight">use</span> estimation skills to verify <span class="highlight">the</span> reasonableness <span class="highlight">of</span> their solutions. They make reasonable estimates with whole numbers <span class="highlight">for</span> sums, differences, products and quotients. They also make reasonable estimates <span class="highlight">for</span> sums and differences <span class="highlight">of</span> <span class="highlight">fractions</span> and decimals. Performance Objectives Process Integration Explanations and Examples Students are expected to: PO 1. Make estimates appropriate to a given situation or computation with whole numbers, <span class="highlight">fractions</span>, and decimals Connections: M05-S1C1
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade5.pdf#page=27
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
strategies, draw logical conclusions, develop and describe solutions, and recognize their applications. Concept 1: Algorithms and Algorithmic Thinking <span class="highlight">Use</span> reasoning to solve mathematical problems. In Grade 5, students extend their work analyzing common algorithms <span class="highlight">for</span> calculation with <span class="highlight">fractions</span> and decimals, explaining why <span class="highlight">the</span> procedures work <span class="highlight">on</span> <span class="highlight">the</span> basis <span class="highlight">of</span> properties <span class="highlight">of</span> operations and place value. They also <span class="highlight">use</span> their understanding <span class="highlight">of</span> geometric properties to develop algorithms <span class="highlight">for</span> calculating area and
GRADE 7
the reasonableness of the solution. In addition to general translations among these representations, students are expected to demonstrate quick recall of equivalent forms of common fractions, decimals, ratios, and percents. They are also expected to translat...
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the reasonableness of the solution. In addition to general translations among these representations, students are expected to demonstrate quick recall of equivalent forms of common fractions, decimals, ratios, and percents. They are also expected to translate between negative fractions and decimals. Continued on next page
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade7.pdf#page=1
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
<span class="highlight">the</span> reasonableness <span class="highlight">of</span> <span class="highlight">the</span> solution. In addition to general translations among these representations, students are expected to demonstrate quick recall <span class="highlight">of</span> equivalent forms <span class="highlight">of</span> common <span class="highlight">fractions</span>, decimals, ratios, and percents. They are also expected to translate between negative <span class="highlight">fractions</span> and decimals. <span class="highlight">Continued</span> <span class="highlight">on</span> next page
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade7.pdf#page=7
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
information related to <span class="highlight">the</span> solution to a problem. Students estimate using all four operations with whole numbers, <span class="highlight">fractions</span>, and decimals. Estimation skills include identifying when estimation is appropriate, determining <span class="highlight">the</span> level <span class="highlight">of</span> accuracy needed, selecting <span class="highlight">the</span> appropriate method <span class="highlight">of</span> estimation, and verifying solutions or determining <span class="highlight">the</span> reasonableness <span class="highlight">of</span> situations using various estimation strategies. Estimations are compared to actual calculations when appropriate. Estimation strategies <span class="highlight">for</span>
GRADE 6
the reasonableness of the solution. Students need many opportunities to use multiple representations in meaningful contexts. Continued on next page...
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the reasonableness of the solution. Students need many opportunities to use multiple representations in meaningful contexts. Continued on next page
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade6.pdf#page=1
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
<span class="highlight">the</span> reasonableness <span class="highlight">of</span> <span class="highlight">the</span> solution. Students need many opportunities to <span class="highlight">use</span> multiple representations in meaningful contexts. <span class="highlight">Continued</span> <span class="highlight">on</span> next page
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade6.pdf#page=2
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
∗ 3 = 12) • What is <span class="highlight">the</span> least common multiple (LCM) <span class="highlight">of</span> 24 and 36? How can you <span class="highlight">use</span> <span class="highlight">the</span> prime factorizations to find <span class="highlight">the</span> LCM? (solution: 2 3 ∗ 3 2 = 72) PO 3. Demonstrate an understanding <span class="highlight">of</span> <span class="highlight">fractions</span> as rates, division <span class="highlight">of</span> whole numbers, parts <span class="highlight">of</span> a whole, parts <span class="highlight">of</span> a set, and locations <span class="highlight">on</span> a real number line. Connections: M06-S1C1-01, M06-S1C1- 04, M06-S4C4-02, M06-S4C4-03 M06-S5C2-05. Represent a problem situation using multiple representations, describe <span class="highlight">the</span> process used to solve <span class="highlight">the</span> problem
GRADE 8
integrating content from each of the other strands. In Grade 8, students continue to use estimation strategies to check solutions for reasonableness. They extend their knowledge of estimation to approximate the location of real numbers on a nu...
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integrating content from each of the other strands. In Grade 8, students continue to use estimation strategies to check solutions for reasonableness. They extend their knowledge of estimation to approximate the location of real numbers on a number line. Performance Objectives Process Integration Explanations and Examples Students are expected to: PO 1. Make estimates appropriate to a given situation. Connections: M08-S1C2-03, M08-S1C3- 02, M08-S2C1-02, M08-S2C3-02, M08- S3C3-02, M08-S3C4-02
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade8.pdf#page=5
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
integrating content from each <span class="highlight">of</span> <span class="highlight">the</span> other strands. In Grade 8, students continue to <span class="highlight">use</span> estimation strategies to check solutions <span class="highlight">for</span> reasonableness. They extend their knowledge <span class="highlight">of</span> estimation to approximate <span class="highlight">the</span> location <span class="highlight">of</span> real numbers <span class="highlight">on</span> a number line. Performance Objectives Process Integration Explanations and Examples Students are expected to: PO 1. Make estimates appropriate to a given situation. Connections: M08-S1C2-03, M08-S1C3- 02, M08-S2C1-02, M08-S2C3-02, M08- S3C3-02, M08-S3C4-02
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade8.pdf#page=21
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
compare mathematical strategies <span class="highlight">for</span> efficient problem solving; select and <span class="highlight">use</span> one or more strategies to solve a problem. <span class="highlight">The</span> properties <span class="highlight">of</span> real numbers and properties <span class="highlight">of</span> equality include but are not limited to <span class="highlight">the</span> following: associative, commutative, distributive, identity, zero, reflexive, and transitive. <span class="highlight">The</span> property <span class="highlight">of</span> closure is not expected at this grade level. <span class="highlight">Continued</span> <span class="highlight">on</span> next page
GRADE HS
student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the proces...
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student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all mathematical strands. Strand 1: Number and Operations Number sense is the understanding of numbers and how they relate to each other and how they are used in specific context or
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGradeHS.pdf#page=1
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
student should understand and <span class="highlight">use</span> all concepts and skills from <span class="highlight">the</span> previous grade levels. <span class="highlight">The</span> standard is designed so that new learning builds <span class="highlight">on</span> preceding skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are <span class="highlight">the</span> process standards that are embedded throughout <span class="highlight">the</span> teaching and learning <span class="highlight">of</span> all mathematical strands. Strand 1: Number and Operations Number sense is <span class="highlight">the</span> understanding <span class="highlight">of</span> numbers and how they relate to each other and how they are used in specific context or
GRADE 2
Arizona Mathematics Standard Articulated by Grade Level The bulleted items within a performance objective indicate the specific content to be taught. Explanations and Examples Updated 1.19.09 Grade 2 Arizona Department of Education: Standards and Assessment Division 1 Approve...
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Arizona Mathematics Standard Articulated by Grade Level The bulleted items within a performance objective indicate the specific content to be taught. Explanations and Examples Updated 1.19.09 Grade 2 Arizona Department of Education: Standards and Assessment Division 1 Approved 6.24.08 GRADE 2 Every student should understand and use all
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade2.pdf#page=1
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Arizona Mathematics Standard Articulated by Grade Level <span class="highlight">The</span> bulleted items within a performance objective indicate <span class="highlight">the</span> specific content to be taught. Explanations and Examples Updated 1.19.09 Grade 2 Arizona Department <span class="highlight">of</span> Education: Standards and Assessment Division 1 Approved 6.24.08 GRADE 2 Every student should understand and <span class="highlight">use</span> all
GRADE K
objects and recognize that a number represents a specific quantity. Once this is established, students can begin to read and write numerals (numerals are the symbols for the quantities). Continued on next page...
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objects and recognize that a number represents a specific quantity. Once this is established, students can begin to read and write numerals (numerals are the symbols for the quantities). Continued on next page
1
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGradeK.pdf#page=1
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
objects and recognize that a number represents a specific quantity. Once this is established, students can begin to read and write numerals (numerals are <span class="highlight">the</span> symbols <span class="highlight">for</span> <span class="highlight">the</span> quantities). <span class="highlight">Continued</span> <span class="highlight">on</span> next page
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