Handout 2.1 SAP Focus Math K-8
10
This doument shows where students and teahers should spend the large majority of their time in order to meet the expetations of the Standards. CCSS WHERE TO FOCUS KINDERGARTEN MATHEMATICS MATH MATHEMATICS K KINDERGARTEN F FOCUS Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice. To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade. Students should spend the large majority 1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade. 2, 3 MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR KINDERGARTEN Emphases are given at the cluster level. efer to the Common Core State Standards for Mathematics for the specifc standards that fall within each cluster. Key: Major Clusters Supporting Clusters Additional Clusters Know number names and the count sequence. K.CC.A Count to tell the number of objects. K.CC.B Compare numbers. Understand addton as puttng together and addng to, and understand subtracton as takng K.CC.C K.OA.A apart and takng from. K.NBT.A Work wth numbers 11–19 to gan foundatons for place value. K.MD.A Descrbe and compare measureable attrbutes. K.MD.B Classfy objects and count the number of objects n categores. Identfy and descrbe shapes. K.G.A K.G.B Analyze, compare, create, and compose shapes. REQUIRED FLUENCIES FOR KINDERGARTEN HIGHLIGHTS OF MAJOR WORK IN GRADES K–8 K–2 3–5 6 7 8 Addition and subtraction – concepts, skills, and problem solving; place value Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving atios and proportional relationships; early expressions and equations atios and proportional relationships; arithmetic of rational numbers Linear algebra and linear functions Add/subtract within 5 K.OA.A.5 1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources 2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers. at achievethecore.org 1
Transcript of Handout 2.1 SAP Focus Math K-8
Handout 2.1 SAP Focus Math K-8This do ument shows where students
and tea hers should spend the large majority of their time in order
to meet the expe tations of the Standards.
CCSS WHERE TO FOCUS KINDERGARTEN MATHEMATICS
MATH MATHEMATICS
K KINDERGARTEN
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR KINDERGARTEN Emphases are given at the cluster level. efer to the Common Core State Standards for Mathematics for the specifc standards that fall within each cluster.
Key: Major Clusters Supporting Clusters Additional Clusters
Know number names and the count sequence.K.CC.A
Count to tell the number of objects.K.CC.B
Compare numbers.
Understand add t on as putt ng together and add ng to, and understand subtract on as tak ng
K.CC.C
K.OA.A apart and tak ng from.
K.NBT.A Work w th numbers 11–19 to ga n foundat ons for place value.
K.MD.A Descr be and compare measureable attr butes.
K.MD.B Class fy objects and count the number of objects n categor es.
Ident fy and descr be shapes.K.G.A
K.G.B Analyze, compare, create, and compose shapes. REQUIRED FLUENCIES FOR KINDERGARTEN
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving
atios and proportional relationships; early expressions and equations
atios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
Add/subtract within 5K.OA.A.5
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This do ument shows where students and tea hers should spend the large majority of their time in order to meet the expe tations of the Standards.
CCSS WHERE TO FOCUS GRADE 1 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 1 Emphases are given at the cluster level Refer to the Common Core State Standards for Mathematics for the specifc standards that fall within each cluster
Key: Major Clusters Supporting Clusters Additional Clusters
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
1.OA.A
1.OA.B
1.OA.C
1.OA.D
1.NBT.A
1.NBT.B
1.NBT.C
1.MD.A
1.MD.B
1.MD.C
1.G.A
Represent and solve problems involving addition and subtraction.
Understand and apply properties of operations and the relationship bet een addition and subtraction.
Add and subtract ithin 20.
Work ith addition and subtraction equations.
Extending the counting sequence.
Addition and subtraction – concepts, skills, and problem solving; place value
Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
Use place value understanding and properties of operations to add and subtract.
Measure lengths indirectly and by iterating length units.
Tell and rite time.
Represent and interpret data. REQUIRED FLUENCIES FOR GRADE 1
1.OA.C.6 Add/subtract within 10Reason ith shapes and their attributes.
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This document shows where students and teachers should spend the large majority of their time in order to meet the expectations of the Standards
CCSS WHERE TO FOCUS GRADE 2 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 2 Emphases are given at the cluster level. Refer to the Common Core State Standards for athematics for the specifc standards that fall within each cluster.
Key: ajor Clusters Supporting Clusters Additional Clusters
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
2.OA.A
2.OA.B
2.OA.C
2.NBT.A
2.NBT.B
2.MD.A
2.MD.B
2.MD.C
2.MD.D
2.G.A
Add and subtract within 2 .
Work with equal groups of objects to gain foundations for multiplication.
Understand place value.
Use place value understanding and properties of operations to add and subtract.
Measure and estimate lengths in standard units.
Relate addition and subtraction to length.
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
ultiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
Work with time and money.
Represent and interpret data.
Reason with shapes and their attributes. REQUIRED FLUENCIES FOR GRADE 2
Single-digit sums and differences (sums from 2 OA B 2 memory by end of Grade 2)
Add/subtract within 100 2 NBT B 5
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This ocument shows where stu ents an teachers shoul spen the large majority of their time in or er to meet the expectations of the Stan ar s.
CCSS WHERE TO FOCUS GRADE 3 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 3 Emphases are given at the cluster level. Refer to the Common Core State Standards for Mathematics for the specifc standards that fall within each cluster.
Key: Major Clusters Supporting Clusters Additional Clusters
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
and masses of objects.
Represent and interpret data.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition. REQUIRED FLUENCIES FOR GRADE 3
Geometric measurement: recognize perimeter as an attribute of plane fgures and distinguish 3.OA.C.7 between linear and area measures.
Reason with shapes and their attributes. 3.NBT.A.2
3.OA.A
3.OA.B
3.OA.C
3.OA.D
3.NBT.A
3.NF.A
ultiply and divide within 100.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Develop understanding of fractions as numbers.
Solve problems involving measurement and estimation of intervals of time, liquid volumes,
Single-digit products and quotients (Products from memory by end of rade 3)
Add/subtract within 1000
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This document shows where students and teachers should spend the large majority of their time in order to meet the expectations of the Standards
CCSS WHERE TO FOCUS GRADE 4 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 4 Emphases are given at the cluster level. Refer to the Common Core State Standards for athematics for the specifc standards that fall within each cluster.
Key: ajor Clusters Supporting Clusters Additional Clusters
4.OA.A
4.OA.B
4.OA.C
4.NBT.A
4.NBT.B
4.NF.A
4.NF.B
4.NF.C
4.MD.A
4.MD.B
4.MD.C
4.G.A
Use the four operations with whole numbers to solve problems.
Gain familiarity with factors and multiples.
Generate and analy e patterns.
Generali e place value understanding for multi-digit whole numbers.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Extend understanding of fraction equivalence and ordering.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Understand decimal notation for fractions, and compare decimal fractions.
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
Represent and interpret data.
Geometric measurement: understand concepts of angle and measure angles.
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
REQUIRED FLUENCIES FOR GRADE 4
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
ultiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
4 NBT B 4 Add/subtract within 1,000,000
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This document shows where students and teachers should spend the large majority of their time in order to meet the expectations of the Standards
CCSS WHERE TO FOCUS GRADE 5 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 5 Emphases are given at the cluster level. Refer to the Common Core State Standards for athematics for the specifc standards that fall within each cluster.
Key: ajor Clusters Supporting Clusters Additional Clusters
5.OA.A
5.OA.B
5.NBT.A
5.NBT.B
5.NF.A
5.NF.B
5.MD.A
5.MD.B
5.MD.C
5.G.A
5.G.B
Analyze patterns and relationships.
erform operations with multi-digit whole numbers and with decimals to hundredths.
Use equivalent fractions as a strategy to add and subtract fractions.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Convert like measurement units within a given measurement system.
Represent and interpret data.
Geometric measurement: understand concepts of volume and relate volume to multiplication
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
ultiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
and to addition.
Graph points on the coordinate plane to solve real-world and mathematical problems.
REQUIRED FLUENCIES FOR GRADE 5
5 NBT B 5 ulti-digit multiplication Classify two-dimensional fgures into categories based on their properties.
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This document shows where students and teachers should spend the large majority of their time in order to meet the expectations of the Standards
CCSS WHERE TO FOCUS GRADE 6 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 6 Emphases are given at the cluster level. Refer to the Common Core State Standards for athematics for the specifc standards that fall within each cluster.
Key: ajor Clusters Supporting Clusters Additional Clusters
Understand ratio concepts and use ratio reasoning to solve problems.
Apply and extend previous understandings of multiplication and division to divide
6.RP.A
6.NS.A fractions by fractions.
6.NS.B ompute fuently with multi-digit numbers and fnd common factors and multiples.
6.NS. Apply and extend previous understandings of numbers to the system of rational numbers.
6.EE.A Apply and extend previous understandings of arithmetic to algebraic expressions.
Reason about and solve one-variable equations and inequalities.6.EE.B
Represent and analyze quantitative relationships between dependent and independent variables. 6.EE.
6.G.A Solve real-world and mathematical problems involving area, surface area, and volume.
6.SP.A Develop understanding of statistical variability.
6.SP.B Summarize and describe distributions.
) and, where appropriate, additional work ( ) can
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
K–2 Addition and subtraction – concepts, skills, and problem solving; place value
3–5 ultiplication and division of whole numbers and fractions – concepts, skills, and problem solving
6 Ratios and proportional relationships; early expressions and equations
7 Ratios and proportional relationships; arithmetic of rational numbers
8 Linear algebra and linear functions
REQUIRED FLUENCIES FOR GRADE 6
6 NS B 2 ulti-digit division
ulti-digit decimal operations6 NS B 3
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This document shows where students and teachers should spend the large majority of their time in order to meet the expectations of the Standards
CCSS WHERE TO FOCUS GRADE 7 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 7 Emphases are given at the cluster level. Refer to the Common Core State Standards for athematics for the specifc standards that fall within each cluster.
Key: ajor Clusters Supporting Clusters Additional Clusters
7.RP.A
7.NS.A
7.EE.A
7.EE.B
7.G.A
7.G.B
7.SP.A
7.SP.B
7.SP.C
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Apply and e tend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Use properties of operations to generate equivalent e pressions.
Solve real-life and mathematical problems using numerical and algebraic e pressions and equations.
Draw, construct and describe geometrical fgures and describe the relationships between them.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Use random sampling to draw inferences about a population.
Draw informal comparative inferences about two populations.
Investigate chance processes and develop, use, and evaluate probability models.
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
ultiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This document shows where students and teachers should spend the large majority of their time in order to meet the expectations of the Standards
CCSS WHERE TO FOCUS GRADE 8 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 8 Emphases are given at the cluster level. Refer to the Common Core State Standards for athematics for the specifc standards that fall within each cluster.
Key: ajor Clusters Supporting Clusters Additional Clusters
8.NS.A
8.EE.A
8.EE.B
8.EE.C
8.F.A
8.F.B
8.G.A
8.G.B
8.G.C
8.SP.A
Know that there are numbers that are not rational, and approximate them by rational numbers.
Work with radi als and integer exponents.
Understand the onne tions between proportional relationships, lines, and linear equations.
Analyze and solve linear equations and pairs of simultaneous linear equations.
Defne, evaluate, and ompare fun tions.
Use fun tions to model relationships between quantities.
Understand ongruen e and similarity using physi al models, transparen ies, or geometry software.
Understand and apply the Pythagorean Theorem.
Solve real-world and mathemati al problems involving volume of ylinders, ones and spheres.
Investigate patterns of asso iation in bivariate data.
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
ultiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
CCSS WHERE TO FOCUS GRADES K–8 MATHEMATICS
An important subset of t e major work in grades K–8 is t e progression t at leads toward middle sc ool algebra.
K 1 2 3 4 5 6 7 8
Know number Represent and solve Represent and solve Represent & solve Use the four Understand the place Apply and Apply and extend Work w th rad cal and names and the count problems nvolv ng problems nvolv ng problems nvolv ng operat ons w th whole value system extend prev ous prev ous understand ng nteger exponents sequence add t on and add t on and mult pl cat on and numbers to solve understand ngs of of operat ons w th
subtract on subtract on d v s on problems Perform operat ons mult pl cat on and fract ons to add, Understand the Count to tell the w th mult -d g t whole d v s on to d v de subtract, mult ply, connect ons between number of objects Understand and Add and subtract Understand propert es General ze place numbers and dec mals fract ons by fract ons and d v de rat onal proport onal
apply propert es w th n 20 of mult pl cat on value understand ng to hundredths numbers relat onsh ps, l nes, and Compare numbers of operat ons and and the relat onsh p for mult -d g t whole Apply and l near equat ons**
the relat onsh p Understand place value between mult pl cat on numbers Use equ valent extend prev ous Analyze proport onal Understand add t on between add t on and and d v s on fract ons as a strategy understand ngs of relat onsh ps and Analyze and solve as putt ng together subtract on Use place value Use place value to add and subtract numbers to the system use them to solve l near equat ons and and add ng to, and understand ng Mult ply & d v de understand ng fract ons of rat onal numbers real-world and pa rs of s multaneous understand subtract on Add and subtract and propert es of w th n 100 and propert es of mathemat cal problems l near equat ons as tak ng apart and w th n 20 operat ons to add and operat ons to perform Apply and Understand rat o tak ng from subtract Solve problems mult d g t ar thmet c extend prev ous concepts and use rat o Use propert es of Defne, evaluate, and
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sequence prev ous mathemat cal problems quant t es Relate add t on and Develop understand ng Bu ld fract ons Geometr c understand ngs of us ng numer cal and
Understand place value subtract on to length of fract ons as numbers from un t fract ons measurement: ar thmet c to algebra c algebra c express ons by apply ng and understand concepts express ons and equat ons
Use place value Solve problems extend ng prev ous of volume and understand ng nvolv ng measurement understand ngs of relate volume to Reason about and and propert es of and est mat on of operat ons mult pl cat on and to solve one-var able operat ons to add and ntervals of t me, l qu d add t on equat ons and subtract volumes, & masses of Understand dec mal nequal t es
objects notat on for fract ons, Graph po nts n the Measure lengths and compare dec mal coord nate plane Represent and nd rectly and by Geometr c fract ons to solve real-world analyze quant tat ve terat ng length un ts measurement: and mathemat cal relat onsh ps between
understand concepts problems* dependent and of area and relate area ndependent var ables to mult pl cat on and to add t on
CCSS WHERE TO FOCUS KINDERGARTEN MATHEMATICS
MATH MATHEMATICS
K KINDERGARTEN
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR KINDERGARTEN Emphases are given at the cluster level. efer to the Common Core State Standards for Mathematics for the specifc standards that fall within each cluster.
Key: Major Clusters Supporting Clusters Additional Clusters
Know number names and the count sequence.K.CC.A
Count to tell the number of objects.K.CC.B
Compare numbers.
Understand add t on as putt ng together and add ng to, and understand subtract on as tak ng
K.CC.C
K.OA.A apart and tak ng from.
K.NBT.A Work w th numbers 11–19 to ga n foundat ons for place value.
K.MD.A Descr be and compare measureable attr butes.
K.MD.B Class fy objects and count the number of objects n categor es.
Ident fy and descr be shapes.K.G.A
K.G.B Analyze, compare, create, and compose shapes. REQUIRED FLUENCIES FOR KINDERGARTEN
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving
atios and proportional relationships; early expressions and equations
atios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
Add/subtract within 5K.OA.A.5
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This do ument shows where students and tea hers should spend the large majority of their time in order to meet the expe tations of the Standards.
CCSS WHERE TO FOCUS GRADE 1 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 1 Emphases are given at the cluster level Refer to the Common Core State Standards for Mathematics for the specifc standards that fall within each cluster
Key: Major Clusters Supporting Clusters Additional Clusters
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
1.OA.A
1.OA.B
1.OA.C
1.OA.D
1.NBT.A
1.NBT.B
1.NBT.C
1.MD.A
1.MD.B
1.MD.C
1.G.A
Represent and solve problems involving addition and subtraction.
Understand and apply properties of operations and the relationship bet een addition and subtraction.
Add and subtract ithin 20.
Work ith addition and subtraction equations.
Extending the counting sequence.
Addition and subtraction – concepts, skills, and problem solving; place value
Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
Use place value understanding and properties of operations to add and subtract.
Measure lengths indirectly and by iterating length units.
Tell and rite time.
Represent and interpret data. REQUIRED FLUENCIES FOR GRADE 1
1.OA.C.6 Add/subtract within 10Reason ith shapes and their attributes.
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This document shows where students and teachers should spend the large majority of their time in order to meet the expectations of the Standards
CCSS WHERE TO FOCUS GRADE 2 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 2 Emphases are given at the cluster level. Refer to the Common Core State Standards for athematics for the specifc standards that fall within each cluster.
Key: ajor Clusters Supporting Clusters Additional Clusters
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
2.OA.A
2.OA.B
2.OA.C
2.NBT.A
2.NBT.B
2.MD.A
2.MD.B
2.MD.C
2.MD.D
2.G.A
Add and subtract within 2 .
Work with equal groups of objects to gain foundations for multiplication.
Understand place value.
Use place value understanding and properties of operations to add and subtract.
Measure and estimate lengths in standard units.
Relate addition and subtraction to length.
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
ultiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
Work with time and money.
Represent and interpret data.
Reason with shapes and their attributes. REQUIRED FLUENCIES FOR GRADE 2
Single-digit sums and differences (sums from 2 OA B 2 memory by end of Grade 2)
Add/subtract within 100 2 NBT B 5
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This ocument shows where stu ents an teachers shoul spen the large majority of their time in or er to meet the expectations of the Stan ar s.
CCSS WHERE TO FOCUS GRADE 3 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 3 Emphases are given at the cluster level. Refer to the Common Core State Standards for Mathematics for the specifc standards that fall within each cluster.
Key: Major Clusters Supporting Clusters Additional Clusters
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
and masses of objects.
Represent and interpret data.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition. REQUIRED FLUENCIES FOR GRADE 3
Geometric measurement: recognize perimeter as an attribute of plane fgures and distinguish 3.OA.C.7 between linear and area measures.
Reason with shapes and their attributes. 3.NBT.A.2
3.OA.A
3.OA.B
3.OA.C
3.OA.D
3.NBT.A
3.NF.A
ultiply and divide within 100.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Develop understanding of fractions as numbers.
Solve problems involving measurement and estimation of intervals of time, liquid volumes,
Single-digit products and quotients (Products from memory by end of rade 3)
Add/subtract within 1000
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This document shows where students and teachers should spend the large majority of their time in order to meet the expectations of the Standards
CCSS WHERE TO FOCUS GRADE 4 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 4 Emphases are given at the cluster level. Refer to the Common Core State Standards for athematics for the specifc standards that fall within each cluster.
Key: ajor Clusters Supporting Clusters Additional Clusters
4.OA.A
4.OA.B
4.OA.C
4.NBT.A
4.NBT.B
4.NF.A
4.NF.B
4.NF.C
4.MD.A
4.MD.B
4.MD.C
4.G.A
Use the four operations with whole numbers to solve problems.
Gain familiarity with factors and multiples.
Generate and analy e patterns.
Generali e place value understanding for multi-digit whole numbers.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Extend understanding of fraction equivalence and ordering.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Understand decimal notation for fractions, and compare decimal fractions.
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
Represent and interpret data.
Geometric measurement: understand concepts of angle and measure angles.
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
REQUIRED FLUENCIES FOR GRADE 4
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
ultiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
4 NBT B 4 Add/subtract within 1,000,000
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This document shows where students and teachers should spend the large majority of their time in order to meet the expectations of the Standards
CCSS WHERE TO FOCUS GRADE 5 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 5 Emphases are given at the cluster level. Refer to the Common Core State Standards for athematics for the specifc standards that fall within each cluster.
Key: ajor Clusters Supporting Clusters Additional Clusters
5.OA.A
5.OA.B
5.NBT.A
5.NBT.B
5.NF.A
5.NF.B
5.MD.A
5.MD.B
5.MD.C
5.G.A
5.G.B
Analyze patterns and relationships.
erform operations with multi-digit whole numbers and with decimals to hundredths.
Use equivalent fractions as a strategy to add and subtract fractions.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Convert like measurement units within a given measurement system.
Represent and interpret data.
Geometric measurement: understand concepts of volume and relate volume to multiplication
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
ultiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
and to addition.
Graph points on the coordinate plane to solve real-world and mathematical problems.
REQUIRED FLUENCIES FOR GRADE 5
5 NBT B 5 ulti-digit multiplication Classify two-dimensional fgures into categories based on their properties.
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This document shows where students and teachers should spend the large majority of their time in order to meet the expectations of the Standards
CCSS WHERE TO FOCUS GRADE 6 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 6 Emphases are given at the cluster level. Refer to the Common Core State Standards for athematics for the specifc standards that fall within each cluster.
Key: ajor Clusters Supporting Clusters Additional Clusters
Understand ratio concepts and use ratio reasoning to solve problems.
Apply and extend previous understandings of multiplication and division to divide
6.RP.A
6.NS.A fractions by fractions.
6.NS.B ompute fuently with multi-digit numbers and fnd common factors and multiples.
6.NS. Apply and extend previous understandings of numbers to the system of rational numbers.
6.EE.A Apply and extend previous understandings of arithmetic to algebraic expressions.
Reason about and solve one-variable equations and inequalities.6.EE.B
Represent and analyze quantitative relationships between dependent and independent variables. 6.EE.
6.G.A Solve real-world and mathematical problems involving area, surface area, and volume.
6.SP.A Develop understanding of statistical variability.
6.SP.B Summarize and describe distributions.
) and, where appropriate, additional work ( ) can
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
K–2 Addition and subtraction – concepts, skills, and problem solving; place value
3–5 ultiplication and division of whole numbers and fractions – concepts, skills, and problem solving
6 Ratios and proportional relationships; early expressions and equations
7 Ratios and proportional relationships; arithmetic of rational numbers
8 Linear algebra and linear functions
REQUIRED FLUENCIES FOR GRADE 6
6 NS B 2 ulti-digit division
ulti-digit decimal operations6 NS B 3
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This document shows where students and teachers should spend the large majority of their time in order to meet the expectations of the Standards
CCSS WHERE TO FOCUS GRADE 7 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 7 Emphases are given at the cluster level. Refer to the Common Core State Standards for athematics for the specifc standards that fall within each cluster.
Key: ajor Clusters Supporting Clusters Additional Clusters
7.RP.A
7.NS.A
7.EE.A
7.EE.B
7.G.A
7.G.B
7.SP.A
7.SP.B
7.SP.C
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Apply and e tend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Use properties of operations to generate equivalent e pressions.
Solve real-life and mathematical problems using numerical and algebraic e pressions and equations.
Draw, construct and describe geometrical fgures and describe the relationships between them.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Use random sampling to draw inferences about a population.
Draw informal comparative inferences about two populations.
Investigate chance processes and develop, use, and evaluate probability models.
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
ultiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
This document shows where students and teachers should spend the large majority of their time in order to meet the expectations of the Standards
CCSS WHERE TO FOCUS GRADE 8 MATHEMATICS
MATH MATHEMATICS
F FOCUS
Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others ased on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the Standards can safely e neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.2, 3
MAJOR, SUPPORTING, AND ADDITIONAL CLUSTERS FOR GRADE 8 Emphases are given at the cluster level. Refer to the Common Core State Standards for athematics for the specifc standards that fall within each cluster.
Key: ajor Clusters Supporting Clusters Additional Clusters
8.NS.A
8.EE.A
8.EE.B
8.EE.C
8.F.A
8.F.B
8.G.A
8.G.B
8.G.C
8.SP.A
Know that there are numbers that are not rational, and approximate them by rational numbers.
Work with radi als and integer exponents.
Understand the onne tions between proportional relationships, lines, and linear equations.
Analyze and solve linear equations and pairs of simultaneous linear equations.
Defne, evaluate, and ompare fun tions.
Use fun tions to model relationships between quantities.
Understand ongruen e and similarity using physi al models, transparen ies, or geometry software.
Understand and apply the Pythagorean Theorem.
Solve real-world and mathemati al problems involving volume of ylinders, ones and spheres.
Investigate patterns of asso iation in bivariate data.
HIGHLIGHTS OF MAJOR WORK
IN GRADES K–8
Addition and subtraction – concepts, skills, and problem solving; place value
ultiplication and division of whole numbers and fractions – concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and equations
Ratios and proportional relationships; arithmetic of rational numbers
Linear algebra and linear functions
1 At least 65% and up to approximately 85% of class time with Grades K–2 nearer the upper end of that range should be devoted to the major work of the grade. For more information see Criterion #1 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. Find additional resources
2 Refer also to criterion #3 in the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics www.achievethecore.org/publisherscriteria. 3 Note the critical areas are a survey of what will be taught at each grade level; the major work is the subset of topics that deserve the large majority of instructional time during a given year to best prepare students for college and careers.
at achievethecore.org 1
CCSS WHERE TO FOCUS GRADES K–8 MATHEMATICS
An important subset of t e major work in grades K–8 is t e progression t at leads toward middle sc ool algebra.
K 1 2 3 4 5 6 7 8
Know number Represent and solve Represent and solve Represent & solve Use the four Understand the place Apply and Apply and extend Work w th rad cal and names and the count problems nvolv ng problems nvolv ng problems nvolv ng operat ons w th whole value system extend prev ous prev ous understand ng nteger exponents sequence add t on and add t on and mult pl cat on and numbers to solve understand ngs of of operat ons w th
subtract on subtract on d v s on problems Perform operat ons mult pl cat on and fract ons to add, Understand the Count to tell the w th mult -d g t whole d v s on to d v de subtract, mult ply, connect ons between number of objects Understand and Add and subtract Understand propert es General ze place numbers and dec mals fract ons by fract ons and d v de rat onal proport onal
apply propert es w th n 20 of mult pl cat on value understand ng to hundredths numbers relat onsh ps, l nes, and Compare numbers of operat ons and and the relat onsh p for mult -d g t whole Apply and l near equat ons**
the relat onsh p Understand place value between mult pl cat on numbers Use equ valent extend prev ous Analyze proport onal Understand add t on between add t on and and d v s on fract ons as a strategy understand ngs of relat onsh ps and Analyze and solve as putt ng together subtract on Use place value Use place value to add and subtract numbers to the system use them to solve l near equat ons and and add ng to, and understand ng Mult ply & d v de understand ng fract ons of rat onal numbers real-world and pa rs of s multaneous understand subtract on Add and subtract and propert es of w th n 100 and propert es of mathemat cal problems l near equat ons as tak ng apart and w th n 20 operat ons to add and operat ons to perform Apply and Understand rat o tak ng from subtract Solve problems mult d g t ar thmet c extend prev ous concepts and use rat o Use propert es of Defne, evaluate, and
Work w th add t on and nvolv ng the four understand ngs of reason ng to solve operat ons to generate compare funct ons Work w th numbers 11- subtract on equat ons Measure and est mate operat ons, and Extend understand ng mult pl cat on and problems equ valent express ons 19 to ga n foundat ons lengths n standard dent fy & expla n of fract on equ valence d v s on to mult ply and Use funct ons to model for place value Extend the count ng un ts patterns n ar thmet c and order ng d v de fract ons Apply and extend Solve real-l fe and relat onsh ps between
sequence prev ous mathemat cal problems quant t es Relate add t on and Develop understand ng Bu ld fract ons Geometr c understand ngs of us ng numer cal and
Understand place value subtract on to length of fract ons as numbers from un t fract ons measurement: ar thmet c to algebra c algebra c express ons by apply ng and understand concepts express ons and equat ons
Use place value Solve problems extend ng prev ous of volume and understand ng nvolv ng measurement understand ngs of relate volume to Reason about and and propert es of and est mat on of operat ons mult pl cat on and to solve one-var able operat ons to add and ntervals of t me, l qu d add t on equat ons and subtract volumes, & masses of Understand dec mal nequal t es
objects notat on for fract ons, Graph po nts n the Measure lengths and compare dec mal coord nate plane Represent and nd rectly and by Geometr c fract ons to solve real-world analyze quant tat ve terat ng length un ts measurement: and mathemat cal relat onsh ps between
understand concepts problems* dependent and of area and relate area ndependent var ables to mult pl cat on and to add t on
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