Concepts and Skills Progression and the State Standards for Mathematics Grades K 8
Envision Success for All Your Mathematics Students Give your students a cohesive and rigorous path to mathematics success with Pearson s envision Series : envisionmath for Grades K 6, digits for Grades 6 8, and Pearson High School Mathematics for Grades 9 12 These three programs share a core authorship team that ensures integrated development of math concepts and skills, and a consistent pedagogy across the grades. These programs are completely aligned to the State Standards for Mathematics. 2 Instruction aligned to the State Standards The envision Series is exclusively written to help you teach the State Standards. The Standards for Mathematical Practice are embedded in every lesson to support long-term learning goals. Deeper understanding through visual learning The envision Series has visual learning as one of its foundational concepts. Only Pearson partners with Stuart Murphy, a visual learning specialist and author of the popular MathStart books. Bar diagrams, step-by-step visual models, and frequent visual cues help to clarify abstract concepts. Technology that fits your classroom envisionmath and Pearson High School Mathematics Common Core allow you to choose from print only, a blend of print and digital, or a totally digital delivery. digits is designed specifically for instruction using an interactive whiteboard and any time, anywhere online resources. Digital instruction and content support the ways you want to teach and motivate students to learn. Problem-solving through interactive exploration The envision Series focuses on problem solving, reasoning, and communication. Every lesson begins with Problem-Based Interactive Learning as both a vehicle for instruction and an opportunity to demonstrate understanding. This document shows how the envision Series for Grades K 8 aligns to the State Standards for Mathematics. Each CC standard is fully covered in the context of a coherent progression of conceptual knowledge and skill mastery. See at a glance the cohesive and rigorous path of content coverage from kindergarten through Grade 8, meeting every Standard in depth. Go to PearsonSchool.com or contact your local Pearson representative for more information on these programs. 3
Number and Operations Number Meanings and Relationships Understand Number Systems Addition and Subtraction Multiplication and Division Multiplicative Reasoning Count objects K.CC.4, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5 Count in sequence K.CC.1, K.CC.2, 1.NBT.1, 2.NBT.2 Name and write numbers K.CC.3, 1.NBT.1, 2.NBT.3, 3.NBT.1, 4.NBT.2, 4.NF.6, 5.NBT.3, 5.NBT.3.a, 6.NS.4, 7.NS.1, 8.EE.3 Compare and order numbers K.CC.6, K.CC.7, 1.NBT.3, 2.NBT.4, 3.NF.3.d, 4.NBT.2, 4.NF.7, 5.NBT.3.b, 5.NF.5.a, 6.NS.6.c, 6.NS.7, 6.NS.7.a, 6.NS.7.b Round numbers 3.NBT.1, 4.NBT.3, 5.NBT.4 Place value in the base-ten system K.NBT.1, 1.NBT.2, 1.NBT.2.a, 1.NBT.2.b, 1.NBT.2.c, 2.NBT.1, 2.NBT.1.a, 2.NBT.1.b, 3.NBT.2, 4.NBT.1, 5.NBT.1 Fractions 1.G.3, 2.G.3, 3.NF.1, 3.NF.2, 3.NF.2.a, 3.NF.2.b, 3.G.2, 4.NF.1, 5.NF.5.a System of 6.NS.5, 6.NS.6, 6.NS.6.a, 6.NS.6.b, 6.NS.7.c, 6.NS.7.d, 7.NS.2.c, 8.NS.1 System of ir 8.NS.2, 8.EE.2 Properties of operations 1.OA.3, 1.OA.7, 2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.9, 3.OA.5, 3.OA.7, 3.OA.9, 3.NBT.2, 3.NBT.3, 4.NBT.5, 4.NF.3.c, 5.NBT.7, 6.EE.3, 6.EE.4, 7.EE.1, 7.EE.3, 8.EE.1 Whole numbers K.OA.2, K.OA.5, 1.OA.4, 1.OA.5, 1.OA.6, 1.NBT.4, 1.NBT.5, 1.NBT.6, 2.OA.2, 2.OA.4, 2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.8, 2.NBT.9, 2.MD.5, 2.MD.6, 3.NBT.2, 3.MD.7.d, 4.NBT.4, 4.MD.2, 4.MD.7, 5.MD.5.c Fractions 4.NF.3, 4.NF.3.a, 4.NF.3.b, 4.NF.3.c, 4.NF.3.d, 4.NF.5, 4.MD.2, 5.NF.1, 5.NF.2 Decimals 4.MD.2, 5.NBT.7, 6.NS.3 Rational numbers 7.NS.1, 7.NS.1.a, 7.NS.1.b, 7.NS.1.c, 7.NS.1.d, 7.NS.3, 8.EE.4 Whole numbers 2.G.2, 3.OA.6, 3.OA.7, 3.NBT.3, 3.MD.7, 3.MD.7.a, 3.MD.7.b, 3.MD.7.c, 4.NBT.5, 4.NBT.6, 4.MD.2, 5.NBT.5, 5.NBT.6, 5.MD.5.a, 5.MD.5.b, 6.NS.2 Fractions 4.NF.4, 4.NF.4.a, 4.NF.4.b, 4.NF.4.c, 4.MD.2, 5.NF.3, 5.NF.4, 5.NF.4.a, 5.NF.5.b, 5.NF.6, 5.NF.7, 5.NF.7.a, 5.NF.7.b, 5.NF.7.c, 6.NS.1 Decimals 4.MD.2, 5.NBT.7, 6.NS.3 Rational numbers 7.NS.2, 7.NS.2.a, 7.NS.2.b, 7.NS.2.c, 7.NS.2.d, 7.NS.3, 8.EE.4 Determine fraction equivalence 3.NF.3, 3.NF.3.a, 3.NF.3.b, 3.NF.3.c, 4.NF.1, 4.NF.2 Understand ratio concepts 5.NF.5, 5.NF.5.a, 6.RP.1, 6.RP.2, 7.G.1, 8.G.3 Use ratio reasoning to solve problems 6.RP.3, 6.RP.3.a, 6.RP.3.b, 6.RP.3.c, 6.RP.3.d Analyze proportional relationships and use to solve problems 7.RP.1, 7.RP.2, 7.RP.2.a, 7.RP.2.b, 7.RP.2.c, 7.RP.2.d, 7.RP.3, 8.EE.5 Topics 1, 2, 3, 6 counting and cardinality Topics 4, 5, 6 to 100 by 1s, 10s Topics 1, 2, 3 Topics 2, 4 Topics 10, 11 two-digit within 10; fluently within 5 Topic 7 to 120 Topic 7, 9 two-digit partitioning Topics 1, 2, 4, 5 addition, subtraction, equivalence Topics 2, 4, 6, 8 11, 15 within 100; fluently within 10 Topics 5, 6, 10 to 1000 by 5s, 10s, 100s Topics 5, 10 Topics 5, 10 Topics 5, 10 three-digit partitioning Topics 2, 3, 6, 8, 11 addition, subtraction, Topics 1 11, 15 within 1000; add fluently within 100; subtract fluently within 20 partitioning 0 fractions in whole number operations, 14 unit fractions on number line Topics 2 5, 7 multiplication, division, Topics 2, 3 fluently within 1000 Topics 5 8, 14 fluently within 100; relate to area 0 compare (like denominators) Topics 3, 13, Topics 3, 13, Topics 5, 7 Topics 3, 10 multi-digit equivalence in operations Topics 5 8, 12 addition, subtraction fractions Topics 4, 13 16 multi-digit using fluently within 1,000,000 Topics 12, 15 like denominators distance, time, liquid volume Topics 5 10, 15 4-digit by 1-digit; 2-digit by 2-digit Topics 13, 15 fraction by whole number; measurements Topics 13, 15 measurements compare (unlike denominators) fraction products, multi-digit whole numbers and in operations with adding volume unlike denominators to hundredths Topics 3, 4, 5, 12, multiply multi-digit numbers fluenty fraction dividend, whole number divisor to hundredths scaling GCF, LCM, integers, 0 0 integers, fractions Topics 2, 4 divide multi-digit numbers fluently, Topics 6, 8, 9 fraction dividend and divisor Topics 12, 13 unit rate, ratio relationship Topics 12, 13, 14 equivalent ratios, percents Topics 2, 8, 9 GCF, LCM, integers, Topics 8, 9 integers, fractions Topic 7 divide multi-digit numbers fluently, Topics 5, 7 fraction dividend and divisor Topics 6, 7 Topics 10, 11 unit rate, ratio relationship equivalent ratios, percents decimal forms with linear expressions, negative negative scale factor Topics 1, 2, 3 constant of proportionality, percent powers of 10 decimal expansion Topics 1, 3 square, cube root, ir integer exponents scientific notation scientific notation 0 dilations graph relationships 4 5
Algebraic Thinking Solve Equations Represent Problems/Operations Patterns Identify and explain numeric patterns 2.OA.3, 3.OA.9, 4.OA.4, 5.NBT.2, 6.SP.5.c, 7.RP.2, 8.SP.1 Generate and analyze patterns 4.OA.5, 5.OA.3 Addition K.OA.1, K.OA.3, K.OA.4, 1.OA.1, 1.OA.5, 2.OA.1, 3.OA.8, 4.OA.3, 5.NF.2 Subtraction K.OA.1, 1.OA.1, 1.OA.4, 1.OA.5, 1.OA.8, 2.OA.1, 3.OA.8, 4.OA.3, 5.NF.2 Multiplication 3.OA.1, 3.OA.3, 3.OA.5, 3.OA.8, 4.OA.1, 4.OA.2, 4.OA.3, 4.NF.3.c, 5.NF.6 Division 3.OA.2, 3.OA.3, 3.OA.6, 3.OA.8, 4.OA.2, 4.OA.3, 5.NF.3, 6.NS.1 Quantitative relationships between variables 6.EE.9, 7.RP.2, 7.RP.2.a, 8.SP.1, 8.SP.2 Exponential 8.EE.2 Apply properties 1.OA.3, 1.OA.7, 2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.9, 3.NBT.2, 3.NBT.3, 3.OA.5, 3.OA.7, 3.OA.9, 4.NBT.5, 4.NF.3.c, 5.NBT.7, 5.MD.5.a, 6.NS.4, 6.EE.2.c, 6.EE.3, 6.EE.4, 7.NS.1.d, 7.NS.2.a, 7.EE.1, 7.EE.3, 8.EE.1 Numeric equations 1.OA.1, 1.OA.2, 1.OA.8, 2.OA.1, 3.OA.3, 3.OA.4, 3.OA.8, 4.OA.2, 4.OA.3, 4.NF.4.c, 4.MD.4, 4.MD.7, 5.NF.2, 5.NF.3, 5.NF.6, 5.MD.5, 6.RP.3, 6.EE.5, 7.EE.3 Algebraic equations 6.EE.7, 7.EE.4.a, 8.EE.7, 8.EE.7a, 8.EE.7b Pairs of simultaneous equations 8.EE.8, 8.EE.8a, 8.EE.8b, 8.EE.8c Topics 7, 9 use objects for unknown Topic 8 use objects for unknown Topics 1, 4, 5 Topics 2, 3, 4, 6 Topics 1, 2, 4, 5 add, subtract; equivalence Topics 1, 4, 5, 6 determine unknown odd/even Topics 1, 2, 4, 6, 8, 9 Topics 1, 3, 7, 9 Topics 2, 3, 6, 8, 11 add, subtract; Topics 1 9 1- and 2-step equations; add, subtract Topics 2, 4, 5, 7 arithmetic patterns Topics 2, 3 Topics 2, 3 Topics 4, 5, 6 Topics 2, 3, 4, 5, 7 multiply, divide; Topics 2, 3, 5 8 determine unknown; four operations, Topics 1, 11 factors, multiples, prime, composite Topics 1, 2 numeric or shape with 1 rule multi-step equation; Topics 1, 7, 13 ; multiplicative comparison Topics 1, 9 ; interpret remainder 8, 12 add, subtract fractions; distributive property Topics 1, 4 10 multi-step equations; all operations Topics 6, 7 in multiplication by powers of 10 Topics 8, 16 numeric with 2 rules fractions with unlike denominators; use models fractions with unlike denominators; use models fractions, mixed numbers; use models fraction quotients; use models Topics 2, 12 with Topics 10, 11, 12 fractions with unlike denominators; with volume 9 in measure of center fractions; use models Topics 12, 15 Topics 2, 4 Topics 3, 12 use ratio reasoning, substitution Topics 4, 15 form of x + p = q in measure of center fractions; use models Topics 3, 11 use ratio reasoning, substitution form of x + p = q in proportional relationships in proportional relationships with linear expressions, Topics 4, 5, 8 multi-step equations, Topic 8 form of px + q = r in bivariate data in bivariate data square, cube roots integer components linear equations linear equations Write and Evaluate Expressions Functions Inequality Numerical expressions 5.OA.1, 5.OA.2, 6.EE.1, 6.EE.2.b, 7.NS.1, 7.NS.1.c Algebraic expressions 6.EE.2, 6.EE.2.a, 6.EE.2.b, 6.EE.2.c, 6.EE.6, 6.EE.9, 7.EE.2, 7.EE.3, 7.EE.4, 8.EE.2 Understand inequality 6.EE.5 Write and solve inequalities 6.EE.8, 7.EE.4, 7.EE.4.b Define, evaluate, and compare functions 6.EE.9, 7.RP.2, 8.F.1, 8.F.2, 8.F.3 Use functions to model relationships between quantities 8.EE.6, 8.F.4, 8.F.5 Topics 3, 8 with parentheses or brackets whole number exponents Topics 2, 3, 12, 15 order of operations meaning of inequality form of x > c and x < c Topics 12, 15 whole number exponents Topics 1, 2, 3 order of operations meaning of inequality form of x > c and x < c Topics 8, 9 rewrite in equivalent forms px + q > r and px + q < r in proportional relationships integer exponents, radicals properties of functions linear functions 6 7
Measurement and Geometry Explore and Manipulate Shapes and Their Attributes Identify and describe shapes and their attributes; compose shapes K.MD.1, K.G.1, K.G.2, K.G.3, 1.G.2, 2.G.1, 3.G.1, 4.G.1, 5.G.3, 6.G.4, 7.G.2, 7.G.3 Topics 12, 14, 15, 16 2D and 3D shapes Analyze shapes; classify by attrribute or property K.G.4, K.G.5, K.G.6, 1.G.1, 2.G.1, 3.G.1, 4.G.2, 5.G.3, 5.G.4 2D and 3D shapes create composite 2D and 3D shapes defining vs. non-defining attributes draw shapes 2D figures quadrilaterals hierarchy of attributes geometric figures (points, lines, segments, angles, rays) 2D figures Symmetry 4.G.3 line symmetry 2D figures classify 2D figures based on hierarchy 8 3D shapes from nets 3D shapes from nets 2D figures in 3D shapes Compare measurable attributes K.MD.2, 1.MD.1, 2.MD.4 direct comparison Measure and estimate lengths in standard units 1.MD.2, 2.MD.1, 2.MD.2, 2.MD.3, 2.MD.9 order objects by length iterate units to measure length measure to compare length Topics 15, 16 use two different units to measure length Geometric Measurement Measurements Work with time and money 1.MD.3, 2.MD.7, 2.MD.8, 3.MD.1 3 time to half hour Topics 13, 14, 16 time to five minutes, money time to minutes Solve problems involving measurements 3.MD.2, 4.MD.2 liquid volumes, mass Topics 13, 14, 15 distance, liquid volumes, mass, money Measurement units 4.MD.1, 5.MD.1, 6.RP.3.d, 7.RP.1, 8.EE.4 equivalence between units Angle measures 4.MD.5, 4.MD.5.a, 4.MD.5.b, 4.MD.6, 4.MD.7, 5.G.3, 6.G.3, 7.G.5, 8.G.5 Perimeter 3.MD.8, 4.MD.3, 7.G.4 Topics 13, 14 polygons Area 3.MD.5, 3.MD.5.a, 3.MD.5.b, 3.MD.6, 3.MD.7, 3.MD.7.a, 3.MD.7.b, 3.MD.7.c, 3.MD.7.d, 4.MD.3, 5.NF.4.b, 6.G.1, 7.G.4, 7.G.6 find by counting; relate to multiplication measure with proctractor, add measures use formula for rectangles use formula for rectangles 3 convert within a system in polygons rectangle with fractional side lengths ratio reasoning in polygons Topics 8, 11 triangles, quadrilaterals Surface area 6.G.4; 7.G.6 8 use nets Volume 5.MD.3, 5.MD.3a, 5.MD.3b, 5.MD.4, 5.MD.5, 5.MD.5a, 5.MD.5b, 5.MD.5c, 6.G.2, 7.G.6, 8.G.9 use cubes and formula, right rectangular prism Topics 10, 18 right prisms with fractional edge lengths ratio reasoning 3 in polygons 3 triangles, quadrilaterals use nets right prisms with fractional edge lengths unit rates 0 supplementary, complementary, vertical, adjacent circles circles 3 cubes, right prisms 3 cubes, right prisms express in scientific notation within a system exterior angles, transverals 3 cones, cylinders, spheres Connecting Algebra and Geometry Use the coordinate plane 5.OA.3, 5.G.1, 5.G.2, 6.NS.8, 6.G.3, 7.RP.2.d, 8.EE.5, 8.EE.6, 8.G.8 Topics 14, 16 graph points in Quadrant I 0 find distance (one coordinate the same) find distance (one coordinate the same) points in proportional relationship Transformations: congruence and similarity 7.G.1, 8.G.1, 8.G.1.a, 8.G.1.b, 8.G.1.c, 8.G.2, 8.G.3, 8.G.4 scale factor find distance between points rotations, translations, reflections, dilations, The Pythagorean Theorem 8.G.6, 8.G.7, 8.G.8 also converse 8 9
Statistics and Probability Probability Concepts Statistical Variability Represent and Interpret Data Organize objects in categories; count objects in categories K.MD.3, 1.MD.4 Bar graphs 2.MD.10, 3.MD.3 Picture graphs 2.MD.10, 3.MD.3 Line plots 2.MD.9, 3.MD.4, 4.MD.4, 5.MD.2, 6.SP.4 Understanding of statistical variability 6.SP.1 Measures of center 6.SP.2, 6.SP.3 Describing data distributions 6.SP.5, 6.SP.5a, 6.SP.5b, 6.SP.5c, 6.SP.5d Understanding of random sampling 7.SP.1, 7.SP.2 Compare two populations based on sampling 7.SP.3, 7.SP.4 Investigate and interpret bivariate data 8.SP.1, 8.SP.2, 8.SP.3, 8.SP.4 Understand probability models 7.SP.5 Predict relative frequency of an event given the probability 7.SP.6 Develop probability models 7.SP.7, 7.SP.7.a, 7.SP.7.b Find probability of compound events 7.SP.8, 7.SP.8.a, 7.SP.8.b, 7.SP.8.c 3 sort, categorize, count interpret data with 3 categories 4 categories; single-unit scale 4 categories; single-unit scale 4 categories; single-unit scale scaled graphs scaled graphs fractional units on scale fractional measurements fractional measurements 9 box plots, histograms, dot plots 9 statistical questions 9 distribution of data 9 measures of center box plots, histograms, dot plots statistical questions distribution of data measures of center draw inferences compare measures of center, variability theoretical probability experimental probability compare model to experimental results 7 tree diagrams, organized lists, tables, simulations Topics 14, 15 scatter plots, linear associations 10 11
envisionmath envisionmath was written for the State Standards and is organized by the Domains, so teaching is highly focused, manageable, and coherent. Based on critical foundational research and proven classroom results, envisionmath develops conceptual understanding through Problem-Based Interactive Learning and step-by-step Visual Learning; uses bar diagrams to help students understand number and operation meanings in problem solving; and provides solid and effective intervention that makes it easy for teachers to respond to students individual needs. www.pearsonschool.com/envisionmathcommoncore digits digits, Pearson s new middle grades math curriculum, combines any time, anywhere web-based applications with point-of-use interactive whiteboard resources to meet the needs of 21st Century learners and teachers. With digits, time spent grading or reviewing homework is freed up for focused in-class teaching. Readiness assessments and autoscored homework pinpoint students understanding of content so teachers can focus on individual needs during class. digits also meets today s students where they live in the digital world. This one-of-a-kind program engages students with individualized learning paths and self-guided exploration options that make the learning of math highly visual, fun, and engaging. www.digitsmath.com Pearson High School Mathematics Edition Built around the State Standards, Pearson Algebra 1, Geometry, and Algebra 2 Editions not only address the Standards for Mathematical Content but also infuses the Standards for Mathematical Practice in every lesson. This blended print and digital curriculum creates an environment where teachers can engage students, teach for understanding through Problem- Based Interactive Learning, and promote mastery with data-driven differentiated instruction. Using the latest in digital instructional technology, PowerAlgebra.com and PowerGeometry.com provide a pedagogically relevant interface to support classroom instruction. PearsonSchool.com 800-848-9500 Copyright Pearson Education, Inc., or its affiliates. All rights reserved. ADV: 978-0-328-72202-0 www.pearsonschool.com/hsmath2012