The Common Core is a set of high-quality academic standards in mathematics and English language arts (ELA).
In 2009 the state school chiefs and governors that comprise CCSSO and the NGA Center coordinated a stateled effort to develop the Common Core State Standards. Designed through collaboration among teachers, school chiefs, administrators, and other experts, the standards provide a clear and consistent framework for educators.
The standards were created to ensure that all students graduate from high school with the skills and knowledge necessary to succeed in college, career, and life, regardless of where they live. The standards define the knowledge and skills students should gain throughout their K-12 education in order to graduate high school prepared to succeed in entrylevel careers, introductory academic college courses, and workforce training programs.
Forty-two states , the District of Columbia, four territories, have voluntarily adopted and are moving forward with the Common Core.
目錄：
Grade 1
PART 1 OPERATIONS AND ALGEBRAIC THINKING (OA)
Chapter 01
USE ADDITION AND SUBTRACTION WITHIN 20 TO SOLVE WORD PROBLEMS.(OA.1)
Chapter 02
SOLVE WORD PROBLEMS WITH THE ADDITION OF THREE WHOLE NUMBERS. (OA. 2)
Chapter 03
APPLY PROPERTIES OF OPERATIONS AS STRATEGIES TO ADD AND SUBTRACT. SHOW UNDERSTANDING OF THE COMMUTATIVE PROPERTY OF ADDITION AND THE ASSOCIATIVE PROPERTY OF ADDITION. (OA. 3)
Chapter 04
UNDERSTAND SUBTRACTION AS AN UNKNOWN ADDITION PROBLEM. (OA. 4)
Chapter 05
RELATE COUNTING TO ADDITION AND SUBTRACTION. (OA. 5).
Chapter 06
ADD AND SUBTRACT WITHIN 20, DEMONSTRATING FLUENCY FOR ADDITION AND SUBTRACTION WITHIN 10. USE VARIOUS STRATEGIES TO ADD AND SUBTRACT.(OA.6)
Chapter 07
UNDERSTAND THE MEANING OF THE EQUAL SIGN, AND DETERMINE IF EQUATIONS INVOLVING ADDITION AND SUBTRACTION ARE TRUE OR FALSE. (OA. 7)
Chapter 08
DETERMINE THE UNKNOWN WHOLE NUMBER IN AN ADDITION OR SUBTRACTION EQUATION RELATING THREE WHOLE NUMBERS. (OA. 8)
PART 2 NUMBER AND OPERATIONS IN BASE TEN (NBT)
Chapter 09
COUNT TO 120, STARTING AT ANY NUMBER LESS THAN 120. READ AND WRITE NUMERALS AND REPRESENT A NUMBER OF OBJECTS WITH A WRITTEN NUMERAL. (NBT. 1)
Chapter 10
UNDERSTAND THAT THE TWO DIGITS OF A TWO-DIGIT NUMBER REPRESENT AMOUNTS OF TENS AND ONES. 10 CAN BE THOUGHT OF AS A BUNDLE OF TEN ONES. TWO DIGIT NUMBERS ENDING IN 1 THROUGH 9 ARE COMPOSED OF TENS AND ONES. TWO DIGIT NUMBERS ENDING IN ZERO ARE COMPOSED OF TENS AND ZERO ONES. (NBT. 2)
Chapter 11
COMPARE TWO TWO-DIGIT NUMBERS BASED ON MEANINGS OF THE TENS AND ONES DIGITS, RECORDING THE RESULTS OF COMPARISONS WITH THE SYMBOLS ＞, = AND ＜. (NBT. 3)
Chapter 12
ADD WITHIN 100, USING CONCRETE MODELS OR DRAWINGS AND STRATEGIES BASED ON PLACE VALUE, PROPERTIES OF OPERATIONS, AND THE RELATIONSHIP BETWEEN ADDITION AND SUBTRACTION. (NBT. 4)
Chapter 13
USE MENTAL MATHS TO FIND 10 MORE OR 10 LESS THAN A NUMBER, WITHOUT COUNTING ON. (NBT. 5)
Chapter 14
SUBTRACT MULTIPLES OF 10 IN THE RANGE 10-90, USING CONCRETE MODELS OR DRAWINGS AND STRATEGIES BASED ON PLACE VALUE, PROPERTIES OF OPERATIONS, AND/OR THE RELATIONSHIP BETWEEN ADDITION AND SUBTRACTION. (NBT. 6)
……
Grade 2
PART 1 OPERATIONS AND ALGEBRAIC THINKING (OA)
Chapter 01
USE ADDITION AND SUBTRACTION WITHIN 100 TO SOLVE ONE AND TWOSTEP WORD PROBLEMS (OA. 1)
Chapter 02
FLUENTLY ADD AND SUBTRACT WITHIN 20 USING MENTAL STRATEGIES. (OA. 2)
Chapter 03
DETERMINE WHETHER A GROUP OF OBJECTS HAS AN ODD OR EVEN NUMBER OF MEMBERS (OA. 3)
Chapter 04
USE ADDITION TO FIND THE TOTAL NUMBER OF OBJECTS ARRANGED IN RECTANGULAR ARRAYS (OA. 4)
PART 2 NUMBER AND OPERATIONS IN BASE TEN (NBT)
Chapter 05
UNDERSTAND THAT THE THREE DIGITS OF A THREE-DIGIT NUMBER REPRESENT AMOUNTS OF HUNDREDS, TENS, AND ONES. (NBT. 1)
Chapter 06
COUNT WITHIN 1000； SKIP-COUNT BY 5S, 10S, AND 100S. (NBT. 2)
Chapter 07
READ AND WRITE NUMBERS TO 1000 USING BASE-TEN NUMERALS, NUMBER NAMES, AND EXPANDED FORM. (NBT. 3)
Chapter 08
COMPARE TWO, THREE-DIGIT NUMBERS BASED ON VALUES OF THE HUNDREDS, TENS, AND ONES DIGITS, USING ＞, = AND ＜ SYMBOLS. (NBT. 4)
Chapter 09
FLUENTLY ADD AND SUBTRACT WITHIN 100 USING STRATEGIES BASED ON PLACE VALUE, PROPERTIES OF OPERATIONS, AND THE RELATIONSHIP BETWEEN ADDITION AND SUBTRACTION. (NBT. 5)
Chapter 10
ADD UP TO FOUR TWO-DIGIT NUMBERS USING STRATEGIES BASED ON PLACE VALUE AND PROPERTIES OF OPERATIONS. (NBT. 6)
Chapter 11
ADD AND SUBTRACT WITHIN 1000, USING MODELS, DRAWINGS AND STRATEGIES. ADD AND SUBTRACTING USING REGROUPING. (NBT. 7)
Chapter 12
MENTALLY ADD AND SUBTRACT 10 OR 100 TO A GIVEN NUMBER 100-900. (NBT. 8)
Chapter 13
EXPLAIN WHY ADDITION AND SUBTRACTION STRATEGIES WORK, USING PLACE VALUE AND THE PROPERTIES OF OPERATIONS. (NBT. 9)
……
Grade 3
PART 1 OPERATIONS AND ALGEBRAIC THINKING (OA)
Chapter 01
INTERPRET PRODUCTS OF WHOLE NUMBERS (OA. 1)
Chapter 02
INTERPRET WHOLE NUMBER QUOTIENTS (OA. 2)
Chapter 03
USE MULTIPLICATION AND DIVISION TO SOLVE WORD PROBLEMS (OA. 3)
Chapter 04
DETERMINE THE UNKNOWN WHOLE NUMBER IN A MULTIPLICATION OR DIVISION EQUATION. (OA. 4)
Chapter 05
APPLY PROPERTIES OF OPERATIONS TO MULTIPLY AND DIVIDE (OA. 5)
Chapter 06
UNDERSTAND DIVISION AS AN UNKNOWN FACTOR PROBLEM (OA. 6)
Chapter 07
MULTIPLY AND DIVIDE WITHIN 100 USING STRATEGIES OR PROPERTIES OF OPERATIONS (OA. 7)
Chapter 08
SOLVE 2 STEP WORD PROBLEMS USING THE FOUR OPERATIONS. (OA. 8)
Chapter 09
IDENTIFY ARITHMETIC PATTERNS (OA. 9)
PART 2 NUMBER AND OPERATIONS IN BASE TEN (NBT)
Chapter 10
USE PLACE VALUE TO ROUND WHOLE NUMBERS TO THE NEAREST 10 OR 100 (NBT.1)
Chapter 11
ADD AND SUBTRACT WITH 4 DIGIT NUMBERS (NBT. 2)
Chapter 12
MULTIPLY ONE DIGIT WHOLE NUMBERS BY MULTIPLES OF 10 (NBT. 3)
PART 3 NUMBER AND OPERATIONS-FRACTIONS (NF)
Chapter 13
UNDERSTAND FRACTIONS AS A PARTS OF A WHOLE (NF. 1)
Chapter 14
UNDERSTAND FRACTIONS USING A NUMBER LINE (NF. 2)
Chapter 15
RECOGNIZE EQUIVALENT FRACTIONS AND COMPARE FRACTIONS. (NF. 3)
……
Grade 4
PART 1 OPERATIONS AND ALGEBRAIC THINKING (OA)
Chapter 01
INTERPRETING MULTIPLICATION EQUATIONS (OA. 1)
Chapter 02
USING MULTIPLICATION AND DIVISION TO SOLVE MULTIPLICATIVE WORD PROBLEMS (OA. 2)
Chapter 03
SOLVING MULTISTEP WORD PROBLEMS (OA. 3)
Chapter 04
FINDING FACTOR PAIRS (OA. 4)
Chapter 05
GENERATING AND ANALYZING PATTERNS (OA. 5)
PART 2 NUMBER AND OPERATIONS IN BASE TEN (NBT)
Chapter 06
CONCEPTS OF PLACE VALUE (NBT. 1)
Chapter 07
COMPARING TWO MULTI-DIGIT NUMBERS (NBT. 2)
Chapter 08
ROUNDING MULTI-DIGIT WHOLE NUMBERS (NBT. 3)
Chapter 09
ADDING AND SUBTRACTING WHOLE NUMBERS (NBT. 4)
Chapter 10
MULTIPLYING WHOLE NUMBERS (NBT. 5)
Chapter 11
DIVIDING MULTI-DIGIT WHOLE NUMBERS (NBT. 6)
……
Grade 5
PART 1 OPERATIONS AND ALGEBRAIC THINKING (OA)
Chapter 01
USE PARENTHESES, BRACKETS, OR BRACES IN NUMERICAL EXPRESSIONS (OA. 1)
Chapter 02
CREATING EXPRESSIONS USING PARENTHESES (OA. 2)
Chapter 03
ANALYZE PATTERNS AND RELATIONSHIPS (OA. 3)
PART 2 NUMBER AND OPERATIONS IN BASE TEN (NBT)
Chapter 04
RECOGNIZE THAT IN A MULTI-DIGIT NUMBER, A DIGIT IN ONE PLACE IS 10 TIMES AS MUCH AS IT IS IN THE PLACE TO ITS RIGHT AND 1/10 WHAT IT IS IN THE PLACE TO ITS LEFT. (NBT. 1)
Chapter 05
EXPLAIN PATTERNS IN THE NUMBER OF ZEROS OF THE PRODUCT WHEN MULTIPLYING A NUMBER BY POWERS OF 10, AND EXPLAIN PATTERNS IN THE PLACEMENT OF THE DECIMAL POINT WHEN A DECIMAL IS MULTIPLIED OR DIVIDED BY A POWER OF 10. USE WHOLE-NUMBER EXPONENTS TO DENOTE POWERS OF 10. (NBT. 2)
Chapter 06
READ, WRITE, AND COMPARE DECIMALS TO THOUSANDTHS (NBT. 3)
Chapter 07
USE PLACE VALUE UNDERSTANDING TO ROUND DECIMALS TO ANY PLACE (NBT. 4)
Chapter 08
FLUENTLY MULTIPLY MULTI-DIGIT WHOLE NUMBERS USING THE STANDARD ALGORITHM. (NBT. 5)
Chapter 09
FIND WHOLE-NUMBER QUOTIENTS OF WHOLE NUMBERS WITH UP TO FOURDIGIT DIVIDENDS AND TWO-DIGIT DIVISORS (NBT. 6)
PART 3 NUMBERS AND OPERATIONS — FRACTIONS (NF)
Chapter 10
ADD AND SUBTRACT FRACTIONS WITH UNLIKE DENOMINATORS (INCLUDING MIXED NUMBERS) BY REPLACING GIVEN FRACTIONS WITH EQUIVALENT FRACTIONS IN SUCH A WAY AS TO PRODUCE AN EQUIVALENT SUM OR DIFFERENCE OF FRACTIONS WITH LIKE DENOMINATORS (NF. 1)
……
Grade 6
PART 1 RATIOS AND PROPORTIONAL RELATIONSHIPS (RP)
Chapter 01
UNDERSTAND THE CONCEPT OF A RATIO AND USE RATIO LANGUAGE TO DESCRIBE A RELATIONSHIP BETWEEN TWO QUANTITIES. (RP. 1)
Chapter 02
UNDERSTAND THE CONCEPT OF A UNIT RATE ASSOCIATED WITH A RATIO AND USE RATE LANGUAGE IN THE CONTEXT OF A RATIO RELATIONSHIP. (RP. 2)
Chapter 03
USE RATIO AND RATE REASONING TO SOLVE REAL-WORLD AND MATHEMATICAL PROLEMS: TABLES AND EQUIVALENT RATIOS (RP. 3A)
Chapter 04
SOLVING UNIT RATE PROBLEMS. (RP. 3B)
Chapter 05
UNDERSTANDING PERCENT AS A RATE. (RP. 3C)
Chapter 06
USE RATIO REASONING TO CONVERT MEASUREMENT UNITS. (RP. 3D)
PART 2 THE NUMBER SYSTEM (NS)
Chapter 07
DIVISION OF FRACTIONS BY FRACTION. (NS. 1)
Chapter 08
FLUENTLY DIVIDE MULTI-DIGIT NUMBERS USING THE STANDARD ALGORITHM. (NS. 2)
Chapter 09
FLUENTLY ADD, SUBTRACT, MULTIPLY AND DIVIDE MULTI-DIGIT DECIMALS USING STANDARD ALGORITHMS. (NS. 3)
Chapter 10
FINDING GREATEST COMMON FACTORS AND LEAST COMMON MULTIPLES. (NS. 4)
Chapter 11
POSITIVE AND NEGATIVE NUMBERS. (NS. 5)
……
Grade 7
PART 1 RATIOS AND PROPORTIONAL RELATIONSHIPS (RP)
Chapter 01
COMPUTE UNIT RATES ASSOCIATED WITH RATIOS OF FRACTIONS, INCLUDING RATIOS OF LENGTHS, AREAS AND OTHER QUANTITIES MEASURED IN LIKE OR DIFFERENT UNITS. (RP. 1)
Chapter 02
RECOGNIZE AND REPRESENT PROPORTIONAL RELATIONSHIPS BETWEEN QUANTITIES. DECIDE WHETHER TWO QUANTITIES ARE IN A PROPORTIONAL RELATIONSHIP. (RP. 2A)
Chapter 03
RECOGNIZE AND REPRESENT PROPORTIONAL RELATIONSHIPS BETWEEN QUANTITIES. IDENTIFY THE CONSTANT OF PROPORTIONALITY (UNIT RATE) IN TABLES, GRAPHS, EQUATIONS, DIAGRAMS, AND VERBAL DESCRIPTIONS OF PROPORTIONAL RELATIONSHIPS. (RP. 2B)
Chapter 04
RECOGNIZE AND REPRESENT PROPORTIONAL RELATIONSHIPS BETWEEN QUANTITIES. REPRESENT PROPORTIONAL RELATIONSHIPS BY EQUATIONS. (RP. 2C)
Chapter 05
RECOGNIZE AND REPRESENT PROPORTIONAL RELATIONSHIPS BETWEEN QUANTITIES. EXPLAIN WHAT A POINT (X, Y) ON THE GRAPH OF A PROPORTIONAL RELATIONSHIP MEANS IN TERMS OF THE SITUATION, WITH SPECIAL ATTENTION TO THE POINTS (0, 0) AND (1, R) WHERE R IS THE UNIT RATE. (RP. 2D)
Chapter 06
USE PROPORTIONAL RELATIONSHIPS TO SOLVE MULTISTEP RATIO AND PERCENT PROBLEMS. (RP. 3)
PART 2 THE NUMBER SYSTEM (NS)
Chapter 07
APPLY AND EXTEND PREVIOUS UNDERSTANDINGS OF ADDITION AND SUBTRACTION TO ADD AND SUBTRACT RATIONAL NUMBERS； REPRESENT ADDITION AND SUBTRACTION ON A HORIZONTAL OR VERTICAL NUMBER LINE DIAGRAM. DESCRIBE SITUATIONS IN WHICH OPPOSITE QUANTITIES COMBINE TO MAKE 0. (NS. 1A)
Chapter 08
UNDERSTAND P + Q AS THE NUMBER LOCATED A DISTANCE |Q| FROM P, IN THE POSITIVE OR NEGATIVE DIRECTION DEPENDING ON WHETHER Q IS POSITIVE OR NEGATIVE. SHOW THAT A NUMBER AND ITS OPPOSITE HAVE A SUM OF 0. INTERPRET SUMS OF RATIONAL NUMBERS BY DESCRIBING REAL-WORLD CONTEXTS. (NS. 1B)
……
Grade 8
PART 1 NUMBER SYSTEMS (NS)
Chapter 01
RATIONAL NUMBERS AND DECIMAL EXPANSION (NS. 1)
Chapter 02
COMPARING IRRATIONAL NUMBERS (NS. 2)
PART 2 EXPRESSIONS AND EQUATIONS (EE)
Chapter 03
EXPONENTS AND EQUIVALENT EXPRESSIONS (EE. 1).
Chapter 04
EXAMINING SQUARE AND CUBE ROOTS (EE. 2)
Chapter 05
EVALUATING SCIENTIFIC NOTATION (EE. 3)
Chapter 06
OPERATIONS INVOLVING SCIENTIFIC NOTATION (EE. 4).
Chapter 07
GRAPHING PROPORTIONAL RELATIONSHIPS (EE. 5)
Chapter 08
SLOPE AND LINEAR EQUATIONS (EE. 6)
Chapter 09
LINEAR EQUATIONS WITH ONE VARIABLE (EE. 7A)
Chapter 10
ADVANCED ONE VARIABLE LINEAR EQUATIONS (EE. 7B)
Chapter 11
GRAPHS AND TWO VARIABLE SYSTEMS (EE. 8A)
Chapter 12
SOLVING TWO VARIABLE SYSTEMS (EE. 8B)
Chapter 13
LINEAR EQUATION WORD PROBLEMS (EE. 8C)
……
內容試閱：
序言
继《Smart Reading: 跟美国学生同步练阅读》和《Smart Science: 跟美国学生同步学科学》之后，这套以美国现行教学大纲（Common Core State Standards，简称CCSS）为蓝本、由加拿大英语教师编写的《Smart Math: 跟美国学生同步做数学》终于问世了！这三套书，对应西方学校1-8 年级开设的英语语言艺术（ELA）、数学（Math）和科学（Science）三门主要学科，统一按美国现行通用教学标准编写，旨在为出国留学的孩子提升语言能力、用英语训练学科知识与技能提供一定帮助。这些辅导书可以让他们换个角度练英语、换种语言学知识，这应该是件一举多得的事儿。
近些年，出国留学的孩子人数大增，去往的目的地更广、趋于低龄化。留学之路，对一个家庭和孩子未来的发展而言，都是需要慎重考虑和决定的大事，切不可盲从和草率而定。如果定下来要送出去读，出国前应尽可能做些铺垫，如语言训练、兴趣培养、对西方的认知等。多做点这方面的功课，比单纯提高托福、雅思分数要有用得多。
对于“共同核心标准”（CCSS）这一概念，中国家长和学生可能有些陌生。它是美国从幼儿园至高中所使用的统一教学标准，加拿大很多学校也会参考这一标准。在美国和加拿大，学校教育系统主要由各个州（省）政府所监管。这意味着，阿肯色州与俄勒冈州的孩子们在学校所学的内容会不太相同。当他们完成K12 教育、继续接受高等教育或步入职业生涯时，如果所受教育采用不一样的标准，便会产生一些问题。尤其当某个家庭从一个州搬迁至另一个州时，孩子的续读或许会出现一些麻烦。“共同核心标准”正是着力于解决这类问题。它是由美国一些著名教育家与政界、商界很有影响力的人物极力倡导而制定，尽量弥合各州之间教学标准的差异。目前为此，美国42 个州、哥伦比亚地区、四个领地都在使用这一教学标准。比尔? 盖茨先生也极力赞助这一标准的推广。
共同核心标准，涵盖了幼儿园至12 年级，旨在培养学生的批判性思考能力，传授各年级学科知识。让他们学会设立问题、自我思考，将所学内容进行关联和牵引。共同核心标准，首先注重的是教学生如何思考，然后是学习内容。注重记忆基础之上的知识与技能训练和相互关联。这一标准具有以下特点：
1. 建立在大量研究与事实基础之上而制定；
2. 标准清晰、易于理解并保持教学的延续性；
3. 结合未来的大学教育与职业发展；
4. 丰富的内容与知识应用，高度训练学生的思考能力；
5. 融汇了各州教学标准的优势；
6. 参考了其他国家的教育优点，让学生未来更好地适应全球化经济与社会。
目前，共同核心标准包括两类课程：一是英语语言艺术（English Language Arts，简称“ELA”），另一门是数学。ELA 又包括阅读、写作、听说等各个领域。这些语言能力，也是学习其他科目的关键，如科学、历史与信息技术等。所以它不是一门简单的英语科目。数学大纲，不是重点强调记忆，而是让学生在训练技能的同时，能获取解决数学问题的方法。要求学生运用数学知识和技能解决真实世界中的问题。因此数学对学生来讲，会变得更加有趣而充满真实感。
2014 年，Holybird Publishing 在加拿大西海岸美丽的维多利亚市注册成立，这为我们利用北美教育资源与作者队伍提供了便利的条件，使得CCSS 这一系列图书的出版成为可能。这些作者具有丰富的英语教学经验，有的在亚洲从事过多年英语教学，他们非常乐意完成这一工作。经过几年的努力，这套书能呈现给中国读者，满足部分学生的需求，作为出版者，我们十分高兴。由于各种原因，书中难免出现一些错误和不足，恳请批评指正，并期待听到家长和老师的反馈，便于我们更好地改进。衷心祝愿所有求学之路上的孩子们心存大志、学有所成！
Edward Liu
Editor-in-chief
of Holybird Publishing
in Victoria, BC, Canada
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