K 3 Mathematics Core Course Objectives

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1 K 3 Mathematics Core Course Objectives The Massachusetts Department of Elementary and Secondary Education (ESE) partnered with WestEd to convene panels of expert educators to review and develop statements of essential curriculum content,, for approximately 100 different grades/subjects and courses. In conjunction with the Massachusetts Curriculum Frameworks, the CCOs were used by a team of WestEd evaluators to ensure content alignment in the identification and evaluation of example assessments suitable for use as District-Determined Measures (DDMs). Districts can utilize the CCOs themselves or the process of developing CCOs in their own work when selecting DDMs. At each meeting, educators developed highquality CCOs that met the following criteria: Scope: The CCO describes an overarching learning goal. Assess-ability: The CCO describes knowledge, skills, or abilities that are readily able to be measured. are statements that: describe different elements of core, essential content (knowledge, skills, or abilities); are pulled, created, or synthesized from a larger set of curriculum standards; and clarify key knowledge, skills, and abilities that many educators and other content experts working together agree are most critical in that content area, grade, or course. Each CCO should be high-level and represent broad enough learning goals to be taught using a wide variety of instructional tools or methods (scope), while also focused enough that students growth in learning that knowledge or skill can be measured by an assessment (assess-ability). Centrality: The CCO describes a critically important concept, skill, or ability that is central to the subject/grade or course. Relevance: The CCO represents knowledge, skills, and abilities that are consistent with Massachusetts s values and goals. After public review, WestEd s content specialists reviewed the comments submitted by educators and other stakeholders. The CCOs that emerged from this process are presented below. Note: Listed below are the CCOs for mathematics grades K-2. Initial CCO development was focused on high- priority non-tested grades and subjects. Because grade 3 is a tested grade in Massachusetts, it was not included among those grades and subjects targeted for development in summer

2 Mathematics Grade: K 1 Students count forward from a given number within the known sequence, instead of beginning at one, and continue as far as Students count orally by tens to Students write and recognize numbers from 0 to 20 and represent a number of objects with a written numeral 0 to Students say the number names in standard order, pairing each object with one and only one number and each number with one and only one object (1 to 1). 5 Students count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as ten things in a scattered configuration; and given a number from 1 to 20, count out that many objects. 6 Students compare two sets of objects and/or two written numerals and identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. (Include groups with up to ten objects.) 7 Students solve addition and subtraction situations within ten with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations (number stories, word problems). 8 Students decompose numbers less than or equal to ten into pairs in more than one way by using objects or drawings, and record each decomposition by drawing or equation. 9 Students name, describe, construct, and/or manipulate both two-dimensional and three-dimensional shapes in their environment using mathematical vocabulary and spatial reasoning. 10 Students analyze and compare two-dimensional and three-dimensional shapes, in different sizes and orientations, using informal language to describe similarities, differences, parts (number of sides, vertices, corners ), and other attributes (e.g., having sides of equal length). 11 Students directly compare two objects with a measurable attribute by describing the measurable attribute and determining which object has more or less of that attribute. Note: These Core Course Objectives were developed by Massachusetts educators in summer They are intended to provide districts with information about the content taught in this course. Source documents used are as follows: Massachusetts Mathematics Curriculum Framework (2011); Learning Progressions Frameworks Designed for Use with The Common Core State Standards in Mathematics K 12 (NCIEA) (2011). 2

3 Mathematics Grade: 1 1 Students illustrate or show that the two digits of a two-digit number represent amounts of tens and ones using models such as drawings, base-ten blocks, ten frames, or hundreds charts; or given a model students will write the two-digit number. 2 Students compare two two-digit numbers and record the results of comparisons using the symbols >, =, and <. 3 Students add and subtract within 100 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 4 Students subtract multiples of ten using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 5 Students solve addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, by using objects, drawings, and equations, with a box or pictorial representation for the unknown number to represent the problem. 6 Students add and subtract within 20, demonstrating fluency for addition and subtraction within ten, using mental strategies such as: counting on/back; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums (e.g., adding six plus seven by creating the known equivalent). 7 Students write and solve number sentences from problem situations, demonstrating understanding of the equal sign. 8 Students express the length of an object as a whole number of length units, by laying multiple copies of a shorter object end to end with no gaps or overlaps, using standard units of length. 9 Students sequence three objects by length and compare the lengths of three objects indirectly by using a third object. 10 Students identify values and use the values of all U.S. coins in the solution of problems, using appropriate notation. 11 Students distinguish between defining attributes of shapes versus non-defining attributes and draw shapes to possess defining attributes. 3

4 12 Students compose two-dimensional shapes or three-dimensional shapes (e.g., cubes, rectangular prisms, circular cones, and circular cylinders) to create a composite shape (an object composed of a combination of two or more basic shapes), and compose new shapes from the composite shape. Note: These Core Course Objectives were developed by Massachusetts educators in summer They are intended to provide districts with information about the content taught in this course. Source documents used are as follows: Massachusetts Mathematics Curriculum Framework (2011); Learning Progressions Frameworks Designed for Use with The Common Core State Standards in Mathematics K 12 (NCIEA) (2011). 4

5 Mathematics Grade: 2 1 Students explain that the three digits of a three-digit number represent amounts of hundreds, tens, and ones and compare three-digit numbers based on meanings of the hundreds, tens, and ones digits using words and symbols for more than, less than, and/or equal to. 2 Students fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Mentally add ten to a given number, and mentally subtract ten from a given number. Explain why addition and subtraction strategies work, using place value and the properties of operations. 3 Students add and subtract within 1,000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction and relate the strategy to a written method. Mentally add ten or 100 to a given number , and mentally subtract ten or 100 from a given number Students add and subtract within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g., by using drawings and equations with a symbol for the unknown number) to represent the problem. Most work with two-step problems should involve single-digit addends. Word problems about length and about money can be included. 5 Students fluently add and subtract within 20 using mental strategies. By end of grade 2, know from memory all sums of two one-digit numbers. By the end of grade 2, know from memory related subtraction facts of sums of two one-digit numbers. 6 Students recognize and draw shapes having specified attributes. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 7 Students measure the length of an object in units of inches, feet, centimeters, and/or meters, by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. (Units of measure were identified to correlate to the appropriate measuring tool.) 8 Students tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 9 Students draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories and solve simple put-together, take-apart, and compare problems, using information presented in a bar graph. 5

6 Note: These Core Course Objectives were developed by Massachusetts educators in summer They are intended to provide districts with information about the content taught in this course. Source documents used are as follows: Massachusetts Mathematics Curriculum Framework (2011); Learning Progressions Frameworks Designed for Use with The Common Core State Standards in Mathematics K 12 (NCIEA) (2011). 6