Lincoln, Massachusetts Public Schools Mathematics Curriculum

MATHEMATICS

INTRODUCTION

The Lincoln Public Schools has completed a K-8 curriculum content overview for mathematics as well as documents that specify the learning expectations for each strand of mathematics at each grade level. The work was influenced by the standards found in the Massachusetts Mathematics Curriculum Frameworks and the standards published by the National Council of Teachers of Mathematics. During the process we confirmed coherence across the grades and agreed to learning expectations that will be applied consistently at our two campuses. There is ongoing communication to maintain compatibility with the mathematics programs at the high schools our students typically attend---Bedford High School and Lincoln-Sudbury Regional High School. The current curriculum development focus in mathematics is the creation of common assessments for each grade level.

Our mathematics program has been organized so that instruction occurs in each mathematical strand at each grade with the exception of the algebra level where geometry and measurement receive limited attention. The order of topics within a grade may vary. Some topics lend themselves to concentrated work in a specific unit and other topics receive attention throughout the school year. The “Content Overview” includes the “Big Ideas” for each strand of mathematics. Each grade also has a link to a PDF document that provides the specific Learning Expectations.

K-8 CONTENT OVERVIEW FOR MATHEMATICS

Grade	Lincoln Campus and Hanscom Campus
Kindergarten Kindergarten Math Learning Expectations	Patterns, Relations and Algebra repeating patterns, focusing on AB patterns Number Sense and Operations numbers and numerals (reading, writing, naming) numbers, sets of numbers and quantities (counting, comparing, sequencing) Geometry properties of two-dimensional shapes location and position of objects Data, Statistics and Probability collection, interpretation and applications of simple data sets Measurement language and concepts of common measurable properties using non-standard units (recognizing, naming, comparing)
One First Grade Math Learning Expectations	Patterns, Relations and Algebra geometric and simple number patterns, focusing on AAB, ABC Number Sense and Operations money: names of coins (penny, nickel, dime and quarter and equivalences to 25¢); $1 bill conceptual understanding of addition and subtraction, several meanings (combining, how many more needed?) place value of base 10 system through tens Geometry symmetry and congruency of two-dimensional shapes Data, Statistics and Probability interpretation of explicit information on simple charts, tables, graphs and pictographs data gathering (e.g. recording, interviewing) Measurement introduction of standard measurement: inches, telling time to hour and half hour comparison of length and weight of two objects
Two Second Grade Math Learning Expectations	Patterns, Relations and Algebra sorting of shapes and figures by attributes number patterns that “grow” addition and subtraction equations with an unknown quantity Number Sense and Operations money: names of all denominations through $20 bill; equivalences to $5 conceptual understanding of subtraction (comparison, separation) conceptual understanding of unit fractions 1/2, 1/3, 1/4 place value of base 10 system through hundreds Geometry introduction to attributes of three-dimensional shapes shape translations (slides, flips, turns) Data, Statistics and Probability predictions and/or analysis based on simple charts, tables, graphs and pictographs organization and representation of gathered data Measurement properties of standard linear measurement concept of standard linear measurement (e.g. inch) & skills for simple linear measurement time: a.m./p.m. and five-minute interval
Three Third Grade Math Learning Expectations	Patterns, Relations and Algebra understanding of complex and multi-step number patterns equations in all 4 operations with an unknown generalization of rules for number patterns Number Sense and Operations efficiency with addition and subtraction showing understanding of numerical relationships conceptual understanding of multiplication and division non-unit fractions: addition and subtraction of common fractions using models place value of base 10 system through ten-thousands classes of numbers: odd, even, multiples, factors Geometry identification of similar figures introduction to angles: right, greater than, less than introduction to lines: parallel, perpendicular, intersecting classification of shapes using attributes Data, Statistics and Probability graphing skills: axes, scale, range introduction to probability introduction to permutations (combination problems) Measurement area and perimeter of regular polygons elapsed time
Four Fourth Grade Math Learning Expectations	Patterns, Relations and Algebra representation of a variable as an unknown quantity using a letter or symbol equations with variables in all portions (not just after = sign) Number Sense and Operations place value of base 10 system through millions introduction to decimals and connections to fractions---conceptual understanding, reading, writing mixed numbers, equivalent fractions and improper fractions efficiency with multiplication and division showing understanding of numerical relationships Geometry ordered pairs: graph, locate, identify on single coordinate grid two-dimensional and three-dimensional geometric shapes: classifying, distinguishing Data, Statistics and Probability probability and the likelihood of an event occurring combination problems Measurement area and perimeter of irregular polygons and triangles conversions within standard systems
Five Fifth Grade Math Learning Expectations	Patterns, Relations and Algebra rules for extending simple progressions substitution for variables to solve simple equations (“let x =___”) Number Sense and Operations fractions decimals percents number theory concepts: prime and composite numbers, prime factorization, common factors and order of operations, exponents, divisibility Geometry points on the 4 quadrant Cartesian plane (graphing, locating, identifying) triangles and quadrilaterals (identifying, describing and classifying) Data, Statistics and Probability circle graphs with simple fractional components central tendency: mean, median, mode, range, outlier Measurement angles: measuring, identifying, classifying volume and surface area of prisms
Six Sixth Grade Math Learning Expectations	Patterns, Relations and Algebra use of mathematical properties (i.e. Property of Equality) skills for solving 1- and 2-step equations with variables graphs representing relationships between variables Number Sense and Operations multiplication and division of fractions and mixed numbers operations involving integers exponents: squaring and cubing numbers up to 10 Geometry rotational symmetry specific properties of 3D shapes ordered pairs: points on a 4 quadrant graph (identify and graph) Data, Statistics and Probability stem and leaf plots circle graphs: computing fractional components tree diagrams to represent outcomes ratios to represent probability Measurement construction of angles, triangles and quadrilaterals relationship of radius, diameter, circumference, pi
Pre-Algebra Pre-Algebra Learning Expectations	Patterns, Relations and Algebra Slope Linear equations from verbal, tabular and graphical representations Graphing applications of formulas Number Sense and Operations Negative numbers--computation Introduction of irrational numbers Percents Geometry Perimeter, area, volume, surface area Identification of 3-D figures (prisms, pyramids) Pythagoream Theorem Data, Statistics and Probability Experimental and theoretical probability Venn Diagrams, box and whisker plots Combinations (basic: i.e. fundamental counting principle) Construction and analysis of graphs Measurement Scale factor Conversions
Algebra Algebra Learning Expectations	Patterns, Relations and Algebra Quadratic and exponential equations Polynomials (+, -, x, /) Inequalities---solve equations, graphs, etc. Linear equations Factoring polynomials Pythagorean Theorem Number Sense and Operations Properties: distributive, associative, commutative, inverse, identity Evaluative expressions with irrational numbers Negative exponents Geometry The Algebra level does not include instruction concentrated on the Geometry strand. Data, Statistics and Probability Multiplication counting principle Spreadsheets/statistics Probability without counting Measurement The Algebra level does not include instruction concentrated on the Measurement strand.

The faculty members responsible for facilitating curriculum work for Mathematics are Lincoln School Math Specilalist Kathy O'Connell, Hanscom Primary School Math Specialist Claire Groden, and Hanscom Middle School Math Specialist Carolyn Shannon.