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Grade 5 Mathematics Content Whole Numbers Place Value through millions Read, write, compare, order, round numbers through millions Addition, subtraction, multiplication, division Basic Facts Addition with regrouping Subtraction across zeroes Division with and without remainders Estimating of sums, differences, products, and quotients Order of Operations Introduction to expanded notation Rounding of whole numbers and decimals Percent and Ratio Express a ratio Express ratio in different forms Understand that percent means part of means part of 100, and write percent as fractions and decimals Decimals Place value Order and compare Rounding decimals Estimating decimals Addition, subtraction, multiplication and division of decimals Interpreting the remainder Fraction Concepts and Operations Divisibility Prime Factors Least common multiple Greatest common factor Equivalent fractions and simplest form Mixed numbers and fractions Compare and Order fractions Recognize proper and improper fractions Convert Improper fractions to mixed numbers, and mixed numbers to improper fractions Reduce to simplest form Add and subtract fractions with like and unlike denominators Geometry Lines, rays, angles Congruence, similar figures, symmetry Identify and classify polygons and triangles by properties of their angles and sides Know that the sum of the interior angles of a triangle is 180 degrees Know that the sum of the interior angle of a quadrilateral is 180 degrees Calculate the perimeter of regular and irregular polygons Identify pairs of congruent and similar triangles Identify and draw lines of symmetry of basic geometric shapes Identify the ratio of corresponding sides of similar triangles Identify and plot points in the first quadrant Plot points to form basic geometric shapes Calculate perimeter of basic geometric shapes drawn on a coordinate plane Quadrilaterals, triangles, and solid figures Integers Solid figures – face, edge, vertex Measurement Customary length Customary metric Changing linear units Determine the tool and technique to measure with an appropriate level of precision: lengths and angles Measure and draw angles using a protractor Calculate elapsed time in hours and minutes Determine personal references for customary and metric units of length Statistics and Probability Collecting and organizing data Mean of a group of numbers Making a graph with a problem solving strategy Analyzing graphs such as bar, line, circle, and pictograph Graphing ordered pairs Formulate conclusions and make predictions from line graphs and histograms Algebra and Functions Define and use appropriate terminology when referring to constants, variables, and algebraic expressions Translate simple verbal expressions into algebraic expressions Substitute assigned values into variable expressions and evaluate using order of operations Evaluate the perimeter formula for given input values Create and explain patterns and algebraic relationships algebraically (e.g.: 2n (doubling)) Problem solving (Strategies used in all units) Make a table, model, graph or organized list Estimate or find exact answers Justify the reasonableness of estimates Draw conclusions Sequence information Choose the correct operation(s) Solve a simpler problem Write an equation Predict and test Find a pattern Draw a diagram New York State Education Department Learning Standard for Mathematics Students will understand the concepts of and become proficient with the skills of mathematics; communicate and reason mathematically; become problem solvers by using appropriate tools and strategies through the integrated study of number sense and operations, algebra, geometry, measurement, and statistics and probability. Content Strands Strand 1: Number Sense and Operations Definition Example Students will understand numbers, multiple ways of representing numbers, 1. Verbally count by 1’s to 20. relationships among numbers, and number systems; understand meanings 2. Solve proportions using equivalent fractions. of operations and procedures, and how they relate to one another; compute accurately and make reasonable estimates. Strand 2: Algebra Students will represent and analyze algebraically a wide variety of problem solving situations; perform algebraic procedures accurately; recognize, use, and represent patterns, relations, and functions algebraically. 1. Use a variety of manipulative materials to create patterns using attributes of color, size, or shape. 2. Solve simple one-step equations using basic whole number facts. Strand 3: Geometry Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes; identify and justify geometric relationships, formally and informally; apply transformations and symmetry to analyze problem solving situations; apply coordinate geometry to analyze problem solving situations. 1. Identify and appropriately name twodimensional shapes: circle, square, rectangle, and triangle (both regular and irregular). 2. Classify angles as acute, obtuse, right and straight. Strand 4: Measurement Students will determine what can be measured and how, using appropriate methods and formulas; use units to give meaning to measurements; understand that all measurement contains error and be able to determine its significance; develop strategies for estimating measurements. 1. Compare the length of two objects by representing each length with string or a paper strip. 2. Identify radius, diameter, chords, and central angles of a circle. Strand 5: Statistics and Probability Students will collect, organize, display, and analyze data; make predictions that are based upon data analysis; understand and apply concepts of probability. 1. Display data in bar graphs using concrete objects with intervals of one. 2. Calculate the mean for a given set of data and use it to describe a set of data. S:\Ci\MS Word\Math\New Parent Handouts 2005\Gd.2. Parent Handout.doc 1. Example for Primary Instruction. 2. Example for Intermediate Instruction.