Grade 6 Mathematics Content Estimate sums, differences, products and quotients Whole Number Applications Percent Addition, subtraction, multiplication, division Basic facts Properties: associative, commutative, distributive, identity, inverse and zero Estimation of sums, differences, products, quotients Addition with regrouping Subtraction across zeroes Division with and without remainders Order of operations Rounding Exponential notation Evaluate expressions with exponents Estimating Place value to trillions Change a decimal to a percent Change a fraction to a percent Find the percent of a number Estimate a percent of a quantity Decimals Customary and metric units of measure Perimeter and circumference Area of a triangle, rectangle, square, circle, and irregular polygons Capacity and volume of a rectangular prism Identify customary and metric units of capacity Identify equivalent units Estimate volume, area and circumference Order and compare decimals Estimating decimals Rounding decimals Addition, subtraction, multiplication and division of decimals Place value Decimal expressions and equations Interpreting the remainder Fraction Concepts and Operations Divisibility rules Prime factors Least common multiple Greatest common factor Equivalent fractions and simplest form Mixed numbers and fractions Compare and order fractions Change improper fractions to mixed numbers Change fractions to decimals and percents Multiplicative inverse (reciprocals) Addition, subtraction, multiplication and division of fractions and mixed numbers Algebra and Functions Identify, write and evaluate algebraic expressions with a variable Number patterns and functions Absolute value Rational Numbers Translate 2 step verbal expressions into algebraic expressions Use substitution to evaluate an expression Solve 2 step equations Measurement Statistics and Probability Collect, organize and display data Determine and justify the most appropriate graph to display a set of data (pictograph, bar graph, line graph, histogram, or circle graph) Find the range, mean, median and mode Construct Venn Diagrams Read and interpret graphs List possible outcomes for compound events Determine the probability of dependent events Use the Fundamental Counting Principle Geometry Calculate the length of corresponding sides of similar triangles using proportions Recognize similarity and congruence Classify polygons Recognize geometric figures Find the area of triangles and quadrilaterals Use strategies to find the area of regular and irregular polygons Find the volume of rectangular prisms Identify radius, diameter, chords and central angles of a circle Understand diameter and radius and circumference Find the area and circumference of a circle Find the area of a sector of a circle Identify and plot points in all four quadrants Calculate the area of basic polygons on a coordinate plane Ratio and Proportion Venn Diagrams Describe and compare 2 sets of data using ratios Write ratios and proportions Sample space Solve a proportion Identify the probability of certain events Conduct and predict outcomes of experiments Rate Solve proportions using equivalent fractions Integers Understand integers and rational numbers Compare and order rational numbers Additive inverse Addition and subtraction of integers on a number line Problem Solving (Strategies used in all units) Make a table, model, graph, or organized list Estimate or find exact answers Draw conclusions, sequence information Choose the correct operation(s), Find a pattern Write an equation 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.