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Core Content and Skills
Math Grade 6
2007-2008
BOE Approved

Unit I-Number Sense, Patterns, and Algebraic Think  Content   Skills  Problem Solving Strategy: Find a Pattern   Continue numerical patterns by describing and extending number patterns and sequences Describe the pattern match the pattern with its description Match the pattern with its description   Introduction to Algebra   Introduction to vocabulary - variable, constant, expression Distinguish between an expression and an equation Understand what an equations is. Determine if an equation is true or false Translate simple verbal expressions into algebraic expressions Find the variable of the equation that makes it true by using inverse operation to solve one and two step linear equations with one variable   Exponents Order of Operations   Simplify and evaluate expressions with exponents Use exponents to express numbers Use grouping symbols (parentheses) to clarify the intended order of operations Use order of operations rules to solve arithmetic problems. Substitute assigned values into variable expressions and evaluate using order of operations   Review Place Value Review rounding Review comparing Review ordering Estimating sums,differences, products, and quotients   Distinguish between rounding and estimating. Use zero trick for addition, subtraction, multiplication and division Use rounding to estimate sums, differences, products and quotients   Commutative Property of Addition and Multiplication Identity property of addition (Additive Identity is 0) Inverse property of addition and multiplication Associative Property of Addition and Subtraction Zero property of multiplication Distributive Property of multiplication over addition Identity property of multiplication (Multiplicative Identity is 1)   Analyze an equation to determine the number property. Use distributive property to solve multiplication equations mentally Define and identify the commutative and associative properties of addition and multiplication Define and identify the distributive property of multiplication over addition Define and identify the identity of addition and multiplication   Area of a rectangle   Determine the area of a rectangle and square   Five Step Problem Solving Process using graphic organizer   Understand the question by restating in their own words Analyze the Data by listing the important data below the problem Develop a plan Solve the problem Validate the answer by comparing it to the question and data provided

Unit II- Decimals  Content   Skills  Basic decimal concepts   Write numbers in decimal notation Represent decimal numbers using a grid model Round decimal numbers Compare and order decimals with and without number lines   Estimation of sums, differences, products, and quotients   Round numbers to the same place when estimating sums and differences, drop zeros after decimal Round to the leading digit, drop zeros after the decimal, then multiply leading digits and tack on any zeros. Round the divisor, change the quotient so it is compatible with the divisor, cancel zeros and divide using zero trick.   Addition and Subtraction of decimals Multiplication and Division of decimals   Solve algebra equations that involve adding and subtracting decimals Multiply a whole number by a decimal Divide a decimal number by a whole number Divide a decimal number by a decimal number   Introduction to Metric System and its relation to the decimal number system   Measure length with a metric unit Be familiar with prefixes milli, centi, kilo and symbols mm, km, cm and know the metric unit which is used to measure length, namely the meter Make effective use of the ruler for making measurements Relate metric units to customary units via approximations   scientific notation   Represent numbers in scientific notation Convert numbers in scientific notation to standard form Convert large numbers in standard form to scientific notation     Unit III- Statistics and Graphing  Content   Skills  Use of statistical methods and measures of central tendencies to display, describe and compare data Date representations include: bar graphs, line graphs, circle graphs, tally graphs, frequency charts, line plots, scatterplots and stem and leaf diagrams   Read numbers from different types of graphs Compare numbers within the same graph Identify common ways that a graph can suggest misleading information Determine if a scatterplot suggests a trend Organize data using tallies and frequency charts Make a single and double bar and line graph Organize large sets of data into stem and leaf diagrams Calculate the mean, median, mode and range for a given set of data Collect and organize simple data sets to answer questions Understand that a summary of data should include where the middle is and how much spread is around it Determine if an outlier affects the analysis of the data set Problem Solving: Analyzing a graph or chart

Unit IV - Patterns and Number theory  Content   Skills  Number Theory - divisibility, primes, composite, prime factorization, factors and multiples Basic fraction concepts Problem Solving:Venn Diagram Problem Solving: Draw a picture   Learn and memorize divisibility rules for 2, 3, 5, 6, 9 and 10 Learn the difference between prime and composite number Use factoring technique for factor lists Find the prime factorization of a number Find the least common multiple for two numbers Represent values between whole numbers as fractions Write a fraction in lowest terms Convert between improper and mixed numbers Convert between fractions and decimals Compare and order fractions Construct Venn diagrams to sort data

Customary Measurement  Content   Skills  Customary Units of Measurement for length, capacity, and weight   Identify customary units of capacity (cups, pints, quarts, and gallons) Identify equivalent customary units of capacity (cups to pints, pints to quarts, and quarts to gallons)     Unit V- Operations with Fractions  Content   Skills  Adding and subtracting fractions Adding and subtracting mixed numbers Multiplying fractions and mixed numbers Dividing fractions   Add and subtract fractions with unlike denominators Solve equations by adding and subtracting fractions Add and subtract mixed numbers Subtract a mixed number from a whole number Multiply whole numbers by fractions Multiply a fraction by another fraction (two methods) Divide a whole number by a fraction Divide a fraction by a fraction or a whole number

Unit VI - Ratio, Proportion and Percent  Content   Skills  Ratios Rates Proportion Unit Rate Problem Solving: Percent of a number, Percents Justify the reasonableness of answers using estimation (including rounding)   Express 2 quantities as a ratio 3 different ways Find ratios equal to a given ratio by relating fractional notation to a ratio Express 2 quantities with different units as a rate Solve simple proportions within context Test to see if 2 ratios form a proportion Solve proportions using cross products and algebra and unit rates Learn what similar figures are. Calculate the length of corresponding sides of similar triangles, using proportional reasoning Explore the concept of percent with 100 square grid paper Express a quantity as a percent Estimate percent Express percents as fraction and decimals Express fractions and decimals as percents Find a percent of a number by evaluating formulas for determining interest or discounts Find a whole when given a percent and a part Calculate the length of corresponding sides of similar triangles using proportional reasoning Evaluate formulas for given input values (speed = distance/time) Estimate a percent of quantity (0% to 100%) Justify the reasonableness of answers using estimation (including rounding)     Unit VI- Algebra- Solving Equations  Content   Skills  One step equations- solving for the unknown variable Algebraic expressions vs. equations   Translate two-step verbal expressions into algebraic expressions Translate simple verbal expressions into algebraic expressions Solve simple one-step equations using basic whole-number facts. Substitute assigned values into variable expressions and evaluate using order of operations Define and identify the inverse properties of addition and multiplication Solve and explain simple one step equations using inverse operations involving whole numbers

Unit VII Probability  Content   Skills  Introduction to probability Fairness   Find the probability of an event Develop the concept of sampling when collecting data from a population and decide the best method to collect data for a particular question. Calculate probability from geometric models Make tree diagrams Find the probability to a compound event Tell if a game is fair List possible outcomes for compound events Determine the probability of dependent events Determine the number of possible outcomes for a compound event by using the fundamental counting principle and use this to determine the probabilities of events when the outcomes have equal probability     Unit VIII - Geometry  Content   Skills  Units of measurement Area of polygons Circles Volume Congruent and similar figures Area of a sector of a circle Estimating Circumference, Area, and Volume Customary units of measure for capacity Problem Solving Strategy: Using a proportion to solve for an unknown   Find the perimeter of any geometric figure introduce customary measurement system to measuring length, weight and volume Converting between metric units of measurement Develop formulas and find the area of squares and rectangles Develop formulas and find the area of parallelograms Develop formulas and find the area of triangles Identify the parts of a circle Find the circumference of a circle Find the area of a circle Find and calculate the volume of a rectangular prisms and the area of irregular polygons Find the area of a sector of a circle Calculate the area of a sector of a circle, given the measure of the central angle of a circle and the radius of the circle. Calculate the length of corresponding sides of similar triangles using proportional reasoning Estimate the volume, area and circumference Evaluate formulas for given input values (circumference, area, volume)

Unit IX - Integers  Content   Skills  Integers and the coordinate plane Graphing on the coordinate plane Absolute Value Rational Numbers Number Lines   Learn what an integer is Order integers Learn what an opposite is Plot points on an coordinate plane or number line Read the coordinates of points on an coordinate plane Define absolute value and determine the absolute value of rational numbers (including positive and negative) Locate rational numbers on a number line (including positive and negative) Order rational numbers (including positive and negative) Calculate the area of basic polygons drawn on a coordinate plane( rectangles and shapes composed of rectangles having sides with integer lengths

Unit XI- Algebra  Content   Skills  Two step equations Inequalities   Solve and explain two-step equations involving whole numbers using inverse operations Translate two step verbal sentences into algebraic equations Use substitution to evaluate algebraic expressions(may include exponents of one, two, or three)     X- Operations with Integers  Content   Skills  Operations with Integers   Add and Subtract Integers Multiply and Divide Integers

XII- Compound Probability  Content   Skills  Number Sets and Probability Tree Diagrams The Counting Principle Permutations and Combinations Independent and Dependent Events

Survey Project  Content   Skills  Graphs- Single or Double Line Graph, Single or Double Bar Graph, Circle Graph or Pie Chart, Stem and Leaf, Frequency Table or Histogram, Tally Chart   Choose an appropriate display for the data collected. Design a survey Create a form to survey people with question or questions to be answered.