Grade 6 Math Checklist 6A Students can demonstrate knowledge and use of numbers and their many representations in a broad range of theoretical and practical settings. _____ Represent and compare place values through billions, using powers of 10. _____ Order, compare and graph integers. _____ Identify fractional pieces that have the same value but different shapes. _____ Compare and order fractions and decimals efficiently and find their approximate position on a number line. _____ Represent repeated factors using exponents. (a a a = a ) 6B Students can investigate, represent and solve problems using number facts, operations, and their properties, algorithms, and relationships. _____ Identify prime and composite numbers. _____ Write prime factorizations of numbers. _____ Determine the least common multiple and the greatest common factor. _____ Demonstrate the meaning of multiplications of fractions (e.g., ½ x 3 is 1/2 of a group of 3 objects. _____ Simplify simple arithmetic expressions with rational numbers using the order of operations. (2+(3x4)= ___ 2+12 = ___ _____ Recognize and use the inverse relationships of addition and subtraction, multiplication and division to simplify computations and solve problems. _____ Add and subtract fractions (students should use factoring to find common denominator) _____Solve multiplication number sentences and word problems with whole numbers and fractions and mixed numbers (with and without grouping), like or unlike denominators of 12 or less. 6C Students can compute and estimate using mental mathematics, paper-and-pencil methods, calculators, and computers. _____Select and use appropriate operations, methods and tools to compute or estimate using whole numbers with natural number exponents (not zero). _____ Decide which methods is needed for problems with whole numbers, familiar fractions and decimals. 6D Students can solve problems using comparison of quantities, ratios, proportions, and percents. _____ Solve number sentences and word problems using percents. _____ Demonstrate and explain the meaning of percents, including greater than 100 and less than 1. _____ Create and explain a pattern that shows a constant ratio. _____ Analyze situations to determine whether ratios are appropriate to solve problems. _____ Determine equivalent ratios. 7A Students can measure and compare quantities using appropriate units, instruments, and methods. _____ Measure any angle using a protractor or ruler. 7B Students can estimate measurements and determine acceptable levels of accuracy. _____ Estimate distance, weight, temperature, and elapsed time using reasonable units. 7C Students can select and use appropriate technology, instruments, and formulas to solve problems, interpret results, and communicate findings. _____ Select, use and justify an appropriate formula to find the area of triangles, parallelograms and trapezoids. _____ Select, use an appropriate formula or strategy to find the surface area and volume of rectangular and triangular prisms. _____ Calculate the surface area of a cube, rectangular prism and triangular prism. _____ Develop and use formulas for determining the circumference and area of circles. 8A Students can describe numerical relationships using variables and patterns. _____ Analyze arithmetic and geometric sequences of numbers. _____ Evaluate (solve) algebraic expressions for given values. (1+x = 3) _____ Express properties of numbers and operations using variables (commutative property is m+n=n+m) _____ Simplify algebraic expressions involving like(similar) terms. 8B Students can interpret and describe numerical relationships using tables, graphs, and symbols. _____ Graph simple inequalities on a number line. _____ Solve an equation and plot the points on a Cartesian plane. _____ Describe verbally, symbolically, and graphically, a simple relationship presented by a set of ordered pairs of numbers. 8C Students can solve problems using systems of numbers and their properties. _____ Identify and explain incorrect uses of the commutative, associative and distributive properties. _____ Identify and provide examples of the identity property of addition & multiplication _____ Identify and provide examples of inverse operations. _____ Explain why division by zero is undefined. 8D Students can use algebraic concepts and procedures to represent and solve problems. _____Create, model and solve algebraic equations using concrete materials. _____ Solve linear equations (with coefficients). 9A Students can demonstrate and apply geometric concepts involving points, lines, planes and space. _____ Plot and read ordered pairs of numbers in all 4 quadrants. _____ Describes sizes, positions, and orientations of shapes under transformations including dilations. _____ Perform simple constructions (equal segments, angle and segment bisectors, or perpendicular lines, inscribing a hexagon in a circle) with a compass and straightedge or mira. _____ Determine and described the relationship between pi, the diameter, the radius, and the circumference of a circle. _____ Determine the unknown angle measures using angle relationships and properties of a triangle or a quadrilateral. 9B Students can identify, describe, classify and compare relationships using points, lines, planes and solids. _____ Determine the relationships between the number of vertices or sides in a polygon, then number of diagonals, and the sum of its angles. _____ Solve problems that involve vertical, complementary and supplementary angles. _____ Analyze quadrilaterals for defining characteristics. _____ Create a 3-dimensional object from any 2-dimensional representation of the object, including multiple views, nets, or technological representations. 9C Students can construct convincing arguments and proofs to solve problems. _____ Make, test and prove your thinking (justify conjectures based on theory) about various quadrilateral and triangle relationships, including the triangle inequality. _____ Justify the relationship between vertical angles. _____ Justify the sum of the angles of a triangle is 180 degrees. 10A Students can organize, describe and make predictions from existing data. _____ Construct, read, interpret, infer, predict, draw conclusions, and evaluate data from various displays, including circle graphs _____ Recognize and explain misleading displays of data due to inappropriate intervals on a scale. 10B Students can formulate questions, design data collection methods, gather and analyze data and communicate findings. _____ Gather data by conducting simple simulations. _____ Collect data over time with or without technology. 10C Students can determine, describe, and apply the probabilities of events. _____ Record probabilities as fractions, decimals, or percents. _____ Demonstrate that the sum of all probabilities equals one. (4 out of 5 & 1 out of 5 = 1) _____ Determine from experiment and observation (empirical) probabilities from a set of data provided. _____ Discuss the effect of sample size (# of people or objects used in research) on the empirical (based on experiments and observation) probability compared to the theory (guess) probability. _____ List outcomes by a variety of methods. _____ Determine theoretical probabilities of simple events.
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