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Sixth Grade Standards (k-12math.info)
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California 2007 U.S. Sixth grade (average age 11 years old ) mathematics standards:
Number Sense
1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages:
1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.
1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations ( a/b, a to b, a:b ).
1.3 Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/ 21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems.
1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.
2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:
2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.
2.2 Explain the meaning of multiplication and division of positive fractions and perform the calculations (e.g., 5/8 รท 15/16 = 5/8 x 16/15 = 2/3).
2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.
2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).
Algebra and Functions
1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results:
1.1 Write and solve one-step linear equations in one variable.
1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.
1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process.
1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator.
2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions:
2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).
2.2 Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.
2.3 Solve problems involving rates, average speed, distance, and time.
3.0 Students investigate geometric patterns and describe them algebraically:
3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1/2bh, C = pd - the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).
3.2 Express in symbolic form simple relationships arising from geometry.
Measurement and Geometry
1.0 Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems:
1.1 Understand the concept of a constant such as p; know the formulas for the circumference and area of a circle.
1.2 Know common estimates of π (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements.
1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base x height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.
2.0 Students identify and describe the properties of two-dimensional figures:
2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.
2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.
2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).
Statistics, Data Analysis, and Probability
1.0 Students compute and analyze statistical measurements for data sets:
1.1 Compute the range, mean, median, and mode of data sets.
1.2 Understand how additional data added to data sets may affect these computations of measures of central tendency.
1.3 Understand how the inclusion or exclusion of outliers affects measures of central tendency.
1.4 Know why a specific measure of central tendency (mean, median) provides the most useful information in a given context.
2.0 Students use data samples of a population and describe the characteristics and limitations of the samples:
2.1 Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample.
2.2 Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.
2.3 Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached.
2.4 Identify data that represent sampling errors and explain why the sample (and the display) might be biased.
2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.
3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events.
3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.
3.2 Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven).
3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1- P is the probability of an event n
3.4 Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.
3.5 Understand the difference between independent and dependent events.
Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
2.4 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.5 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.6 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.7 Make precise calculations and check the validity of the results from the context of the problem.
3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.
Florida 2007 U.S. Sixth grade mathematics standards:
MA.6.A.1.1 Explain and justify procedures for multiplying and dividing fractions and decimals.
MA.6.A.1.2 Multiply and divide fractions and decimals efficiently.
MA.6.A.1.3 Solve real-world problems involving multiplication and division of fractions and decimals
MA.6.A.2.1 Use reasoning about multiplication and division to solve ratio and rate problems.
MA.6.A.2.2 Interpret and compare ratios and rates
MA.6.A.3.1 Write and evaluate mathematical expressions that correspond to given situations.
MA.6.A.3.2 Write, solve, and graph one- and two- step linear equations and inequalities.
MA.6.A.3.3 Works backward with two-step function rules to undo expressions.
MA.6.A.3.4 Solve problems given a formula.
MA.6.A.3.5 Apply the Commutative, Associative, and Distributive Properties to show that two expressions are equivalent.
MA.6.A.3.6 Construct and analyze tables, graphs and equations to describe linear functions and other simple relations using both common language and algebraic notation
MA.6.G.4.1 Understand the concept of pi, know common estimates of pi (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles.
MA.6.G.4.2 Find the perimeters and areas of composite two-dimensional figures, including non-rectangular figures (such as semicircles) using various strategies.
MA.6.G.4.3 Determine a missing dimension of a plane figure or prism, given its area or volume and some of the dimensions, or determine the area or volume given the dimensions
MA.6.A.5.1 Use equivalent forms of fractions, decimals, and percents to solve problems.
MA.6.A.5.2 Compare and order fractions, decimals, and percents, including finding their approximate location on a number line.
MA.6.A.5.3 Estimate the results of computations with fractions, decimals, and percents and judge the reasonableness of the results.
MA.6.S.6.1 Determine the measures of central tendency (mean, median, and mode) and variability (range) for a given set of data.
MA.6.S.6.2 Select and analyze the measures of central tendency or variability to represent, describe, analyze and/or summarize a data set for the purposes of answering questions appropriately
Oregon 2007 U.S. Sixth grade mathematics standards:
It is essential that these standards be addressed in contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations.
6.1 Number and Operations: Develop an understanding of and fluency with multiplication and division of fractions and decimals.
6.1.1 Select and use appropriate strategies to estimate fraction and decimal products and quotients.
6.1.2 Use and analyze a variety of strategies, including models, for solving problems with multiplication and division of fractions.
6.1.3 Use and analyze a variety of strategies, including models, for solving problems with multiplication and division of decimals.
6.1.4 Develop fluency with efficient procedures for multiplying and dividing fractions and decimals and justify why the procedures work.
6.1.5 Apply the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions and justify why they work.
6.1.6 Apply the properties of operations to simplify calculations.
6.1.7 Use the relationship between common decimals and fractions to solve problems including problems involving measurement.
6.2 Number and Operations and Probability: Connect ratio, rate, and percent to multiplication and division.
6.2.1 Develop, analyze, and apply the meaning of ratio, rate, and percent to solve problems.
6.2.2 Determine decimal and percent equivalents for common fractions, including approximations.
6.2.3 Understand the meaning of probability and represent probabilities as ratios, decimals, and percents.
6.2.4 Determine simple probabilities, both experimental and theoretical.
6.2.5 Develop the concept of pi as the ratio of the circumference of a circle to its diameter.
6.3 Algebra: Write, interpret, and use mathematical expressions and equations.
6.3.1 Use order of operations to simplify expressions that may include exponents and grouping symbols.
6.3.2 Develop the meanings and uses of variables.
6.3.3 Write, evaluate, and use expressions and formulas to solve problems.
6.3.4 Identify and represent equivalent expressions (e.g., different ways to see a pattern).
6.3.5 Represent, analyze, and determine relationships and patterns using tables, graphs, words and when possible, symbols.
6.3.6 Recognize that the solutions of an equation are the values of the variables that make the equation true.
6.3.7 Solve one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation.
Australia , China , Japan, Malaysia, New Zealand, Singapore, and other APEC countries
Link to math standards for 9 APEC members (The Asia-Pacific Economic Cooperation group). Note that some have rather large PDF files.
