GRADE 6

 

Number and Operations

1.   Students compare and order fractions, decimals, and mixed numbers.  They solve problems involving 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 to show the relative sizes of two quantities and use proportions to solve problems

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, understanding it as the multiplication of both sides of an equation by a multiplicative inverse

1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips

2.   Students calculate and solve problems involving addition, subtraction, multiplication and division of rational numbers:

2.1 Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use

2.2 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations that use positive numbers and combinations of these operations

2.3 Determine the least common multiple and greatest common divisor of whole numbers.  Use them to solve problems with fractions

Understand the concepts and perform addition, subtraction, and simple multiplication of fractions

 

Algebra and Functions

1.   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 and apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions and justify each step in the process

2.   Students analyze and use tables, graphs, and rules to solve problems involving

      rates and proportions:

2.1 Demonstrate that rate in a measure of one quantity per unit value of another

3.   Students investigate geometric patterns and describe them algebraically.

4.   Students will represent relationships with tables, graphs in the coordinate plane, and verbal or symbolic rules.

 

Measurement and Geometry

1.   Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems:

1.1 Precisely describe, classify, and understand two- and three dimensional objects using their defining properties

1.2 Draw geometric objects with specified properties, such as side length or angle measures

1.3 Develop and use formulas to determine the circumference of circle, the areas of triangles, parallelograms, trapezoids, and circles, and develop strategies to find the areas of more complex shapes

1.4 Understand the meaning of ¹.  Know the formula for the circumference and area of a circle

1.5 Know common estimates of ¹ and use these to estimate and calculate the circumference and the area of circles; compare with actual measurements

1.6 Know and use the formulas for volume of a triangular prism and cylinder, compare and explain the similarity between these formulas and the formula for the volume of a rectangular solid

2.   Students identify and describe the properties of two-dimensional figures:

2.1 Identify angles as vertical, adjacent, complementary, and/or supplementary and provide descriptions of these terms

2.2 Use the properties of complementary and supplementary angles and the angles of a triangle to solve problems involving an unknown angle

2.3 Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume

2.4 Understand both metric and customary systems of measurement

2.5 Understand relationships among units and convert from one unit to another within the same system

 

Data Analysis and Probability

1.   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 can effect these computations of measures of central tendency

1.3 Understand how the inclusion or exclusion of outliers affect measures of central tendency

1.4 Know why a specific measure of central tendency (mean, median, mode) provides the most useful information in a given context

2.   Students use data samples of a population and describe the characteristics and limitations of the samples:

2.1 Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population

2.2 Analyze data displays and explain how the way a question was asked might have influenced the results obtained, and/or how the way the results were displayed might have influenced the conclusions reached      

2.3 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims

3.   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 Represent probabilities as fractions and decimals between 0 and 1, and percents between 0 and 100 and check that probabilities computed are reasonable; know that if P is the probability of an event, 1-P is the probability of the event not occurring

4.   Students will collect and organize data and display data with appropriate tables, charts, and graphs, including scatterplots and stem and leaf plots.

5.   Students will analyze data with respect to characteristics of frequency and distribution, including mode and range, and other measures of central tendency and make conclusions and recommendations based on data analysis.

 

Problem Solving and Mathematical Reasoning

1.   Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant 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.   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 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models to explain mathematical reasoning

2.4 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

2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy

2.6 Make precise calculations and check validity of the results from the context of the problem

3.   Students move beyond a particular problem by generalizing to other situations:

3.1 Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tool

3.2 Evaluate the reasonableness of the solution in the context of the original situation

3.3 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems

3.4 Develop generalizations of the results obtained and apply them in other circumstances

3.5 Use the language of mathematics to express mathematical ideas precisely