Sixth Grade - Math Indicators

Numbers, Number Sense and Operations 

Number and Number Systems
  • Decompose and recompose whole numbers using factors and exponents 
    (e.g., 32 = 2X2X2X2X2 = 25), and explain why "squared" means "second power" and "cubed" means "third power."
  • Find and use the prime factorization of composite numbers.  For example,
    a.  Use the prime factorization to recognize the greatest common factor (GCF);
    b.  Use the prime factorization to recognize the least common multiple (LCM);
    c.  Apply the prime factorization to solve problems and explain solutions.
  • Explain why a number is referred to as being "rational" and recognize that the expression a/b can mean a parts of size 1/b each, 
    a divided by b, or the ratio of a to b.
  • Describe what it means to find a specific percent of a number, using real-life examples.
  • Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100.
Meaning of Operations
  • Use the order of operations, including the use of exponents, decimals and rational numbers, to simplify numerical expressions.
  • Use simple expressions involving integers to represent and solve problems; e.g., if a running back loses 15 years on the first carry but gains 8 yards on the second carry, what is the net gain/loss?.
  • Represent multiplication and division situations involving fractions and decimals with models and visual representations; e.g., show with pattern blocks 2 2/3 / 1/6.
  • Give examples of how ratios are used to represent comparisons; e.g., part-to-part, part-to-whole, whole-to-part.
  • Recognize that a quotient may be larger than the dividend when the divisor is a fraction; e.g., 6 / 1/2 = 12.
Computation and Estimation
  • Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams mathematical reasoning.
  • Develop and analyze algorithms for computing with fractions and decimals, and demonstrate fluency in their use.
  • Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., 7/8 + 12/14 ~ 2 and 4.23 X 5.8 ~ 25.
  • Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions.
  • Determine the percent of a number and solve related problems; e.g., find the percent markdown if the original price was $140, and the sale price is $100.

Measurement 

Measurement Units Understand and describe the difference between surface area and volume.
Use Measurement Techniques & Tools
  • Use strategies to develop formulas for finding circumference and areas of circles, and to determine the area of sectors; e.g., 1/2 circle, 2/3 circle, 1/3 circle, 1/3 circle.
  • Estimate perimeter or circumference and area of circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by:
    a.  estimating lengths using string or links, areas using tiles or grid, and volumes using cubes;
    b.  measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms.
  • Determine which measure (perimeter, area, surface area, volume) matches the context for a problem situation, e.g., perimeter is the context for fencing a garden, surface area is the context for painting a room.
  • Understand the difference between perimeter and area, and demonstrate that two shapes may have the same perimeter, but different areas or may have the same area, but different perimeters.
  • Describe what happens to the perimeter and area of a two-dimensional shape when the measurements of the shape are changed, e.g., length of sides are doubled.

 

Geometry and Spatial Sense 

Characteristics & Properties
  • Classify and describe two-dimensional and three-dimensional geometric figures and objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides, congruent angles/sides.
  • Use standard language to define geometric vocabulary, vertex, face, altitude, diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate.
  • Use multiple classification criteria to classify triangles; e.g., right scalene triangle.
  • Identify and define relationships between planes; i.e., parallel, perpendicular and intersecting.
Spatial Relationships Predict and describe sizes, positions and orientations of two-dimensional shapes after transformations such as reflections, rotations, translations and dilations.
Transformations & Symmetry Draw similar figures that model proportional relationships; e.g., model similar figures with a 1 to 2 relationship by sketching two of the same figure, one with corresponding sides twice the length of the other.
Visualization & Geometric Models Build three-dimensional objects with cubes, and sketch the two-dimensional representations of each side; i.e., projection sets.

Patterns, Functions and Algebra 

Use Patterns, Relations & Functions
  • Represent and analyze patterns, rules and functions, using physical materials, tables and graphs.
  • Use words and symbols to describe numerical and geometric patterns, rules and functions.
Use Algebraic Representations
  • Recognize and generate equivalent forms of algebraic expressions, and explain how the commutative, associative and distributive properties can be used to generate equivalent forms; e.g., perimeter as 2(l + w) or 2l + 2w.
  • Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs.
  • Produce and interpret graphs that represent the relationship between two variables.
  • Evaluate simple expressions by replacing variables with given values, and use formulas in problem-solving situations.
Analyze Change
  • Identify and describe situations with constant or varying rates of change, and compare them.
  • Use technology to analyze change; e.g., use computer applications or graphing calculators to display and interpret rate of change.

Data Analysis and Probability 

Data Collection
  • Read, construct and interpret line graphs, circle graphs and histograms.
  • Select, create and use graphical representations that are appropriate for the type of data collected.
  • Compare representations of the same data in different types of graphs, such as a bar graph and circle graph.
Statistical Methods
  • Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range).
  • Describe the frequency distribution of a set of data, as shown in a histogram or frequency table, by general appearance or shape; e.g,, number of modes, middle of data, level of symmetry, outliers.
  • Make logical inferences from statistical data.
Probability Design an experiment to test a theoretical probability and explain how the results may vary.