Mathematics

Mathematics 6 Course Description

In Grade 6, instructional time should focus on four critical areas:

  1. connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems;

  2. completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers;

  3. writing, interpreting, and using expressions and equations; and

  4. developing understanding of statistical thinking.

Academic Transition Mathematics 6 Course Description

Numbers and Operations

  • Divide, a fraction by a fraction. For example, (2/3) / (3/4) = 8/9.

  • Solve addition, subtraction, multiplication, and division problems with decimals.

  • Find the greatest common factor and/or the least common multiple of two numbers. For example, the least common multiple of two numbers. For example, the least common multiple of 6 and 8 is 24.

  • Locate negative numbers on number lines.

  • Compare negative numbers in real-word contexts. For example, -4F > -8F because -4F is warmer than -8F.

  • Pilot points in the coordinate plane using all four quadrants and answer questions about those points. For example, given a graph of the points. For example, given a graph of the points (-6, 4) and (2, 4), determine that the two points are 8 units apart.

  • Use ratio language (3 to 4, 3:4, ¾).

  • Find unit rates and use them to solve problems.

  • Find a percent of a quantity as a rate per 100 and use percentages to solve problems.

Geometry

  • Use formulas to find the area of triangles, trapezoids, and parallelograms.

  • Find the areas of polygons by breaking them into shapes with known area formulas. For example, the area of a pentagon shaped like “home plate” can be found by finding the area of a triangle and the area of a rectangle.

  • Find the volumes of right rectangular prisms. For example, a box with the dimensions 10 (3/4) cm × 8 (1/2) cm × 6 cm has a volume of 548 (1/4) cm3.

  • Represent prisms and pyramids using nets made of rectangles and triangles.

  • Find the surface areas of prisms.

Algebraic Concepts

  • Evaluate expressions with exponents. For example, 53 is the same as 5 × 5 × 5 or 125.

  • Write expressions using numbers and variables. For example, “three less than 5 times a number” is 5n– 3.

  • Evaluate expressions by substituting a number for a variable. For example, evaluate b2 – 5 when b = 4.

  • Use the distributive property to find equivalent expressions. For example, 2(x– 5) = 2x– 10.

  • Solve one‐step equations. For example,

  • 3x = 12 means that x = 4, or 5 + y = 17 means that y = 12.

  • Model real‐world situations with inequalities and show the solution using number lines. For example, model “the temperature in the freezer is always n colder than 32F” with the inequality t < 32.

  • Write equations using two variables. For example, “Jim is paid 8 dollars per hour” can be modeled with p = 8h.

  • Use tables, graphs, and equations to look at the relationship between variables.

Measurement, Data, and Probability

  • Display numerical data in dot plots, histograms, and box‐and‐whisker plots.

  • Compute mean, median, and mode to measure the “center” of a data set. Compute range, interquartile range, and mean absolute deviation to measure the variability of a data set.