## Grade 6 Mathematics

## OVERVIEW

How do mathematicians think, write, and speak? Find out in Grade 6 Mathematics, where students will experience new ways of solving problems through interactive and engaging activities. With a focus on hands-on learning and real-world application, students will be exposed to foundational concepts needed for higher-level math study, including integer operations, equations, and statistics.

## MAJOR TOPICS AND CONCEPTS

**MAJOR CONCEPTS**

**Segment One**

- Multiply and divide positive multi-digit numbers with decimals to the thousandths
- Solve multi-step, real-world problems involving any of the four operations with positive multi-digit decimals or positive fractions, including mixed numbers
- Compute products and quotients of positive fractions by positive fractions, including mixed numbers
- Rewrite positive rational numbers in different but equivalent forms, including fractions, terminating decimals, and percentages
- Define, plot, order, and compare rational numbers
- Represent and compare rational numbers that have opposite direction on a number line and explain the meaning of zero within a real-world context
- Find, interpret, and compare the absolute values of rational numbers as the distance from zero on a number line, given a mathematical or real-world context
- Define, plot, order, and compare rational numbers
- Evaluate positive rational numbers and integers with natural number exponents
- Rewrite the sum of two composite whole numbers having a common factor, as a common factor multiplied by the sum of two whole numbers
- Express composite whole numbers as a product of prime factors with natural number exponents
- Find the greatest common factor and least common multiple of two whole numbers given a mathematical or real-world context
- Add, subtract, multiply, and divide integers
- Translate written descriptions into algebraic expressions and translate algebraic expressions into written descriptions given a mathematical or real-world context
- Evaluate algebraic expressions using substitution and order of operations
- Apply the properties of operations to generate equivalent algebraic expressions with integer coefficients
- Determine which values make the equation or inequality true or false given an equation or inequality and a specified set of integer values
- Write and solve one-step equations in one variable using addition, subtraction, multiplication, and division within a mathematical or real-world context
- Translate a real-world written description into an algebraic inequality and represent the solution on a number line
- Add, subtract, multiply, and divide rational numbers (accelerated)
- Solve real-world problems involving any of the four operations with rational numbers (accelerated)
- Solve mathematical problems using multi-step order of operations with rational numbers including grouping symbols, whole-number exponents, and absolute value (accelerated)
- Apply properties of operations to add and subtract linear expressions with rational coefficients (accelerated)
- Determine whether two linear expressions are equivalent (accelerated)
- Write and solve one-step inequalities in one variable within a mathematical context and represent solutions algebraically or graphically (accelerated)

**Segment Two**

- Write and interpret ratios to show the relative sizes of two quantities given a real-world context
- Solve mathematical and real-world problems involving ratios, rates, and unit rates, including comparisons, mixtures, ratios of lengths and conversions within the same measurement system
- Determine a rate for a ratio of quantities with different units, and calculate and interpret the corresponding unit rate given a real-world context
- Generate or complete a two- or three-column table to display equivalent part-to-part ratios and part-to-part-to-whole ratios
- Apply ratio relationships to solve mathematical and real-world problems involving percentages using the relationship between two quantities
- Solve multi-step, real-world percent problems (accelerated)
- Apply ratios to solve real-world problems involving proportions (accelerated)
- Recognize and formulate a statistical question that would generate numerical data
- Find and interpret mean, median, mode, and range given a numerical data set within a real-world context
- Determine the minimum, the lower quartile, the median, the upper quartile, and the maximum given a box plot within a real-world context and use a summary of the data to describe the spread and distribution of the data
- Create box plots and histograms to represent sets of numerical data within real-world contexts
- Describe and interpret the spread and distribution of the data, including any symmetry, skewness, gaps, clusters, outliers, and the range given a histogram or line plot within a real-world context
- Determine and describe how changes in data values impact measures of center and variation given a real-world scenario
- Determine an appropriate measure of center or measure of variation to summarize numerical data, represented numerically or graphically, taking into consideration the context and any outliers (accelerated)
- Use the measure(s) of center and measure(s) of variability to make comparisons, interpret results, and draw conclusions about two populations given two numerical or graphical representations of data (accelerated)
- Use proportional relationships to make predictions about a population, given categorical data from a random sample (accelerated)
- Plot rational number ordered pairs in all four quadrants and on both axes and identify the x- or y-axis as the line of reflection when two ordered pairs have an opposite x- or y-coordinate
- Find distances between ordered pairs, limited to the same x-coordinate or the same y-coordinate, represented on the coordinate plane
- Solve mathematical and real-world problems by plotting points on a coordinate plane, including finding the perimeter or area of a rectangle
- Derive a formula for the area of a right triangle using a rectangle and apply the formula to find the area of a triangle
- Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles
- Apply formulas to find the areas of trapezoids, parallelograms, and rhombi (accelerated)
- Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals (accelerated)
- Find the surface area of right rectangular prisms and right rectangular pyramids using the figure’s net given a mathematical or real-world context
- Solve mathematical and real-world problems involving the volume of right rectangular prisms with positive rational number edge lengths
- Determine the sample space for a simple experiment (accelerated)
- Find the theoretical probability of an event related to a simple experiment (accelerated)
- Interpret the likelihood of a chance event occurring and compare the probabilities of chance events (accelerated)
- Find experimental probabilities and compare them to theoretical probabilities (accelerated)

## Fee Details

Progam | Regular | Advanced |

Fee Component | Course Fee | |

Amount (USD) | $ 450 | $ 475 |

Description | To be paid by the student at the time of Enrollment. |

## Grade Level

## Grade 6

## Duration

## Annual

## Requirements

- Scientific Calculator
- Unity Web Player