6th grade math

Program of study for 6th grade

The CCSS core curriculum for 6th grade covers a range of categories, including:

• Number
  Students reinforce their understanding of place value, including whole numbers up to millions, decimals, and negative numbers. They work with operations such as addition, subtraction, multiplication, and division of whole numbers and decimals. Students develop their understanding of fractions, decimals, and percentages. They work on operations with fractions, including simplification and finding equivalent fractions. They convert between fractions, decimals, and percentages and solve problems involving percentages.

• Algebra
  Students are introduced to algebraic concepts. They learn about algebraic notation, expressions, and equations. They solve simple linear equations and work with formulas and functions. They explore patterns and relationships and use algebraic methods to solve problems.

• Ratio and proportion
  Students explore ratio and proportion, including ratio notation, simplification, and comparison. They solve problems involving direct and indirect proportion and apply proportional reasoning in various contexts.

• Geometry & measures
  Students study the properties of geometric shapes, including angles, triangles, quadrilaterals, and circles. They learn about transformations such as reflections, rotations, and translations. They explore properties of 2D and 3D shapes and work with coordinates in the Cartesian plane.

• Probability
  Students learn about probability, including theoretical and experimental probability. They calculate probabilities, explore the concept of sample space, and solve problems involving simple and compound events.

• Statistics
  Students develop skills in handling data, including data collection, representation, and interpretation. They construct and interpret graphs and charts, calculate measures of central tendency, and understand basic concepts of probability.

In addition to these specific topics, students will also develop their fluency with mathematical concepts and their ability to solve mathematical problems. They will be able to use mathematical reasoning to solve problems in other areas of their lives, such as science, technology, and engineering.

• Order positive integers
  
  Select the set of positive integers that are in ascending order
• Order negative integers
  
  Arrange negative integers in ascending order from smallest to largest
• Arrange integers ascending
  
  Choose the set of positive and negative integers that are in correct ascending order
• Identify unit fractions
  
  Identify the fractions that are unit fractions, or will simplify to unit fractions
• Identify improper fractions
  
  Identify the fraction or fractions that are improper fractions
• Identify mixed fractions
  
  Identify the fraction or fractions that are mixed fractions
• Identify equivalent fractions
  
  Identify the pairs of fractions that are equivalent
• Calculate fractions of amounts
  
  Calculate fractions of quantities, e.g. one third of 12 grams, etc.
• Add decimals
  
  Add decimals by first aligning the decimal points of each number
• Subtract decimals
  
  Subtract decimals by first aligning the decimal points
• Multiply decimals
  
  Multiply decimals by initially removing the decimal point
• Divide decimals by integers
  
  Divide decimal numbers by integers
• Divide integers by decimals
  
  Divide integer values by decimal numbers
• Divide decimals by decimals
  
  Divide decimals by decimals
• Identify square numbers
  
  Identify the square numbers in each of the given groups of integers
• Lowest common multiples
  
  Identify the lowest common multiple (LCM) of 2 numbers
• Round numbers: nearest 10
  
  Round each of the given numbers to the nearest 10
• Round numbers: nearest 100
  
  Round each given number to the nearest 100
• Round numbers: nearest 1000
  
  Round each of the given numbers to the nearest 1000
• Round decimals: nearest integer
  
  Round each of the given decimals to the nearest whole number (integer)
• Add fractions: common denominator
  
  Add fractions with a common denominator
• Add fractions: scale denominator
  
  Add fractions by scaling up the fraction with the smaller denominator; simplify answers where possible
• Add fractions using LCD
  
  Add fractions by finding the lowest common denominator (LCD); simplify your answers where possible
• Convert exponents to expanded form
  
  Convert between base with exponent and expanded form e.g. 3³ <=> 3 x 3 x 3
• Find percentages: multiples of 10
  
  Find a percentage using multiples of 10
• Multiply decimals by 10 100 1000
  
  Multiply by powers of 10 up to 1000 by moving the digits the correct number of columns to the left
• Divide decimals by 10 100 1000
  
  Divide by powers of 10 up to 1000 by moving the digits the correct number of columns to the right
• Identify factors
  
  Identify the correct set of factors for numbers up to 50
• Highest common factor
  
  Identify the Highest Common Factor (HCF) for the given sets of numbers
• Subtract fractions: common denominator
  
  Subtract fractions which share a common denominator
• Subtract fractions: scale denominator
  
  Subtract fractions by scaling up the fraction with the smaller denominator
• Subtract fractions: LCD
  
  Subtract fractions by finding the lowest common denominator (LCD) of the two fractions
• Prime numbers
  
  Identify the prime number or numbers in each of the given lists
• Positive decimals
  
  Choose the set of positive decimals that are in ascending order
• Positive fractions: ascending order
  
  Arrange these sets of positive fractions in ascending order
• Decimals to fractions
  
  Convert terminating decimals to their equivalent, simplified fractions
• Fractions to decimals
  
  Convert fractions to their equivalent terminating decimals
• Multiply simple fractions
  
  Multiply pairs of simple fractions and simplify your answers where possible
• Multiply fractions with cancelling
  
  Multiply fractions by cross cancelling numbers first
• Fractions of amounts
  
  Find fractions of amounts by first dividing by the fraction denominator then multiplying by the numerator
• Percentages to fractions
  
  Identify the correct, simplified fraction for each of the given percentages
• Percentages to decimals
  
  Identify the correct decimal for each of the given percentages
• Fractions to percentages
  
  Identify the correct percentage for each of the given fractions
• Fractions and percentages
  
  Compare by converting both fractions and percentages to decimals; select the larger decimal
• Divide fractions
  
  Divide fractions by flipping one of the fractions (get the reciprocal of the fraction) and multiplying them

• Next term
  
  For each given arithmetic sequence, find the next term
• Find the rule
  
  For each arithmetic or geometric sequence find the rule to extend the sequence
• Find term from rule
  
  Find the specified term given the first term and the rule
• Two positive integer variables
  
  Calculate the value of J by substituting in the given positive integer values for the 2 variables k and m
• Coordinates of a point
  
  In each instance identify the correct coordinates for the point on the graph
• Plotting coordinates
  
  Take the plotted points and the additional point coordinates to identify the polygon that is formed
• Perimeter: squares
  
  Form an expression for the perimeter of each of the given squares in terms of x
• Perimeter: rectangles
  
  Form an expression for the perimeter of each of the rectangles in terms of x and y
• Add like terms
  
  Simplify expressions by adding algebraic like terms such as a + a or b² + 3b² or 5c³ + 3c³
• Subtract like terms
  
  Simplify expressions by subtracting quantities of like terms such as 5x - 3x or 13x² - 5x²
• Add and subtract like terms
  
  Simplify expressions by adding and subtracting like terms such as 5x - 3x + 6x
• Add & subtract unlike terms
  
  Simplify expressions by adding and subtracting unlike terms e.g. a + a - b or 2x - 3y + 5x
• Identify like & unlike terms
  
  Decide whether each expression consists of like terms or unlike terms
• Count terms in expressions
  
  Count the number of terms in each of the given expressions
• Interpret algebraic notation
  
  For each expression, convert between algebraic notation and expanded form e.g. 3c = c + c + c
• Match expressions to descriptions
  
  Match simple algebraic expressions to the correct word description of the expression
• Multiply like terms
  
  Simplify expressions by multiplying like terms with no exponents to give answers raised to a power
• Multiply unlike terms
  
  Simplify expressions by multiplying quantities of unlike terms with no exponents e.g. 2b x 3c
• Terms on one side, one-step equations
  
  In each instance use simple algebraic methods to solve for the given variable in these one-step equations
• Terms on one side, two-step equations
  
  For each two-step equation use algebraic methods to solve for the given variable

• Convert mm into cm
  
  Convert lengths given in millimeters (mm) to centimeters (cm) by dividing the value by 10
• Convert cm to m
  
  Convert lengths given in centimeters (cm) into meters (m) by dividing the value by 100
• Convert m to km
  
  Convert distances given in meters (m) into kilometers (km) by dividing the value by 1000
• Convert km to m
  
  Convert distances given in kilometers (km) into meters (m) by multiplying by 1000
• Convert m to cm
  
  Convert lengths given in meters (m) into centimeters (cm) by multiplying by 100
• Convert cm to mm
  
  Convert lengths given in centimeters (cm) into millimeters (mm) by multiplying by 10
• Express quantities as ratios
  
  Express each of the sets of quantities as a part to part ratio, simplified if possible
• Ratio in its simplest form
  
  Use division to express each ratio in its simplest form
• Equivalent ratios
  
  Identify the ratios that are equivalent e.g. 1:2 and 3:6
• Convert grams to milligrams
  
  Convert masses given in grams (g) to milligrams (mg) by multiplying the value by 1000
• Convert kilograms to grams
  
  Convert masses given in kilograms (kg) to grams (g) by multiplying the value by 1000
• Convert tonnes to kilograms
  
  Convert masses given in tonnes (t) into kilograms (kg) by multiplying by 1000
• Convert cm³ or ml to liters (L)
  
  Convert volumes given in cubic centimeters (cm³) or milliliters (ml) to liters (L) by multiplying by 1000
• Convert liters to milliliters
  
  Convert volumes given in liters (L) into milliliters (ml) by multiplying by 1000
• Convert liters to cm³
  
  Convert liters (L) to cubic centimeters (cm³) by multiplying by 1000
• Share a quantity into parts
  
  Add up the parts and divide the quantity by the total number of parts to get the different shares

• Count edges of 3D shapes
  
  Work out the total number of edges for each of the given solids
• Count vertices of 3D shapes
  
  Work out the total number of vertices for each of the given solids
• Count faces of 3D shapes
  
  Work out the total number of faces for each of the given solids
• Perimeter of rectangles
  
  Use the formula P=2(L+W) to calculate the perimeters of the given rectangles
• Perimeter of triangles
  
  Use the formula P = 3L to calculate the perimeters of each of the equilateral triangles
• Perimeter of parallelograms
  
  Use the formula Perimeter = 2(Base + Side) to calculate the perimeters of the given parallelograms
• Perimeter of trapezoids
  
  Calculate the perimeters of the given trapezoids by adding the lengths of all its sides
• Perimeter of compound shapes
  
  Calculate the perimeters of the given compound shapes constructed from parallelograms
• Identify the quadrilateral
  
  Use the given properties to identify the quadrilateral
• Parts of the circle 1
  
  Identify the following parts of a circle: radius, diameter, circumference; calculate radius and diameter
• Lines of symmetry: quadrilaterals
  
  How many lines of symmetry does each of the given shapes have?
• Identify types of triangle
  
  Using standard conventions identify isosceles, equilateral, right-angle and scalene triangles
• Angles on a straight line
  
  Use the angles on a straight line rule to find the missing angles
• Angles around a point
  
  Use the angles around a point rule to find the missing angles
• Angles in a triangle
  
  Use the fact that angles within a triangle sum to 180° to find the missing angles
• Area of rectangles
  
  Calculate the areas of the given rectangles using the formula area = length x height, A = L x W
• Area of triangles
  
  Use the formula area = ½ x base x height to calculate the areas of the given equilateral triangles
• Area of parallelograms
  
  Calculate the areas of the given parallelograms
• Area of compound shapes
  
  Calculate the areas of the given compound shapes constructed from parallelograms to 2 d.p.
• Calculate the volume of cuboids
  
  Use the standard formula (length x width x height) to calculate the volume of cuboids

• How likely is the event?
  
  Decide whether each of the given events is likely, unlikely, certain or impossible
• Standard events
  
  For each scenario work out the probability of the outcome as a fraction

• Calculate the mean
  
  Calculate the mean for each set of positive integers
• Calculate mean: include negative integers
  
  Calculate the mean of each set of both positive and negative integers
• Match bar charts to data
  
  Select the data that is correctly represented in each of the bar charts
• Read bar chart values
  
  Read off correct values from each bar chart
• Match data to frequency table
  
  In each instance decide whether the frequency table correctly matches the given raw data
• Match vertical line chart to data
  
  In each instance decide whether the given vertical line chart matches the frequency table data
• Pictograms: interpret data
  
  For each of the given pictograms identify the number of people who like different fruit