Grade 6 Math Curriculum
Numerical Expressions and Factors
Numerical expressions are mathematical statements made with a combination of numbers and math operators. Sixth grade math students will learn to evaluate expressions and factorize numbers present in expressions.
Evaluating power and exponents
Power is a math expression that can be used in the place of repeated multiplication of the same number. Sixth graders will learn how to evaluate expressions involving the powers of numbers.
Perfect squares
Evaluating order of operations
Math expressions can have multiple terms and different operators, and they can be solved in different ways—but they can lead to incorrect results, if not solved in the right order. Here, 6th grade math students will learn to solve math operations in the right order.
Prime factorization of a number
Any number can be written as the multiple of two numbers, also known as factors. Bigger numbers will have multiple factors. The process of representing a number as a multiple of its prime factors is known as prime factorization.
Greatest common factor
Two numbers can have multiple common factors. Sixth graders need to learn how to find the greatest common factors, or GCF, as it will help them simplify math expressions.
Least common multiple
Two different numbers can have the same multiples. Students need to learn to know how to find the least common multiple, or LCM, as this concept is used to solve several math problems.
GCF and LCM
Fractions and Decimals
Fractions are numbers that exist between two whole numbers. They can be expressed as decimal numbers with the whole number part and the fractional part separated by a decimal point. Here, students will solve sixth grade math problems to understand the relationship between fractions and decimals.
Operation on fractions
Fractions are numbers that lie between two whole numbers. We can perform arithmetic operations on fractions, similar to how we do with whole numbers.
Operations on fractions using division of mixed fractions
Mixed fractions, or mixed numbers, are expressed as a combination of whole numbers and fractions. Students will solve math problems for sixth graders to get acquainted with operations on fractions.
Decimals, percents and fractions
Students will learn to express a quantity as a decimal, percent, or a fraction. They will also solve sixth grade math problems based on this concept.
Multiplying decimals
Sixth grade math students will learn different strategies that can be used to multiply decimal numbers easily.
Dividing decimals
The steps followed while dividing decimal numbers are similar to the steps followed for whole numbers. Students will understand the steps by solving math problems for sixth graders.
Ratio and Rates
A ratio is a comparison of quantities that have the same units. On the other hand, a rate is a comparison between two quantities that have different units. Students will learn how to represent rates and ratios and solve simple problems based on them.
Understanding ratios
A ratio is a relationship between two quantities showing the number of times one quantity is contained in the other. Sixth graders will learn to form ratios and solve questions based on them.
Equivalent ratios
Ratios, just like fractions, can be expressed in multiple ways using different combinations of numbers. The ratios that have the same value, despite having different numbers, are known as equivalent ratios.
Creating ratio tables
A ratio table helps students list down equivalent ratios. Here, 6th grade math students will learn to create a ratio table using different methods and use them to solve math problems.
Graphing ratio relationships
The relationship between two quantities, or ratios, can be graphed by plotting the data in the form of ordered pairs in a coordinate plane. Students will learn to use this concept to solve sixth grade math problems.
Unit rates
A rate is a ratio that compares two quantities having different units. A unit rate compares a quantity with one unit of another quantity. Students will learn some real-life instances where unit rates are used.
Converting measures
A single quantity can be measured using different units. Here, 6th graders will learn to convert quantities measured in one unit into another unit.
Percents
A percent is a number or ratio expressed as a fraction of 100. Students will learn various real-life applications of percents, and they will solve math problems based on the same concept.
Percents and fractions
Percents are fractions in which the denominator is 100. Students will learn to convert percents into fractions, and fractions into percents.
Comparing and ordering fractions, decimals and percents
Now that sixth grade math students know how to convert fractions, decimals, and percents interchangeably, they will learn to compare and order them by converting them into a common form.
Solving problems based on percent
Here, students will solve sixth grade math problems related to percents, which will enhance their understanding of percents.
Difference between percentage and percentile
Percent error
Algebraic Expressions and Properties
Algebraic expressions are mathematical statements made up of numbers, operators and unknown quantities known as variables. Students will learn how to express statements using algebraic expressions.
Algebraic expressions
Mathematical statements made up of numbers, operators, and variables are known as algebraic expressions.
Algebra symbols
Writing algebraic expression
Students learn how to write a given statement in the form of an algebraic expression. These math problems for sixth graders build their foundation to solve further difficult problems on the same topic.
Properties of addition and multiplication
Students will learn the properties of addition and multiplication that can be used to express statements as algebraic expressions.
The distributive property
The distributive property is a number property that can be used to simplify numerical and algebraic expressions.
Factoring expressions
Sixth graders will learn how to factorize algebraic expressions. This online math course gives students a clearer picture on how terms are grouped and in turn be factored.
Equations
Equations are mathematical formulas that state the equality between two expressions using the ‘equal to’ (=) sign. Here, 6th grade math students will be introduced to the various strategies used to solve equations.
Writing equations in one variable
Equations can be numerical or algebraic. Algebraic equations can have any number of variables. Students will start off by learning to work with equations in one variable.
Writing equations in two variables
Now that students are acquainted with algebraic equations, they will start writing equations that have two variables.
Area, Surface Area, and Volume
Area and volume are quantities used to describe the size of objects. We use the concept of area to measure the size of two-dimensional objects, and we use surface area and volume to measure the size of three-dimensional objects.
Parallelograms
Triangles
Parallelogram-Trapezoids-Kites
Square
Parallelograms
A parallelogram is a quadrilateral in which the opposite sides are equal and parallel. Students will learn the properties related to parallelograms and solve questions based on them.
Area of parallelogram
Triangles
A triangle is a simple polygon. It has three sides and three angles. Here, students will learn further properties of triangles and also learn how to calculate the area of a triangle.
Area of triangles
Parallelograms, trapezoids and kites
Quadrilaterals are polygons that have four sides. A few examples of quadrilaterals are: parallelograms, trapezoids and kites. Students will learn the properties of each of these quadrilaterals.
Trapezoids
Area of trapezoids and kite
Area of shapes
Three-dimensional figures
A three-dimensional figure can be defined as a solid figure or a shape that has three dimensions which are length, breadth and height. Students will learn about different types of three-dimensional figures and solve questions based on them.
Vertices faces edges
Prism
A prism is a three-dimensional shape comprising two congruent polygonal faces. Students will learn about different types of prisms and their properties.
Rectangular prisms
Triangular prisms
Cube
Surface area of a prism
Pyramids
A pyramid has a polygonal base and lateral triangular faces that join at a common point of intersection called the apex. Students will learn about different types of pyramids and their properties.
Square pyramid
Triangular pyramid
Surface area of a pyramid
Rectangular prisms
A rectangular prism, also known as a cuboid, is a three-dimensional shape made up of six rectangular faces. Sixth graders will learn the properties of rectangular prisms with the help of some real-life examples.
Volume of rectangular prisms
Integers, Number Lines, and the Coordinate Plane
Sixth graders are already familiar with whole numbers, decimals and fractions. Now, they will learn about a new set of numbers known as integers. They will also learn how integers are represented on the number line and the coordinate plane.
Integers
An integer is a number that can be written without a fractional component. So, integers include all negative numbers, zero, and all positive numbers that do not have a fractional part.
Properties of integers
Integers on a number line and their comparison
Sixth graders will learn the comparison of integers using a number line with the help of sixth grade math problems.
Comparison and the absolute value of rational numbers
Here, sixth graders will learn to compare rational numbers by considering their absolute values.
The coordinate plane
The coordinate plane is a two-dimensional plane formed by the intersection of the x-axis (horizontal axis) and y-axis (vertical axis). A coordinate plane can be used to represent data by plotting the ordered pairs.
Polygons in the coordinate plane
Sixth graders will learn to represent polygons on a coordinate plane by plotting the vertices in a coordinate plane and joining the adjacent vertices with line segments to form a polygon.
Finding distances between points
Inequalities
Inequalities are relations that make a comparison between numbers or mathematical expressions.
Properties of inequalities
Solving inequalities
Here, sixth grade math students will learn to solve inequalities using simple arithmetic operations.
Solving inequalities using different operations: Addition and Subtraction
Solving inequalities using different operations: Multiplication and Division
Statistical Measures
Statistics is a branch of math that deals with the collection, organization, analysis, interpretation, and presentation of data. Sixth grade students will be introduced to the basic concepts of statistics.
Introduction to statistics
Statistics is an area of study that interprets and analyzes the data collected. In the 6th grade math curriculum, students learn about basic statistical concepts.
Mean of data
The mean of a data set is the average value of the data set. Sixth graders will learn the formula used to calculate the mean of any data set and also solve fun problems on the same concept.
Average
Difference between average and mean
Central tendency
The central tendency of a data set is a single central value that can be used to describe the whole set. Students will learn different ways to calculate the central tendency of data sets.
Median of data
Mode of data
Difference between mean median and mode
Difference between mean and median
Measures of variation
Variation of a data set is described as the spread or the dispersion of data values against the central value. Students will learn the concept of range and more in this section.
Interquartile range
Data Displays
Now that sixth graders have learned to collect, organize, analyze, and interpret data, it is time for them to learn how to display data. Students will learn various ways to display data in an easily comprehensible manner.
Arranging the data
Students will learn different methods to arrange and display data. This will help them build organizational skills, an important skill in the sixth grade skills checklist.
Knowing histograms
Sixth grade math students will learn the most common method of representing data—histograms. A histogram looks similar to a bar graph but has different characteristics.
Drawing and distribution of data
Sixth graders will learn different types of data distribution with the help of some examples.
Make your child Math confident for life
Ace concepts of mathematics with personalized learning
Make your child Math confident for life
Ace concepts of mathematics with personalized learning
Helpful Resource for your Kids
Some of the benefits of solving grade 6 math worksheets are as follows: improved problem-solving, facilitates time management, interactive learning and revision of portions. Click the links below to download our free math worksheets.
Statistics is an important subject as it has applications in many fields including economics, finance, and so on. Hence, students start learning statistical concepts in detail starting from sixth grade.
Sixth graders are already aware of decimals, whole numbers, and fractions. But real-life math problems require the knowledge of a wider set of numbers, which include integers and rational numbers.
The math concepts discussed in 6th grade have a wide range of real-life applications. Ratios and rates are used to express relationships between quantities like speed, price per quantity, and so on. We use percents to express scores and discounts. We also use concepts like area and volume in geometry to solve math problems related to the physical world.
The three methods of calculating the central tendency of data sets are mean, median, and mode.
Knowing the volume of a shape can help us determine how much space a solid takes up. For example, we can calculate the number of boxes that can be stacked in a room by knowing the volume of the boxes and the volume or space available in the room. In some cases, it can also help us determine the amount of substance that can fit inside a shape—the space available inside a water bottle will tell us how much water can be filled in.