Grade 5 Math Curriculum
Place Value
Each digit in multi-digit numbers has a different value. The value of a digit is determined by its position in the number—known as place value. Using this free online math resource, students will revise the concept of place values and apply it to simplify math operations.
Place values with whole numbers
Whole numbers are often termed as counting numbers. The set of whole numbers include 0, 1, 2, 3, and so on. In the fifth grade math curriculum, students will learn the place value system in whole numbers which is covered in this section.
Pattern and power of 10
Power is an expression that represents the repeated multiplication of the same number. It is important for a fifth grade math student to learn the powers of 10, which will create a strong foundation for solving more challenging problems on powers. Students will observe some patterns among the powers of 10.
Place values with decimals
In decimal numbers, the whole number part and fractional part are separated by a decimal point. In math for 5th graders, students will learn the place value of digits in the fractional part and brush up their knowledge on the place value of digits in the whole number part.
Comparing decimals using place values
Comparison of numbers is one of the many applications of place value and is an important topic in the 5th grade math curriculum. Fifth grade students will learn to compare decimal numbers using the place value system. They also learn more about the symbols and terminologies involved.
Greater than symbol
Less than symbol
Equal sign
Greater than and less than symbol
Rounding off
Rounding off is a method of estimation that helps us save time while doing calculations. While rounding off a number, its value is changed to the nearest usable value. Mastering this 5th grade math concept helps students solve more challenging problems.
Numerical Expression
An expression is a mathematical statement containing numbers, variables, and operators. Fifth graders are already familiar with the basic operations of numbers. Here, they will learn to use number properties and order of operations to write and evaluate expressions.
Number properties
Number properties are a set of properties that can be used to simplify expressions. Fifth grade math students need to learn the number properties as it helps them evaluate math expression easily.
More on number properties
Here, 5th grade students will learn more about number properties. They will also solve fifth grade math problems related to number properties.
Numerical expressions
Numerical expressions represent mathematical statements using numbers and operators. Students will learn to write and evaluate numerical expressions with the help of number properties and order of operations.
Adding and subtracting decimals
Fifth grade students are already fluent in the addition and subtraction of whole numbers. Now, they will learn to perform the same operation with decimal numbers.
Estimation of Numbers
In the 5th grade math curriculum, students will learn to find the approximate result of math operations using the concept of estimation. They will also learn more about compatible numbers and the rounding of numbers.
Using models to add and subtract
Models are used to visualize decimals. In this section, fifth grade math students will use models to perform the addition and subtraction of numbers. Visually solving these fifth grade math problems will act as a solid base to directly solve addition and subtraction problems.
Adding and subtracting decimals
Students will learn to perform addition and subtraction of decimals and solve fifth grade math problems based on the same concept. They will also strengthen their understanding of place values and regrouping.
Multiply whole numbers
Repeated addition of the same number is termed multiplication. Fifth grade students are already fluent in the multiplication of whole numbers. But they need to revise multiplication facts before moving on to more complex topics.
Multiply whole numbers
Estimation of products of whole numbers
Multiplication of two-digit numbers
Whole Number
The set of whole numbers includes 0, 1, 2, and so on. They are also called counting numbers. In other words, natural numbers in addition to 0 are termed as whole numbers.
Multiply whole numbers
Fifth graders will revise the concept of multiplication of whole numbers before moving on to advanced topics. They will learn about multiplication by ones, tens, and hundreds.
More on multiplication
Here, students will solve fifth grade math problems related to multiplication and further hone their skills in multiplication.
Estimation of products of whole numbers
Fifth graders will learn to estimate the product of whole numbers to perform math operations quickly. Students learn about estimates so that they will be able to predict the approximate answer before performing the multiplication.
Multiplication of single-digit numbers
This section discusses the multiplication of a number with single-digit numbers. Practicing these math problems is a good way to practice and strengthen their understanding on multiplication.
Multiplication of two-digit numbers
Now that students are fluent in the multiplication of single-digit numbers, they will move on to the multiplication of two-digit numbers, in which a number is multiplied by two-digit numbers. They also learn about partial products.
Multiply decimals
Decimals are numbers whose whole number part and fractional part are separated by a decimal point. Here, 5th graders will learn to evaluate expressions involving the multiplication of decimals and multiplication of decimals with whole numbers.
Multiplication of decimals with powers of 10
Estimation of products of decimals and whole number
Using partial products to multiply decimals
Multiplying decimals
Using properties to multiply decimals
Multiplication of decimals with powers of 10
Multiplication of decimals with powers of 10 leads to some interesting results. Fifth grade students will learn how the decimal point shifts places when it is multiplied by a power of 10. They also revise the concepts of place values.
Multiplying decimals
Learn how to multiply decimal numbers with the help of some solved online fifth grade math problems.
Multiplication of decimals by models
Students learn about the 10 by 10 grid model that is used to represent decimals. Using models for the multiplication of decimals will help students understand the concept much better and also visualize the process.
Estimation of products of decimals and whole number
Here, fifth graders will learn to estimate the product of a decimal number and a whole number. They also revise concepts of rounding and compatible numbers.
Using partial products to multiply decimals
In this section, fifth grade students will learn to use the concept of partial products to multiply decimals. They will also refresh their concepts in place values.
Using properties to multiply decimals
Fifth graders will learn to multiply decimals using the properties of multiplication. This will help them evaluate expressions involving the multiplication of decimals easily.
Divide whole numbers
Division is the inverse operation of multiplication. Fifth grade math students will recollect what they have learned about the division of numbers in the fourth grade. They revise terminologies such as dividend, divisor, quotient, and remainder.
Division of two-digit numbers by single-digit number
Division by single-digit numbers
Divide multi-digit numbers by single-digit numbers
Estimating quotients
Students will learn to estimate the value of quotients without actually performing the division operation. Students learn how to use division facts and compatible numbers to estimate quotients.
Division of whole numbers
In this section, students will recollect the division of whole numbers and solve fifth grade math questions based on the same concept. They also learn how to relate division with multiplication.
Division of 1-digit, 2-digit and 3-digit numbers
This section is an extension of what students have already learned. Students will solve problems related to the division involving divisors of 1-digit, 2-digit, and 3-digit numbers.
Use partial quotients
Here, students will learn the concept of partial quotients and how they can be used for division operations. Visualizations of partial quotients using an area model make learning easier and faster.
Division of two-digit numbers by single-digit number
Here, students will recollect the division of two-digit numbers by single-digit numbers, and they will solve math problems for fifth graders on the same concept.
Division by single-digit numbers
Students will recollect the division of single-digit numbers and solve problems based on the same concept.
Divide multi-digit numbers by single-digit numbers
Students will recollect the division of multi-digit numbers by single-digit numbers and solve problems based on this concept.
Divide Decimals
Now that students are familiar with the division of whole numbers, it is time to move on to the division of decimal numbers. Students will solve fifth grade math problems to be acquainted with this operation.
Estimating quotients for decimals
Divide decimals by whole numbers
Division of decimals
Division of decimal numbers is carried out in a similar manner as compared to division of whole numbers. The only difference is the presence of a decimal point. 5th grade math students will also learn about shifting the decimal point as a result of the division operation.
Divide decimals using models
Dividing decimal numbers using models will help students gain a visual picture of the operation.
More on division of decimals
Here, fifth grade math students will solve problems related to division of decimals, which will enable students to improve their skills in division.
Estimating quotients for decimals
Students will learn to estimate the value of the quotient of a division operation without actually performing the operation with the help of compatible numbers.
Divide decimals by whole numbers
Students will learn to divide decimals by whole numbers. This part should be easy as they are already familiar with the process. They also revise concepts of regrouping.
Add and Subtract Fractions
Fractions are numbers that exist between whole numbers. Students will learn the addition and subtraction of fractions with the help of math problems for fifth graders.
Simplest form
Like fractions and unlike fractions
Mixed fractions
Estimate sums and differences of fractions
Simplest form
The simplest form of a fraction is a fraction which cannot be simplified further. In other words, the numerator and denominator of a fraction in the simplest form do not have any common factors other than 1.
Addition and subtraction of fractions
Students will learn the steps involved in the addition and subtraction of fractions.
Like fractions and unlike fractions
Like fractions are fractions that have the same denominator. On the other hand, unlike fractions are fractions that have different denominators.
Mixed fractions
Mixed fractions or mixed numbers are numbers that have a fractional part and a whole number part. Students will perform arithmetic operations on mixed fractions.
Estimate sums and differences in fractions
Here, fifth graders will learn to estimate the approximate value of the sum or difference of two fractions without actually performing the operation.
Multiply Fractions
Students can solve repetitive addition of the same fraction by replacing it with a multiplication operation. Fifth grade students will learn various strategies to carry out this arithmetic operation and solve questions based on the concept.
Comparing factors and products
Multiply fractions and whole numbers
Students will start with the easiest multiplication operation involving fractions—multiplication by whole numbers. They also learn about unit fractions. They will solve math problems for fifth graders based on the same topic.
Multiplication of fractions using models
Multiplication of fractions may seem a bit complicated compared to the multiplication of whole numbers. Models can be used to represent the numbers being multiplied. Students can perform the multiplication operation using models to make it easier.
Area of rectangles
The area of a rectangle is calculated by multiplying its length by its breadth. Students can learn to multiply two fractions using the same concept by finding the area of a rectangle whose length and breadth are fractional values.
Multiplication operation on mixed numbers
Here, students will learn to perform multiplication on mixed numbers and solve challenging questions based on the same topic. In these online math problems for fifth graders, students also learn more about improper fractions and area models.
Comparing factors and products
Students will learn the difference between factors and products. They learn how to compare the product of two fractions.
Dividing fractions
Fractions are closely related to the division operation. In fact, any division operation can be expressed as a fraction. By solving math problems for fifth graders, students will learn to divide a fraction by another number.
Fractions as divisions
Division including fractions and whole numbers
Fractions as divisions
Fraction is basically an alternate method for expressing division. Here, 5th graders will learn the relationship between fractions and division operations. They will understand the division process using visual aids such as models.
Mixed numbers as quotients
Mixed numbers have a whole number part and a fractional part. Students learn how to express improper fractions as mixed numbers. They also understand further with the help of area models and tape diagrams.
Division including fractions and whole numbers
Here, students will learn the division of fractions by whole numbers. They learn about unit fractions and also visualize the division process using tape diagrams and area models. Students will learn the steps involved in the operation and solve questions based on the concept.
Convert and display units
Units are standard quantities used to express the measure of physical quantities. A single quantity can be measured using more than one unit. Here, fifth grade math students will learn to convert a quantity measured in one unit into another unit.
Measurement of length in metric units
Measurement of length in customary units
Mass & Capacity in metric units
Weight & Capacity in customary units or Mass & Capacity in customary units
Creation & Interpretation of line plots
Measurement of length in metric units
Length is a property of a physical object. We measure the length of objects to describe size or distance. In this section, students will learn the metric units of length.
Inches to centimeter converter
Relation between inch and centimeter
Centimeter to inches converter
Measurement of length in customary units
The units of measurement mostly belong to either the metric system or the customary system of units. Here, fifth graders will learn the customary units used to measure length.
Metric units and customary units
The units of measurement are broadly classified into two groups: the metric system and the customary system. In the 5th grade math curriculum, students will learn about the units of measurement in both systems.
Mass and capacity in metric units
Mass and capacity are properties of an object. We measure mass and capacity using different units. Using these free online math courses, students will learn the metric units used to measure the mass and capacity of objects.
Convert and display units of measure
Fifth graders will learn to convert and display different units of measurement.
Mass and capacity in customary units
Students will learn the customary units used to measure the mass and capacity of objects. They will also solve fifth grade math problems related to the same concept.
Coordinate Plane
A coordinate plane is a two-dimensional plane formed by the intersection of two axes: the x-axis (horizontal axis) and the y-axis (vertical axis). By using these free online math courses, students will learn concepts related to the coordinate plane and its applications.
Polygons in the Coordinate Plane
Interpret line graphs
Analyzing graphs
Introduction to coordinate plane
The coordinate plane is two-dimensional and can be used to plot data. The location of each data point is described by its x-coordinate and y-coordinate.
Creation and interpretation of line plots
Students will learn to create and interpret line plots that display data values.
Graphing and plotting data in a coordinate plane
Fifth graders learn how to plot ordered pairs onto the coordinate plane and, in turn, learn how to graph data. This concept is important to master as this is the basic idea behind all types of graphs and acts as a vital skill in the fifth grade skills checklist.
Polygons in the coordinate plane
Students will learn to plot polygons on the coordinate plane using the coordinates of the vertices.
Interpret line graphs
Here, students will learn to interpret data from line graphs.
Analyzing graphs
Students will learn to analyze different types of graphs. This will get students accustomed to different methods of data representation.
Volume
The amount of space occupied by a three-dimensional object is known as its volume. As the size of the object increases, the volume occupied by it also increases. Fifth grade students will learn to find the volume of different types of solids.
Prism
Understand the concept of volume
The amount of space occupied by a solid body is the volume of the body. Here, students will learn how to calculate the volume of different figures. They will solve fifth grade math problems based on the same topic.
Difference between area and volume
Prism
Cube
Cuboid And cube
Rectangular prism
Rectangular prisms are three-dimensional figures that have six rectangular faces. Fifth grade students can learn more about these solids.
Volumes of right rectangular prisms
A solid that has six rectangular faces with congruent bases ia known as a rectangular prism. In right rectangular prisms, the sides and bases are perpendicular to each other. In the 5th grade math curriculum, students can learn about finding the volume of right rectangular prisms.
Volumes of rectangular prisms
Solids having six rectangular faces are termed as rectangular prisms. 5th grade students learn how to find the volume of rectangular prisms by solving problems.
Volumes of composites shapes
Composite shapes are three-dimensional shapes made up of a combination of different three-dimensional shapes. Here, students will learn to find the volume of composite shapes by finding the sum of the volume of the individual shapes.
Classifying triangles
Triangle is a polygon. It has three sides and three angles. Triangles can be classified based on two categories: sides and angles. Students will learn about different types of triangles in this section.
Triangle
Properties of triangle
Classification of triangles based on sides
Classification of triangles based on angles
Classify quadrilaterals by their angles and sides
Quadrilaterals and their properties
Types-Of-Quadrilaterals
Classify quadrilaterals by their angles and sides
Quadrilaterals and their properties
Triangle
A triangle is a polygon that has three sides and three angles. It is one of the most basic shapes in geometry. Here, 5th grade students will learn properties related to triangles and solve problems based on them.
Properties of triangle
Triangles have unique properties relating to the length of their sides and the measure of their angles.
Classification of triangles based on sides
Triangles can be classified into different categories based on the length of their sides. Fifth graders will learn properties related to each category of triangles.
Equilateral triangle
Isosceles triangle
Isosceles right triangle
Properties of isosceles triangle
Scalene triangle
Classification of triangles based on angles
Triangles can also be classified based on the measure of their angles. Students will learn the properties related to each type of these triangles.
Acute triangle
Obtuse triangle
Right triangle
Equiangular triangle
Classifying Quadrilaterals Based on Their Angles and Sides
Just like triangles, quadrilaterals can also be classified on the basis of the length of their sides and the measure of their angles. Students will learn about each type of quadrilateral and solve questions based on them.
Quadrilaterals and their properties
Quadrilaterals are shapes that have four sides. Quadrilaterals are divided into different types based on the length of their sides and the measure of their angles. Students will learn the properties associated with each type of quadrilateral.
Types of quadrilaterals
Quadrilaterals are two-dimensional shapes that have four sides and four angles. There are different types of quadrilaterals that can be classified based on the properties of their lengths or angle measures. Here, students will learn in detail about different types of quadrilaterals.
Trapezoid
Parallelogram
Rectangle
Rhombus
Square
Classify quadrilaterals by their angles and sides
Quadrilaterals are classified into different types based on the length of their sides and the measure of their angles. Fifth grade students will learn to classify quadrilaterals based on these properties.
Quadrilaterals and their properties
In this section, students will learn about different types of quadrilaterals and the unique properties associated with each type. They will also solve fifth grade math problems based on the same concept.
Helpful Resource for your Kids
Our grade 5 online math worksheets are sure to help your child cover all the important concepts and formulas in the grade 5 math syllabus. Click the link below to download the online math worksheets.
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Ace concepts of mathematics with personalized learning
Fifth grade students can improve their math skills by practicing lots of questions. Check out the free online classes offered by BYJU’S Math from the fifth grade math checklist.
The geometric concepts discussed in fifth grade are unit conversions, coordinate geometry, the volume of three-dimensional shapes, the classification of triangles, and the classification of quadrilaterals.
Triangles are classified based on the length of their sides and the measure of their angles.
Two-dimensional shapes don’t have volume as they don’t take up space in three dimensions. Volume is a property of three-dimensional shapes. We use both surface area and volume to describe the size of three-dimensional shapes, but we only use area and perimeter in the case of two-dimensional shapes.
Students will use fractions frequently to solve math problems in higher grades. Hence, it is important for a fifth grader to learn how to perform operations with fractions. The free online math courses by BYJU’S Math will help fifth grade students strengthen their conceptual understanding of fractions.