### 5th Grade Math Worksheets (Grade 5 - For Ages 10 to 11)

These worksheets are designed for children age nine to ten years old. At this point, students have mastered basic decimal operations and are starting to get more comfortable with fractions and percentages. We have a really big mix here for you. This is the grade where math gets a good deal more difficult.

- Decimal Division | Answer Key - Decimal quotients to the thousandths place. We use the vertical division setup.
- Products of Decimals | Answer Key - This worksheet involves multiplying decimals to the thousandths by whole numbers.
- Fraction Addition | Answer Key - Add the fractions with the same denominators. Make sure to reduce the fraction as far as you can.
- Fraction Multiplication | Answer Key - Find the product of a whole number and a fraction.
- Triple Digit Multiple Tables | Answer Key - Multiply triple digit numbers in a rule or table format. This is some great practice.
- Quadruple Digit Multiplication Tables | Answer Key - When you are multiplying very large numbers you can some times lose your place within the problem.
- Tens and Hundreds Decimal Multiplication | Answer Key - These problems can take a good bit of time. So make sure to plan accordingly.
- Subtracting Fractions (Same Denominator) | Answer Key - Find the differences between two fractions that have a common denominator. A critical skill towards understanding fractions.
- Grade 5 Do Now Math Sheets - Aligned to the core curriculum at this grade level. Quick problems; great for warm-ups.
- Solving Expressions | Answer Key - This is one of your first steps towards using PEMDAS. The order of operations used is a key skill.
- Writing and Solving the Expression | Answer Key - This involves a bit of skilled thinking on the part of students. They first convert number sentences to expressions. Then they solve the expression.
- How Many Times More or Less? | Answer Key - Students think about comparisons in number sentences form.
- Standard and Exponential Forms | Answer Key - Convert exponential form to standard format and then change it back.
- Writing Integers in Expanded Form | Answer Key - Sometimes the expanded form can be very expanded. Just be forewarned.
- Compare the Decimals and Number Forms | Answer Key - This is a nice mix of comparing expanded, exponential, and standard format.
- Fill and Drill Equations | Answer Key - The variable for x will change, but not the equation. This is also referred to as "plugging and chugging" the variables into the equation.
- Hard Fraction Word Problems | Answer Key - We include a visual fraction problem at the bottom. This type of question is appearing more and more on standard exams.
- Resizing and Math (Scale) | Answer Key - All the word problems involving scaled geometry to some extent. These types of problems are tackled in the work place on a regular basis.
- Convert Units of Measurement | Answer Key - We start with basic metric unit conversion and then we progress into word problems.
- Volume of Rectangular Prisms | Answer Key - We get into basic volume problems with rectangles and then we move into analytical thinking within that concept.
- How Many Blocks Apart? Real World Coordinate | Answer Key - Determine how far different points are apart on coordinate grid system.

## What Do Students Learn in 5th Grade Math?

The first few years of studying math at school are foundational. During this time, students learn all the basic concepts of math and practice to create a strong basic comprehension that will allow them to excel at the subject.

There will be some more complex concepts that teachers will introduce students to in fifth grade while building on concepts taught before. They will experience quite a jump in the difficulty level and bear in mind that not every child will learn at the same pace. You need to be aware of the difference in their cognitive skills.

These are some concepts a student will learn in fifth grade.

**Numerical Expressions**

Since first grade, students have solved mathematical problems based on addition, subtraction, multiplication, and division. Students will take this a step ahead in fifth grade and start addressing numerical expressions. Students will learn to solve math statements requiring different numbers with one or more math symbols.

An example of a numerical expression would look like this…

11 + 10

or

11 + 9 - 6

To solve numerical expressions, children will also learn the concept of BODMAS, an abbreviation for (Bracket Open, Divide, Multiply, Add, Subtract). BODMAS is the standard order of operation in which students should solve any given math equation or problem. Students will effectively use this rule with every math question.

**Geometry**

In fifth grade, students will build on their understanding of basic geometry. They will learn to classify shapes into categories based on their properties such as number of side and angles. Students will learn how to find the area of different triangles and quadrilateral shapes.

By this point, students also have a sound understanding of 3D shapes. In fifth grade, children will also learn to calculate the volume of 3D shapes.

Help your children identify 3D shapes at home as well, and engage them in conversations about finding their volumes.

**Algebra**

As students in fifth grade, students will be introduced to the topic of algebra. Students will be required to utilize basic math skills like addition, subtraction, multiplication, and division, but this time, we are introducing alphabet into the mix.

From this concept, students will now develop the necessary understanding of the representation of patterns and other functions through words, tables, and graphs. In fifth grade, teachers help students learn and understand algebraic expressions and equations.

Students will be introduced to the basic concepts of algebra like exponent, expression, polynomial, and other parts of algebra. In addition to that, students will also learn how to find out the values in equations that have a missing term, which is usually referred to by some alphabet.

An example of an algebraic equation would look like this…

x + 12 = 6

or

2y – 8 = 5y

**Statistics and Probability**

The lesson plan for fifth grade students includes the topic of probability. Teach them probability through coin flips in class. This can be made more engaging by asking them school-related questions and asking about the chances of those events happening.

As part of their learning, students will also learn about statistics. For more interactive learning sessions, students will design their own surveys for which they will collect data. Students will then analyze the findings of the data.

Students will create bar graphs and learn to label them correctly to represent a set of data from their findings. These surveys and data could be based on the students and the school to In fifth grade, students will start to understand the real world more when they discuss the actual need for data and data collection.

**Ratios**

In previous classes, children have learned the concepts of fractions and decimals; in fifth grade, they will use this understanding to comprehend the concepts of ratios.

Students will learn to explain and see the relationship between two similar numbers and understand how to compare the two numbers. For example, they can use ratios as a way to compare the number of students in the class who enjoy math and the number of students in the class who enjoy English.

They will also connect the concept of ratios to their basic concepts like multiplication and division. Students will use various models like diagrams and number lines to make sense of these connections.

An example of a ratio would look like this...

10:7

**Unitary Method**

Studying the unitary method will help students to find the value of one unit from the given value of different units and vice versa. An example to demonstrate this is...

Josh went to the bakery and purchased 5 donuts for the price of $7.5. The next day Josh again went to the bakery and purchased 3 donuts. What is the price Josh would pay for 3 donuts?

It may seem complex, but the way to find the answer is rather simple.

If 5 donuts = $7.5

Divide $7.5 by 5

Single donut would cost $1.50.

Now you can multiply $1.50 by 3 to find the price of 3 donuts.

**Final Thoughts**

By the end of fifth grade, students should be able to understand how what they are taught in the classroom applies to the real world. They should be able to identify that unitary method can be used in grocery shopping, whereas ratios are a great way of representing the country’s opinion on politics.

These concepts can seem like they are too complicated However, the more students practice, the more solid their math foundation would be. The purpose of these early math classes is to help students build their basic math concepts.