Place value and decimals
Students start the year working with bigger numbers and the digits to the right of a decimal point. They read, write, and compare numbers like 3.45 and 3.405, and round them to a given place.
What does a student learn in
This is the year math stretches past whole numbers into decimals and fractions that students can add, subtract, and multiply with confidence. Students start writing short expressions and equations to show how numbers relate, not just solving problems someone else set up. They also measure and sort shapes and read data from tables and graphs. By spring, students can add fractions with different denominators and multiply a decimal like 2.4 by 3.
- Decimals
- Fractions
- Expressions and equations
- Shapes and volume
- Graphs and data
Year at a glance
How the year usually goes. Every school and district set their own curriculum, so treat this as a guide, not official pacing.
- 1
- 2
Operations with whole numbers and decimals
Students multiply and divide larger numbers and add, subtract, multiply, and divide with decimals. Money problems and measurement problems become the everyday practice.
- 3
Fractions as numbers
Students add and subtract fractions with different bottom numbers, like 1/3 plus 1/4. They also multiply fractions and divide with unit fractions, often using recipes and rulers as the setup.
- 4
Expressions and the coordinate grid
Students write number sentences with parentheses and follow the order of operations. They also plot points on a grid with an x and y axis and use it to show patterns.
- 5
Shapes, volume, and measurement
Students sort shapes by their sides and angles and find the volume of boxes by counting unit cubes or using length times width times height. They also convert between units like inches and feet or grams and kilograms.
- 6
Data, graphs, and chance
Students make line plots and other graphs from measurements they collect, then find averages and describe what the data shows. They also talk about how likely different outcomes are.
Mastery Learning Standards
The required skills a student should display by the end of Grade 5.
K-8 Mathematics
K-8 Mathematics
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Numbers and Operations
Students work with whole numbers, fractions, and decimals together, adding, subtracting, multiplying, and dividing them to solve real problems. This is the foundation for most of fifth-grade math.
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Algebraic Concepts
Students write and solve math sentences that compare or balance quantities, like finding a missing value or deciding which side of an equation is larger. The focus is on expressing real relationships with numbers and symbols, not just calculating an answer.
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Geometry
Students sort and measure flat and solid shapes, like rectangles, triangles, and cubes, then describe what makes each one different using sides, angles, and faces.
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Measurement and Data
Students collect numbers, organize them into tables or graphs, and use basic measures like averages to describe what the data shows.
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Probability and Statistics
Students look at real data sets and start asking "how likely is that?" They organize results into graphs or tables and describe what the numbers show.
| Standard | Definition | Code |
|---|---|---|
| Numbers and Operations | Students work with whole numbers, fractions, and decimals together, adding, subtracting, multiplying, and dividing them to solve real problems. This is the foundation for most of fifth-grade math. | PA-MATH.K8.5.1 |
| Algebraic Concepts | Students write and solve math sentences that compare or balance quantities, like finding a missing value or deciding which side of an equation is larger. The focus is on expressing real relationships with numbers and symbols, not just calculating an answer. | PA-MATH.K8.5.2 |
| Geometry | Students sort and measure flat and solid shapes, like rectangles, triangles, and cubes, then describe what makes each one different using sides, angles, and faces. | PA-MATH.K8.5.3 |
| Measurement and Data | Students collect numbers, organize them into tables or graphs, and use basic measures like averages to describe what the data shows. | PA-MATH.K8.5.4 |
| Probability and Statistics | Students look at real data sets and start asking "how likely is that?" They organize results into graphs or tables and describe what the numbers show. | PA-MATH.K8.5.5 |
Assessments
The state tests students at this grade and subject take.
PSSA Mathematics (Grades 3-8)
PSSA Mathematics is the spring summative math test for grades 3 through 8, aligned to PA Core Math.
- When given:
- spring
- Frequency:
- annual
Common Questions
What math will students learn this year?
Students work with bigger whole numbers, decimals, and fractions, including adding and subtracting fractions with different bottom numbers. They also write simple expressions, measure shapes, and read graphs and tables. Multiplying and dividing get faster and more accurate.
How can I help with fractions at home?
Cook together and ask students to double a recipe or cut it in half. Measuring cups make fractions real. When a recipe needs 3/4 cup twice, ask how much that is in total before you pour.
What should students know about decimals by spring?
Students should read, write, and compare decimals to the hundredths place, like 0.45 and 0.4. Money and sports stats are the easiest way to practice. Ask which player has the higher batting average, or count change from a five-dollar bill.
How should I sequence the year?
Start with place value and whole-number operations so students have a strong base for decimals. Move into fraction addition and subtraction in the middle of the year, then multiplication and division of fractions. Save volume and the coordinate plane for the last stretch.
Which topics usually need the most reteaching?
Fraction operations with unlike denominators trip up the most students, especially subtraction. Decimal place value is the other common gap, since students confuse 0.5 and 0.05. Build in spiral review for both across the year.
My child says math is harder this year. Is that normal?
Yes. Fifth grade is the year fractions and decimals become a real workout, and the numbers get bigger. A few minutes of practice most nights helps more than a long session on the weekend.
What does mastery look like by the end of the year?
Students should add, subtract, multiply, and divide whole numbers and decimals with accuracy, and add and subtract fractions with unlike denominators. They should also find the volume of a box and plot points on a grid. Word problems should feel manageable, not mysterious.
How do I know if students are ready for sixth grade math?
Check whether students can solve a multi-step word problem with fractions or decimals and explain their thinking. If they can handle that and read a graph without help, sixth grade ratios and percents will land on solid ground.
What is a quick way to practice at home in ten minutes?
Pick one number skill and one real object. Use a measuring tape to find the volume of a cereal box, or use the grocery receipt to add decimals and check the total. Short and real beats long and abstract.