Place value and decimals
Students extend place value to the right of the decimal point. They read, write, and compare decimals to the thousandths, and they multiply and divide whole numbers by 10, 100, and 1,000.
What does a student learn in
This is the year math moves from whole numbers into decimals and fractions as real quantities. Students add and subtract fractions with unlike denominators, multiply and divide with decimals to the hundredths, and start to see how place value shifts when you multiply or divide by ten. Word problems get longer, and students learn to write expressions that match the steps they took. By spring, they can solve a multi-step problem with fractions and explain the reasoning behind each move.
- Fractions
- Decimals
- Place value
- Multi-step word problems
- Volume
- Coordinate grids
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 larger numbers and divide with two-digit divisors. They also add, subtract, multiply, and divide decimals using money and measurement problems from daily life.
- 3
Adding and subtracting fractions
Students add and subtract fractions with unlike denominators, including mixed numbers. They use these skills in recipes, rulers, and other situations where parts of a whole show up.
- 4
Multiplying and dividing fractions
Students multiply fractions and divide whole numbers by unit fractions. They learn what it means to take a fraction of a fraction and how that connects to area.
- 5
Measurement, graphs, and volume
Students convert between units like inches and feet or grams and kilograms. They read line plots, and they find the volume of boxes by counting and multiplying unit cubes.
- 6
Shapes and the coordinate plane
Students plot points on a coordinate grid and use it to solve problems. They also sort two-dimensional shapes by their properties, such as which quadrilaterals share the same features.
Mastery Learning Standards
The required skills a student should display by the end of Grade 5.
Standards for Mathematical Practice
Standards for Mathematical Practice
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Make Sense of Problems
Students read a math problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work.
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Reason Abstractly
Students take a word problem apart to work with the numbers, then put the numbers back into the story to check that the answer makes sense in real life.
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Construct Arguments
Students explain why their math answer is correct, using examples or logic to back it up. They also listen to a classmate's reasoning and say specifically what works or what doesn't.
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Model with Mathematics
Students use math to make sense of real situations: drawing a diagram, writing an equation, or reading a graph to figure out an answer that actually matters outside of school.
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Use Tools Strategically
Students choose the right tool for the math in front of them: a calculator for large numbers, pencil and paper for working something out by hand, or a quick estimate to check if an answer makes sense.
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Attend to Precision
Students choose words and units carefully when solving problems, like labeling an answer "miles per hour" instead of just "miles." Exact language and correct calculations matter as much as getting the right number.
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Use Structure
Students notice patterns and internal rules in numbers, shapes, and equations, then use those patterns as shortcuts to solve problems. Recognizing that 8 x 7 is the same as 7 x 8 is one example.
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Express Regularity
Students notice when the same steps keep appearing in a problem and use that pattern as a shortcut or rule. Instead of starting from scratch each time, they ask why the pattern works and apply it to new problems.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students read a math problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work. | IL-MATH.MP.5.1 |
| Reason Abstractly | Students take a word problem apart to work with the numbers, then put the numbers back into the story to check that the answer makes sense in real life. | IL-MATH.MP.5.2 |
| Construct Arguments | Students explain why their math answer is correct, using examples or logic to back it up. They also listen to a classmate's reasoning and say specifically what works or what doesn't. | IL-MATH.MP.5.3 |
| Model with Mathematics | Students use math to make sense of real situations: drawing a diagram, writing an equation, or reading a graph to figure out an answer that actually matters outside of school. | IL-MATH.MP.5.4 |
| Use Tools Strategically | Students choose the right tool for the math in front of them: a calculator for large numbers, pencil and paper for working something out by hand, or a quick estimate to check if an answer makes sense. | IL-MATH.MP.5.5 |
| Attend to Precision | Students choose words and units carefully when solving problems, like labeling an answer "miles per hour" instead of just "miles." Exact language and correct calculations matter as much as getting the right number. | IL-MATH.MP.5.6 |
| Use Structure | Students notice patterns and internal rules in numbers, shapes, and equations, then use those patterns as shortcuts to solve problems. Recognizing that 8 x 7 is the same as 7 x 8 is one example. | IL-MATH.MP.5.7 |
| Express Regularity | Students notice when the same steps keep appearing in a problem and use that pattern as a shortcut or rule. Instead of starting from scratch each time, they ask why the pattern works and apply it to new problems. | IL-MATH.MP.5.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Students work with whole numbers, fractions, and basic positive and negative numbers, using what they know about how our number system is built to solve grade-level problems.
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Operations and Algebraic Thinking
Students solve word problems and write equations using addition, subtraction, multiplication, and division. They work with expressions that combine these operations and explain how they fit together.
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Measurement and Data
Students read and build tables and graphs to make sense of real data, like survey results or recorded measurements. They also summarize what the data shows in plain terms.
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Geometry
Students sort and measure flat shapes like triangles and rectangles alongside solid shapes like cubes and cones. They use what they know about angles, sides, and faces to explain what makes each shape different from the rest.
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Ratios and Proportional Relationships
Students use ratio reasoning to solve real-world math problems, such as figuring out how many cups of juice to mix with water when scaling a recipe up or down.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students work with whole numbers, fractions, and basic positive and negative numbers, using what they know about how our number system is built to solve grade-level problems. | IL-MATH.K8.5.1 |
| Operations and Algebraic Thinking | Students solve word problems and write equations using addition, subtraction, multiplication, and division. They work with expressions that combine these operations and explain how they fit together. | IL-MATH.K8.5.2 |
| Measurement and Data | Students read and build tables and graphs to make sense of real data, like survey results or recorded measurements. They also summarize what the data shows in plain terms. | IL-MATH.K8.5.3 |
| Geometry | Students sort and measure flat shapes like triangles and rectangles alongside solid shapes like cubes and cones. They use what they know about angles, sides, and faces to explain what makes each shape different from the rest. | IL-MATH.K8.5.4 |
| Ratios and Proportional Relationships | Students use ratio reasoning to solve real-world math problems, such as figuring out how many cups of juice to mix with water when scaling a recipe up or down. | IL-MATH.K8.5.5 |
Assessments
The state tests students at this grade and subject take.
Illinois Assessment of Readiness Mathematics (Grades 3-8)
IAR Mathematics is the spring summative math test for grades 3 through 8, aligned to the Illinois Learning Standards for Mathematics.
- When given:
- spring
- Frequency:
- annual
Common Questions
What math should students know by the end of the year?
Students should add, subtract, multiply, and divide with larger numbers, work with decimals to the hundredths, and add and subtract fractions with unlike bottom numbers. They should also read graphs, find the volume of a box, and plot points on a grid.
How can I help with fractions at home?
Cook together and double or halve a recipe. Cutting a pizza into eighths and asking how many slices make three quarters builds the same thinking students need on paper. Ten minutes a few times a week goes a long way.
My child says math is harder this year. Is that normal?
Yes. Fractions with different bottom numbers and decimal place value are a real jump from last year. Expect some frustration in the fall and steadier confidence by spring as students get more practice.
Which topics usually need the most reteaching?
Adding and subtracting fractions with unlike denominators, dividing with two-digit divisors, and decimal place value tend to need a second pass. Plan a short review block after the first unit on each before moving into harder problems.
How should I sequence the year?
A common path is place value and decimals first, then multi-digit multiplication and division, then fraction operations, then volume and the coordinate grid. Saving fractions until students are solid with multiplication helps, since finding common denominators leans on that fluency.
What does mastery look like at this grade?
Students can solve a multi-step word problem, explain why their answer makes sense, and pick a reasonable tool such as paper, mental math, or estimation. They should also catch their own errors when a unit or decimal point is off.
How do I know students are ready for next year?
Check that students can multiply and divide confidently, add and subtract fractions with unlike bottom numbers, and reason about decimals to the hundredths. Comfort with these three areas is the strongest signal for sixth grade ratios and early algebra.
How can I practice math facts without flashcards?
Use real numbers from the day. Ask students to figure the tip, double a recipe, or compare unit prices at the store. Short, frequent practice in everyday moments sticks better than long drills.
What should I do if my child gets stuck on homework?
Ask them to read the problem aloud and draw a picture or write what they already know. If they are still stuck after five minutes, stop and send a short note to the teacher. Pushing past frustration usually backfires.