Ratios and rates
Students learn to compare two amounts, like 3 cups of flour for every 2 eggs. They use this to figure out unit prices, mixing recipes, and speed.
What does a student learn in
This is the year math shifts from arithmetic to reasoning with ratios and variables. Students compare prices and recipes using ratios, rates, and percents, and they start writing simple equations with a letter standing in for an unknown number. They also work with negative numbers on a number line and learn to read graphs that summarize a set of data. By spring, students can solve a word problem by setting up an equation like 3x + 5 = 20.
- Ratios and rates
- Percents
- Equations with variables
- Negative numbers
- Data and graphs
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
Dividing fractions
Students move past adding and subtracting fractions and start dividing them. They figure out how many half-cups fit in a recipe or how many quarter-pound burgers come from two pounds of meat.
- 3
Decimals and negative numbers
Students work fluently with decimals in all four operations and meet negative numbers on a number line. They place temperatures, elevations, and bank balances above and below zero.
- 4
Expressions and equations
Letters start standing in for numbers. Students write short expressions like 3x + 5, solve simple one-step equations, and see how a formula can describe a real situation.
- 5
Area, surface area, and volume
Students find the area of triangles and odd shapes by breaking them apart. They also calculate the volume of boxes with fractional side lengths and the surface area of 3D shapes using nets.
- 6
Statistics and data
Students learn that a good question has a range of answers, not just one. They summarize a data set with the mean, median, and range, and read what a graph is really showing.
Mastery Learning Standards
The required skills a student should display by the end of Grade 6.
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 real situation, turn it into numbers and equations to solve it, then translate the answer back into what it means in real life.
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Construct Arguments
Students explain how they solved a problem and point out flaws in someone else's reasoning. They use examples and numbers to back up their thinking, not just their gut feeling.
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Model with Mathematics
Students take a real-world problem, like splitting a bill or planning a garden, and use math to figure it out. The numbers and equations match something that actually exists outside the classroom.
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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 to show steps, 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. They label answers with the right units (miles, degrees, square feet) and use math terms correctly so their reasoning is clear.
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Use Structure
Students notice patterns and hidden structure in math problems, like spotting that a fraction, a ratio, and a division problem are all asking the same thing. Recognizing that structure helps students solve new problems faster.
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Express Regularity
Students notice when a pattern keeps showing up in their work and use it as a shortcut. Instead of solving the same type of problem from scratch each time, they spot the repeating steps and turn them into a rule.
| 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.6.1 |
| Reason Abstractly | Students take a real situation, turn it into numbers and equations to solve it, then translate the answer back into what it means in real life. | IL-MATH.MP.6.2 |
| Construct Arguments | Students explain how they solved a problem and point out flaws in someone else's reasoning. They use examples and numbers to back up their thinking, not just their gut feeling. | IL-MATH.MP.6.3 |
| Model with Mathematics | Students take a real-world problem, like splitting a bill or planning a garden, and use math to figure it out. The numbers and equations match something that actually exists outside the classroom. | IL-MATH.MP.6.4 |
| Use Tools Strategically | Students choose the right tool for the math in front of them: a calculator for large numbers, pencil and paper to show steps, or a quick estimate to check if an answer makes sense. | IL-MATH.MP.6.5 |
| Attend to Precision | Students choose words and units carefully when solving problems. They label answers with the right units (miles, degrees, square feet) and use math terms correctly so their reasoning is clear. | IL-MATH.MP.6.6 |
| Use Structure | Students notice patterns and hidden structure in math problems, like spotting that a fraction, a ratio, and a division problem are all asking the same thing. Recognizing that structure helps students solve new problems faster. | IL-MATH.MP.6.7 |
| Express Regularity | Students notice when a pattern keeps showing up in their work and use it as a shortcut. Instead of solving the same type of problem from scratch each time, they spot the repeating steps and turn them into a rule. | IL-MATH.MP.6.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Sixth graders work with whole numbers, fractions, and negative numbers to solve grade-level problems. They use number-system reasoning to compare, place, and operate on all three types of numbers.
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Operations and Algebraic Thinking
Sixth graders use addition, subtraction, multiplication, and division to write expressions and solve word problems. They move from basic arithmetic into algebra by replacing unknown values with letters and solving for what those letters represent.
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Measurement and Data
Students read and build tables, graphs, and basic statistical summaries to make sense of real data. They pull meaning from the numbers, not just record them.
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Geometry
Students sort, describe, and measure flat shapes like triangles and rectangles, and solid shapes like cubes and cylinders. They use angle measures, side lengths, and other properties to compare and classify what they find.
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Ratios and Proportional Relationships
Students use ratio reasoning to solve real-world problems: comparing quantities, finding rates, and scaling amounts up or down. Think recipes, maps, or unit prices.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Sixth graders work with whole numbers, fractions, and negative numbers to solve grade-level problems. They use number-system reasoning to compare, place, and operate on all three types of numbers. | IL-MATH.K8.6.1 |
| Operations and Algebraic Thinking | Sixth graders use addition, subtraction, multiplication, and division to write expressions and solve word problems. They move from basic arithmetic into algebra by replacing unknown values with letters and solving for what those letters represent. | IL-MATH.K8.6.2 |
| Measurement and Data | Students read and build tables, graphs, and basic statistical summaries to make sense of real data. They pull meaning from the numbers, not just record them. | IL-MATH.K8.6.3 |
| Geometry | Students sort, describe, and measure flat shapes like triangles and rectangles, and solid shapes like cubes and cylinders. They use angle measures, side lengths, and other properties to compare and classify what they find. | IL-MATH.K8.6.4 |
| Ratios and Proportional Relationships | Students use ratio reasoning to solve real-world problems: comparing quantities, finding rates, and scaling amounts up or down. Think recipes, maps, or unit prices. | IL-MATH.K8.6.5 |
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 be doing well by the end of the year?
By spring, students should work fluently with fractions, decimals, and percents, including dividing fractions and finding a percent of a number. They should also write and solve simple equations with a letter standing in for an unknown, and reason about ratios like 3 cups of flour to 2 cups of sugar.
What is the biggest new idea this year?
Ratios and rates. Students start comparing two quantities, like miles per hour or price per ounce, and using that thinking to solve problems. This is the foundation for proportions next year and most of the algebra that follows.
How can families help with math at home in 10 minutes?
Cook and shop together. Ask students to double a recipe, figure out the price per ounce on two cereal boxes, or calculate a 15 percent tip. These small conversations build the ratio and percent reasoning that drives most of the year.
What should families do when a student gets stuck on homework?
Ask students to read the problem aloud and explain what it is asking before touching a pencil. Then ask what they already know and what one small step might be. The goal is to get them talking through the problem, not to hand them the answer.
How should the year be sequenced?
Most plans open with ratios and rates, move into fraction division and decimal operations, then build into expressions and one-step equations. Save statistics and the work with mean, median, and variability for later in the year, once students are comfortable reasoning with numbers in context.
Which skills usually need the most reteaching?
Dividing fractions, negative numbers on a number line, and writing an equation from a word problem. Students often memorize the fraction division trick without understanding why it works, which falls apart when problems get harder. Build time into each unit for revisiting these.
Do students still need to know their multiplication facts?
Yes. Sixth grade work moves fast, and students who still count on their fingers for 7 times 8 fall behind on bigger problems. Five minutes of fact practice a few nights a week pays off all year.
What does mastery of ratios look like by June?
Students can describe a ratio in words, set up a table of equivalent ratios, plot pairs on a graph, and solve a real problem like a unit price comparison or a scaled recipe. They should also recognize that a percent is just a ratio out of 100.
How will families know if a student is ready for seventh grade?
A ready student can divide fractions and explain what the answer means, solve a problem involving a percent or a unit rate, and write a short equation for a word problem. If any of these feel shaky in May, a few weeks of summer practice on that one skill helps a lot.