Working with positive and negative numbers
Students learn to add, subtract, multiply, and divide with negative numbers. Temperatures below zero, money owed, and elevation below sea level start to make sense as numbers students can actually use.
What does a student learn in
This is the year math leans hard on negative numbers, percents, and proportions. Students work with all rational numbers, adding and multiplying through zero and into the negatives, and they use ratios to handle tips, discounts, and scale drawings. Algebra grows up too, as students solve multi-step equations with variables on both sides. By spring, students can figure out a sale price or a tip in their head and solve an equation like 3x + 5 = 20 on paper.
- Negative numbers
- Ratios and proportions
- Percents
- Solving equations
- Probability
- Scale drawings
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
Ratios, rates, and proportions
Students compare quantities using ratios and unit rates. They figure out the better deal at the store, scale a recipe up or down, and use proportions to solve problems with maps and similar shapes.
- 3
Percent in the real world
Students apply percent thinking to tips, taxes, discounts, and interest. They also work with percent increase and decrease, so a sale price or a markup is something they can calculate on their own.
- 4
Expressions and equations
Students write and solve equations with variables, including problems with two steps. They learn to rewrite expressions in simpler forms and use equations to answer real questions about money, distance, and time.
- 5
Geometry, area, and volume
Students find the area of circles and the surface area and volume of boxes and prisms. They also work with angles and draw shapes to scale, the kind of math behind blueprints and packaging.
- 6
Statistics and probability
Students use samples to make predictions about larger groups and compare two sets of data. They also start working with probability, figuring out the chances of events from coin flips to spinners.
Mastery Learning Standards
The required skills a student should display by the end of Grade 7.
Standards for Mathematical Practice
Standards for Mathematical Practice
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Make Sense of Problems
Students read a 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-world problem, strip it down to numbers and symbols to solve it, then translate the answer back into plain language that fits the situation.
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Construct Arguments
Students build a case for their answer using numbers, examples, or diagrams, then explain why a classmate's reasoning is right or where it breaks down.
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Model with Mathematics
Students use math to make sense of real situations, like figuring out a budget, reading a chart, or splitting a bill. The goal is to see math as a tool for problems that actually come up outside of school.
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Use Tools Strategically
Students choose the right tool for the math in front of them. That might mean a calculator for big numbers, a sketch on paper for a geometry problem, or a quick mental estimate to check whether an answer makes sense.
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Attend to Precision
Students choose exact words, labels, and units when explaining math. A calculation means little without the right label, so "14" becomes "14 square inches" or "14 miles per hour."
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Use Structure
Students learn to spot patterns and built-in rules in math problems, like noticing that the same shortcut works across different equations. Recognizing that structure saves time and makes harder problems easier to solve.
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Express Regularity
Students notice when the same steps keep showing up across different problems and use that pattern to find a shortcut or write a general rule.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students read a problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work. | IL-MATH.MP.7.1 |
| Reason Abstractly | Students take a real-world problem, strip it down to numbers and symbols to solve it, then translate the answer back into plain language that fits the situation. | IL-MATH.MP.7.2 |
| Construct Arguments | Students build a case for their answer using numbers, examples, or diagrams, then explain why a classmate's reasoning is right or where it breaks down. | IL-MATH.MP.7.3 |
| Model with Mathematics | Students use math to make sense of real situations, like figuring out a budget, reading a chart, or splitting a bill. The goal is to see math as a tool for problems that actually come up outside of school. | IL-MATH.MP.7.4 |
| Use Tools Strategically | Students choose the right tool for the math in front of them. That might mean a calculator for big numbers, a sketch on paper for a geometry problem, or a quick mental estimate to check whether an answer makes sense. | IL-MATH.MP.7.5 |
| Attend to Precision | Students choose exact words, labels, and units when explaining math. A calculation means little without the right label, so "14" becomes "14 square inches" or "14 miles per hour." | IL-MATH.MP.7.6 |
| Use Structure | Students learn to spot patterns and built-in rules in math problems, like noticing that the same shortcut works across different equations. Recognizing that structure saves time and makes harder problems easier to solve. | IL-MATH.MP.7.7 |
| Express Regularity | Students notice when the same steps keep showing up across different problems and use that pattern to find a shortcut or write a general rule. | IL-MATH.MP.7.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Students work with whole numbers, fractions, and negative numbers to solve grade-level problems. They use what they know about how numbers are built and related to reason through calculations and comparisons.
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Operations and Algebraic Thinking
Students use addition, subtraction, multiplication, and division to set up and solve word problems, then write the math as an expression or equation.
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Measurement and Data
Students read and build tables and graphs to make sense of real data. They use basic statistics to describe what the numbers show and spot patterns worth noticing.
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Geometry
Students sort and measure flat shapes like triangles and rectangles alongside 3-D figures like prisms and pyramids. They use angle measures, side lengths, and other properties to explain what makes each shape what it is.
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Ratios and Proportional Relationships
Students use ratios and rates to solve everyday problems, like figuring out how much something costs for a different quantity or how long a trip will take at a given speed. The math connects two quantities and scales them up or down.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students work with whole numbers, fractions, and negative numbers to solve grade-level problems. They use what they know about how numbers are built and related to reason through calculations and comparisons. | IL-MATH.K8.7.1 |
| Operations and Algebraic Thinking | Students use addition, subtraction, multiplication, and division to set up and solve word problems, then write the math as an expression or equation. | IL-MATH.K8.7.2 |
| Measurement and Data | Students read and build tables and graphs to make sense of real data. They use basic statistics to describe what the numbers show and spot patterns worth noticing. | IL-MATH.K8.7.3 |
| Geometry | Students sort and measure flat shapes like triangles and rectangles alongside 3-D figures like prisms and pyramids. They use angle measures, side lengths, and other properties to explain what makes each shape what it is. | IL-MATH.K8.7.4 |
| Ratios and Proportional Relationships | Students use ratios and rates to solve everyday problems, like figuring out how much something costs for a different quantity or how long a trip will take at a given speed. The math connects two quantities and scales them up or down. | IL-MATH.K8.7.5 |
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 will students work on this year?
Most of the year focuses on ratios, percents, and working with positive and negative numbers. Students also solve equations with a variable, study probability, and find the area and surface area of shapes. A lot of word problems show up.
How can families help with math at home?
Cooking, shopping, and sports stats are full of ratios and percents. Ask questions like how much a sale price saves, how to double a recipe, or what a batting average means. Five minutes of real talk about numbers beats a worksheet.
What should students know by the end of the year?
Students should be comfortable adding, subtracting, multiplying, and dividing with negative numbers and fractions. They should solve a two-step equation, find a percent of a number, and reason about chance. These skills set up algebra next year.
My child gets stuck on word problems. What helps?
Have students read the problem out loud, then say in their own words what is being asked. Drawing a quick picture or labeling the numbers with units helps a lot. The goal is to slow down before grabbing a calculator.
Which topics usually need the most reteaching?
Operations with negative numbers and fraction division tend to be sticky, especially when both show up in the same problem. Percent increase and percent decrease also trip students up. Plan for spiral review across units rather than a single unit and move on.
How should ratios and proportional reasoning be sequenced?
Start with unit rates and scaling in familiar contexts like recipes or maps, then move into percents as a special kind of ratio. Save proportional equations and graphs for after students can reason about a table. This order keeps the meaning ahead of the procedure.
Do students still need to practice math facts?
Yes. Quick recall of multiplication facts and common fractions to decimals makes harder work much easier. A few minutes of flashcards or a card game a couple times a week is enough.
How do I know students are ready for eighth grade math?
Look for fluent work with negative numbers, confident solving of two-step equations, and clear explanations of ratio and percent problems. Students should also be able to defend an answer with a sentence, not just a number. Writing about reasoning matters more this year.