This is the year math becomes the language of proportions. Students stretch ratios into percent change, scale drawings, and interest on a savings account, and they start working fluently with negative numbers in real situations like temperature drops or money owed. Expressions and equations grow into tools for solving multi-step word problems. By spring, students can find a unit rate, work with negatives without flipping the signs, and solve a problem like figuring out the original price after a 20 percent discount.
Students extend arithmetic to negative numbers. They add, subtract, multiply, and divide using number lines, temperature changes, and money owed, and they learn why a negative times a negative gives a positive.
Students compare quantities using ratios and unit rates, then solve real problems like recipe scaling, gas mileage, and best-buy shopping. They learn to recognize when two quantities grow in proportion.
Students use proportional thinking to handle tips, taxes, discounts, interest, and percent change. They move between fractions, decimals, and percents to answer questions about money and growth.
Students write and solve equations with variables to model real situations, including problems with two steps. They also rewrite expressions to see the same quantity in different ways.
Students work with scale drawings, angles, and circles, finding circumference and area. They calculate surface area and volume of boxes, prisms, and other everyday 3D shapes.
Students use samples to make claims about a larger group and compare two data sets side by side. They also predict the chance of events using fractions, percents, and simple experiments.
Students read a problem all the way through, figure out what it's actually asking, and keep working even when the first approach doesn't pan out.
Students take a word problem apart to work with the numbers, then put the context back together to check that the answer makes sense in the real situation.
Students explain why their math answer is correct, using examples or logic to back it up. They also listen to how classmates solved the same problem and point out where the thinking holds up or falls apart.
Students use math to make sense of real situations, like figuring out a budget, reading a graph, or estimating a trip. The goal is to see numbers and equations as tools for solving problems that actually come up in life.
Students choose the right tool for the job, whether that means grabbing a calculator, sketching by hand, or making a quick estimate. The goal is knowing when each approach makes sense, not just reaching for the same tool every time.
Students use the right math words, label answers with correct units (like inches or dollars), and check their calculations carefully.
Students learn to spot patterns and hidden structure in math problems, like noticing that the same rule works across different numbers or shapes. Recognizing that structure lets them solve new problems faster without starting from scratch.
When solving a problem the same way several times, students pause to notice the pattern and write a shortcut or rule that works every time, not just once.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students read a problem all the way through, figure out what it's actually asking, and keep working even when the first approach doesn't pan out. | DC-MATH.MP.7.1 |
| Reason Abstractly | Students take a word problem apart to work with the numbers, then put the context back together to check that the answer makes sense in the real situation. | DC-MATH.MP.7.2 |
| Construct Arguments | Students explain why their math answer is correct, using examples or logic to back it up. They also listen to how classmates solved the same problem and point out where the thinking holds up or falls apart. | DC-MATH.MP.7.3 |
| Model with Mathematics | Students use math to make sense of real situations, like figuring out a budget, reading a graph, or estimating a trip. The goal is to see numbers and equations as tools for solving problems that actually come up in life. | DC-MATH.MP.7.4 |
| Use Tools Strategically | Students choose the right tool for the job, whether that means grabbing a calculator, sketching by hand, or making a quick estimate. The goal is knowing when each approach makes sense, not just reaching for the same tool every time. | DC-MATH.MP.7.5 |
| Attend to Precision | Students use the right math words, label answers with correct units (like inches or dollars), and check their calculations carefully. | DC-MATH.MP.7.6 |
| Use Structure | Students learn to spot patterns and hidden structure in math problems, like noticing that the same rule works across different numbers or shapes. Recognizing that structure lets them solve new problems faster without starting from scratch. | DC-MATH.MP.7.7 |
| Express Regularity | When solving a problem the same way several times, students pause to notice the pattern and write a shortcut or rule that works every time, not just once. | DC-MATH.MP.7.8 |
Students work with whole numbers, fractions, and negative numbers to solve grade-level problems. That includes comparing, ordering, and calculating with all three number types.
Students use addition, subtraction, multiplication, and division to write expressions and solve word problems. The focus is on setting up the math correctly, not just getting an answer.
Students read and build tables and graphs, then use those displays to draw conclusions about real data. They also summarize what the numbers show, including typical values and how spread out the data is.
Students sort and measure flat shapes like triangles and rectangles alongside solid shapes like cylinders and pyramids. They use angle measures, side lengths, and other properties to describe what makes each shape what it is.
Students use ratios and proportions to solve everyday problems, like figuring out unit prices, scaling a recipe, or finding a missing measurement when two quantities stay in the same relationship.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students work with whole numbers, fractions, and negative numbers to solve grade-level problems. That includes comparing, ordering, and calculating with all three number types. | DC-MATH.K8.7.1 |
| Operations and Algebraic Thinking | Students use addition, subtraction, multiplication, and division to write expressions and solve word problems. The focus is on setting up the math correctly, not just getting an answer. | DC-MATH.K8.7.2 |
| Measurement and Data | Students read and build tables and graphs, then use those displays to draw conclusions about real data. They also summarize what the numbers show, including typical values and how spread out the data is. | DC-MATH.K8.7.3 |
| Geometry | Students sort and measure flat shapes like triangles and rectangles alongside solid shapes like cylinders and pyramids. They use angle measures, side lengths, and other properties to describe what makes each shape what it is. | DC-MATH.K8.7.4 |
| Ratios and Proportional Relationships | Students use ratios and proportions to solve everyday problems, like figuring out unit prices, scaling a recipe, or finding a missing measurement when two quantities stay in the same relationship. | DC-MATH.K8.7.5 |
DC's spring summative math test for grades 3 through 8, aligned to DC's Common Core-based math standards.
Alternate assessment for students with the most significant cognitive disabilities, given in grades 3-8 and high school in ELA, math, and science.