Adding and subtracting within 20
Students start the year getting quick and confident with sums and differences up to 20. By the end of this stretch, most basic facts come from memory instead of finger counting.
This is the year math stretches past 100 and into the hundreds. Students learn that a number like 247 is built from hundreds, tens, and ones, and they use that idea to add and subtract larger numbers in their heads and on paper. Word problems get longer, and students have to figure out which step comes first. By spring, they can add and subtract within 100 quickly and measure an object with a ruler in inches or centimeters.
Students start the year getting quick and confident with sums and differences up to 20. By the end of this stretch, most basic facts come from memory instead of finger counting.
Students learn that a three-digit number is built from hundreds, tens, and ones. They count by 5s, 10s, and 100s, compare numbers, and read them out loud.
Students use what they know about place value to add and subtract numbers up to 100, and then up to 1,000. Expect to see them line up tens and ones and trade groups when needed.
Students measure with rulers in inches and centimeters, read a clock to the nearest five minutes, and count coins and dollar bills. They also start making simple bar graphs and picture graphs.
Students name and draw shapes by their sides and corners, and split rectangles and circles into halves, thirds, and fourths. This sets the table for fractions next year.
Students read a math problem carefully, figure out what it's asking, and keep trying even when the first approach doesn't work.
Students take a word problem and turn it into numbers and symbols to solve it, then explain what the answer actually means in real life. Math and meaning connect in both directions.
Students explain why their math answer makes sense and listen to how classmates solved the same problem. They practice agreeing or disagreeing with a reason, not just a result.
Students use math to make sense of real situations, like figuring out how many chairs fit at a table or how much money something costs. The math connects to something outside the classroom.
Students choose the right tool for the job, picking a ruler to measure, pencil and paper to work out a problem, or a calculator when it makes sense. The goal is knowing which tool fits, not just grabbing whatever is nearby.
Students use the right math words, label answers with the correct units (inches, dollars, minutes), and check their arithmetic carefully.
Students notice patterns and rules in math, like how adding zero never changes a number or how shapes can be broken into smaller parts. Spotting those patterns helps students solve new problems faster.
Students notice when the same steps keep working the same way, like adding zero always leaving a number unchanged. They use that pattern as a shortcut instead of starting from scratch each time.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students read a math problem carefully, figure out what it's asking, and keep trying even when the first approach doesn't work. | CT-MATH.MP.2.1 |
| Reason Abstractly | Students take a word problem and turn it into numbers and symbols to solve it, then explain what the answer actually means in real life. Math and meaning connect in both directions. | CT-MATH.MP.2.2 |
| Construct Arguments | Students explain why their math answer makes sense and listen to how classmates solved the same problem. They practice agreeing or disagreeing with a reason, not just a result. | CT-MATH.MP.2.3 |
| Model with Mathematics | Students use math to make sense of real situations, like figuring out how many chairs fit at a table or how much money something costs. The math connects to something outside the classroom. | CT-MATH.MP.2.4 |
| Use Tools Strategically | Students choose the right tool for the job, picking a ruler to measure, pencil and paper to work out a problem, or a calculator when it makes sense. The goal is knowing which tool fits, not just grabbing whatever is nearby. | CT-MATH.MP.2.5 |
| Attend to Precision | Students use the right math words, label answers with the correct units (inches, dollars, minutes), and check their arithmetic carefully. | CT-MATH.MP.2.6 |
| Use Structure | Students notice patterns and rules in math, like how adding zero never changes a number or how shapes can be broken into smaller parts. Spotting those patterns helps students solve new problems faster. | CT-MATH.MP.2.7 |
| Express Regularity | Students notice when the same steps keep working the same way, like adding zero always leaving a number unchanged. They use that pattern as a shortcut instead of starting from scratch each time. | CT-MATH.MP.2.8 |
Second graders work with whole numbers up to 1,000, learning how to count, compare, and break them into hundreds, tens, and ones. They also take their first steps with fractions, like splitting a shape or a set of objects into equal parts.
Second graders practice adding, subtracting, multiplying, and dividing to solve word problems. They learn to write number sentences that match real situations, like sharing objects equally or combining groups.
Students read and build simple picture graphs, bar graphs, and tables to answer questions about data. They count, compare, and draw conclusions from the information in front of them.
Students sort flat and solid shapes by their sides, corners, and faces. They also measure and describe shapes like squares, triangles, and cubes using what they notice about each one.
Students use ratio reasoning to solve everyday math problems at the second-grade level, such as figuring out how many more objects are needed to match a given group or how two quantities relate to each other.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Second graders work with whole numbers up to 1,000, learning how to count, compare, and break them into hundreds, tens, and ones. They also take their first steps with fractions, like splitting a shape or a set of objects into equal parts. | CT-MATH.K8.2.1 |
| Operations and Algebraic Thinking | Second graders practice adding, subtracting, multiplying, and dividing to solve word problems. They learn to write number sentences that match real situations, like sharing objects equally or combining groups. | CT-MATH.K8.2.2 |
| Measurement and Data | Students read and build simple picture graphs, bar graphs, and tables to answer questions about data. They count, compare, and draw conclusions from the information in front of them. | CT-MATH.K8.2.3 |
| Geometry | Students sort flat and solid shapes by their sides, corners, and faces. They also measure and describe shapes like squares, triangles, and cubes using what they notice about each one. | CT-MATH.K8.2.4 |
| Ratios and Proportional Relationships | Students use ratio reasoning to solve everyday math problems at the second-grade level, such as figuring out how many more objects are needed to match a given group or how two quantities relate to each other. | CT-MATH.K8.2.5 |
Connecticut's spring summative math test for grades 3 through 8, aligned to the Connecticut Core Standards for Mathematics.
By spring, students should add and subtract within 100 quickly and explain how they got the answer. They should also tell time on a clock, count coins, measure with a ruler, and read simple bar graphs.
Use real life. Count change at the store, measure ingredients with a ruler or cup, and ask what time dinner starts and how long until then. Five minutes of this a few times a week builds more number sense than a worksheet.
Not yet. Fingers and drawings are normal tools at this age. The goal this year is for students to move toward quick recall of sums within 20, so practice short bursts of addition facts a couple of times a week.
Start with tens and ones using bundles or blocks, then move to hundreds. Build addition and subtraction within 100 on top of that work, and save three-digit numbers and mental math with 10 and 100 for later in the year once students trust the structure.
Subtraction across a ten, telling time to five minutes, and counting mixed coins. Plan to revisit these in short warm-ups for weeks after the unit ends, not just during the unit itself.
Students should solve one and two-step problems with addition and subtraction within 100, draw a picture or write an equation, and explain why the answer makes sense. A correct number with no reasoning is not mastery yet.
Listen for them adding and subtracting two-digit numbers in their head or on paper without panic, telling time on a round clock, and naming shapes like pentagons and cubes. If those feel shaky in June, a little summer practice helps a lot.
Yes. Students are expected to know sums of two single-digit numbers from memory by the end of the year. Short, friendly practice with flash cards or quick games beats long drills.