What does a student learn in StateVirginia,GradeGrade 2,SubjectMathematics?

Students count, group, and describe amounts up to 200, using strategies like skip-counting by 5s or 10s to get there faster. The focus is on building number sense, not just reciting a sequence.

Students count by 2s starting from different even numbers, using tools like a number line or hundreds chart to show the pattern as they go.

Students count forward by 5s, 10s, and 25s (like nickels and dimes) starting from different numbers, then show those patterns on a number line or hundreds chart.

Skip counting means jumping forward by the same number each time, like counting by 5s or 10s instead of one by one. Students practice these patterns and use them to figure out what number comes next in a sequence.

Counting by 100s, students practice jumping from 0 to 100 to 200 and beyond, reaching at least 1,000. They use tools like number lines or charts to see and show the pattern those big jumps make.

Students count backward by 10s starting from any number up to 200, using tools like a number line or hundreds chart to track the pattern as the numbers decrease.

Starting at any number up to 200, students count backward by tens (200, 190, 180...) and explain why each number comes next.

Students pick the most sensible number from a short list of choices when a real-life question involves a large quantity. They rule out answers that are obviously too small or too big.

Students show that even numbers can be split into two equal groups. For example, 12 becomes two groups of 6, or the addition sentence 6 + 6 = 12.

Students sort objects into two equal groups to show why odd numbers always leave one extra. For example, 7 becomes three and three, with one left over, or 3 + 3 + 1.

Students sort a pile of up to 50 objects into two equal groups to decide if a number is even or odd, then explain how they know.

Reading, writing, and comparing numbers up to 999 by understanding that each place in a number means tens or hundreds of the one before it. Students use that pattern to say which number is bigger or smaller.

Students look at a picture or group of blocks arranged in hundreds, tens, and ones, then write the number those blocks show, such as writing 347 when they see three flats, four rods, and seven cubes.

Students read and write numbers like 347 in three ways: as the numerals (347), as words (three hundred forty-seven), and broken apart by place value (300 + 40 + 7). Blocks or pictures help show what each digit actually means.

Reading a three-digit number, students name the place of each digit (ones, tens, hundreds) and say what it's worth. In 352, the 5 sits in the tens place and stands for 50.

Students use blocks or drawings to show that 10 ones make a ten, and 10 tens make a hundred. The goal is understanding why our number system groups by tens, not just memorizing the rule.

Students break a number like 156 into hundreds, tens, and ones in more than one way, then put those parts back together. A number can be split up differently and still be the same amount.

Students place a number on a number line by deciding which marked tick mark it belongs on or between. The number line might count by 1s, 2s, 5s, 10s, or 25s.

Students look at two numbers up to 999 and decide which is greater, which is smaller, or whether they match. They use the symbols >, <, and = and explain how they know.

Students put up to three numbers (each no bigger than 999) in order from smallest to biggest or biggest to smallest, whether the numbers are shown as pictures, blocks, or written digits.

Students cut shapes or objects into equal pieces and figure out how to show halves, thirds, fourths, sixths, and eighths. They explain why their parts are equal.

Students divide shapes or objects into equal parts and name each part as a fraction. A pizza cut into 4 equal slices means each slice is one-fourth of the whole.

Students explore why cutting a pizza into 8 slices gives you smaller pieces than cutting it into 4. The more equal parts you split something into, the smaller each part gets.

Given one piece of a whole, students figure out how many pieces of that same size it takes to complete the whole shape or amount.

Students count equal-sized fraction pieces in order, like counting slices of a pizza cut into fourths: one-fourth, two-fourths, three-fourths, four-fourths, and beyond. The counting keeps going past one whole shape into a second.

Students look at a shape or object split into equal parts and write the fraction that names one or more of those parts, like 1/4 for one piece of something cut into four equal pieces.

Students split shapes like circles and squares into equal parts, such as halves or fourths, using drawings or physical pieces. The focus is on making sure every part is the same size.

Students split a line, strip, or number line into equal parts to show fractions like halves, thirds, and fourths. The focus is on length, not shape, so students learn that equal parts must be the same size from end to end.

Students split a group of objects (like chips or cubes) into equal shares and name each share as a half, a third, a fourth, a sixth, or an eighth.

Students compare simple fractions like one-half and one-fourth by looking at shaded shapes or marked lengths, then decide which piece is bigger, smaller, or the same size using the symbols >, <, and =.

Students count coins and bills to make amounts up to $2.00, then solve simple word problems about buying and making change. They work with pennies, nickels, dimes, quarters, and dollar bills.

Students learn what a quarter looks like, what 25 cents means, and how to make that same amount using different combinations of pennies, nickels, and dimes.

Students count a mix of coins and dollar bills to find the total amount, up to $2.00. They skip-count by ones, fives, tens, and twenty-fives to add it all up.

Students pick a combination of coins and bills that adds up to a given amount, like 75 cents or $1.50. The total has to be $2.00 or less.

Students count a mix of coins and dollar bills, then write the total using a dollar sign, cent sign, and decimal point. Amounts stay at $2.00 or less.

Students practice adding and subtracting numbers up to 100 until the answers come automatically. They also solve word problems and show how they got their answer.

Students practice making quick ballpark guesses before adding or subtracting two numbers up to 100. They round to the nearest ten or look for numbers that work well together to check whether their final answer makes sense.

Students use strategies like place value or drawing a picture to add or subtract two numbers up to 100. They might break apart a number by tens and ones, or use what they know about addition to check a subtraction problem.

Students read a short story problem and figure out whether to add or subtract to find the answer. Numbers stay at 100 or below, and students explain how they know their answer makes sense.

Students practice adding and subtracting numbers up to 20 using mental shortcuts, like knowing that 6+7 is just one more than 6+6, or that adding 9 is nearly the same as adding 10.

Students know their addition and subtraction facts up to 20 from memory, no counting on fingers required. Think 7 + 8 or 15 - 6, answered instantly.

Students learn that flipping the order of two numbers in an addition problem gives the same answer, and that adding zero to any number leaves it unchanged. These patterns help students add faster and with more confidence.

Students figure out the missing number in an addition or subtraction equation, like 3 + ? = 5 or 5 - ? = 3. They use objects or drawings to show how they got the answer.

Given one addition or subtraction fact, students write the other three related facts in the same family. If they know 3 + 4 = 7, they can also write 4 + 3 = 7, 7 - 4 = 3, and 7 - 3 = 4.

Students learn that the "not equal" sign (≠) means two amounts are different, not the same. They practice explaining why, using numbers or objects to back up their thinking.

Students show whether two math expressions have the same value or different values, using the equals sign or a not-equal sign. For example, they check whether 9 + 24 gives the same total as 10 + 23.

Students measure real objects by length, weight, and liquid volume using rulers, scales, and measuring cups. They estimate before measuring and compare results using whole units like inches, pounds, and cups.

Measurement tools each have a job. Students learn what a ruler, a scale, and a measuring cup are for and practice using each one correctly to measure length, weight, or liquid.

Students learn that a ruler is the right tool for measuring how long something is, not for weighing it or checking how much liquid it holds.

Scales are tools for measuring how heavy something is. Students learn to recognize different kinds, like a kitchen scale or a balance scale, and understand that each one measures weight.

Students learn that measuring cups come in different sizes and that each one is a tool for finding how much liquid something holds.

Students estimate and measure lengths, weights, and liquid volumes using inches, feet, pounds, and cups, then check whether their estimate was close to the actual measurement.

Students measure how long an object is to the nearest inch using a ruler. They line up the ruler correctly and read the number where the object ends.

Students weigh real objects on a scale and record the result to the nearest whole pound.

Students measure how much liquid a container holds by pouring it into a measuring cup and reading the amount to the nearest cup.

Students read analog and digital clocks and tell time to the nearest five minutes. They connect the position of clock hands to the matching digital display.

Students learn that an hour holds 60 minutes and a day holds 24 hours. These two facts are the building blocks for reading any clock or planning any schedule.

Students decide which unit of time fits a real activity best, such as whether brushing teeth takes minutes, not hours. Then they explain why that unit makes sense.

Students read and write times like 3:15 or 7:45 on both a clock face with hands and a digital display, rounding to the nearest five-minute mark.

Students match a digital time like 6:20 to the same time on a clock face with hands. Both show the same moment, just written two different ways.

Students find the line where a shape folds into two matching halves, then use that idea to explain why both sides are equal in size and shape. Works with circles, triangles, squares, and rectangles.

Students fold, draw, or trace a shape to find the line where both halves match exactly. That matching line is called a line of symmetry.

Students fold, draw, or build shapes where one side mirrors the other exactly. A square, triangle, or rectangle with a line of symmetry looks the same on both halves.

Students fold a shape along its line of symmetry and see that both halves match exactly, same shape and same size.

Students sort flat shapes and 3-D objects by comparing what makes them alike and different. A square and a cube, for example, share corners and straight edges, but one is flat and the other has depth.

Students trace the flat sides of a box or cube onto paper to see which shapes make up that solid. It connects 3-D objects to the flat shapes hidden on their surfaces.

Students look at real boxes and flat cutout patterns that fold into boxes, then describe how cubes and rectangular prisms are alike and different by counting their flat faces, edges, and corners.

Students look at a 3-D shape, like a cube or a box, and describe what they notice: how many corners it has, how many edges, and what the flat faces look like.

Students sort flat shapes and 3D solids by counting their faces, edges, and corners. A square has four flat sides, while a cube has six flat faces but otherwise looks like its flat cousin.

Students gather information to answer a real question, then sort it into a picture graph or bar graph and explain what the numbers show.

Students come up with questions worth investigating, like "What is your favorite lunch?" then collect answers from classmates. They work with no more than 25 responses spread across six categories.

Students pick a question they want answered, then figure out what information they need to collect. They gather that data by voting, making lists, or using tally marks.

Students sort a set of information into a pictograph where each picture stands for 1 or 2 items, then create a key so readers know what each picture means.

Students sort collected information into categories and draw a bar graph with a title and labeled sides, using scales that count by 1s or 2s, with up to six groups and no more than 25 total items.

Students read a pictograph or bar graph and explain what the data shows, such as which category had the most or least and how the numbers compare.

Students read a picture chart or bar graph and answer questions about it, like which group has the most or how many more apples were picked than oranges. Charts use simple scales so each picture stands for 1, 2, 5, or 10 items.

Students look at a finished pictograph or bar graph and answer questions about what the data shows, then use what they see to predict what might happen next.

Students look at a number pattern, figure out the rule, and continue it. They also build their own patterns using addition, objects, or pictures.

Students look at a sequence of shapes, numbers, or objects and figure out the rule that makes it repeat or grow. They describe what comes next and explain the pattern they see.

Students look at a repeating or growing pattern, figure out the rule behind it, and use that rule to keep the pattern going. They work with objects, pictures, and numbers.

Students make their own repeating or growing pattern using objects, drawings, or numbers. For example, they might arrange blocks in a repeating color order or write numbers that keep increasing by the same amount.

Students take a pattern shown one way, such as with shapes or pictures, and redraw it using numbers or objects instead. Then they explain how the two versions match.