What does a student learn in
California, Grade 2, Mathematics ?

Students sort and draw shapes by counting their sides and corners. They name specific shapes like triangles, four-sided figures, pentagons, and hexagons, and they recognize a cube by its equal square faces.

Students divide a rectangle into equal-sized squares arranged in rows and columns, then count all the squares to find the total. It's an early look at how multiplication and area work.

Cutting circles and rectangles into equal pieces, students name those pieces halves, thirds, or fourths and explain how the pieces make up the whole. Two equal shares of the same shape can look different and still be the same size.

Students partition rectangles into rows and columns of same-size squares and count how many squares fit inside. This builds an early picture of multiplication and area before those words even show up.

Students use what they know about place value to solve addition and subtraction problems, choosing the right tool for the job, whether that's a number line, base-ten blocks, or mental math.

Students measure lengths using the same unit throughout, like repeating a ruler end-to-end without gaps or overlaps. Getting that detail right is what makes a measurement mean something.

Students look at shapes or number patterns and spot the hidden structure, like noticing a rectangle is made of rows of equal squares. Finding that structure helps students solve problems without starting from scratch each time.

Students sort and describe shapes by their sides and angles, grouping squares with squares and triangles with triangles. They learn that shapes in the same category share specific features, like equal sides or right corners.

Students pick the right measuring tool for the job and use it to find how long something is. A short pencil calls for a ruler; a longer object might need a yardstick or measuring tape.

Students measure the same object twice using two different tools (like a paper clip and a ruler), then explain why the numbers come out different. The shorter the tool, the bigger the count.

Students guess how long something is before measuring it, using inches, feet, centimeters, or meters. It builds the habit of sizing up an object with their eyes before reaching for a ruler.

Students measure two objects with a ruler, then subtract to find the difference. They practice saying things like "the pencil is 3 inches longer than the crayon."

Students solve story problems about measuring lengths, adding or subtracting numbers up to 100 to find a missing measurement. They might draw a ruler or write an equation with a blank to show their thinking.

Students place whole numbers on a number line by marking equal spaces from zero, then use the same number line to add and subtract numbers up to 100.

Students read both kinds of clocks and write the time to the nearest five minutes, noting whether it is a.m. or p.m. They also learn basic time facts, like how many minutes are in an hour or days in a week.

Students figure out how much a mix of coins and dollar bills adds up to, then write the total with the right symbol, like 23¢ or $1.05.

Students measure a handful of objects with a ruler, record each length to the nearest inch or centimeter, and then plot the results on a number line. The finished chart shows how the measurements spread out across whole numbers.

Students collect data, sort it into up to four groups, and draw a picture graph or bar graph to show what they found. Then they use the graph to answer simple questions, like how many more or fewer items are in one group than another.

Students learn that every three-digit number is built from hundreds, tens, and ones. In 706, the 7 means seven hundreds, the 0 means no tens, and the 6 means six ones.

Students count up to 1,000 and practice jumping by 2s, 5s, 10s, and 100s, like counting nickels or dimes in a piggy bank. Seeing the pattern in those jumps builds the number sense students use in everyday math.

Students read and write numbers up to 1,000 three ways: as digits (325), as words ("three hundred twenty-five"), and as a sum that shows each part (300 + 20 + 5).

Students compare two three-digit numbers by looking at hundreds first, then tens, then ones, and write which number is greater, equal, or less using the symbols >, =, and <.

Students add and subtract any two numbers up to 100 quickly and accurately. They use what they know about tens and ones, not just memorized steps, to find the answer.

Students add up to four two-digit numbers at a time by grouping tens together and ones together. They use what they know about how numbers are built to make the addition easier.

Students add and subtract numbers up to 1000 by working with hundreds, tens, and ones separately. When a column has too many or too few, students regroup across place values and show how the written math matches what they did.

Students read short story problems and use addition or subtraction to find a missing number, working with totals up to 100. The unknown can appear anywhere in the problem, so students draw pictures or write equations to figure it out.

Adding and subtracting numbers up to 20 from memory, without counting on fingers or using a number line. Students also practice arranging objects into equal groups as a first step toward multiplication.

Students sort a group of up to 20 objects into pairs to decide if the total is odd or even. If everything pairs up cleanly, the number is even, and students write it as two equal parts added together.

Students count objects arranged in a grid of rows and columns, then write an addition sentence to show the total. For example, 3 rows of 4 dots becomes 4 + 4 + 4 = 12.