What does a student learn in
New York, Grade 4, Mathematics ?

Students draw and label basic shape parts: points, lines, rays, and angles. Then they spot those same parts inside flat shapes like triangles and rectangles.

Students learn to spot the invisible fold line that splits a shape into two matching halves. They identify which shapes have that line and draw it in.

Students sort triangles by their angles. A right triangle has one square corner, an obtuse triangle has one wide angle, and an acute triangle has all sharp angles.

Quadrilaterals come in many types. Students learn to spot which ones count as parallelograms by checking for two pairs of sides that run parallel to each other, like opposite sides of a rectangle or a slanted diamond shape.

Students look at four-sided shapes and decide which ones are rectangles by checking for four right angles. A square counts too.

Students learn how many inches fit in a foot, centimeters in a meter, and seconds in a minute. Then they convert bigger units into smaller ones and record the results in a two-column table.

Word problems here involve measuring things like distance, time, money, and weight. Students add, subtract, multiply, or divide to find answers, work with fractions and decimals, and use number lines to show their work.

Students use formulas to find the distance around a rectangle and the space inside it. They apply both to real problems, like figuring out how much fencing a yard needs or how much tile covers a floor.

Students collect measurements in fractions like 1/2 or 1/4, plot them on a number line graph, then add or subtract those fractions to answer questions about the data.

An angle is the opening formed when two straight lines meet at a point. Students learn that a full circle has 360 degrees, and an angle is measured by how much of that circle it takes up.

Students use a protractor to measure angles and record the degrees. They also draw angles when given a specific degree measurement.

Angles can be split into smaller angles, and the parts always add up to the whole. Students find missing angle sizes by adding or subtracting the pieces they already know.

Each spot in a whole number is worth ten times the spot just to its right. The 4 in 400 is worth ten 40s, not one.

Students practice rounding whole numbers to the nearest ten, hundred, thousand, or beyond. They use what they know about place value to decide which round number a given number is closest to.

Students add and subtract large numbers quickly and accurately using the standard written method, lining up place values and carrying or borrowing as needed.

Students multiply large numbers, like 1,234 times 6 or 47 times 23, by breaking them apart by place value. They show their thinking with diagrams or equations, not just an answer.

Students divide numbers up to four digits by a single digit and find any remainder left over. They show how they solved it using a picture, a rectangle, or an equation.

Students read and write numbers up to the millions in three ways: as digits (304,000), as words ("three hundred four thousand"), and broken apart by place value (300,000 + 4,000).

Students look at two large numbers and decide which is bigger, smaller, or equal by checking the value of each digit by place. They record the result using the symbols >, =, or <.

A multiplication equation can show comparison, not just counting groups. Students read "35 = 5 x 7" as "35 is 5 times as many as 7" and write equations from phrases like "four times as many as six."

Word problems ask students to figure out when one amount is a certain number of times larger than another. Students choose multiplication or division, draw a diagram, and write an equation to solve it, telling apart "5 more than" from "5 times as many."

Students read a multi-step word problem, write an equation using a letter for the missing number, and solve it using addition, subtraction, multiplication, or division. Then they check whether the answer makes sense by estimating.

Students find every pair of whole numbers that multiply to make a given number, then decide whether that number is prime (only 1 and itself divide it evenly) or composite (more pairs exist). Work stays within numbers up to 100.

Follow a rule to build a number or shape pattern, then notice things about that pattern the rule never told you. For example, a rule might say "add 3" but students also spot that every result is odd.