What does a student learn in
California, Grade 4, Mathematics ?

Students draw and name basic parts of geometry: points, lines, line segments, rays, and angles. They also spot where lines cross at right angles or run side by side in flat shapes.

Students sort flat shapes by their sides and corners, deciding whether sides run parallel, meet at a right angle, or both. Right triangles get their own category.

Students identify lines of symmetry in two-dimensional shapes, explaining why a fold matches both halves. They practice spotting symmetry in everyday shapes like letters, flags, and simple figures.

Students use fraction models like number lines and area diagrams to show how fractions work. They connect the math they write to pictures and real objects, checking that their representations make sense.

Students identify lines of symmetry in flat shapes, checking whether one half folds exactly onto the other. They sort shapes by the number of lines of symmetry they have.

Students sort flat shapes like squares, triangles, and rectangles into groups based on what they have in common, such as equal sides or right corners.

Students learn how units of measurement relate to each other, like knowing 1 foot equals 12 inches or 1 kilogram equals 1,000 grams. They convert between larger and smaller units and record the pairs in a table.

Students solve word problems involving measurements like hours, miles, gallons, and dollars, using addition, subtraction, multiplication, or division. They also convert larger units into smaller ones, like turning 2 hours into 120 minutes, and draw number lines to show their work.

Students use the area and perimeter formulas for rectangles to solve real problems, like finding a missing side length when they know the total area. The math connects multiplication to the shape of a room or a floor.

Students record measurements like half-inch or quarter-inch lengths on a line plot, then use that chart to add and subtract fractions. For example, they might find how much longer the longest leaf is than the shortest.

An angle is the opening between two straight lines that meet at a point. Students learn that a full circle has 360 degrees, use a protractor to measure angles in whole-number degrees, and draw angles of a given size.

When a large angle is split into smaller angles, the pieces add up to the whole. Students find missing angle sizes by adding or subtracting the known parts, the way they would find a missing piece of a puzzle.

Each spot in a number is worth ten times more than the spot to its right. A 7 in the hundreds place is worth ten 7s in the tens place.

Students read, write, and compare large numbers in three ways: as numerals, as words, and as expanded form (like 3,000 + 400 + 20 + 5). They also use the symbols >, =, and < to show which number is larger or smaller.

Students round large numbers to the nearest ten, hundred, or thousand by looking at which digits matter most. This builds the number sense they use when adding and subtracting bigger numbers by hand.

Students add and subtract large numbers quickly and accurately using the step-by-step method taught in class. Think carrying and borrowing across multiple columns, done reliably without a calculator.

Students multiply large numbers, like 1,234 times 6 or 47 times 23, by breaking them into smaller, easier pieces based on place value. They show how the math works using diagrams and equations, not just the answer.

Students divide numbers up to the thousands by a single digit and find what is left over. They show how they solved it using drawings, arrays, or equations.

Students learn why 1/2 and 2/4 are the same amount, even though the pieces look different. They use diagrams to see how slicing a shape into more parts doesn't change the total, then use that idea to find and create equivalent fractions.

Students decide which of two fractions is larger, even when the bottom numbers don't match. They use symbols like > or < to record the comparison and explain their reasoning with a drawing or model.

Students work with fractions whose bottom numbers are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100. Fractions like one-half, three-fourths, and seven-tenths are fair game; anything with a bottom number outside that list is not covered yet.

Multiplying a fraction by a whole number. Students find out how many times a fraction fits into a larger amount, like figuring out how many quarter-miles make up three miles.

Students learn to rewrite a fraction like 3/10 as 30/100, then use that swap to add two fractions whose bottoms are 10 and 100. It builds the groundwork for working with decimals and cents.

Fractions with 10 or 100 on the bottom can be written as decimals. Students practice switching between forms, like seeing that 62/100 and 0.62 mean the same thing, then placing that number on a number line.

Students compare decimal numbers like 0.3 and 0.27, deciding which is larger or smaller using symbols like > and <. They back up their thinking with a number line or visual model.

Students learn that multiplication equations describe "times as many" relationships. For example, 35 = 5 x 7 means 35 is five times as many as 7, and students translate that kind of statement into an equation.

Word problems ask students to figure out when one amount is a certain number of times bigger than another. Students choose whether to multiply or divide to find the missing number, and explain why that's different from simply asking how much more one amount is than another.

Students read multi-step word problems and solve them using addition, subtraction, multiplication, and division. They use a letter to stand for the unknown number, then check whether their answer makes sense by estimating or rounding.

Students find every pair of numbers that multiply to make a given number, then decide if that number is prime (only divisible by 1 and itself) or composite (divisible by more numbers). They also spot and extend number patterns.

Students follow a rule (like "add 3" or "double it") to build a number or shape pattern, then notice something the rule never mentioned, such as every other number being odd.