What does a student learn in StateKansas,GradeGrade 4,SubjectMathematics?

Students learn that multiplication equations can describe comparisons. For example, 35 = 5 x 7 means 35 is five times as many as 7. They also turn comparison phrases like "four times as many as 6" into equations.

Word problems ask students to figure out how many times bigger or longer one amount is than another. Students write a multiplication or division equation to solve it, using a box or letter to stand in for the missing number.

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

Students find every pair of whole numbers that multiply to make a given number, then decide whether that number is prime (only divisible by 1 and itself) or composite (divisible by smaller numbers too).

Students follow a rule (like "add 3") to build a number or shape pattern, then notice something the rule never mentioned, such as the numbers keep switching between odd and even. They explain in plain words why that keeps happening.

Each place in a number is worth ten times the place to its right. The 4 in 400 is worth ten times the 4 in 40.

Students read, write, and compare large whole numbers in multiple ways: as numerals, as words, and broken apart by place value. They use symbols like > and < to show which number is bigger or smaller.

Students learn to round any large number to the nearest ten, hundred, thousand, or beyond. They look at the digits around a given place to decide whether to round up or down.

Students add and subtract large whole numbers quickly and accurately, using a method that makes sense to them. The focus is on getting the right answer reliably, not on using one specific procedure.

Students multiply large numbers, like 1,234 times 6 or 47 times 23, by breaking them into smaller, friendlier pieces. They show their thinking using pictures, grids, or equations.

Students divide numbers up to four digits by a single digit and find any remainder left over. They show how they got the answer using a drawing, a grid, or an equation.

Students collect measurements in fractions and plot them on a line plot or bar graph. Then they use that graph to add and subtract the fractions they see.

Students learn how units of measurement relate to each other, like how many centimeters fit in a meter or minutes in an hour. They practice converting a larger unit into its smaller equivalent and recording those pairs in a simple table.

Students use addition, subtraction, multiplication, and division to solve word problems about miles, minutes, gallons, pounds, and dollars. They also draw number lines to show measurements like half a meter or 1.5 hours.

Students use formulas to find the area and perimeter of rectangles, then explain why they chose square units for area or linear units for perimeter. Problems connect to real situations like flooring a room or fencing a yard.

Students draw and name the basic building blocks of geometry: points, lines, rays, and angles (including right, acute, and obtuse). They also spot these features inside flat shapes like triangles and rectangles.

Students sort flat shapes by their angles and sides. A triangle with all equal sides gets a different label than one with a corner like a right angle, and rectangles get sorted apart from other four-sided shapes based on whether their sides run parallel or meet at a square corner.

Students learn to spot the fold line on a shape that splits it into two matching halves. They also draw those fold lines on shapes like letters, stars, and other flat figures.

Students learn why 1/2 and 2/4 name the same amount, even though one pizza is cut into fewer, bigger slices. They use pictures and diagrams to find other fractions that land in the same spot on the number line.

Students compare two fractions with different top and bottom numbers and decide which is larger, smaller, or equal. They explain their reasoning using pictures or number lines and write the answer using symbols like > or <.

Adding fractions means combining smaller "unit" fractions that all share the same bottom number. Students learn that 3/4 is just three one-fourths added together, the same way 3 ones add up to 3.

Adding fractions means joining pieces of the same whole. Subtracting fractions means removing pieces from that same whole, the way students might add or remove slices from one pizza.

Students break a fraction into smaller pieces that add back up to the original, then write an equation to show their thinking. For example, 3/4 can be written as 1/4 + 1/4 + 1/4, or as 2/4 + 1/4.

Students add and subtract mixed numbers that share the same bottom number, like 2 3/4 plus 1 1/4. They can convert the mixed numbers into fractions first or use what they know about addition and subtraction to solve.

Students solve story problems that add or subtract fractions with the same bottom number, like figuring out how much pizza is left after two slices are eaten. They may draw a picture or write an equation to show their work.

Multiplying a fraction by a whole number means figuring out, say, how much total pizza you'd have if each person gets 2/3 of a pie and there are 4 people. Students build on what they know about multiplication to solve problems like that.

Multiplying a fraction by a whole number starts with seeing that any fraction is just several copies of one small piece. For example, 3/4 means three copies of 1/4, the way 3 apples means three single apples.

Multiplying a fraction by a whole number means seeing 3 x (2/5) as three groups of two one-fifth pieces. Students learn to find the total by multiplying the top number while keeping the bottom number the same.

Word problems ask students to multiply a fraction by a whole number, like finding how many cups are needed if each batch uses 2/3 of a cup and you make 4 batches. Students set up the math and solve it.

Students learn that 3/10 is the same as 30/100, then use that idea to add tenths and hundredths together. This builds the foundation for working with decimals and money.

Fractions with 10 or 100 on the bottom can be written as decimals. A fraction like 3/10 becomes 0.3, and 45/100 becomes 0.45.

Students look at two decimal numbers, like 0.35 and 0.4, and decide which is larger or smaller. They use the symbols >, <, or = to record the comparison and explain their reasoning with a number line or grid.