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

Students use addition, subtraction, multiplication, and division to solve word problems with whole numbers. The focus is on choosing the right operation, not just calculating an answer.

Students read a multiplication equation and explain what it means as a comparison: 35 = 5 x 7 means 35 is five times as many as 7. They also write equations when a comparison is described in words.

Word problems ask students to compare two amounts by multiplying or dividing. For example, "six times as many" or "three times as long" means students set up a multiplication or division equation to find the missing number.

Word problems that take more than one step to solve, using addition, subtraction, multiplication, or division. Students figure out what to do with a remainder when division doesn't come out evenly.

Students write math equations using a letter like n to stand for the missing number in a word problem. The letter acts as a placeholder until they solve for it.

Students check whether an answer makes sense by rounding numbers or estimating in their head before or after solving a problem. If the real answer is way off from the estimate, they know to look for a mistake.

Students learn to break a number apart into the smaller numbers that multiply to make it, and to find numbers that a given number divides into evenly.

Students list every pair of whole numbers that multiply together to reach a given number, like finding that 4 and 6 both multiply to make 24. They do this for any number up to 100.

Students learn that if a number divides evenly into another, the bigger number is a multiple of it. For example, since 3 divides evenly into 12, that makes 12 a multiple of 3.

Students pick a number between 1 and 100 and figure out whether it can be divided evenly by a single-digit number, like checking if 36 is a multiple of 4.

Students decide whether a number up to 100 can only be divided evenly by 1 and itself, or whether it has other divisors too. That distinction is the difference between a prime and a composite number.

Students practice spotting rules in number or shape patterns, then use those rules to predict what comes next or explain why the pattern works.

Students create a pattern by following a rule (like "add 3 each time"), then notice something extra the rule never said, such as all the numbers being odd. They explain what they spotted.

Students learn how the position of a digit in a number changes its value. A 3 in the hundreds place means something very different from a 3 in the thousands place, and students work with numbers all the way up to one million.

Each place in a number is worth ten times more than the place just to its right. The 4 in 400 is worth ten times as much as the 4 in 40.

Students read, write, and compare large numbers up to one million in three ways: as digits (304,000), as words (three hundred four thousand), and broken apart by place value. They also use the symbols >, =, and < to show which number is bigger or smaller.

Students round large numbers to the nearest ten, hundred, thousand, or beyond. They use what they know about place value to decide whether a number like 34,871 rounds up or down.

Students add, subtract, multiply, and divide large whole numbers up to one million by thinking carefully about place value. They learn the patterns that make working with big numbers manageable.

Students add and subtract large numbers, up to a million, using the standard stacking method with regrouping. The goal is accuracy and speed, not just getting the right answer sometimes.

Students multiply large numbers by a single digit and multiply two two-digit numbers together, such as 1,234 x 6 or 47 x 23, using place value to keep track of each step.

Students multiply large numbers by breaking them into hundreds, tens, and ones, then combining the parts. This is the thinking behind the standard multiplication algorithm.

Students show how they solved a multiplication problem by drawing a rectangle split into sections or writing out an equation. The picture or equation explains the thinking behind the answer, not just the answer itself.

Dividing a big number (up to four digits) by a single digit, students find how many times it goes in evenly and what's left over. Think 2,748 divided by 6, with a remainder.

Students divide large numbers by breaking them into smaller, friendlier parts, using what they know about place value and how multiplication and division work together.

Students show how they solved a division problem by drawing a rectangle broken into parts or writing an equation, so the math is visible, not just the answer.

Fractions can look different but mean the same amount. Students find equal fractions and put fractions in order from smallest to largest, using what they know about how fractions are built.

Students learn that 1/2 and 2/4 take up the same amount of space, even though the pieces are different sizes. They use drawings or diagrams to show why two fractions that look different can be equal, and practice creating their own equivalent pairs.

Students compare two fractions that have different top and bottom numbers by finding a common denominator or by checking each fraction against a familiar landmark like one-half. They decide which fraction is larger, smaller, or equal.

Two fractions are only worth comparing when they refer to the same-sized whole. Half a small pizza and half a large pizza are both "one half," but they are not equal amounts.

Students compare two fractions and write >, =, or < between them. Then they back up their answer by drawing a fraction model or explaining in words why one fraction is larger, smaller, or equal.

Students use what they already know about adding and subtracting whole numbers to build fractions from smaller pieces. A unit fraction like 1/4 is the building block, and students combine or break apart those pieces to work with larger fractions.

Adding fractions means combining smaller same-denominator pieces into a larger one. Students see that 3/4 is just three 1/4 pieces added together, the same way they would add whole numbers.

Adding fractions means joining pieces of the same whole. Subtracting fractions means removing pieces from that same whole, the way you'd add or remove slices from one pizza, not two different-sized ones.

Students break one fraction into smaller pieces that add up to the same amount, finding more than one way to do it. For example, 3/4 can be written as 1/4 + 2/4 or as 1/4 + 1/4 + 1/4, then shown with a drawing or explained in words.

Students add and subtract mixed numbers (like 2 1/4 + 1 3/4) when the fractions share the same bottom number. They convert mixed numbers into fractions or use what they know about addition and subtraction to find the answer.

Students solve story problems that add or subtract fractions and mixed numbers that share the same bottom number, then explain their answer using a fraction bar, number line, or their own words.

Multiplying a fraction by a whole number means finding the total when the same fraction repeats. If you eat 2/3 of a pizza three times, students find that total by multiplying, the same way they would with whole numbers.

A fraction like 3/4 is just the unit fraction 1/4 counted three times. Students learn to see any fraction as a whole number of equal-sized pieces stacked together.

Multiplying a fraction by a whole number works like repeated addition. Students learn that 3 x (2/5) is the same as adding 2/5 three times, which gives them 6/5.

Word problems ask students to multiply a fraction by a whole number, like finding how many cups of juice are needed if each person gets 3/4 of a cup. Students use a drawing or equation to show their thinking and find the answer.

Students learn that fractions like 3/10 can also be written as 0.3, and that decimals on a number line or hundredths grid can be compared to find which is larger.

Students learn that 3/10 is the same as 30/100, then use that swap to add fractions like 3/10 and 4/100 by giving them a matching denominator.

Students write fractions with a 10 or 100 in the bottom as decimals. So 3/10 becomes 0.3 and 47/100 becomes 0.47.

Students compare two decimal numbers, like 0.4 and 0.37, and explain which is larger by thinking about what each number actually represents. They show their reasoning, not just the answer.

Comparing decimals only works when both numbers describe the same whole. Seven tenths of a small pizza is not the same as seven tenths of a large one, so students learn to check that both decimals refer to the same-size whole before deciding which is greater.

Students compare two decimals and write >, =, or < between them. Then they explain their thinking using a number line, a drawing, or a sentence.

Students measure and convert units, like turning feet into inches or hours into minutes. They practice changing a bigger unit into the matching number of smaller units to solve real problems.

Students learn how the units inside a measurement system relate to each other: a foot is 12 inches, a pound is 16 ounces, an hour is 60 minutes. They practice converting from bigger units to smaller ones and recording what they find.

Students learn that bigger units of measurement can be broken into smaller ones. For example, 1 foot equals 12 inches, 1 hour equals 60 minutes, and 1 kilogram equals 1,000 grams.

Students fill in a two-column table that pairs a larger unit with its smaller equivalent, such as feet next to inches or hours next to minutes.

Word problems ask students to add, subtract, multiply, or divide measurements like hours, miles, pounds, and dollars. Students pick the right operation and solve, showing their work.

Students solve measurement word problems that include fractions or decimals, such as finding a total length in feet and inches or a weight in pounds and half-pounds.

Students practice converting bigger units into smaller ones, like turning 3 feet into 36 inches or 2 hours into 120 minutes. They solve word problems where the answer requires working in the smaller unit.

Students draw a number line with a measurement scale to show distances, lengths, or other amounts. This helps them place measurements in order and see how far apart two values are.

Students find the area and perimeter of rectangles by using formulas, then apply those skills to real problems like figuring out how much carpet a room needs or how much fencing surrounds a yard.

Students read and build graphs, line plots, and charts using measurement data. They answer questions about what the data shows, like comparing totals or finding differences between groups.

Students collect measurements in halves, quarters, or eighths and plot each one as a dot on a number line. Then they use that chart to add and subtract fractions.

Students learn what an angle is and how to measure it in degrees, the way you might measure a turn of a clock hand. They use a protractor to find the size of angles in real shapes.

Two straight lines that meet at a point form an angle. Students learn what angles are, how they're measured in degrees, and why a larger angle means a wider opening between the two lines.

An angle is a slice of a circle. Students learn that the size of an angle depends on how much of the circle it cuts through, measured from the point where two lines meet at the center.

Students learn that an angle's measure is just a count of one-degree turns. An angle that sweeps through 47 of those turns measures 47 degrees.

Students use a protractor to measure angles in whole-number degrees, then draw angles when given a specific degree. Think of it like reading a clock face, but for the exact opening between two lines.

Students figure out a missing angle by adding or subtracting the angles they already know. For example, if a corner is split into two parts and one part measures 50 degrees, students find what the other part must be.

Students find a missing angle by writing an equation, the way they'd write 90 = 55 + ? to figure out what's left after one angle takes up part of a corner.

When a big angle is split into smaller angles, the smaller angles add up to the whole. Students use this to find a missing angle size when part of the measurement is already known.

Students sort shapes by their angles and sides, spotting right angles, parallel lines, and other features that tell one shape from another.

Students learn to draw and name the basic parts of geometry: points, lines, rays, and angles (sharp, square, and wide-open). They also spot these features inside flat shapes like triangles and rectangles.

Students sort shapes by whether their sides run parallel, meet at a right angle, or neither. They also learn to spot right triangles by their square corner.

Students learn to spot the fold line that splits a shape into two matching halves, then draw that line themselves. A butterfly's wings or a heart are good examples of shapes with this kind of symmetry.