What does a student learn in StateAlaska,GradeGrade 5,SubjectMathematics?

Parentheses change which part of a math problem gets solved first. Students read and write expressions like (3 + 2) x 4, following the order the symbols set.

Students write math expressions like (4 + 3) x 2 to describe a calculation, then read someone else's expression and explain what it means without actually solving it.

Students follow two different counting rules to build two number sequences, then compare how the sequences relate to each other. They plot matching pairs of numbers on a grid to see that relationship as a picture.

Each digit in a number is worth 10 times more than the same digit one step to its right. The 4 in 400 is worth ten 4s in 40, and ten times less than the 4 in 4,000.

Students learn why multiplying by 10, 100, or 1,000 shifts digits to the left and dividing shifts them right. They also practice writing those powers of 10 using exponents, like 10^2 instead of 100.

Students read, write, and compare decimal numbers down to the thousandths place (like 3.847). They understand what each digit means and can say which of two decimals is larger or smaller.

Students read and write decimal numbers three places past the decimal point in three ways: as a standard number, as words, and broken into each digit's value (like 347.392 = 3 hundreds + 4 tens + 7 ones + 3 tenths + 9 hundredths + 2 thousandths).

Students compare decimal numbers out to the thousandths place and record which is greater, lesser, or equal using the symbols >, <, and =. The comparison depends on what each digit is worth in its position, not just how the numbers look.

Students practice rounding decimal numbers to a chosen place, like the nearest tenth or whole number. They use their understanding of place value to decide whether a number rounds up or down.

Students multiply large whole numbers quickly and accurately using the standard step-by-step method taught in class. Think multiplying a three-digit number by a two-digit number, carrying digits and working column by column.

Students divide large numbers (up to four digits) by a two-digit number and show how they got the answer. They use tools like number lines, arrays, or real-life situations to explain their thinking.

Students add, subtract, multiply, and divide decimal numbers like $1.25 or $3.40. They use place value and real models to work out the math, then explain in writing why their method makes sense.

Students practice switching between units of measurement, like converting inches to feet or centimeters to meters, then use those conversions to solve real-world math problems that take more than one step.

Students figure out the time difference between cities in different parts of the world. For example, if it's 3 p.m. in New York, what time is it in Tokyo?

Students collect measurements in fractions and plot each one on a number line graph. Then they use that graph to answer questions, like which measurement shows up most or how much larger one group is than another.

Students look at graphs and data sets from real-world problems, then explain what the numbers show. They find the mean (the average) and the median (the middle value) to describe what the data tells them.

Students learn that volume measures how much space a solid object takes up. They figure out how many same-size cubes would fill a box or other 3-D shape, which sets up the formulas they use to calculate volume later.

A unit cube is a small cube where every side measures 1 unit. Students use it as the basic building block for measuring volume, the same way a ruler uses inches to measure length.

Students learn that volume is just a count of how many small cubes fill a solid shape with no gaps. If 24 cubes pack a box perfectly, the box holds 24 cubic units.

Students figure out how much space a 3-D shape holds by counting the small cubes packed inside it. They practice with cubes measured in centimeters, inches, or feet.

Students figure out how much space a 3-D shape holds by counting the small cubes packed inside it. They practice with cubes measured in inches, centimeters, or feet.

Students find the volume of boxes and other rectangular shapes by multiplying length, width, and height, or by breaking a shape into pieces and adding the volumes together. They apply both methods to solve real-world problems.

Students figure out how much space fits inside a box by imagining it packed with small cubes, then check that multiplying the three side lengths gives the same answer. Both methods count the same space.

Students use two volume formulas to find how much space fits inside a box-shaped object. They practice with real measurements, like figuring out how many cubic feet fill a storage bin or a classroom aquarium.

Students find the total volume of an irregular solid by splitting it into two box-shaped pieces, calculating each piece separately, and adding the results together.

Students add and subtract fractions that have different bottom numbers, like 1/2 and 1/3, by rewriting them so the bottom numbers match. This works with mixed numbers too, like 2 1/4 plus 1 1/3.

Students solve story problems that add or subtract fractions with different bottom numbers, like 1/2 plus 1/3. They also use familiar fractions such as 1/2 to quickly check whether their answer makes sense.

Dividing a whole number by another whole number sometimes gives an answer that is a fraction or mixed number. Students learn that 3/4 means "3 divided by 4," then solve real-world problems where sharing or splitting leads to those kinds of answers.

Multiplying a fraction by another fraction or a whole number. Students find a part of a part, like figuring out what half of three-quarters actually is, and learn why the answer is often smaller than the numbers they started with.

Multiplying a fraction by a whole number means splitting that whole number into equal parts and taking some of those parts. For example, (2/3) x 6 means splitting 6 into 3 equal parts and taking 2 of them.

Students find the area of a rectangle whose sides are fractions by multiplying those side lengths together. They also show why that multiplication works by filling the rectangle with small equal squares.

Multiplying a number doesn't always make it bigger. Students learn to predict whether a product will be larger or smaller than the starting number based on what the second number looks like as a fraction.

Multiplying a number by a fraction less than 1 makes the result smaller than what you started with. Students figure this out by thinking about the fraction's size, not by doing the multiplication.

Students explain why multiplying a number by a fraction bigger than 1 makes the answer larger, and why multiplying by a fraction smaller than 1 makes the answer smaller. They connect that idea to what happens when a fraction is multiplied by 1.

Students multiply fractions and mixed numbers to solve everyday problems, like finding the area of a garden that is 2 and a half by 3 and three-quarters feet. They may draw a picture or write an equation to show their thinking.

Dividing a fraction like 1/3 by a whole number, or dividing a whole number by a fraction like 1/4. Students learn what happens to the size of a number when you split it into fractional parts or group it by a fraction.

Dividing a fraction by a whole number means splitting that fraction into even smaller pieces. Students figure out, for example, how much of a pizza each person gets when one-third is shared among 4 people.

Dividing a whole number by a fraction means asking how many of those fraction-sized pieces fit into the whole. Students solve problems like 3 divided by 1/4 and explain what the answer means.

Students solve everyday problems that involve splitting a fraction into equal groups or dividing a whole number into fractional pieces. They draw diagrams or write equations to show their thinking.

Students learn to plot points on a grid using two numbers, like (3, 5). The first number shows how far to move across, the second shows how far to move up.

Students plot points on a grid using two numbers (across, then up) to show real-world information, like mapping a route or tracking data. They also read a point's location and explain what it means in the problem.

A rectangle is a parallelogram, so every rule that applies to parallelograms also applies to rectangles. Students learn that shape categories work like nesting dolls: properties of a broader group carry down to every shape inside it.

Shapes belong to families. Students sort polygons like rectangles and rhombuses into overlapping groups based on shared traits, such as equal sides or right angles, and explain why one shape can belong to more than one category.