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

Fractions with denominators like 10 or 25 can be rewritten as decimals. Students convert between the two forms and explain why they name the same amount.

Fractions and decimals are two ways to write the same amount. Students learn that one-half and 0.5 mean the same thing, and practice switching between fraction and decimal form for numbers with denominators like 10 or 100.

Students switch between fraction and decimal form for the same number, like writing 0.25 as 1/4 or 3/4 as 0.75. Both forms name the same amount, just written differently.

Students compare fractions and decimals out to three places after the decimal point, then use >, =, or < to show which is larger, smaller, or equal. They also explain how they know.

Adding, subtracting, multiplying, and dividing fractions and decimals. Students work through problems that mix both, building the number sense they need before algebra.

Before adding, subtracting, or multiplying fractions and decimals, students predict roughly what the answer should be. That quick check helps them catch mistakes before they happen.

Before multiplying two fractions, students predict whether the answer will be bigger or smaller than the numbers they started with. They use what they know about the size of each fraction to make a reasonable guess before doing any math.

Multiplying by a fraction bigger than 1 (like 5/4) makes the answer larger than the number you started with. Students explain why that happens, not just calculate it.

Multiplying by a fraction smaller than 1 shrinks the number. Students explain why, using a picture or words to show that taking part of something gives you less than what you started with.

Multiplying the top and bottom of a fraction by the same number keeps its value the same. Students explain why this works, connecting it to the idea that any number divided by itself equals 1.

Adding and subtracting fractions gets harder when the bottom numbers don't match. Students find a common denominator, rewrite the fractions so they match, then add or subtract, including problems that mix whole numbers with fractions.

Students connect fraction multiplication to rectangle area by seeing that multiplying two fractions gives the same result as finding how much space a rectangle covers when its sides are measured in fractions of a foot, inch, or other unit.

Students multiply a fraction by a whole number and a whole number by a fraction, then explain what the answer means in context. For example, they work out what three-quarters of 12 looks like, or how many groups of 8 fit into a fraction problem.

Students multiply two fractions that are each smaller than 1 and explain what the answer means. For example, finding half of a quarter gives a smaller piece than either fraction started with.

Dividing a fraction by a whole number means splitting a fraction into even smaller pieces. Students find the answer and explain what it means, like figuring out how much of a pizza each person gets when half a pizza is shared among three people.

Students divide a whole number by a fraction like 1/2 or 1/4 and explain what the answer means. For example, how many quarter-cups fit in 3 cups? Students find that number and describe what it represents in the problem.

Students look at number patterns and figure out the rule behind them. Then they use that rule to predict what comes next or describe how two quantities change together.

Students follow two separate counting rules to build two number sequences, then look at how the sequences relate to each other. For example, one rule might say "add 3" and another "add 6."

Students take two number patterns and pair up their matching terms as coordinates, like (2, 6), ready to plot on a graph.

Students plot pairs of numbers from a pattern onto a grid with an x-axis and a y-axis, then look at the shape the points form to describe the relationship between the two values.

Students look at two number patterns side by side and describe how one relates to the other, such as noticing that one sequence is always double the other.

Students look at a sequence of numbers and write a rule that explains how it works, such as "multiply by 3 each time" or "add 5 to the previous number."

Students use addition, subtraction, multiplication, and division to set up and solve word problems. The focus is writing the math sentence that fits the situation, not just finding the answer.

Multi-step word problems ask students to use addition, subtraction, multiplication, or division across two or more steps, with some values replaced by a letter standing in for an unknown number. Students solve and explain how they got the answer.

Students sort flat shapes like squares and triangles, and solid shapes like cubes and cones, into groups based on their properties, such as the number of sides or whether faces are flat or curved.

Students sort shapes into groups and subgroups based on their properties. A square belongs under rectangles, which belongs under quadrilaterals, building a family tree of shapes from most specific to most general.

Students measure how much space a 3D shape takes up by counting unit cubes or using a formula. This is volume, and fifth graders apply it to rectangular boxes.

A unit cube is a perfect cube where every edge measures 1 unit. Students use it as the basic building block for measuring volume, the same way a square tile measures area.

Students figure out the volume of a box-shaped object by thinking about it as stacked layers. Multiply the area of the bottom face by the number of layers to get the total space inside.

Students plot points on a grid using two numbers, one for how far across and one for how far up, then use that grid to solve math problems.

Students plot points on a grid where two number lines cross at zero. Reading the grid means finding how far right and how far up a point sits from that corner.

Students read any dot on a grid by naming two numbers: how far it sits to the right and how far it sits up. Those two numbers, written as a pair, give the dot its exact address on the graph.

The first number in a coordinate pair tells how far to move right from the starting point (0,0) before moving up or down. Students use that number to place or read points on a grid.

The second number in an ordered pair tells how far up a point sits from the starting corner of the grid. Students use that count to plot or read any location on the coordinate plane.

Students convert between units in the same system, like inches to feet or grams to kilograms, and use those conversions to solve word problems.

Students convert between units like inches and feet, or ounces and pounds, to solve problems that take more than one step. The focus is on knowing when a conversion is needed and carrying it through the full problem.

Students collect data, display it in graphs or tables, and draw conclusions from what the numbers show.

Students plot measurements on a number-line graph, then study the results to answer questions. They identify values that stand apart from the rest and find the middle value in the data set.