Standards - Mathematics

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and illustrate using visual fraction models, drawings, and equations to represent the problem.

Create a story context for a unit fraction divided by a whole number, and use a visual fraction model to show the quotient.

Create a story context for a whole number divided by a unit fraction, and use a visual fraction model to show the quotient.

Make a line plot to display a data set of measurements in fractions of a unit ($\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{8}$).

Add, subtract, multiply, and divide fractions to solve problems involving information presented in line plots.

Note: Division is limited to unit fractions by whole numbers and whole numbers by unit fractions.

Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems.

Identify volume as an attribute of solid figures, and measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised (non-standard) units.

Pack a solid figure without gaps or overlaps using n unit cubes to demonstrate volume as n cubic units.

Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume.

Use the associative property of multiplication to find the volume of a right rectangular prism and relate it to packing the prism with unit cubes. Show that the volume can be determined by multiplying the three edge lengths or by multiplying the height by the area of the base.

Apply the formulas $V = l \times w \times h$ and $V = B \times h$ for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.

Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the two parts, applying this technique to solve real-world problems.

Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.

Classify triangles according to side length (isosceles, equilateral, scalene) and angle measure (acute, obtuse, right, equiangular).

Classify quadrilaterals in a hierarchy based on properties.

Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Use appropriate notations [a/b, a to b, a:b] to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities.

Use unit rates to represent and describe ratio relationships.

Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

Interpret and compute quotients of fractions using visual models and equations to represent problems.

Use quotients of fractions to analyze and solve problems.

Fluently divide multi-digit whole numbers using a standard algorithm to solve real-world and mathematical problems.

Add, subtract, multiply, and divide decimals using a standard algorithm.

Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.

Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

Use factors and multiples to determine prime factorization.

Use signed numbers to describe quantities that have opposite directions or values and to represent quantities in real-world contexts.

Locate integers and other rational numbers on a horizontal or vertical line diagram.

Define opposites as numbers located on opposite sides of 0 and the same distance from 0 on a number line.

Use rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.

Find the position of pairs of integers and other rational numbers on the coordinate plane.

Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

Identify (a,b) and (a,-b) as reflections across the x-axis.

Identify (a,b) and (-a,b) as reflections across the y-axis.