Search the California Content Standards

Cluster:
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Standard:
Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Cluster:
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Standard:
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Cluster:
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Standard:
Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

Cluster:
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Standard:
Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Apply the formulas V = l × w × h and V = b × 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.

Cluster:
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Standard:
Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems.

Cluster:
Understand ratio concepts and use ratio reasoning to solve problems.

Standard:
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

Cluster:
Understand ratio concepts and use ratio reasoning to solve problems.

Standard:
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

Footnote:
Expectations for unit rates in this grade are limited to non-complex fractions.

Cluster:
Understand ratio concepts and use ratio reasoning to solve problems.

Standard:
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Cluster:
Understand ratio concepts and use ratio reasoning to solve problems.

Standard:
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Cluster:
Understand ratio concepts and use ratio reasoning to solve problems.

Standard:
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.