Search the California Content Standards

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:
Use equivalent fractions as a strategy to add and subtract fractions.

Standard:
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Cluster:
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Standard:
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Cluster:
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Standard:
Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Cluster:
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Standard:
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, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

Overarching Standard Description:
The student will organize, synthesize, create, and communicate information.

Standard:
Use information and technology creatively to answer a question, solve a problem, or enrich understanding: a. Use a thesaurus to edit and revise manuscripts to improve the meaning and focus of writing.

Standard:
Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently.

Standard:
Use flowcharts and/or pseudocode to design and illustrate algorithms that solve complex problems.

Descriptive Statement:
Complex problems are problems that would be difficult for students to solve without breaking them down into multiple steps. Flowcharts and pseudocode are used to design and illustrate the breakdown of steps in an algorithm. Students design and illustrate algorithms using pseudocode and/or flowcharts that organize and sequence the breakdown of steps for solving complex problems. For example, students might use a flowchart to illustrate an algorithm that produces a recommendation for purchasing sneakers based on inputs such as size, colors, brand, comfort, and cost. Alternatively, students could write pseudocode to express an algorithm for suggesting their outfit for the day, based on inputs such as the weather, color preferences, and day of the week.