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.

Enduring Understanding: Musicians connect their personal interests, experiences, ideas, and knowledge to creating, performing, and responding.
Essential Question(s): How do musicians make meaningful connections to creating, performing, and responding?
Process Component(s): Synthesize

Performance Standard(s):
Explain and demonstrate how personal interests, experiences, ideas, and knowledge relate to creating, performing, and responding to music.

Enduring Understanding: Musicians connect societal, cultural, and historical contexts when creating, performing, and responding.
Essential Question(s): How do musicians make meaningful connections to societal, cultural, and historical contexts when creating, performing, and responding?
Process Component(s): Relate

Performance Standard(s):
Explain and demonstrate connections between music and societal, cultural, and historical contexts.

Enduring Understanding: The creative ideas, concepts, and feelings that influence musicians’ work emerge from a variety of sources.
Essential Question(s): How do musicians generate creative ideas?
Process Component(s): Imagine

Performance Standard(s):
a. Improvise rhythmic, melodic, and harmonic ideas, and explain connection to specific purpose and context (such as social, cultural, and historical). b. Generate musical ideas (such as rhythms, melodies, and accompaniment patterns) within specific related tonalities, meters, and simple chord changes.

Cluster:
Perform operations with multi-digit whole numbers and with decimals to hundredths.

Standard:
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Cluster:
Perform operations with multi-digit whole numbers and with decimals to hundredths.

Standard:
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

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

Standard:
Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

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. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

Footnote:
Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.