CCSS Math Errata - Content Standards (CA Dept of Education)



Errata Sheet

California Common Core State Standards: Mathematics

Following is a list of corrections to the California Common Core State Standards: Mathematics, published in 2013 by the California Department of Education. These corrections will be implemented in the next printing of the document. Corrections are current as of February 5, 2014.

|Section |Page |Standard Number or Entry |Reads |Should Read |

|Grade 5 |37 |5.NF.5b |b. Explaining why multiplying a given |b. Explaining why multiplying a given |

| | | |number by a fraction greater than 1 |number by a fraction greater than 1 |

| | | |results in a product greater than the |results in a product greater than the |

| | | |given number (recognizing |given number (recognizing |

| | | |multiplication by whole numbers greater|multiplication by whole numbers greater|

| | | |than 1 as a familiar case); explaining |than 1 as a familiar case); explaining |

| | | |why multiplying a given number by a |why multiplying a given number by a |

| | | |fraction less than 1 results in a |fraction less than 1 results in a |

| | | |product smaller than the given number; |product smaller than the given number; |

| | | |and relating the principle of fraction |and relating the principle of fraction |

| | | |equivalence a/b = (n × a)/(n b) to the |equivalence a/b = (n × a)/(n × b) to |

| | | |effect of multiplying a/b by 1. |the effect of multiplying a/b by 1. |

|Grade 8 |54 |8.NS.2 |2. Use rational approximations of |2. Use rational approximations of |

| | | |irrational numbers to compare the size |irrational numbers to compare the size |

| | | |of irrational numbers, locate them |of irrational numbers, locate them |

| | | |approximately on a number line diagram,|approximately on a number line diagram,|

| | | |and estimate the value of expressions |and estimate the value of expressions |

| | | |(e.g., π2). For example, by truncating |(e.g., π2). For example, by truncating |

| | | |the decimal expansion of √2, show that |the decimal expansion of √2, show that |

| | | |√2 is between 1 and 2, then between 1.4|√2 is between 1 and 2, then between 1.4|

| | | |and 1.5, and explain how to continue on|and 1.5, and explain how to continue on|

| | | |to get better approximations. |to get better approximations. |

|Algebra I |64 |N-RN.1 |1. Explain how the definition of the |1. Explain how the definition of the |

| | | |meaning of rational exponents follows |meaning of rational exponents follows |

| | | |from extending the properties of |from extending the properties of |

| | | |integer exponents to those values, |integer exponents to those values, |

| | | |allowing for a notation for radicals in|allowing for a notation for radicals in|

| | | |terms of rational exponents. For |terms of rational exponents. For |

| | | |example, we define 51/3 to be the cube |example, we define 51/3 to be the cube |

| | | |root of 5 because we want (51/3)3 = |root of 5 because we want (51/3)3 = |

| | | |5(1/3)3 to hold, so (51/3)3 must equal |5(1/3)3 to hold, so (51/3)3 must equal |

| | | |5. |5. |

|Algebra II |82 |F-BF.4a |a. Solve an equation of the form f(x) =|a. Solve an equation of the form f(x) =|

| | | |c for a simple function f that has an |c for a simple function f that has an |

| | | |inverse and write an expression for the|inverse and write an expression for the|

| | | |inverse. For example, f(x) =2x3 or f(x)|inverse. For example, f(x) =2x3 or f(x)|

| | | |= (x + 1)/(x × 1) for x ≠ 1. |= (x + 1)/(x – 1) for x ≠ 1. |

|Algebra II |83 |F-TF.8. |Prove the Pythagorean identity sin2(θ) |Prove the Pythagorean identity sin2(θ) |

| | | |+ cos2(θ) = 1 and use it to find |+ cos2(θ) = 1 and use it to find |

| | | |sin(θ), cos(θ), or tan(θ) given sin(θ),|sin(θ), cos(θ), or tan(θ) given sin(θ),|

| | | |cos(θ), or tan(θ) and the quadrant. |cos(θ), or tan(θ) and the quadrant of |

| | | | |the angle. |

|Mathematics II |98 |A-SSE.1b |b. Interpret complicated expressions by|b. Interpret complicated expressions by|

| | | |viewing one or more of their parts as a|viewing one or more of their parts as a|

| | | |single entity. For example, interpret |single entity. For example, interpret |

| | | |P(1 + r)n as the product of P and a |P(1 + r)n as the product of P and a |

| | | |factor not depending on P. ( |factor not depending on P. ( |

|Mathematics II |99 |A-SSE.3c |c. Use the properties of exponents to |c. Use the properties of exponents to |

| | | |transform expressions for exponential |transform expressions for exponential |

| | | |functions. For example, the expression |functions. For example, the expression |

| | | |1.15t can be rewritten as (1.151/12)12t|1.15t can be rewritten as |

| | | |≈ 1.01212t to reveal the approximate |(1.151/12)12t≈ 1.01212t to reveal the |

| | | |equivalent monthly interest rate if the|approximate equivalent monthly interest|

| | | |annual rate is 15%. |rate if the annual rate is 15%. |

|Mathematics II |101 |F-TF.8 |Prove the Pythagorean identity sin2(θ) |Prove the Pythagorean identity sin2(θ) |

| | | |+ cos2(θ) = 1 and use it to find |+ cos2(θ) = 1 and use it to find |

| | | |sin(θ), cos(θ), or tan(θ) given sin(θ),|sin(θ), cos(θ), or tan(θ) given sin(θ),|

| | | |cos(θ), or tan(θ) and the quadrant. |cos(θ), or tan(θ) and the quadrant of |

| | | | |the angle. |

|Mathematics III |110 |F-LE.4 |4. For exponential models, express as a|4. For exponential models, express as a|

| | | |logarithm the solution to abct = d |logarithm the solution to abct = d |

| | | |where a, c, and d are numbers and the |where a, c, and d are numbers and the |

| | | |base b is 2, 10, or e; evaluate the |base b is 2, 10, or e; evaluate the |

| | | |logarithm using technology. ? |logarithm using technology. ( |

| | | |[Logarithms as solutions for |[Logarithms as solutions for |

| | | |exponentials] |exponentials] |

|Number and Quantity |122 |N-VM.1 |1. (+) Recognize vector quantities as |1. (+) Recognize vector quantities as |

| | | |having both magnitude and direction. |having both magnitude and direction. |

| | | |Represent vector quantities by directed|Represent vector quantities by directed|

| | | |line segments, and use appropriate |line segments, and use appropriate |

| | | |symbols for vectors and their |symbols for vectors and their |

| | | |magnitudes (e.g., v, |v|, ||v||, v) |magnitudes (e.g., v, |v|, ||v||, v) |

| | | | | |

| | | | |The last v should not be in bold type. |

|Section |Page |Standard |Reads |Should Read |

| | |Number or Entry | | |

|Modeling |132 |Flowchart at top of page |Formulate Validate |Formulate Validate |

| | | | | |

| | | | | |

| | | | | |

| | | |Compute Compute |Compute Interpret |

| | | | | |

| | | |Because of spatial restrictions in this| |

| | | |errata sheet, only the text from the | |

| | | |center portion of the flowchart appears| |

| | | |here. | |

|Glossary |145 |Line plot and Mean |Line plot. A method of visually |Mean. A measure of center in a set of |

| | | |displaying . . . above a number line. |numerical data, computed by adding the |

| | | |Also known as a dot plot.2 |values in a list and then dividing by |

| | | | |the number of values in the list.2 |

| | | |This footnote was misplaced; it belongs|Example: For the data set {1, 3, 6, 7, |

| | | |in the definition of “Mean,” not “Line |10, 12, 14, 15, 22, 120}, the mean is |

| | | |plot.” |21. |

| | | | | |

| | | | |2. To be more precise, this defines the|

| | | | |arithmetic mean. |

|Glossary |150, Table 3 |Associative property of |(a × b) ? c = a × (b × c) |(a × b) × c = a × (b × c) |

| | |multiplication | | |

© California Department of Education, February 19, 2014

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