 Glendale Unified School District  Glendale, California USA
 Elementary Mathematics
California Common Core Content Standards  Mathematics
K12

California Common Core Mathematics
Transitional Kindergarten – High School
GUSD is committed to offering a highquality mathematics education to all students TK through Grade 12 based on the California State Standards for Mathematics with an emphasis on the Standards for Mathematical Practice. Students will experience mathematics education in ways that will strengthen their conceptual development. Preparing students for college and careers will be achieved through engagement in rigorous and meaningful mathematics education that will shape them into competent mathematicians and ultimately enhance their opportunities for future endeavors.How are the content standards organized?
The standards are clustered into five domains. The domains are listed below.
Note the changes that occur in some domains from K5 to 68 to High School (HS)1^{st}
2^{nd}
3^{rd}
4^{th}
5^{th}
6^{th}
7^{th}
8^{th}
HS
Geometry
Geometry
Measurement and Data
Statistics & Probability
Statistics & Probability
Number & Operations: Base Ten
Number System
Number & Quantity
Operations & Algebraic Thinking
Expressions & Equations
Algebra
Counting & Cardinality
Number & Operations:FractionsRatios & Proportional Relationships
Functions
Functions
What are the Standards for Mathematical Practice?
The Standards for Mathematical Practice (SMPs) describe ways in which students engage with the mathematics content throughout the grade levels. Students apply the practices as they become competent practitioners in the elementary, middle and high school years.Make sense of problems and
persevere in solving them.
Use appropriate tools strategically.
Reason abstractly and quantitatively.
Attend to precision.
Construct viable arguments and
critique the reasoning of others.
Look for and make use of structure.
Model with mathematics
Look for and express regularity
in repeated reasoning.
Standards for Mathematical Practices Chart for Students and Parents
Kinder
1st

enVision Math Parent Letter Translations
Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 Topic 6 Topic 7 Topic 8 Topic 9 Topic 10 Topic 11 Topic 12 Topic 13 Topic 14 Topic 15 California Common Core Content Standards
1^{st} Grade Mathematics
Overview:
First grade students extend their understanding of addition and subtraction by learning to use adding and subtracting to solve word problems within 20. They understand the meaning of the equal sign and are expected to count to 120. Place value knowledge is deepened and students use this knowledge to compare twodigit numbers within 100. Students practice their measurement skills with linear measurement and begin to organize data from surveys. Students also tell and write time in hours and halfhours using analog and digital clocks.
Specifically, your child will…
Operations and Algebraic Thinking
· Solve addition and subtraction word problems within 20
· Understand the relationship between addition and subtraction
· Apply the properties of operations
a. Commutative property of addition:
If you know 8 + 3 = 11, then you know 3 + 8 = 11.
b. Associative property of addition:
To add 2 + 6 + 4, the second two numbers can be
added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.· Add and subtract within 20
Number and Base Ten Operations
· Count to 120, starting at any number
· Understand the meaning of the equal sign
· Understand place value: ones, tens
· Use place value to add and subtract within 100
Measurement and Data
· Measure lengths and tell the measurement in units
· Tell and write time
Geometry
· Build and talk about a graph
Compare shapes by talking about sides, vertices, etc.· Compare twodimensional shapes to threedimensional shapes
Source:
Common Core Standards Parent Handbook
Also see:
Parent Roadmap: Supporting Your Child in Kindergarten Mathematics (PDF)
Standards for Mathematical Practice in Kindergarten(PDF)
2nd

enVision Math Parent Letter Translations
Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 Topic 6 Topic 7 Topic 8 Topic 9 Topic 10 Topic 11 Topic 12 Topic 13 Topic 14 Topic 15 California Common Core Content Standards
2^{nd} Grade Mathematics
Overview:
Second grade students use addition and subtraction within 100 to solve word problems and are expected to know from memory all sums of two onedigit numbers by the end of second grade. Place value understanding is extended to 1000 and students compare three digit numbers based on their knowledge of hundreds, tens and ones. Second grade students compute with money and learn to estimate and compare lengths using appropriate measurement tools. Second graders refine their understanding of geometry by drawing shapes based on the number of faces and angles.Specifically, your child will…
Operations and Algebraic Thinking
· Solve addition and subtraction word problems within 100
· Fluently add and subtract within 20
· Know all sums of two onedigit numbers
Number and Base Ten Operations
· Understand place value: ones, tens, and hundreds
· Use place value to add and subtract within 1000
Measurement and Data
· Measure, estimate, and compare lengths in standard units
· Represent whole number lengths on a number line
· Work with time and money
· Know relationships of time (minutes in an hour, days in a month, etc.)
· Solve work problems using combinations of dollar bills and coins
· Collect data, build a graph, and answer questions about the data presented
Geometry
· Recognize shapes: triangles, quadrilaterals, pentagons, hexagons, and cubes
· Draw shapes by size of the angles or by the number of equal faces
Source:
Common Core Standards Parent Handbook
Also see:
Parent Roadmap: Supporting Your Child in Grade Two Mathematics(PDF)
Standards for Mathematical Practice in 2nd Grade(PDF)
3rd

enVision Math Parent Letter Translations
Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 Topic 6 Topic 7 Topic 8 Topic 9 Topic 10 Topic 11 Topic 12 Topic 13 Topic 14 Topic 15 Topic 16 California Common Core Content Standards
3^{rd} Grade Mathematics
Overview:
Third grade students develop an understanding of multiplication and division and learn to fluently multiply and divide within 100. Students are expected to know from memory all products of two onedigit numbers by the end of third grade. Place value understanding is used for multidigit computation and estimation. Fractions are introduced in the third grade with an emphasis on understanding fractions as numbers and their relative size and placement on the number line. In third grade students understand concepts of area and perimeter and solve problems using liquid volume and mass.
Specifically, your child will…
Operations and Algebraic Thinking
· Solve multiplication and division word problems
· Understand the properties of multiplication
· Commutative property of multiplication:
If you know 6 x 4 = 24, then you know 4 x 6 = 24.
· Associative property of multiplication:
3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30,
or by 5 x 2 = 10, then 3 x 10 = 30.
· Distributive property of multiplication:
If 8 x 5 = 40 and 8 x 2 = 16, then 8 x 7 is:
8 x (5 + 2)
(8 x 5) + (8 x 2)
40 + 16 = 56.
· Fluently multiply and divide within 100
· Know all products of two onedigit numbers
· Solve word problems with addition, subtraction, multiplication, and division
Number and Base Ten Operations
· Understand that multiplication and division are related
· Use place value to round numbers and know the value of each digit in a fourdigit number
· Use place value understanding to solve multidigit arithmetic
Number and Operations – Fractions
· Understand fractions as numbers
· Recognize simple equivalent fractions
· Compare two fractions with the same numerator or the same denominator
Measurement and Data
· Tell and write time to the nearest minute
· Estimate and measure time, volume, and weight
· Understand area and perimeter
Geometry
· Understand that shapes in different categories can also be in a larger category
Source:
Common Core Standards Parent Handbook
Also see:
Parent Roadmap: Supporting Your Child in Grade Three Mathematics(PDF)
Standards for Mathematical Practice in 3rd Grade (PDF)
4th

enVision Math Parent Letter Translations
Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 Topic 6 Topic 7 Topic 8 Topic 9 Topic 10 Topic 11 Topic 12 Topic 13 Topic 14 Topic 15 Topic 16 California Common Core Content Standards
4^{th} Grade Mathematics
Overview:
Fourth graders use their knowledge of place value to generalize to 1,000,000 and learn to round multidigit whole numbers to any place. They fluently add and subtract using the standard algorithm and multiply and divide with multidigit numbers. Fourth graders extend understanding of fractions to include equivalence, ordering and simple decimal notation. Students measure angles and classify geometric shapes by lines (parallel, perpendicular, etc.) and angles (right, acute, obtuse, etc.).
Specifically, your child will…
Operations and Algebraic Thinking
· Use addition, subtraction, multiplication, and division with whole numbers to solve word problems
· Learn about factors and multiples
· Factors of 24: 1, 2, 3, 4, 6, 8, 12
· Multiples of 4: 4, 8, 12, 16, 20
· Make and describe patterns with objects and numbers
Number and Base Ten Operations
· Understand and use place value to generalize to 1,000,000
· Expanded form: 6783 = 6000 + 700 + 80 + 3
· Compute with multidigit numbers
· Solve problems involving using multiplication of multidigit by twodigit numbers
· Divide multidigit numbers by onedigit divisor
· Round multidigit numbers to any place
Number and Operations – Fractions
· Build understanding of equivalent fractions and ordering fractions
· Compare two fractions with different numerators and different denominators by making common denominators
· Add and subtract fractions and mixed numbers with like denominators
· Understand the decimal notation for fractions
· Compare decimals
Measurement and Data
· Solve problems using measurement conversions
· Apply area and perimeter formulas for rectangles
· Organize and explain data using a line plot
Geometry
· Understand and measure angles
· Draw and identify lines and angles
· Describe and sort shapes by their lines and angles
· Recognize lines of symmetry
Source:
Common Core Standards Parent Handbook
Also see:
Parent Roadmap: Supporting Your Child in Grade Four Mathematics(PDF)
Standards for Mathematical Practice in 4th Grade (PDF)
5th

Fifth grade students finalize fluency with multidigit addition, subtraction, multiplication, and division. They apply their understanding of fractions to the addition and subtraction of fractions with unlike denominators, the concept of fraction multiplication and division, and decimal addition and subtraction. They analyze numeric patterns and relationships and graph ordered pairs on a coordinate plane. Students build on their understanding of geometry by recognizing attributes of geometrical shapes and calculating inside angle measurement and area of triangles and parallelograms.
Overview:
Specifically, your child will…
Operations and Algebraic Thinking
 Write and interpret numerical expressions using parentheses, brackets, or braces: “Add 8 and 7, then multiply by 2” is 2(8 + 7)
 Express a whole number (2 – 50) as a product of its prime factors
 Describe more complex patterns by seeing the change
Number and Base Ten Operations
 Understand the place value system from thousandths to millions
 Fluently multiply multidigit numbers using the standard algorithm
 Divide multidigit numbers by twodigit divisors
 Read, write, and compare decimals to the thousandths
 Round decimals to any place
 Compute with multidigit whole numbers and numbers with decimals to the hundredths
Number and Operations – Fractions
 Add and subtract fractions with unlike denominators
 Multiply fractions and mixed numbers
 Divide unit fractions by whole numbers and whole numbers by unit fractions
Measurement and Data
 Convert measurements and use in problem solving: 0.05 m = 5 cm or 2.5 feet = 30 inches
 Organize and explain data using a line plot
 Understand and find the volume of rectangular prisms
 Analyze number patterns
Geometry
 Graph points on a coordinate graph
 Show a graph with an x and y axis with several points labeled by their coordinates
 Sort twodimensional shapes into categories based on their properties
Source:
Common Core Standards Parent Handbook
Also see:
Parent Roadmap: Supporting Your Child in Grade Five Mathematics(PDF)
Standards for Mathematical Practice in 5th Grade (PDF)enVision Math Parent Letter Translations
Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 Topic 6 Topic 7 Topic 8 Topic 9 Topic 10 Topic 11 Topic 12 Topic 13 Topic 14 Topic 15 Topic 16
6th

California Common Core Content Standards
6^{th} Grade Mathematics
Overview:
Sixth grade students use their knowledge of multiplication and division to solve ratio and rate problems. They finalize their understanding of division of fractions and begin the study of negative integers. They understand the use of variables in mathematical expressions, write expressions and equations that correspond to situations, and use expressions and equations to solve problems. Students begin the study of probability and statistics and use their geometrical foundations to solve problems involving area, surface area, and volume.
Specifically, your child will…
Ratios and Proportional Relationships
· Understand ratio concepts and use ratio reasoning to solve problems
· Understand unit rate
· Find a percent of a quantity
The Number System
· Divide fractions by fractions
· Fluently compute with multidigit numbers and multidigit decimals
· Find common factors and multiples of numbers
· Find the greatest common factor and least common multiple of two whole numbers
· Use understanding of positive numbers to understand rational numbers
· Understand positive and negative integers and be able to locate on a fourquadrant coordinate plane
· Order rational numbers
· Understand absolute value
Expressions and Equations
· Use understanding of arithmetic to solve one variable equations and inequalities
· Write expressions and equations to describe real world situations using variables
· Write and solve equations with whole number exponents
· Write an inequality to describe a real world or mathematical problem
· Represent and explain relationships between dependent and independent variables
Geometry
· Solve real world problems involving area, surface area, and volume
Statistics and Probability
· Ask a statistical question (How old are the students in my school?), collect and organize the data on a line plot, graph, histogram, dot plot, box plot, etc.
· Describe and summarize data by noticing the center, spread, and overall shape
· Display numerical data on a number line including dot plots, histograms, and box plots
Source:
Common Core Standards Parent Handbook
Also see:
Parent Roadmap: Supporting Your Child in Grade Six Mathematics (PDF)
Standards for Mathematical Practice in 6th Grade(PDF)