 Glendale Unified School District  Glendale, California USA
 K8 Mathematics
California Common Core Mathematics

GUSD mathematics instruction is based on the California State Standards for Mathematics with an emphasis on the Standards for Mathematical Practice.
How are the content standards organized?
TK/K
1st
2nd
3rd
4th
5th
6th
7th
8th
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
Mathematics Standards by Grade Level
Kinder

Kindergarten Mathematics
Overview
Kindergarten students learn to: Count to 100
 Write numbers to 20
 Classify groups of objects
 Identify basic shapes
 Beginning addition and subtraction
Specific Skills Learned
Counting and Cardinality Know number names and be able to count to 100
 Write numbers 020
 Count objects to tell the number of things in a group up to 20
Number and Base Ten Operations Learn about numbers 1120, with tens and ones
 Compare numbers and groups
Operations and Algebraic Thinking Understand that addition is putting together groups and adding to groups
 Understand that subtraction is taking apart groups and taking from groups
 Fluently add and subtract within 5
Measurement and Data Sort objects into groups
 Classify objects and count the number of objects in categories
Geometry Identify and describe shapes
 Analyze, compare, create, and compose shapes
evVision Math Kindergarten Parent Letters (with 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
1st

1st Grade Mathematics
Overview
First grade students: Are expected to count to 120
 Extend their understanding of addition and subtraction
 Understand the meaning of the equal sign (=)
 Compare twodigit numbers
 Practice measurement skills
 Begin to organize data from surveys
 Tell and write time in hours and halfhours using analog and digital clocks
Specific Skills Learned
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
Operations and Algebraic Thinking Solve addition and subtraction word problems within 20
 Understand the relationship between addition and subtraction
 Apply the properties of operations
 Commutative property of addition (if you know 8 + 3 = 11, then you know 3 + 8 = 11)
 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
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
enVision Math 1st Grade Parent Letters (with 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
2nd

2nd Grade Mathematics
Overview
Second grade students: Are expected to know from memory all sums of two onedigit numbers
 Use addition and subtraction within 100 to solve word problems
 Learn place values to 1,000
 Compare threedigit numbers
 Compute with money
 Estimate and compare lengths using appropriate measurement tools
 Draw shapes based on the number of faces and angles
Specific Skills Learned
Number and Base Ten Operations Understand place value: ones, tens, and hundreds
 Use place value to add and subtract within 1000
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
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
enVision Math 2nd Grade Parent Letters (with 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
3rd

3rd Grade Mathematics
Overview
Third grade students: Learn to multiply and divide within 100
 Are expected to know from memory all products of two onedigit numbers
 Understand fractions as numbers and their relative size and placement on the number line
 Understand concepts of area and perimeter
 Solve problems using liquid volume and mass
Specific Skills Learned
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
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
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
enVision Math 3rd Grade Parent Letters (with 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
4th

4th Grade Mathematics
Overview
Fourth grade students: Use their knowledge of place value to generalize to 1,000,000
 Learn to round multidigit whole numbers to any place
 Add and subtract using the standard algorithm
 Multiply and divide with multidigit numbers
 Extend understanding of fractions to include equivalence, ordering and simple decimal notation
 Measure angles and classify geometric shapes by lines (parallel, perpendicular, etc.) and angles (right, acute, obtuse, etc.)
Specific Skills Learned
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
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
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
enVision Math 4th Grade Parent Letters (with 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
5th

5th Grade Mathematics
Overview
Fifth grade students: Become fluent with multidigit addition, subtraction, multiplication, and division
 Learn to add and subtract fractions with unlike denominators
 Understand the concept of fraction multiplication and division
 Understand the concept of decimal addition and subtraction
 Analyze numeric patterns and relationships
 Graph ordered pairs on a coordinate plane
 Recognize attributes of geometrical shapes
 Calculate inside angle measurement and area of triangles and parallelograms
Specific Skills Learned
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
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
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
enVision Math 5th Grade Parent Letters (with 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

6th Grade Mathematics
Overview
Sixth grade students: Solve ratio and rate problems
 Finalize their understanding of division of fractions
 Begin the study of negative integers
 Understand the use of variables in mathematical expressions
 Write expressions and equations that correspond to situations
 Use expressions and equations to solve problems
 Begin the study of probability and statistics
 Solve problems involving area, surface area, and volume
Specific Skills Learned
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
enVision Math 6th Grade Parent Letters (with Translations)
Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 Topic 6 Topic 7 Topic 8
7th

7th Grade Mathematics
Overview
Seventh grade students: Deepen their understanding of:
 Proportional relationships to solve complicated problems
 Rational numbers to include computation (add, subtract, multiply, and divide)
 Algebraic foundations
 Probability and statistics by describing populations based on sampling
 Learn about irrational numbers
 Investigate chance to develop, use, and evaluate probability models
Specific Skills Learned
Ratios and Proportional Relationships Use proportional relationships to solve multistep operation and percent problems
 Compute unit rates
The Number System Add, subtract, multiply, and divide rational numbers
 Convert fractions to decimals
 Solve multistep problems with positive and negative numbers.
Expressions and Equations Use properties of operations to solve algebraic equations
 Add, subtract, factor, and expand linear expressions
 Use variables to represent numbers in realworld problems
 Construct simple equations and inequalities to solve problems
Geometry Draw, construct, and describe geometrical figures and describe the relationships between them
 Solve problems involving angle measure, area, surface area, and volume (cylinders, cones, and spheres)
 Solve reallife problems involving volume of cylinders, cones, and spheres
 Know the formulas for area and circumference of a circle
 Use facts about supplementary, complementary, vertical, and adjacent angles to solve multistep problems
Statistics and Probability
 Use random sampling to describe and compare populations
 Find, calculate, and explain the probability of a chance event
enVision Math 7th Grade Parent Letters (with Translations)
Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 Topic 6 Topic 7 Topic 8 enVision Math 7th/8th Grade Accelerated Parent Letters (with 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  Deepen their understanding of:
8th

8th Grade Mathematics
Overview
Eighth grade students: Deepen their understanding of rational and irrational numbers
 Compute algebraically with radicals and exponents
 Solve linear equations
 Define, solve, compare, and graph functions
 Understand and use the Pythagorean Theorem
 Solve problems involving volumes of cylinders, cones, and spheres
Specific Skills Learned
Functions Define, solve, and compare functions
 Understand that a function is a rule and the ordered pairs are input and output
 Build and use functions to model relationships
The Number System Understand rational and irrational numbers
Expressions and Equations Work with radicals and integer exponents
 Understand the connection between proportional relationships, lines, and linear equations and be able to graph them
 Understand that the unit rate of a proportional relationship is the slope of the graph
 Use similar triangles to explain slope and understand y = mx + b
 Analyze and solve linear equations with one variable and pairs of simultaneous linear equations
Geometry Understand congruence and similarity
 Understand, use, and apply the Pythagorean Theorem
 Solve problems involving volumes of cylinders, cones, and spheres
Statistics and Probability Investigate patterns of sets of data
 Construct and interpret scatter plots
enVision Math 8th Grade Parent Letters (with Translations)
Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 Topic 6 Topic 7 Topic 8 enVision Math 7th/8th Grade Accelerated Parent Letters (with 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