Overview of Skills Learned

• Counting to 100
• Writing numbers to 20
• Classifying groups of objects
• Identifying basic shapes
• Beginning addition and subtraction

Specific Skills Learned

• Counting and Cardinality
  • Know number names and be able to count to 100
  • Write numbers 0-20
  • Count objects to tell the number of things in a group up to 20
• Number and Base Ten Operations
  • Learn about numbers 11-20, 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

GUSD Curriculum

• enVision Math
   

evVision Math Kindergarten Parent Letters (with translations)

Overview of Skills Learned

• Students should be able to count to 120
• Deeper understanding of addition and subtraction
• Understanding the meaning of the equal sign (=)
• Comparing two-digit numbers
• Practicing measurement skills
• Beginning to organize data from surveys
• Telling and writing time in hours and half-hours 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 two-dimensional shapes to three-dimensional shapes

GUSD Curriculum

• enVision Math
   

enVision Math 1st Grade Parent Letters (with Translations)

Overview of Skills Learned

• Students are expected to know from memory all sums of two one-digit numbers
• Using addition and subtraction within 100 to solve word problems
• Learning place values to 1,000
• Comparing three-digit numbers
• Computing with money
• Estimating and comparing lengths using appropriate measurement tools
• Drawing 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 1,000
• Operations and Algebraic Thinking
  • Solve addition and subtraction word problems within 100
  • Fluently add and subtract within 20
  • Know all sums of two one-digit 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

GUSD Curriculum

• enVision Math
   

enVision Math 2nd Grade Parent Letters (with Translations)

Overview of Skills Learned

• Students are expected to know from memory all products of two one-digit numbers
• Multiplying and dividing within 100
• Understanding fractions as numbers and their relative size and placement on the number line
• Understanding concepts of area and perimeter
• Solving 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 four-digit number
  • Use place value understanding to solve multi-digit 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 one-digit 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

GUSD Curriculum

• enVision Math
   

enVision Math 3rd Grade Parent Letters (with Translations)

Overview of Skills Learned

• Using knowledge of place value to generalize to 1,000,000
• Rounding multi-digit whole numbers to any place
• Adding and subtracting using the standard algorithm
• Multiplying and dividing with multi-digit numbers
• Extending understanding of fractions to include equivalence, ordering and simple decimal notation
• Measuring angles and classifying 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 multi-digit numbers
  • Solve problems involving using multiplication of multi-digit by two-digit numbers
  • Divide multi-digit numbers by one-digit divisor
  • Round multi-digit 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

GUSD Curriculum

• enVision Math
   

enVision Math 4th Grade Parent Letters (with Translations)

Overview of Skills Learned

• Becoming fluent with multi-digit addition, subtraction, multiplication, and division
• Adding and subtracting fractions with unlike denominators
• Understanding the concept of fraction multiplication and division
• Understanding the concept of decimal addition and subtraction
• Analyzing numeric patterns and relationships
• Graphing ordered pairs on a coordinate plane
• Recognizing attributes of geometrical shapes
• Calculating 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 multi-digit numbers using the standard algorithm
  • Divide multi-digit numbers by two-digit divisors
  • Read, write, and compare decimals to the thousandths
  • Round decimals to any place
  • Compute with multi-digit 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 two-dimensional shapes into categories based on their properties

GUSD Curriculum

• enVision Math
   

enVision Math 5th Grade Parent Letters (with Translations)

Overview of Skills Learned

• Solving ratio and rate problems
• Finalizing their understanding of division of fractions
• Beginning the study of negative integers
• Understanding the use of variables in mathematical expressions
• Writing expressions and equations that correspond to situations
• Using expressions and equations to solve problems
• Beginning the study of probability and statistics
• Solving 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 multi-digit numbers and multi-digit 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 four-quadrant 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

GUSD Curriculum

• enVision Math 2.0
   

enVision Math 6th Grade Parent Letters (with translations)

After 6^th grade, students can qualify to take a Math 7/8 Accelerated course. Students who do not qualify in 6^th grade, can have an opportunity to accelerate in a summer class called “Summer Bridge A” between 7^th and 8^th grade. Learn more about accelerated math pathways.

Overview of Skills Learned

• Solving complicated problems using proportional relationships
• Adding, subtracting, multiplying, and dividing rational numbers
• Algebraic foundations
• Probability and statistics by describing populations based on sampling
• Learning about irrational numbers
• Developing, using, and evaluating probability models

Specific Skills Learned

• Ratios and Proportional Relationships
  • Use proportional relationships to solve multi-step operation and percent problems
  • Compute unit rates
• The Number System
  • Add, subtract, multiply, and divide rational numbers
  • Convert fractions to decimals
  • Solve multi-step 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 real-world 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 real-life 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 multi-step problems
• Statistics and Probability
  • Use random sampling to describe and compare populations
  • Find, calculate, and explain the probability of a chance event

GUSD Curriculum

• enVision Math 2.0
   

enVision Math 7th Grade Parent Letters (with translations)

enVision Math 7th/8th Grade Accelerated Parent Letters (with translations)

Students who successfully complete the Math 7/8 Accelerated course in 7^th grade or the Summer Bridge A course between 7^th and 8^th grade can qualify for the Accelerated Math 8B/ Integrated I course. This is a high school level course taken in middle school. Learn more about accelerated math pathways.

Overview of Skills Learned

• Deeper understanding of rational and irrational numbers
• Computing algebraically with radicals and exponents
• Solving linear equations
• Defining, solving, comparing, and graphing functions
• Understanding and using the Pythagorean Theorem
• Solving 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

GUSD Curriculum

• enVision Math 2.0 – Traditional 8^th grade math course
• Houghton Mifflin Harcourt (HMH): Accelerated Integrated I course – Crescenta Valley and Hoover HS
• Core Connections (CPM): Accelerated Integrated I course – Clark Magnet, Daily, and Glendale HS
   

enVision Math 8th Grade Parent Letters (with Translations)

Integrated Math I is the first course of a three-course sequence. It is typically taught in 9^th grade or in 8^th grade for students taking an accelerated math pathway. Learn more about accelerated math pathways.

Integrated I is required for graduation from a GUSD high school.

Overview of Skills Learned

• Describing functions
• Linear relationships
• Dimensional analysis
• Transformations and solving
• Statistical models
• Modeling with two-variable data
• Sequences
• Linear systems and piecewise functions
• Exponential functions
• Congruence and transformations
• Lines, angles, and triangles

GUSD Curriculum

• Houghton Mifflin Harcourt (HMH): Crescenta Valley and Hoover HS
• Core Connections (CPM): Clark Magnet, Daily, and Glendale HS

Integrated Math II is the second course of a three-course sequence. It is typically taught in 10^th grade or in 9^th grade for students taking an accelerated math pathway. Learn more about accelerated math pathways.

Integrated II is required for graduation from a GUSD high school.

Overview of Skills Learned

• Quadratics functions (solving, factoring, and graphing)
• Polynomial functions
• Geometric proofs (lines, angles, triangles, and quadrilaterals)
• Similarity and right triangles
• Trigonometry (intro to trig functions sine, cosine, and tangent)
• Properties of circles
• Volume of solids
• Probability
   

GUSD Curriculum

• Houghton Mifflin Harcourt (HMH): Crescenta Valley and Hoover HS
• Core Connections (CPM): Clark Magnet, Daily, and Glendale HS

Integrated Math III is the third and final course of the Integrated Math sequence. It is typically taught in 11^th grade. In lieu of Integrated III, some students opt to take a more statistical route with Introductions to Data Science. Learn more about accelerated math pathways.

Integrated III is not required for graduation.

Overview of Skills Learned

• Methods of reasoning with geometry
• Transforming parent graphs
• Investigations and functions
• Polynomial functions, expressions, and equations
• Logarithms and triangles (inverse functions)
• Exponential functions
• Trigonometric functions
• Normal distributions and geometric modeling
• Properties of circles
   

GUSD Curriculum

• Houghton Mifflin Harcourt (HMH): Crescenta Valley and Hoover HS
• Core Connections (CPM): Clark Magnet, Daily, and Glendale HS

Introduction to Data Science (IDS) is typically taught in 11^th grade for students who prefer to take a more statistical approach to math instruction. Students may opt to take IDS in lieu of Integrated Mathematics III. IDS could lead to Financial Literacy Statistics or AP Statistics. Learn more about accelerated math pathways.

IDS is not required for high school graduation.

Overview of Skills Learned

• Using large data sets to make convincing arguments
• Following the data cycle to research topics and consider, analyze, and interpret data
• Computer programing
• Presentation skills
• Critical thinking around data

Check out our high school course catalog to learn more about these advanced math opportunities! Learn more about accelerated math pathways.

• Precalculus
• Financial Literacy/ Statistics
• AP Precalculus
• AP Calculus AB
• AP Calculus BC
• AP Statistics