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?

Overview

• Count to 100
• Write numbers to 20
• Classify groups of objects
• Identify basic shapes
• Beginning addition and subtraction   

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 two-digit numbers
• Practice measurement skills
• Begin to organize data from surveys
• Tell and write time in hours and half-hours using analog and digital clocks

Specific Skills Learned

enVision Math 1st Grade Parent Letters (with Translations)

2nd Grade Mathematics

Overview

Second grade students:

• Are expected to know from memory all sums of two one-digit numbers
• Use addition and subtraction within 100 to solve word problems
• Learn place values to 1,000
• Compare three-digit 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 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

enVision Math 2nd Grade Parent Letters (with Translations)

3rd Grade Mathematics  

Overview

Third grade students:

• Learn to multiply and divide within 100
• Are expected to know from memory all products of two one-digit 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 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

enVision Math 3rd Grade Parent Letters (with Translations)

4th Grade Mathematics

Overview

Fourth grade students:

• Use their knowledge of place value to generalize to 1,000,000
• Learn to round multi-digit whole numbers to any place
• Add and subtract using the standard algorithm
• Multiply and divide with multi-digit 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 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

enVision Math 4th Grade Parent Letters (with Translations)

5th Grade Mathematics

Overview

Fifth grade students:

• Become fluent with multi-digit 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 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

enVision Math 5th Grade Parent Letters (with Translations)

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 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

enVision Math 6th Grade Parent Letters (with Translations)

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 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

enVision Math 7th Grade Parent Letters (with Translations)

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

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)

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