# Elementary Math (TK-6)

• ## Why does the math look different?

The language of the Common Core standards, the shifts in mathematics instruction, and the goals of the Standards for Mathematical Practices have transformed the way in which our students are learning mathematics.

# K-12

• California Common Core Mathematics
Transitional Kindergarten – High School

GUSD is committed to offering a high-quality 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 K-5 to 6-8 to High School (HS)

 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: Fractions Ratios & 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

# 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

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 two-digit 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 half-hours using analog and digital clocks.

Operations and Algebraic Thinking

·         Solve addition and subtraction word problems within 20

·         Understand the relationship between addition and subtraction

·         Apply the properties of operations

If you know 8 + 3 = 11, then you know 3 + 8 = 11.

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 two-dimensional shapes to three-dimensional shapes

Source:
Common Core Standards Parent Handbook
Also see:
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

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 one-digit 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.

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

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:|
Also see:

# 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

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 one-digit numbers by the end of third grade.   Place value understanding is used for multi-digit 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.

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

·         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 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

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:
Also see:

# 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

Overview:

Fourth graders use their knowledge of place value to generalize to 1,000,000 and learn to round multi-digit whole numbers to any place.  They fluently add and subtract using the standard algorithm and multiply and divide with multi-digit 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.).

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 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

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:
Also see:

# 5th

• Fifth grade students finalize fluency with multi-digit 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:

## 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 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

## 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

Source:
Also see:

## 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

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.

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

Source:
Also see: