Everyday Mathematicsis a complete kindergarten through sixth grade curriculum that enriches the mathematical experiences of teachers and children. It embraces many of the traditional goals of school mathematics as well as two ambitious goals:

• To substantially raise expectations with respect to the amount and range of mathematics that children can learn.
• To provide materials for children and support for teachers that enable them to meet these higher expectations.

• A curriculum that emphasizes conceptual understanding while building a mastery of basic skills
• A curriculum that explores the full mathematics spectrum, not just basic arithmetic
• A curriculum based on how children learn, what they’re interested in, and the future for which they must be prepared

In Everyday Mathematics, children are expected to master a variety of mathematical skills and concepts, but often not the first time they are encountered. Mathematical content is taught in a repeated fashion, beginning with concrete experiences. Everyday Mathematics students study important concepts over consecutive years through a variety of curricular formats. Each grade level builds on and extends concept understanding so that children approach each new challenge from a firmly established foundation. Examples of this kind of concept development are found in Everyday Mathematics’ six content strands:

• Numeration
• Operations
• Patterns, Functions, and Algebra
• Geometry
• Measurement and Reference Frames
• Data and Chance

Everyday Mathematics is a curriculum of rich content designed to prepare students for more advanced mathematics in middle and high school. A dramatic change has evolved in recent decades in the amount of mathematics used in society. The importance of mathematical ideas is interwoven into the daily lives of everyone. In order to help students prepare for and make the most of these opportunities, a strong mathematics curriculum is needed. Everyday Mathematics is that curriculum.

Kindergarten First through Sixth Grades

Ongoing Daily Routines Numeration

Numeration Operations and Computation

Operations Patterns, Functions, and Algebra

Patterns and Functions Geometry

Geometry Measurement and Reference Frames

Measurement and Reference Frames: Measurement Data and Chance

Measurement and Reference Frames: Money

Measurement and Reference Frames: Clocks and Calendars

Data and Chance
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Kindergarten Everyday Mathematics
Ongoing Daily Routines: Number of the Day and Growing Number Line; Cleanup Count; Job Chart; Weather Observation; Building the Monthly Calendar; Attendance; Recording Daily Temperature.
Numeration: Correct number sequences through rote counting and counting objects. Counting on from a number, backward, skip counting. Experiences with objects of various sizes, shapes, and arrangements. Read and write numbers; use the term "digit".	Counting with an action  Identify small numbers without counting  Counting in sequences; sequencing numbers  Counting on from a number (0-115); back from a number (20-0)  Oral and rote counting to 115 and beyond  Rational counting with objects of various sizes, shapes, and arrangements  One more, one less; before/after  Interrupted counts  Interrupted skip counts  Skip counts by 2s,5s,and 10s  Calculator usage for skip counting, counting on, counting by ones, counting backwards  Tally counting  Estimate quantity  Concept of zero  Concept of zero  Read, write, and illustrate numbers and number words  Compare numbers using greater than and less than  Ordinal numbers  Equivalent names for numbers  Write and use 2- and 3-digit numbers
Operations: Using Operations and relations in solving concrete problems from everyday life; make up and act out number stories; explore the inverse operations of addition and subtraction as "doing" and "undoing"; using relation vocabulary appropriately. The things we "do" with numbers.	Symbolic language for addition and subtraction  Make estimated on a number line  Use relations vocabulary such as: bigger, smaller, more, less, the same, fewer, over, under, higher, lower, on the same level, equivalent  Join sets (objects)  Remove sets ( objects)  Use + and – with pictures, number models, and words  Create and tell addition and subtraction stories: one more and one less number sentences and stories  Work with number families; equivalent numbers  Use the calculator to solve addition and subtraction problems  Tell number stories with a calculator  Find missing addends  Counting-on: on the number line  Fraction: one-half  Halves of a whole group  Subtract by ones to zero  Play operations games  Tell and act out fraction stories
Patterns and Functions: Sorting and categorizing collections; exploring functions  through "What’s My Rule?" games; counting by 1s, 2s,  5s, 10s and so on.	Create patterns with a variety of objects: motions  Create sequential linear patterns  Explore attribute blocks  Look for patterns in surroundings  Sort and categorize objects by sizes and shapes (attributes)  Reproduce patterns  Count in patterns; verbalize patterns  Weave patterns on cardboard looms  Create patterns using 1,2, or 3 objects  Sort and categorize patterns  Copy pattern designs  Introduce functions: find the rule  Relations: input/output based on a defined rule  Function Machine: "What’s My Rule?’ routines
Geometry: Tracing, drawing, constructing, and playing with simple shapes; analyze parts of shapes and relationships among sizes and shapes.	Use geometric shapes to draw pictures  Construct a shape collage  Compare shapes  Describe characteristics of shapes: square, rectangle, circle, triangle, rhombus  Use pattern-block template  Define shapes by feel  Construct shapes using a variety of materials  Change shapes with consistent perimeters  Find triangles and quadrilaterals in random-folded paper  Create shape puzzles  Geoboard explorations  Create a shape museum  Create a shape museum  Explore 3-dimensional shapes  Explore symmetry in nature, with mirrors, with concept of one-half  Construct symmetry cards, designs  Tile with pattern-blocks  Mosaics  Make 2-dimensional shapes
Measurement and Reference Frames: Introduce length, weight, volume or capacity, and elapsed time through matching and comparison activities; using appropriate tools to measure and label various units with U.S. customary and metric systems; drawing, comparing, and recording results; introduce money as a tool to explore place value, fractions, equivalence, decimal system; explore characteristics and values of bills and coins; use money incidentally; develop understanding of time; keep track of time on calendars, clocks, number lines: develop sense of record and sequential order and time.	Measurement  Compare Dry and wet weights  Change in shape does not affect weight  Use vocabulary of weight measurement: weight, the same as, heavy, heavier, less, more, less equal to, equivalent  Weight objects by hand; using a pan to balance  Balance weighted objects  Weigh objects using a bathroom scale  Add and subtract from weighted objects  Order weights from lightest to heaviest  Weigh to illustrate conversation of matter  Estimate measures  Determine distance in feet and steps  Compare lengths  Measure heights  Non-standard and standards units of measurement Money: Buying power of money  Purchasing items with money  Value of money  Recognize and use penny, nickel, dime quarter, $1, $10  Compare coins, equivalence of coins (5 pennies = one nickel, etc.)  Exchanges: pennies, nickels, dimes, and $1 bill  Count coin combinations (pennies, nickels, dimes) to and amount past $1 using skip counting  Play money games  Recognize and write the cent sign  Estimate with money  Conduct a flea market  Equivalent fractional terms of money: quarter is one-fourth of a dollar Clocks and Calendars: Tell time to the hour  Explore concept of minutes  Parts of a clock  Construct a clock  Calendar events: third day, first Monday, birthdays, highest numbered day, two days whose sum is 8, the day that is in the first row and second column, days with 4 in the ones place, etc.  Estimate time  Play time games  Elapsed time  Order of events, time lines  Relate digital time to analog time  Compare times events
Data and Chance: Collect, organize, and display data using concrete objects, tables, charts, and graphs. Male counts and comparisons of data.	Discuss and read a graph for meaning  Discuss outcomes  Bar graphs and pictographs: birthdays, ages, favorite colors, pets, dot cube throws  Use class data to construct, read and interpret a concrete (cubes) graph  Title a graph  Interpret results  Discuss probability  Conduct a survey, "How Did You Come To School?"  Create a linear graph of changing temperatures throughout the seasons  Tally the years when a collection of coins was minted  Use a grid or graph  Use coordinates  Make a Venn diagram

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First Grade Everyday Mathematics
Numeration: Counting; reading and writing numbers; investigating place-value of whole numbers; exploring fractions and money.	Numbers between two numbers on a number line  Identify, order numbers to 4-digits  Verbal counts by 1, by 2, by 3, by 4, by 5, by 6, by 10, by 25  Count by 1 to 1000  Count by ten from any number  Tally Counts  One more; one less; equivalencies  Read and write numbers to 1000  How numbers are used  Calculator: key in numbers; add, subtract; (=/R); place value  Ten digits in our number system  Links between number grid and number line  Make number scrolls  Tens and hundreds exchanges using calculator counts by one  Place value: ones, tens, thousands  Money and Base-10 blocks for place value  Ones, tens, Thousands Exchange Game  Equivalent names for numbers  Fractions as equal parts of wholes  Fractional parts of whole objects and sets of objects  Notation for writing fractions: numerator and denominator  Equivalent fractions  Negative numbers: on a number line, count back on a calculator  Decimal notation for money and parts of a dollar  Rote count by 1s, 2s, 5s, and 10s with objects and money  Compare and order numbers to 3-digits and money using >, < and =  Interrupted counts by 1s, 2s, 5s, 10s  Money and Base-10 block exchanges  Fraction concepts: halves, thirds, fourths  Fraction notation for unit fractions: label fractional parts of geometric figures and pattern blocks
Operations and Computation: Learning addition and subtraction facts, fact families, and extended facts; beginning informal work with properties of numbers and problem solving.	Addition and subtraction games  Vertical and horizontal formats for writing facts  Relation symbols (<, >, =); express relationships  Automatically of basic addition facts (fact power)  Fact games  Fact shortcuts for mastery: turnaround rule, doubles, plus zero, plus one  Inverse relationships between addition facts and subtraction facts  Fact families: dominoes; fact triangles  Addition/subtraction fact table  Add and subtract 0 an1 to/from 2- or 3- digit numbers  Extend addition and subtraction facts to add and subtract tens  Mentally add and subtract tens to any number  Add two 1-digit numbers  Subtract two 1- digit numbers  Add a 1-digit number and a 2-digit number  Subtract a 1-digit number and a 2-digit number  Add two 2-digit numbers  Subtract a 1-digit number from a 3-digit number  Subtract a 2-digit number from a 2-digit number  Add and Subtract coin amounts  Parts-and-Total diagrams  Use tools to solve addition/subtraction problems: number line, number grid, simple drawings, concrete counters, base-10 blocks  Number models for change-to-more and change-to-less situations  Count on/back for simple addition/subtraction facts  Make-up and solve number stories and comparison number stories  Calculator puzzles to practice addition/subtraction facts
Patterns, Functions, and Algebra Exploring attributes, patterns, sequences, relations, and functions finding missing numbers and rules in Frames-and-Arrows and "What’s My Rule/" problems; studying properties of operations.	Patterns in counts by various numbers; on number grids and a circle design  Frames and Arrows: with rule and 1st number; with missing rule; with 1st number missing  Dot patterns on dominoes  Patterns involving shapes, color, and rotation  Patterns involving shapes, color, and rotation  Patterns as being able to predict what comes next  Odd and even numbers  Function Machine and "What’s My Rule?" routines for rule based relationships between pairs of numbers; find missing parts, input, output, rule  Sort blocks by attributes of shape, color, and size, shape with attribute blocks  Patterns in addition facts  Number scrolls into 100’s  Addition/subtraction using number grids, number lines, frames and Arrows, and "What’s My Rule"?
Geometry Exploring 2-and 3- dimensional shapes	Attributes of prisms  Faces and corners of shapes  Identify and draw shapes: triangle, quadrangle, square, rhombus, trapezoid, hexagon, circle, pentagon, heptagon, octagon  Identify: sphere, cone, cylinder, rectangular prism, cube, pyramid  Regular and irregular polygons  Parts of polygons: side, vertex, angle  Name points, line segments, figures  Line symmetry: cutting and folding: constructions  Construct 3-dimensional shapes: triangular prism and rectangular pyramid  Construct polygons  Use tools to construct shapes: Pattern-Block Template; straightedge; geoboard, ruler  Pattern-Block relationships/equivalencies
Measurement and reference Frames Using tools to measure length, capacity, and weight; using clocks, calendars, timelines, thermometers, and ordinal numbers.	Measure children: height, weight  Nonstandard linear measures: fingers, hands, feet, and arms  Order objects using estimated and measured weight using a spring scale, bath scale  Order objects using estimated and measured length  Read temperatures using Celsius and Fahrenheit scales  Ordinal numbers  Patterns and suffixes with relatively large ordinal numbers  Use a.m. and p.m.  Relationships of minute hand and hour hand  Telling time to five minutes (telling time to the minute)  Notate time: 1:00 p.m.; 1:20 p.m.; 11:25 a.m., etc.  Determine intervals between two given times  Estimate and measure using standard units of measure: foot, inch, meter, centimeter  Coin and dollar exchanges  Count mixed collections of coins and dollars; make purchases; count change  Dollar and cents notation  Timelines
Data and Chance Collecting, organizing, and displaying data using tables, charts, and graphs; exploring concepts of chance.	Tally counts  Identify landmarks: range, maximum, minimum, mode, median  Collect, order, display, analyze and interpret real life data and predict outcomes  Display data: bar graph, table, tally chart, line plot  Explore equal-chance events  Collect, analyze, and interpret real-life data

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Second Grade Everyday Mathematics
Numeration: Counting; reading and writing numbers; identifying place-value; working with fractions; using money to develop place-value and decimal concepts.	Explore numbers with calendar activities  Place value to 10,000 (base-10 system)  Skip counting to 1-,000  Counting patterns with a calculator  Count forward and backward by 2, 5, 10, from 1000  Use the number line  Equivalent names for numbers to 10,000  Understand the use of numbers  Context of numbers (label or unit)  Estimation (about approximately)  Fractions as regions  Show equal parts  Equal parts of one  Name sets with fractions  Equivalent fractions  Decimal notation for money  Decimal and fraction names for money  Count/skip on: number grid, number line, calculator  Explain terms: numerator and denominator  Sort and Compare fractions  Value of combinations of $1, $10, $100 bills and exchanges  Number scroll to 1000  Compare numbers using: words, pan-balance, relation symbols (<,>, =) and base-10 blocks  Represent 3-and 4-digit numbers with base-10 blocks
Operations and Computation Recalling addition and subtraction facts; exploring fact families; adding and subtracting with tens and hundreds; beginning multiplication and division; exchanging money amounts.	Add and subtract 1-, 2-, and 3-digit numbers  Master basic addition and subtraction facts  "Parts-and-Total" addition problems  Compare quantities using greater than, less than, or equal to  Find missing addends  Multiples of equal groups  Multiplication using arrays  Diagrams to solve division problems  Memory keys on a calculator  Parentheses to specify order of operations  Relationship between multiplication and division  Multiplication and division diagrams  Order 4-digit numbers  Mental arithmetic to add and subtract, multiply and divide  Mentally add and subtract multiples of 10  Mentally add any 1-digit number to a multiple of 10  Mentally subtract any 1-digit number form a 2-digit number where the difference is a multiple of 10  Fact families/fact triangles for addition/subtraction and multiplication/division Write number models to solve addition/subtraction number stories  Complements of 10 and multiples of 10  Frames-and-arrows for addition and subtraction  Chang-to-more and change-to-less number stories  Use estimation for addition and subtraction  Calculator for addition and subtraction  Algorithms: partial-sums, trade first  Multiplication terms: factor and product  Multiply by 2s, 5s, and 10s
Patterns, Functions, and Algebra Exploring number patterns, rules for number sequences, relations between numbers, and attributes.	Patterns in doubles and halves  Patterns in multiples  Place value patterns on number grids, number lines, Facts Tables  Patterns in numbers  Describe and continue number sequences  Arrow paths  Odd and even numbers  Number pairs related by a singles rule  Addition and subtraction fact table patterns  Frames-and-Arrows; number sequences, money, with 2 rules  Addition puzzles  Sort attribute blocks to match a rule  "What’s My Rule/" and Function Machines  Number models for addition/subtraction and multiplication/division
Geometry Exploring 2-and 3-dimensional shapes; classifying polygons.	Explore regular polyhedrons  Construct a variety of triangles  Construct a "quilt block "  Identify and classify geometric shapes  Similarities and differences between 3-dimensional shapes: prisms, pyramids, cylinders, spheres, cones  Classify 3-dimensionsl shapes by the shape of their bases  Work with polygons: triangles, squares, rectangles, parallelograms, rhombuses, trapezoids, pentagons, hexagons, heptagons, octagons  Similarities and differences between quadrilaterals  Use a straightedge  Define points  Define, name, and draw parallel and nonparallel line segments  Symmetry  Construct symmetrical shapes  Perimeter and area of polygons  Capacities of cylinders  Make, describe, and compare shapes on a geoboard
Measurement and Reference Frames Using tools to measure length, capacity, weight, and volume; using U.S. customary and metric measurement units.	Units of weight/measure weight: pan balance; spring scale; bathroom scale; estimate by feel  Measure with ruler, yard/meter stick  Measure height  Measure in inches, feet, yards miles, millimeters, centimeters, meters  Estimate measures  Equivalent units of measure  Estimate distances  Fractional units of length: one-half inch, one half centimeter  Make up and solve money stories  Money amounts in decimal notation  Estimate money sums  Money equivalents  Decimal and fraction names for money amounts  Solve money problems using a calculator  Tell time to the hour, half hour, quarter hour, 5-minute, minute  Estimate times  Time as an approximation  Read a thermometer: Celsius and Fahrenheit  Compare temperatures  Forecast weather and temperatures  Read and interpret road maps  Timelines  Calendar activities  Nonstandard and standard unit of measure (U.S. customary and metric)  Volumes of base-10 blocks  Estimate and find area and perimeter  Units of capacity; relationships and equivalencies  Make purchases; make change  Money values and exchanges with coins and $1 bills
Data and Chance Collecting, organizing, and interpreting data using tables, charts, and graphs; exploring concepts of chance.	Estimation in working with data  Construct data tables, bar graphs, and tally charts  Collect, organize, and analyze sets of real-life data  Interpret a bar graph  Identify landmarks: median, mode, range, maximum, and minimum  Make a frequency table and line plot  Frequency distributions  Construct a frequency bar graph  Interpret data  Compare pairs of data  Compare climate of data

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Third Grade Everyday Mathematics
Numeration: Counting patterns; place-value; reading and writing whole numbers through 1,000,000; fractions, decimals, and integers.	Enter money amounts on a calculator  Read, write and order numbers to 1,000,000  Numbers and their uses  Counting on and back to 1,000,000  Use of calculators  Equivalent names for numbers  Skip counting on the calculator  Calendar facts  Equal parts  Write fractions  Find a fraction of a number  Money notation  Decimals with base-10 blocks (1 and 2 places)  Decimals to thousandths  Place value in decimals  Exchange measures: 1 ft. for 12 in, 1hr for 60 min  Fraction notation; parts of objects and collections  Fractions in number stories  Fractions and decimals with U.S. customary and metric units of length  Equivalent units of measure and fractions  Equivalent fraction  Fraction names for quantities greater than one  Positive and negative numbers  Show percents as hundredths on a calculator
Operations and Computation Multiplication and division facts extended to multi-digit problems; working with properties; operations with fractions and money.	Inverse relationship between addition and subtraction  Addition with three or more addends  Addition and subtraction facts  Addition of three 1-digit numbers  Number families  Variety of procedures for computation  Multiple of equal groups (rate multiplication)  Multiplication arrays  Equal shares and equal groups  Multiplication and division facts  Inverse relationship between multiplication and division  Square numbers through 10x10  Multiplication facts  Division facts  Write number models with parentheses  Multiplication number models with parentheses  Estimate products of 1-digit numbers by dollars and cents  Multidigit multiplication; multiples of 10, 100, 1000  Automaticity of basic number facts  Divide with multiples of 10, 100, 1000  Partial products algorithm for multiplication 1-digit numbers  Multiplication to find 10% of a number  Identify and find factors of numbers  Explore division procedures by sharing whole dollar amounts  Lattice multiplication with multidigit numbers  Find products of 2-digit numbers  Estimation and mental; arithmetic with multiples  Mental arithmetic to find products of 1-digit numbers by multidigit numbers
Patterns, Functions and Algebra Finding patterns on the number grid solving Frames-and-Arrows puzzles having two rules; completing variations of "What’s My Rule?" activities; exploring the relationship between multiplication and division; using parentheses in writing number models; naming missing parts of number models.	Common attributes among figures in a set  Solve attribute game puzzles  Patterns in a four-digit numbers  Number sequences  Number families (fact families)  Function Machine (input/output)  Parts-and-total number stories with diagram use  Comparison number stories with diagram use  Change number stories and diagrams Number models for area Relationship between addition and subtraction  Relationship between multiplication and division  Number models with parentheses  Multiplication number models using parentheses  Factors of whole numbers
Geometry Exploring 2-and3 dimensional shapes and other geometric concepts	Angles as a way to record rotations or turns  Construct a variety of triangles and quadrilaterals  Construct a variety of polygons of five or more sides  Identify and name polygons  Perimeter of polygons  Construct 3-dimensional shapes  Area of a rectangle  Identify 3-dimensional shapes and 2-dimensional shapes embedded within them  Relation of two or more line segments, rays, or lines intersecting, parallel, forming angles, and segments as sides of polygons  Notate points, segments, rays and lines  Construct pyramids and prisms  Construct angles and label accurately  Measure angles  Estimate angle measure  Center, circumference and diameter of circles/circular objects  Explore volume of rectangular prisms
Measurement and Reference Forms Recording equivalent units of length; recognizing appropriate units of measure for various items; finding the areas of rectangles; using multiplication arrays, coordinate grids, thermometers, and map scales to estimate distances.	Measure of 3-dimensional shapes  Estimate and find areas of rectangles  Use a variety of measuring tools  Estimation in measurement  Nonstandard linear units if measure/personal references  Standard units of length (customary and metric)  Perimeter of polygons  Diameter approximate value of Pi ( P )  Compare measures  Fractions and decimals with U.S. customary and metric units of length  Equivalent use of measure with fractions  Units of length, weight, and capacity and their equivalents, customary and metric  Volume of rectangular prisms  Relationship between weight and volume  Order objects by volume and weight  Equivalent measures and measure conversions  Application of net weight (for example: shipping packages)  Tell time to the minute  Elapsed time  Estimate distances with a map scale  Read and write temperatures-Celsius or Fahrenheit  Coordinate grids; ordered pairs  Dollar-and-cents notation  Estimate costs  Determine exact costs  Enter dollar-and-cents amounts into a calculator  Making change  Calculating sales taxes  Measure circumference and diameter  Measure line segments and perimeters to the nearest 1/8 inch and ½ cm  Make and use an angle measurer  Determine values of set of coins  Positive and negative numbers in relation to zero point in temperatures
Data and Chance Collecting, organizing, and displaying data using tables, charts, and graphs; exploring concepts of chance	Construct: tally charts, bar graphs, line graphs, frequency tables  Collect, record, display and analyze data  Identify landmarks: median, mode, maximum, minimum, range, mean  Plot average rainfall on a centimeter/millimeter scale  Use data to predict outcomes  Language of chance events  Probability of experiments  Find all possible combinations of given objects  Solve problems based on a bar chart and a line graph

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Fourth Grade Everyday Mathematics
Numeration:  Reading, writing, and comparing whole numbers through millions, decimals through thousandths, negative numbers to –20, and fractions; understanding relations between fractions, decimals, and percents; locating fractions and mixed numbers on a number line; generating equivalent fractions.	Relationships between ones, tenths, hundredths, and thousandths  Place value for whole numbers; extend the concepts to decimals  Uses of numbers: counts; measures; locations in reference frames; ratios; percents; scale numbers; identification numbers and codes  Base-10 place value system for naming whole numbers to millions  Read and write numbers in the millions  Meaning of decimals  Dollars and cents notation  Decimal notation to 3-place decimals  Meaning and use of fractions; color fractional parts of regions  Determine the number of objects representing a fractional part in a collection of objects  Compare fractional parts of regions where the regions are of different sizes and shapes  Explore equivalent fractions by matching fractional parts of regions  Formulate and apply a rule of generating sets of equivalent fractions  Compare fractions by comparing fractional parts of regions  Rename fractions as decimals  Using powers of ten with scientific notation  Rounding number to the nearest million  Magnitude estimates  Links between fractions, decimals, and percent notations  Terminating and repeating decimals  Use the percent key on a calculator  Percents  Equivalent names for percents  Use calculator to convert fractions to decimals to percents  Mayan numeration system  Equivalent names for whole numbers, decimals and fractions  Read, write and compare numbers to the hundred-millions  Read, write, and compare decimals to the thousandths  Fill-in-missing numbers on decimal number line  Positive and negative numbers
Operations and Computation: Using paper-and pencil algorithms to add, subtract, multiply, and divide multi-digit whole numbers and decimals; using mental arithmetic to compute exact answers and to estimate; rounding from millions to hundredths; modeling multiplication with arrays and areas; doing operations with fractions.	Add and subtract positive and negative numbers  Exponential notation for powers of 10  Mastery of addition and subtraction facts  Patterns in multiplication/division table  Identify multiplication facts to be memorized; practice through games; "50 facts" tests  Relationships between multiplication and division as a means for solving division facts  Multiply 1-digit times 2, 3-, 4-digit numbers  Multiply 2-digit times 2, 3-digit numbers  Rounding numbers to the nearest million  Multiples of 10, 100, 1000  Estimate sums and products  Find a fractional part of a number  Scientific notation  Estimate and find sums of distance and time measurement  Mental arithmetic with multiplication and division  Missing digit problems  Meaning of percent (ratio)  Write ratios as fractions  Interpreting percents  Recognizing uses of percents and rates in everyday life  Shading percent of a region  Find percent of a number  Explore alternative algorithms for addition and subtraction of multi-digit numbers  Multiplication/division diagrams (equal sharing, equal grouping, scaling, rate multiplication)  Unit-rate strategy  Units analysis in rate problems  A division algorithm as tallying device  Convert between rates  Add and subtract two-place decimals  Multiply by two-digit numbers  Divide by two-digit numbers  Divide by two-digit divisors  Make-up and solve number stories  Relationship of fractions and division Add and subtract fractions and decimals (hundredths) Addition algorithms: partial-sums; column addition  Subtraction algorithms: trade-first; counting up; partial-differences  Multiplication algorithms: partial-products; lattice method  Division algorithms: partial quotient  Solve division problems; with remainders; express remainder as fraction or decimal
Patterns, Functions, and Algebra: Using letters and other symbols for unknowns; simplifying expressions containing parentheses; creating, extending, and describing patterns, using formulas for finding the area of simple geometric figures; determining rules that relate numbers in pairs; finding missing numbers in tables; translating among verbal, numerical, and graphical representations, understanding and writing number models for number stories.	Rate tables  Equivalent fractions by multiplying numerator and denominator by the same number  Determine whether simple number sentences are true or false  Parenthesis in number sentences that involve more than one operation; determine whether such sentences are true or false  Introduce the vocabulary of open sentences  Find the solution of open sentences by replacing the variable with a number that will make the sentence true  Solve open sentences  Formulas  Solve number sentences on a calculator  Place-value puzzles  Missing factors with fraction of a number  Missing number in a number sentence  Number sentences and relation symbols  Solve logic problems
Geometry: Locating points on a coordinate grid; drawing and measuring angles; classifying angles as acute, obtuse, or right; classifying lines as parallel, intersecting, or perpendiculars; recognizing and using transformations, including reflections and rotations; understanding the relationship between reflections and line symmetry; building 3-dimensional shapes; describing, comparing, and analyzing 2-dimensional and 3-dimensional figures.	Develop a definition of polygons  Draw circles with a compass  Vocabulary and notation for line segments, lines rays  Properties of angles, triangles, quadrangles, polygons  Classify quadrangles  Meaning of parallel, classify parallelograms  Compass constructions involving more than one circle; concentric circles  Copy line segments using compass and straightedge  Construct regular hexagons and other designs with compass and straightedge  Clockwise rotations; make a circular protractor and use it to form angles of various degree measures  Use a 360 degree protractor to measure and draw angles less than 360 degrees  Use a half-circle protractor to measure and draw angles less than 180 degrees  Use a transparent mirror  Isometric or congruent transformations: reflection, rotation, translation, similarity  Figures in a coordinate plane  Lines of reflection  Line Symmetry  Geometry puzzles  Construct geometric solids, surface, face, edge, vertex, base, volume, interior  Construct structures from blueprints  Classify angles: acute, obtuse, reflex, right, straight
Measurement and Reference Frames: Using tools to measure length, area, volume, weight, temperature, and time; developing personal references for inches, centimeters, feet meters, and yards; estimating lengths and weights; finding areas and perimeters of rectangles, parallelograms, and triangles; finding volumes or rectangular prisms by counting cubic units; calculating elapsed time; using correct units in all measurements; calculating distances using map scales.	Derive formula for area of a rectangle  Metric linear measurement  Measure objects in metric units, convert measurements to other metric units  Measurement facts for mammals  Make scale drawings  Estimated area (for example: area of your skin)  Geographical area measurement  Formula for the area of parallelograms and triangles  Formula for the volume of rectangular prism  Area and perimeter of irregular polygons  Barometric pressure  Inch, foot, yard, mile  Millimeter, centimeter, decimeter, meter  Cup, pint, quart, half-gallon, gallon  Grid coordinates to identify regions, give directions, and describe routes on a map  Use letter-number coordinate pairs to identify square regions on a grid  Parallel/meridian partitioning on the world globe  Use a globe and a world map to find latitude and longitude of places  Construct a cutaway version of the globe  Locate places on atlas maps  Magnetic compass to specify direction; expressed in degrees with relation to North  Interval estimates  Grid layouts  Ordered pairs on a coordinate grid  Population counts (census data)  Use travel maps  Time to the nearest minute  Heart rate (heartbeats per minute)  Miles per hour  Cost per night  Graph test results over a period of time  Time zones  Time comparisons  Personal references to estimate lengths in US Customary and metric units  Volume concepts and units  Find perimeter and area; draw figures with given perimeter and area; grid squares; formula  Equivalent units of measure; convert measurements  Ounce, pound, gram, kilogram  Use scale to convert map distances to actual distances  Solve elapsed time problems
Data and Chance: Creating, reading and interpreting graphs; identifying landmarks in data sets, including range, median, mode, and mean; listing all possible outcomes in simple situations; using fractions to quantify probabilities; using experimental results to make predictions.	Predict the result of a chance experiment  Perform the experiment to verify the prediction  Collect, organize, display, and analyze a set of data  Maximum, minimum, range, mean, median, mode  Basic concepts and vocabulary for chance events  Find the chances that an event will occur  Analyze pie graphs (estimate shaded portion by percent)  Scale drawings  Read and interpret maps  Post "credits" and "debits"  Display standard-of-living and literacy data  Take a survey  Tabulate survey results  Analyze survey results  Predict outcomes based on data  Use collection words to name a set of things  Evaluate reliability of data  Display and interpret data: line plots, bar graph, tally charts, table  Solve probability problems  Collect and compare rate data; unit price data

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Fifth Grade Everyday Mathematics
Numeration: Reading, writing, and comparing negative numbers, fractions, whole numbers through billions, and decimals through thousandths; reading writing, and interpreting whole number powers of 10; translating between exponential and standard notation; understanding and identifying prime numbers, composite numbers, and square numbers.	Read, write, and compare numbers in the millions, billion, trillions  Represent whole numbers with rectangular arrays  Square numbers: representatives and properties  Equivalent names for numbers  Compare Numbers in exponential notation  Compare and order positive and negative numbers  Place value relationships on the calculator  Place value from trillions to thousandths  Meaning of fractions and fraction notation  Unit fractions; mixed numbers and fractions less than/greater than 1  Equivalent fractions  Fractional parts of a region  Fractions to name a part of a group  Rename fractions as mixed numbers and mixed numbers as fractions  Compare and order fractions (like and unlike denominators)  Repeating decimals  Percent as ratio: percents to compare fractions (like and unlike denominators)  Rename percents as decimals and percent activities  Ratio: meaning, notation, equivalent forms  PI as a ratio  Ratio as a comparison  Populations: ratio and percent activities  Rate as a comparison  Find factor strings and prime factorization  Deficient, abundant, and perfect numbers  Define and identify prime and composite numbers  Standard notation; expanded form, number-and-word notation  Convert among fractions/decimals/percents  Round numbers to given place  Use Probability Meter to display and interpret data  Find greatest common factor and lest common multiple
Operations and Computation: Using paper and pencil algorithms to add, subtract, multiply, and divide multi-digit whole numbers and decimals; using mental arithmetic both to compute exact answers and to estimate; rounding form billions to hundredths; translating among fractions, decimals, and percents; prime factoring; converting between fractions and mixed numbers; adding and subtracting fractions and mixed numbers with unlike denominators; finding least common multiples and greatest common factors; multiplying and dividing fractions.	Multiplication and division factors (mastery) Factors, products, factor pairs, factor rainbows. Prime factorization  Multiples of a number  Magnitude estimate  Simplify fractions  Least common multiples, greatest common factors  Mental arithmetic activities: Multiplication and division facts, including extensions and missing factors; multiplying a number by 9 in the ones place, multiply and divide multiples of ten; fraction-decimal-percent of a number; unit fraction to find thirds, fourths, fifths Divisibility tests for 2,3,4,5,6,9,10  Square roots  Deficient, abundant, and perfect numbers  Fractional parts of whole numbers; number line models  Decimal/fraction/percent equivalencies  Round decimal: up, down, to nearest 0.5  Estimate with percents  Find percent of a number  Use percent and unit fraction to find the whole  Missing parts of equivalent ratios  Scientific notation  Estimate sums and distances  Algorithms and Procedures  Write and solve number stories: addition, subtraction, multiplication and division with positive and negative whole numbers and decimals  Generate equivalent fractions; multiplication rule  Addition algorithms with whole numbers and decimals: same-change; partial sums  Subtraction algorithms with whole number and decimals: opposite-change; partial sums  Subtraction algorithms with whole numbers and decimals: same-change; partial differences  Multiplication algorithms with whole number and decimals: partial-products; lattice method; Egyptian  Division algorithms: partial quotients; successive estimation  Divide with 1-and-2 digit divisors  Fraction multiplication, algorithms: multiply numerator and multiply denominator; multiply fractions and whole number; multiply mixed numbers  Multi-digit addition, subtraction, multiplication and division with whole numbers and decimals  Estimate and find sums and differences of fractions with common denominators, unlike denominators and mixed numbers  Add and subtract positive and negative numbers on a calculator  Order of operations: solve problems with parentheses  Unsquare numbers by successive approximations  Square key and square root key on a calculator  Use a calculator to convert fractions/decimals/percents  Powers key on the calculator  Scientific notation on the calculator  Calculator key for fractions
Patterns, Functions, and Algebra: Evaluating simple algebraic expressions; finding rules for patterns; finding the nth term in a sequence; solving simple open number sentences and simple rate problems; working with equations by doing the same thing to both sides; understanding simple direct proportion; using variables and equations to represent situations; graphing ordered pairs; translating among verbal, numerical, and graphical representations.	Formula for area of rectangle, triangle, parallelogram  Pick’s formula for area of polygons  Formulas for the circumference of an area and circle  Formulas for the volume of a prism, sphere, cylinder  Formula for the relationships among faces, vertices and edges of a polyhedron  Use the Sieve of Eratosthenes to find prime numbers; Formulas for the volume of a prism, sphere, cylinder  Formula for the relationships among faces, vertices and edges of a polyhedron  Use the Sieve of Eratosthenes to find prime numbers; 1-200  Patterns in repeating polygons and their perimeters  "What’s My Rule?" routines (function machine)  Use a rule; find a rule  Algebraic expressions and word to describe "What’s My Rule?"
Geometry: Constructing a circle with a given radius or diameter; defining and creating tessellations; measuring and drawing angles, including reflex and straight angles; identifying and defining right, isosceles, and equilateral triangles; plotting points in four quadrants; using translations, reflections, and rotations; solving perimeter, area, and volume problems; understanding the relationship between the volumes of cones/pyramids and cylinders/prisms; finding the surface area of a cube and the area of a circle; identifying angle relationships in triangles and in quadrilaterals.	Compare prisms, pyramids, cylinders, cones  Two-dimensional shapes  Kites, parallelograms, perimeter  Rectangular and square arrays  Properties of regular polygons,, parallel lines, perpendicular lines  Tessellation with regular polygons, quadrangles, and a special polygon  Names of geometric solids  Properties of geometric solids: edge, face, curved surface, flat, vertex, apex, base, height, regular  Pattern (nets) for geometric solids  2-D and 3_D figures as clues in a measurement hunt  Scale drawings of sports playing fields  Radius and diameter  Use a compass or a Geometry Template to draw a circle; radius; diameter; determine circumference  Draw angles with half-circle and full-circle protractors  Measure angles with a protractor  Angle measures in a circle  Inscribe a square and a regular hexagon in a circle  Equilateral, isosceles, scalene and right triangles  Acute, obtuse, right, reflex, straight, vertical, and adjacent angles  Copy a triangle: with protractor; with compass; with straightedge  Copy line segments  Sum of angle and measure of each angle of regular polygon  Sum of angle measures of any triangle or quadrangle  Clockwise and counterclockwise turns to represent angle measure  Measure finger-separation angles  Congruent figures  Transformations, translations, reflections on a coordinate grid  Similarity on a coordinate grid  Base and height of rectangles, parallelograms, and triangles  Volume experiment dealing with air pressure/displacement  Volume and density of sports balls  Estimate and calculate volume of a cylinder  Area f circles, rectangles, triangles, parallelograms  Surface area of a cylinder  Identify bases of prisms, pyramids, cylinders, and cones
Measurement and Reference Frames: Measuring and estimating length, area, volume, weight, and capacity; converting and computing with common units of measure; creating scale drawings.	Area and notation for square units  Personal reference for area  Perimeter circumference  Estimation challenges: how many footsteps, miles and how much time will it take to go from one place to another; tallying chances in a game to determine fairness, determine land area of local school site  Estimate time for 1 million, 1 billion, 1 trillion finger taps; lengths and distances with a compass; area of a circle by counting squares; equivalent customary and metric measures  Fractions and linear measure  Convert fractions of hours to minutes  Natural measures: span, cubit, fathom  Personal references for natural measures  Equivalent measures  Highest/lowest elevations  Measure in fractions of inches: one-sixteenth inch and millimeter  Fractions, decimals on the number line  Compare measures  Measure to nearest gram  Ratios of linear measure  Rectangular land survey system; measure land in acres  Reasonable measures of volume and capacity  Compare measures of volume (cm3) and capacity  (L, mL) Volume and notation for cubic units  Measure volume of triangular and quadrangular prisms  Compare volumes: volume by the displacement method  Time equivalents  Fractions and equivalent times  Measure pendulum swings in seconds  Convert units of time: minute, hour, day, week, year, decade, century  Time an event to the nearest 0.1 second  Temperature change and negative numbers  Celsius/Fahrenheit equivalents  Slide rule as a number-line model  Positive and negative numbers on a number line  Use parts of map: Legend; direction symbols; scale  Draw, classify; estimate and measure angles  Measure to find sum of angles in polygon  Find personal references and measure length in US customary and metric  Measure line segments; draw line segments of a given length  Locate, plot, read ordered pairs on a coordinate grid
Data and Chance: Comparing probabilities for different outcomes; comparing theoretical and experimental probabilities as fractions, decimals, and percents; drawing justifiable conclusions from data; displaying data in more than one way; formulating a question, carrying out a survey or experiment; recording data, and communicating results; drawing and interpreting, circle graphs and stem-and-leaf plots; understanding measures of central tendency (mean, median, mode).	Find: mean, median, mode, maximum, minimum, range Analyze data Reasonableness of data  Collect data: game winners; states visited; hand and finger measures; candy color; hand-folding; favorite snacks; dominate eye; video data about on and off headlights at dusk; analyzing walking and bicycling data; reaction time data; populations; etc.  Organize data: number-line plot; stem-and-leaf plot  Display data: bar graphs, line graphs, circle graphs, tables, charts  Read and interpret graphs and tables  Relationship between data on temperature and elevation  Analyze fairness of a game  Chance events" certain, likely, 50-50, unlikely, impossible  Use a Probability Meter  Probabilities expressed as words and percents  Predictions using tables of values, formulas, and line graphs  Estimate chances  Random number generators  Survey project: choose sample, develop questions, collect information to analyze  Analyze sample size and reliability of predictions  Frequency of specific occurrence in a sample  Undertake a classroom census  Minimum, maximum, median of sums of circle measures  Use ratios to examine trends in data  Make estimate based on random sample  Construct tree diagrams to represent and count combinations of choices  Find probabilities in "equally likely" situations

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Sixth Grade Everyday Mathematics
Numeration: Reading, writing and comparing whole numbers, negative numbers, fractions, decimals, and percents; reading, writing, and interpreting integer powers of 10; converting between scientific and standard notation and among fractions, decimals, percents, and mixed numbers; renaming fractions and mixed numbers in simplest form.	Equivalent fractions, mixed numbers, decimals, percents  Equivalent names for numbers  Compare and order positive and negative numbers  Positive and negative powers to 10  Add and subtract positive and negative numbers  Place value: whole numbers, decimals  Scientific notation  Standard notation  Compare large numbers in scientific notation  Uses of random numbers  Properties of number systems  Properties of rational numbers  The real number line  Prime and composite numbers  "Memorable" numbers  Square roots  Appropriate use of fractions, decimals, percents  Compare and order fractions and mixed numbers  Rename improper fractions as mixed numbers or whole numbers  Fractions to express probabilities  Numbers between 0 and 1 in decimal and exponential notation  Rates as comparisons  Rename percents as degrees for sectors of circle graphs  Rate, rate units, rate notations, per units rates  Compare rates (unit prices)  Scales (ration comparisons) for models and maps  Ratio: part-to-part and part-to-whole comparisons  Equivalent ratios  Compare ratios  Ratios to describe size-change factor notation  Compare, order, read, and write numbers through trillions; millionths  Translate between notations: number-and-word; standard; scientific  Find equivalent fractions  Rename mixed numbers as fraction; express in simplest form  Find reciprocal of a number  Calculator: powers key; scientific notation  Least common multiple; greatest common factor
Operations and Computation: Using paper-and-pencil algorithms for basic operations with whole numbers, fractions, and decimals; using mental arithmetic to compute exact answers and to estimate; performing operations with integers and with numbers in scientific notation; solving problems using unit rates and ratios; solving proportions; using ratios in scale drawings and size-change factors in similar figures; rounding to any specified place; adding and subtracting fractions and mixed numbers with unlike denominators; multiplying and dividing fractions; finding least common multiples, greatest common factors and prime factors.	Mental Arithmetic and Number Systems Exponents and multiples of 10 ( scientific notation)  Estimate products of decimals  Mental arithmetic: Use whole numbers; divide by 2,4,6,8,10; multiply by 5,50,500; successive whole number calculations; inverse operations with whole numbers; estimate with whole numbers  Mental arithmetic: squares and square roots  Mental arithmetic: calculate with measurements  Mental arithmetic: name ratios and rates  Multiply or divide by powers of 10  Extend multiplication and division facts  Multiples of numbers  Estimate products of whole numbers and decimals (magnitude estimates0 Multiply with fractions, decimals, and percents  Multiplication properties of one; reciprocals property  Fact families for multiplication and division with positive and negative numbers  Squares of numbers and square roots  Estimate square roots  Size-change factors and similar figures (multiplication application)  Figurate numbers (triangular numbers)  Dividend, divisor, quotient, remainder  Fractions in simplest form  Estimate sums of fractions  Estimate percents and fractions of a circle  Estimate percent equivalents for fractions  Estimate a fraction and a percent of a whole  Estimate products and quotients of fractions with positive and negative numbers  Estimate products of decimals  Rate tables and finding per-unit rates  Per-unit rates to solve problems  Rate diagrams  Unit ratios: times as many problems  Ratios and areas of rectangles  Size-change factors as ratios  Ratios to find lengths of corresponding sides of similar polygons  Golden ratio and unit ratios  Estimate distances of rotation and revolution  Calculate minimum distances and estimated travel times between Earth and other planets, add, subtract, multiply, and divide decimals  Round decimals to a given place  Estimate quotients: whole numbers; decimals  Division algorithm: partial quotients  Solve multi-step number stories  Order of operations; evaluate number expressions  Distributive property  Lattice method for multiplication Algorithms and Procedures Covert data tables to fractions and percents  Unit fraction to find the whole  Multiply whole numbers; decimals; by powers of 10  Divide by 1-digit numbers by breaking the dividend into friendly numbers  Division algorithm: use successive estimates  Divide by 1-and2 digit divisors  Generate random numbers with a calculator  Add and subtract positive and negative numbers with a calculator  Computations and the distributive property  Common denominators  Add and subtract fractions with like and unlike denominators  Add and subtract mixed numbers with like and unlike denominators  Fraction multiplication algorithm  Multiply mixed numbers, fractions and mixed numbers  Division of fractions algorithm  Divide mixed numbers  Divide fractions  How to use the percent circle  Percent of a number  Percent of a number using a calculator  Percent one number is of another using a calculator  Unit percent to find the whole  Rename fractions as decimals using a calculator  Scientific notation with a calculator  Convert numbers in exponential to standard notation using a calculator  Area models (partial products for distributive properties  Order of operations and scientific calculators  Enlarge a drawing using a grid  Squares of numbers, square roots, and reciprocals using calculator  Special keys on the calculator
Patterns, Functions, and Algebra: Recognizing, continuing, and describing complex patterns and finding the nth term in a sequence; using variables and opposite number sentences to represent problem situations; writing equations to fit given tables of numbers; evaluating algebra expressions; solving linear equations with one unknown by performing the same operation to both sides of the equation representing linear functions as equations, in tables and grids and verbally as rules; understanding and applying the order operations and the distributive property.	Complete a table given a rule  State the rule given the table  Find patterns in relationships between area and perimeter  Find a pattern and continue a number sequence  General patterns and special cases  Multiplication patterns  Turn-around patterns with positive and negative numbers  "What’s My Rule?" activities  "What’s My Rule?" tables for geometric patterns  Formulas and rules in "What’s My Rule?" tables  Formulas for distance for and speed of free-falling objects  Formulas for finding and average  Formulas for body proportions  Formulas for balancing mobiles  Computer spreadsheets using formulas  Formulas for volume: rectangular prisms, cylinders, spheres  Formulas to solve problems involving temperature conversions  Formulas to solve problems involving temperature conversions  Formulas to solve problems involving age and vocabulary relationships  Formulas to solve problems involving bowling handicaps  Solve problems using formulas for area and volumes of trapezoids and cones  Formulas, tables, and coordinate grids  Pythagorean Theorem  Relationships represented by rules, tables, and coordinate graphs  Relationships among radius, circumference, and area of a circle  Applications of variables in generalizations, number patterns (properties0, formulas and spreadsheets  Variables to state fraction multiplication and division algorithm  Variables to state distributive property of multiplication over addition and subtraction  Write number sentences to solve problems  Solve simple open sentences  Number models for ration number stories  Substitute a given value and evaluate expressions  Use symbols to rewrite English expressions  Number sentences: relation, operation, and grouping symbols  Write and solve simple equations (open sentences)  Pan-balance problems  Pan-balance model for equivalent equations  Equivalent –equation method of solving equations  Algebraic expressions for situations described in words  Evaluate an algebraic expression  Order of operations  Solution sets of inequities  Rewrite expressions using the distributive property