# Scope and Sequence of Elementary Math

## K5 Math

### Numeration

Identify numbers 0–100; Write numbers 0–100

### Number Sense

Compose/decompose numbers; Identify ordinal positions: first–tenth; first, next, last; Determine order: before, after, between; Find patterns in numeration; Develop place value: tens and ones; Identify teen numbers as 10 and some more

### Counting & Cardinality

Count and make sets to 20; Count to 100 by 1s and 10s; Count on from any given number; Represent the quantity of a number using manipulatives or by drawing a picture

### Whole Number Operations: Addition & Subtraction

Sums to 10: join sets; count on; compose/decompose numbers; Differences to 10; take apart; unknown part; count back; Represent addition/subtraction sentences with pictures (manipulatives, draw, act out); Write addition/subtraction sentences (equations); Solve word problems; Tell a story for a number sentence; Explain the sum or difference

### Algebra Readiness

Understand part-whole relationship; Correlate the relationship between addition and subtraction

### Equal Parts of a Whole (Fraction Concepts)

Count equal parts in a whole; Distinguish between equal parts and unequal parts; Partition a whole into equal parts

### Geometry

Describe attributes of flat shapes: circle, square, triangle, rectangle in various orientations; Describe attributes of solid figures: ball shape (sphere), can shape (cylinder), box shape (rectangular solid, cube), cone shape (cone); Construct shapes with manipulatives; Identify spatial relationships: top, middle, bottom; left, right; over, under; inside, outside; on, off; front, back; Extend and construct patterns (color, shape, size)

### Estimation

Number of objects; Length: longer, shorter; Weight: weighs more, weighs less; Capacity: holds more, holds less; Time: more time, less time

### Measurement

Sort and classify objects by attributes (number, color, size, shape); Compare measurable attributes; length (longer/shorter), height (taller/shorter), weight (heavier, lighter), capacity (more, less); Measure: nonstandard units and inches; more than one attribute; Determine temperature: hot, cold; Tell time: read and write time to the hour; daytime, nighttime; sequence events; more time, less time; Read a calendar: days of the week; months of the year; yesterday, today, tomorrow; seasons; Identify and count pennies

### Problem Solving

Solve word problems using manipulatives, drawing pictures, or acting-out situations; Write and solve number sentences (equations)

## Math 1

### Numeration

Read and identify 0-999; Write and picture 0-999; Number words: zero to twenty

### Number Sense

Compose/decompose; Ordinals: first-tenth; first, next, last; before, after, between; Patterns; sequencing: first, next, last; before, after, between

### Number Line

Place Value; Hundreds/tens/ones; 1 more/1 less, 10 more/10 less, 100 more/100 less; Expanded form; Compare with < and >; Even/odd numbers

### Counting

Find patterns in numeration; Count to 999; Count by 1s, 5s, 10s to 200; Count forward and backward

### Addition

100 basic facts (using strategies); Number sentences (equations) and vertical form; Two- and three-digit addends; money; Rename 10 ones as 1 ten

### Subtraction

100 basic facts (using fact families and other strategies); 2-digit minuend and subtrahend; equation; vertical form; money; Word problems: take-away, comparison, missing addend; Subtract 0 rule

### Multiplication Readiness

Repeated addition; counting by 2s, 5s, 10s

### Algebra Readiness

Represent a picture with a number sentence; missing addend; Understand and use Addition Properties (Commutative, Associative, Identity)

### Fractions

Equal parts; halves; fourths (quarter); part of a set of objects

### Geometry

Plane shapes: circle, square, triangle, rectangle; sides and corners; Solid figures: sphere, cylinder, rectangular prism, cube, cone; corners, faces, curved sides; Spatial relationships; patterns; perimeter

### Estimation

Numbers of objects; Length: is longer, is shorter; Weight: weighs more, weighs less; Capacity: holds more, holds less

### Measurement

Length/height: nonstandard units, inch, centimeter; Weight: weighs more, weighs less; Capacity: holds more, holds less; Temperature: Fahrenheit; Celsius; Measuring tools: ruler, scale, thermometer, cup; Time: hour and half hour; elapsed time; Calendar: days, weeks, months; Money: penny, nickel, dime, quarter

### Problem Solving

Word problems; picture, tally charts, bar graph; Reasoning

### Graphs and Data

Pictures, graph, bar graph, tally charts

### Calculators (optional)

Make numbers; addition; subtraction

## Math 2

### Numeration

Identify and write 0–9,999; number words: zero to nine hundred ninety-nine

### Number Sense

Place value: thousands/hundreds/ tens/ones; 10 more/10 less; 100 more/100 less; even/odd numbers; round to the nearest ten and hundred; compare with < and >; expanded form; Ordinals: first–twentieth; Patterns; sequencing: before, after, between; number line

### Counting

Count by 1s, 5s, 10s, and 100s; by 2s to 60; by 3s to 30; by 4s to 40

### Addition

100 basic facts (using fact families and other strategies); 4-digit addends; vertical form addition; rename 10 ones as 1 ten, 10 tens as 1 hundred, 10 hundreds as 1 thousand; money; word problems; strategies; Order Principle, Zero Principle, Grouping Principle

### Subtraction

100 basic facts (using fact families and other strategies); Three- and four-digit minuend and subtrahend; rename 1 ten as 10 ones, 1 hundred as 10 tens, 1 thousand as 10 hundreds; money; Word problems; take-away, comparison, missing addend; strategies; Zero Principle

### Multiplication

Repeated addition; array; number line; equation; vertical form; factors: 0–5, 10; word problems; Order Principle, Identity Principle, Zero Principle

### Division

Equal sets; equation; missing factor; divisor: 1–5; word problems

### Algebra Readiness

Equation; missing addend; missing factor; Order Principle, Grouping Principle, Zero Principle

### Fractions

Equal parts; halves to tenths; part of a set; fair share; compare with common denominators; compare with 1 as the numerator

### Decimals

Money

### Geometry

Plane figures: circle, square, triangle, rectangle, pentagon, hexagon, oval; sides, vertices; similar, congruent; symmetry; slides, flips, turns; Solid figures: sphere, cylinder, rectangular prism, cube, cone, pyramid; faces, edges, vertices, curves; Lines: horizontal/vertical; parallel/intersecting; Area; perimeter; patterns

### Estimation

Round to nearest ten and hundred; Length: inch, foot, yard; centimeter, meter; Weight: more than/less than 1 pound, 1 ounce; Mass: more than/less than 1 kilogram; about 1 gram/more than 1 gram; Capacity: more than/less than 1 cup, 1 pint, 1 quart, 1 gallon; more than/less than 1 liter

### Measurement

Length: inch, foot, yard; centimeter, meter; Capacity: cup, pint, quart, gallon; liter; Weight: ounce, pound; Mass: gram, kilogram; Temperature: Fahrenheit; Celsius; Measuring tools: ruler, scale, thermometer, cup, liter; Time: to five-minute interval; A.M./P.M.; elapsed time; Calendar: day, week, month, year; Money: penny, nickel, dime, quarter, half-dollar, one dollar

### Problem Solving

Word problems; graphs; tables; charts; map skills; probability; money

### Statistics & Graphs

Pictograph; bar graph; coordinate graph; line graph; circle graph; tables; charts; tallies

### Calculators

Addition; subtraction

## Math 3

### Number Sense

Recognize and write 0–1,000,000 with numerals and words; Roman numerals I–XIII; Ordinals; first through ninety-ninth; order; number line; 10 more/10 less; place value; ones to hundred thousands; expanded form; even/odd numbers; round to the nearest ten, hundred, one thousand, compare with > and <

### Counting

Count by 1s, 2s, 5s, 10s, 100s, 1,000s, 10,000s; count by 2s to 20, by 3s to 30, by 4s to 40, by 5s to 50, by 6s to 60, by 7s to 70, by 8s to 80, by 9s to 90

### Addition

100 basic facts; fact families; five-digit addends; vertical form; rename 10 ones as 1 ten to 10 one thousands as 1 ten thousand; money; strategies; word problems; Commutative Property, Associative Property, Identity Property

### Subtraction

100 basic facts; fact families; five-digit minuend and subtrahend; word problems; rename 1 ten as 10 ones to 1 ten thousand as 10 one thousands; money; word problems; strategies; take-away, comparison; missing addend; Zero Principle

### Multiplication

110 basic facts; fact families; multiples; repeated addition; arrays; number line; equation; vertical form; 1 digit factors; 2 to 3 digits by 1 digit; renaming; strategies; word problems; Commutative Property; Associative Property; Identity Property; Zero Property

### Division

110 basic facts; fact families; equal sets; repeated subtraction; measurement; partition/strategies; equation; division frame; word problems; 2 and 3 digits by 1 digit; 1-digit remainders

### Algebra Readiness

Equation; missing addend; missing factor; negative numbers (temperature); Properties

### Fractions

Part of a whole; part of a set; equivalent fractions; compare; order; mixed numbers; add and subtract like fractions

### Decimals

Read and write tenths and hundredths; mixed numbers; compare; order; add and subtract; rename 10 tenths as 1 one and 10 hundredths as 1 tenth; word forms; money; word problems

### Geometry

Plane figures: circle, polygons, square, triangle, rectangle, pentagon, hexagon, octagon; edge, vertex; slides, flips, turns; Solid figures: sphere, cube, cylinder, cone, rectangular prism, rectangular pyramid; faces; edges; vertices; curved surface; Lines: horizontal/vertical; parallel/ intersecting; symmetry; Area; perimeter; patterns

### Estimation

Round to nearest ten, hundred, and one thousand; Length; distance; capacity; weight; mass

### Measurement

Length: ½ inch, foot, yard, mile; centimeter, meter, kilometer; Capacity: cup, pint, quart, gallon; milliliter, liter; Weight: ounce, pound; Mass: gram, kilogram; Temperature: Fahrenheit; Celsius; Time: to 1-minute interval; past and future elapsed time to 5-minute interval; before/after the hour; A.M./P.M.; noon/midnight; Calendar: date, future date; schedule; Money: coins; five-dollar bill; ten-dollar bill; dollar sign; decimal point; addition, subtraction

### Problem Solving

Word problems; graphs; tables; charts; schedule; map skills; logic; probability; money; multi-step problems; problems with too little information; Problem Solving Plan

### Data & Graphs

Bar graph, pictograph; line plot; line graph; coordinate graph; circle graph; tables and charts; tallies

### Calculators

Addition; Subtraction

## Math 4

### Number Sense

Recognize and write 0–100,000,000 with numerals and words; Roman numeraIs I–XXXIX

### Number Patterns

Ordinals; first through ninetyninth; order; number line; 10 more/10 less; Place value: ones to hundred millions; expanded form; even/ odd numbers; round to the nearest ten, hundred, one thousand; compare with >, <, and =

### Counting

Count by 1s, 2s, 5s, 10s, 100s, 1,000s, 10,000s; count by 2s to 20, by 3s to 30, by 4s to 40, by 5s to 50, by 6s to 60, by 7s to 70, by 8s to 80, by 9s to 90

### Addition

100 basic facts; fact families; six-digit addends; vertical form; rename 10 ones as 1 ten to 10 one thousands as 1 ten thousand; Strategies; word problems; money; Commutative property, associative property, identity property

### Subtraction

100 basic facts (using strategies); fact families; six-digit minuend and subtrahend; rename 1 ten as 10 ones to 1 ten thousand as 10 one thousands; Strategies; word problems; money; take-away, comparison; missing addend; unknown part; Zero principle

### Multiplication

110 basic facts; fact families; multiples; repeated addition; arrays; number line; equations; vertical form; one-digit factors; one digit times two to four digits; two digits times two or three digits; renaming; strategies; word problems; Commutative property, associative property, identity property, zero property, multiplication, addition principle

### Division

110 basic facts (using strategies); fact families; equal sets; repeated subtraction; measurement; partition/ strategies; equation; round the division; adjust the quotient; division frame; word problems; finding averages; computation: two to four digits by one digit; two to three digits by two digits; one to two digit remainders; divisibility rules

### Algebra Readiness

Equations; missing addend; missing factor; negative numbers; function tables; variables

### Fractions

Part of a whole; part of a set; add and subtract like fractions and mixed numbers with like fractions; rename improper fractions; Equivalent fractions; compare; order

### Decimals

Read and write tenths and hundredths; mixed numbers; compare; order; add and subtract; rename 10 tenths as 1 one and 10 hundredths as 1 tenth; word forms; money; word problems; round to nearest whole

### Geometry

Plane figures: circle, polygon, square, triangle, rectangle, pentagon, parallelogram, rhombus, hexagon, octagon; edge, vertex; slides, flips, turns; Solid figures: sphere, cube, cylinder, cone, rectangular prism, square prism, triangular prism, rectangular pyramid, square pyramid, triangular pyramid; face, edge, vertex, curved surface; Lines: horizontal/vertical, parallel/ intersecting, segments; points; rays; angles: right, acute, obtuse; Symmetry; similar; congruent; Circle: radius, diameter; Perimeter; area; complex area; volume; patterns

### Estimation

Round to nearest ten, hundred, and one thousand, one million; Round for addition, subtraction, multiplication, and division; Length; distance; capacity; weight; mass

### Measurement

Length: ¼ and ½ inch, foot, yard, mile; centimeter, meter, kilometer, millimeter; Capacity: cup, pint, quart, gallon; milliliter, liter; Weight: ounce, pound, ton; Mass: gram, kilogram; Temperature: Fahrenheit; Celsius; Time: to one-minute interval; past and future elapsed time to five-minute interval; before/ after the hour; a.m./p.m.; noon/ midnight; Calendar: date, future date; schedule; Money: coins; one-, five-, ten-, and twenty-dollar bills; dollar sign; decimal point; addition; subtraction; multiplication; division

### Problem Solving

Use a problem-solving plan: problems; graphs; tables; charts; write word problems; schedule; map skills; logic; probability; money; multistep problems; problems with too little information, fractions

### Data

Pictograph; bar, line, circle, and coordinate graphs; Tables; charts; tallies; line plot; stem-and-leaf plot; Mean, median, mode, range, frequency

### Calculators

Addition; subtraction; division

## Math 5

### Number Sense

Recognizing and writing 0–100,000,000,000 as numerals and words; Roman numerals I–C; Place value: ones to hundred billions; comparing; expanded form; even/odd numbers; positive/negative numbers; number line; expressions and equations

### Addition & Subtraction

Basic facts (fact families and other strategies); six-digit numbers; renaming to hundred thousands; inverse relationship; strategies; word problems; money; compensation; Properties: commutative, associative, identity, zero principle

### Multiplication

Basic facts (fact families and other strategies); multiples; repeated addition; arrays; equations; vertical form; one to three digits times two to four digits; renaming; strategies; word problems; money; factor trees; prime and composite numbers; GCF; LCM; Properties: commutative, associative, identity, zero, distributive over addition

### Division

Basic facts (fact families and other strategies); equal sets; inverse of multiplication; measurement; partition; fraction form; equations; two to four digits by one or two digits; remainders; strategies; word problems; money

### Fractions

Part of a whole; part of a set; equivalent fractions; comparing; ordering; lowest terms; renaming improper fractions and mixed numbers; Adding and subtracting like and unlike fractions; adding and subtracting mixed numbers with like and unlike fractions; Multiplying a whole number times a fraction and a fraction times a whole number; multiplying a fraction times a fraction; multiplying a whole number times a mixed number; multiplying a mixed number times a mixed number; Dividing a whole number by a fraction; dividing a fraction by a fraction; reciprocals

### Decimals

Reading and writing tenths, hundredths, thousandths; writing as fractions and mixed numbers; comparing; ordering; renaming to thousandths; word forms; money; word problems; rounding to nearest hundredth; Multiplying a decimal by a whole number, by a decimal, and by a power of 10; Dividing a decimal by a one-digit whole number; dividing a whole number by a whole number with a decimal quotient; dividing to rename a fraction as a decimal; dividing a decimal by a power of 10

### Geometry

Points; horizontal/vertical lines; parallel/intersecting/perpendicular lines; line segments; rays; angles: right, acute, obtuse; measuring angles; Plane figures: circle, polygon, square, triangle, rectangle, pentagon, hexagon, octagon, quadrilateral, parallelogram, rhombus, trapezoid; edge, vertex; similar, congruent, symmetrical; translation, reflection, rotation; perimeter, circumference, area; Solid figures: sphere, cone, cylinder, polyhedron, cube, prism, pyramid; face, edge, vertex, curved surface; nets; surface area; volume; Circle: center point, radius, diameter, chord, central angles; Triangles: sum of angles = 180º; acute, obtuse, right; isosceles, scalene, equilateral

### Estimation

Rounding to a given place; Rounding for addition, subtraction, multiplication, and division; Whole numbers; fractions; decimals; Length; distance; capacity; weight; mass

### Measurement

Length; capacity; weight; mass; temperature; Time: past and future elapsed time; equivalent units; converting units; adding and subtracting; Calendar; writing dates

### Problem Solving

Use a problem-solving plan: problems; graphs; tables; charts; schedule; map skills; logic; probability; money; multistep problems; problems with too little or too much information

### Data

Tables; charts; tallies; frequency table; line plot; stem-and-leaf plot; Pictograph; bar/double-bar graph; line/double-line graph; circle graph; coordinate graph; Mean, median, mode; range; frequency; scale; interval

### Ratios, Proportions, Percents

Equivalent ratios; unit rate; scale drawings; map scale; Writing percents as fractions and decimals; writing fractions as percents; comparing percents to decimals and fractions; finding the percent of a number

### Calculators

Varied activities

## Math 6

### Number Sense

Recognize and write 0–100,000,000,000 as numerals and words; Roman numerals I–C; Place value: ten thousandths to hundred billions; comparing; expanded form; even/odd, positive/negative, prime/composite numbers; number line; expressions and equations; Part-whole relationships; inverse operations

### Addition & Subtraction

Basic facts; fact families; nine-digit column addition; Mental compensation; Properties: Commutative, Associative, Identity; Zero Principle

### Multiplication

Basic facts; fact families; multiples; repeated addition; vertical form; 1–3 digits times 2–4 digits; renaming; factor trees; prime/ composite numbers; GCF; LCM; Properties: Commutative, Associative, Identity, Zero, Distributive

### Division

Basic facts; fact families; equal sets; measurement/partition; fraction form; equations; mental division by 10; 2–4 digits by 1–2 digits; remainders; mixed number and decimal quotients; decimal equivalent for a fraction

### Equations

Inverse operations; compensation; simplify expressions; evaluate expressions; if-then statements; solve for an unknown

### Pre-Algebra

Missing addend/subtrahend/minuend/factor; add, subtract, multiply, and divide integers; positive/negative numbers; Variables in expressions and equations; solve for a variable in an equation

### Fractions

Part of a whole; part of a set; equivalent fractions; comparing; ordering; lowest terms; renaming improper fractions and mixed numbers; Add, subtract, multiply, and divide like and unlike fractions; cross-products; cancellation; pictorial representations or journal entries to express understanding of operations

### Decimals

Read and write tenths, hundredths, thousandths; write as fractions and mixed numbers; comparing; ordering; renaming to thousandths; word forms; Add and subtract; Multiply a decimal by a whole number, by a decimal, and by a power of 10; Divide a decimal by a 1-digit whole number; divide a whole number by a whole number with a decimal quotient; divide to rename a fraction as a decimal; divide a decimal by a power of 10

### Geometry

Points; lines: parallel, intersecting, perpendicular; line segments; rays; symmetry; similar/congruent; constructions; angles: right, acute, obtuse; measure angles; sum of angles in a triangle = 180°; Plane figures: regular/irregular; polygons; triangles: scalene, isosceles, equilateral; quadrilaterals; parallelograms; transformations: translation, reflection, rotation; perimeter; area; Solid figures: sphere, cone, cylinder, polyhedrons, cube, prisms, pyramids; face, edge, vertex, curved surface; nets; surface area; volume; Circle: center point; radius; diameter; chord; central angles; circumference

### Estimating

Round whole numbers and decimals to a given place; round fractions to the nearest half or whole; front-end estimation; Round to estimate a sum, difference, product, and quotient

### Measurement

Length; capacity; weight; mass; Temperature: Fahrenheit/Celsius; Time: elapsed time; time zones; timeline; 24-hour clock; wages; Rename within the metric and customary systems to add, subtract, multiply, and divide

### Problem Solving

Graphs; tables; charts; schedule; map skills; probability; money; Venn diagram; Using a problem-solving plan; Multi-step problems; problems with too little or too much information; group planning; Strategies: patterns; logic; guess and check; diagram/model; simpler problem; formulas; working backwards; writing an equation

### Statistics & Graphs

Pictograph; bar/double bar graph; line/double line graph; histogram; circle graph; coordinate graph; Tables; charts; tallies; frequency table; line plot; stem-and-leaf plot; box-and-whisker plot; Mean, median, mode; range; frequency; scale; interval

### Ratios, Proportions, Percents

Equivalent ratios; unit rate; scale drawings; map scale; Percents as fractions and decimals; write fractions and decimals as percents; compare percents to decimals and fractions; find the percent of a number; determine the sales price given a discount as a percent; Proportionate geometric figures