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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 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; 2- and 3-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; fact families; 4-digit addends; column 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; fact families; 3- and 4-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 5-minute interval; A.M./P.M.; elapsed time; Calendar: day, week, month, year; Money: penny, nickel, dime, quarter, half-dollar, 1 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; Ordinals; first through ninety-ninth; order; number line; 10 more/10 less; Place value: ones to hundred thousands; compare; 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; column addition; 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; 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; 1-digit factors; 1 digit times 2–4 digits; 2 digits times 2–3 digits; renaming; strategies; word problems; Commutative Property, Associative Property, Identity Property, Zero Property, Multiplication, Addition Principle

Division

110 basic facts; fact families; equal sets; repeated subtraction; measurement; partition/strategies; equation; division frame; word problems; computation: 2–4 digits by 1 digit; 2–3 digits by 2 digits; 1–2 digit remainders

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, polygons, square, triangle, rectangle, pentagon, hexagon, octagon; edge, vertex; slides, flips, turns; Solid figures: sphere, cube, cylinder, cone, rectangular prism, rectangular 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; patterns

Estimation

Round to nearest ten, hundred, and one thousand; 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 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; 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, schedule, map skills, logic, probability, money, multistep problems, problems with too little information

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; 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; multiples; repeated addition; arrays; equations; vertical form; 1–3 digits times 2–4 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; equal sets; inverse of multiplication; measurement; partition; fraction form; equations; 2–4 digits by 1–2 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, one 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 1-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 = 180°; 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 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 ½ 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; Multi-step problems; problems with too little or too much information; Problem-Solving Plan; group planning; Strategies: patterns; logic; guess and check; diagram/model; simpler problem; formulas; work backwards; write 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

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