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
Make 10; 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; thirds; fourths (quarter); part of a set of objects; fair share; probability
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; Venn diagram
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; pound, kilogram; Capacity: holds more, holds less; cup, pint, quart, gallon, liter; 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; Reasoning; Problem-Solving Plan; STEM; Graphs and Data: Pictograph, bar graph, tally chart
STEM
Coding activities
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