Concepts are introduced in the grade specified, and reviewed in subsequent grades.
| Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8 | |
|---|---|---|---|---|---|---|
| Acres | Square feet in acre; acres in square mile | |||||
| Addition | Meaning of; terms; facts; column; endings with/without bridging; carrying to thousands; checking by adding up/by subtraction; choosing the right sum | Carrying to millions; adding like fractions | Carrying to billions; adding mixed numbers, unlike fractions, mixed measures, like/unlike decimals | Adding positive/negative numbers | ||
| Angles | Right | Straight, acute, obtuse, vertex | Reading degrees in: straight, acute, obtuse, reflex; drawing; bisecting | Complementary; supplementary; copying | ||
| Area, finding | Square, rectangle | Triangle | Missing dimensions; parallelograms; circles | Rhomboid; trapezoid | ||
| Average | Finding | |||||
| Bank accounts | Checking; savings | |||||
| Base | used as complete group in Type I, II, II percent problems | |||||
| Bisecting | Lines | |||||
| Business terms | Understanding terms; finding cost; selling price, overhead, profit, margin, commission, discount | Assets, liabilities, loss, profit, promissory notes, recording income, retail, unit price, wholesale | ||||
| Board feet | introduced | |||||
| Calendar Facts | Days, weeks, months, year, leap year, writing dates the short way | Decade, century | Reading and writing year dates; adding/ subtracting year dates; millennium | B.C./A.D.; time line | ||
| Changing Measures | Larger units to smaller units; smaller units to larger units | unequal measures | ||||
| Circles | Recognizing; radius, diameter, semicircle, arc, circumference | Degrees in circle; drawing; finding diameter, radius, circumference, area | ||||
| Commission | Using to find net proceeds, rate of commission, selling price | |||||
| Comparing | Larger numbers to smaller numbers and vice versa; smaller fractions to larger fractions and vice versa | |||||
| Compass | using | compass rose | ||||
| Constructing | Parallel lines, parallelogram, perpendicular lines, square | |||||
| Coordinates | introduced | |||||
| Cord | introduced | |||||
| Counting by | 2, even/odd, 3, 5, 10, 25, 50, 100 | |||||
| Cubic measures | introduced | |||||
| Decimals | To thousandths; mixed decimals; comparing decimals; equivalents; adding/ subtracting like/unlike decimals; multiplying with decimal factors; dividing with decimal dividends; dividing decimals by powers of 10 | To ten thousandths; reducing and comparing decimals; more equivalents; decimal in multiplier/ multiplicand; in dividends; remainders as decimals; changi fractions to decimals; repeating/terminating decimals; decimal divisors; type I, II, III | To hundred trillionths; changing uneven decimals to fractions | |||
| Degrees of direction | introduced | |||||
| Discount | Using discount to find net amount, regular price; successive discount, trade discount | |||||
| Divisibility rules | For 2, 5, 10 | For 3, 4, 6, 9 | ||||
| Division | Meaning of; writing facts 3 ways; terms; families 1-10; table numbers; using zeros; checking by subtraction/ multiplication; label even/uneven division answers; choosing division or multiplication; division with 1 place divisors and 3 place dividends; long division; one step even/uneven; short division; even/uneven; choosing the correct quotient | With money numbers; two uses of division; families 11 and 12; zero in division; checking uneven division; as a fraction; 2-step even and uneven short division; 3-step even and uneven long division; zero in the quotient; remainder as a fraction | Larger dividends for long/short division with 1-digit divisors; 2-digit divisors; apparent/non-apparent quotients; rounding divisors; partial dividends; analyzing remainders; dividing mixed measures; dividing fractions using the common denominator method | 4-digit and more divisors; dividing fractions by inverting divisor; decimals in the dividend/divisor | 15 family | 16 family |
| Dozen/half dozen | introduced | |||||
| Drawing | sketches | |||||
| Estimating | Sums and remainders to nearest ten | Larger numbers; products | ||||
| Equations | Meaning of; recognizing; balancing | Balancing; solving | Rewriting, simplifying | |||
| Estimating | percents | |||||
| Exponents/ base | introduced | |||||
| Factoring | Common factors; greatest common factors; pairs of factors; prime factors | |||||
| Fractions | Of an object or group | Terms; unit fractions; like/unlike fractions; comparing like fractions; more than one part of a whole; fractions equal to one whole; equal fractions; maknig equal fractions; reducing; proper/improper; changing improper fractions | Comparing unlike fractions; finding common denominators; changing whole numbers to improper fractions; using fractions to compare; multiplying fractions; cancellation; dividing fractions using the common denominator method | Dividing fractions; Type I, II, III | ||
| Geometric shapes | Circles, rectangles, squares, triangles | Polygon, pentagon | Heptagon, hexagon, octagon, parallelogram, quadrilateral, rhombus, trapezoid | Solids: rectangular prism, cube, cylinder, cone, pyramid, sphere | Solids: triangular prism, trapezoidal prism | |
| Graphs | Pictograph; horizontal bars | Horizontal/vertical bars; line | Bar graph showing 2 facts; line graph showing several facts; circle graph | Finding the number of degrees in a sector of a circle graph | ||
| Hypotenuse | Finding | |||||
| Increase/ deecrease | Using to find original amount | |||||
| Interest | For part of year; finding rate; compound | |||||
| International date line | introduced | |||||
| Land descriptions | introduced | |||||
| Lateral surface, area of | Cube, rectangular prism, cylinder, pyramid | Trapezoidal prism, cone | ||||
| Lattitude and Longitude | introduced | |||||
| Lines and models | Point, line segment, line, ray, parallel lines | Intersecting lines; perpendicular lines | ||||
| Loss and percent of loss | introduced | |||||
| Mean, median, mode | introduced | |||||
| Measures, Linear | Centimeter, inch, foot, yard, meter, mile | Kilometers; fractions of an inch | Millimeters | Rods | ||
| Measures, Liquid | Teaspoon, tablespoon, cup, pint, quart, liter, gallon | Hectoliters; dry measures: pint, quart, peck, bushel | Kiloliter | |||
| Measures, Speed | introduced | |||||
| Measures, Time | Second, minute, hour, day, week, month, year, leap year | Decade, century | Millenium | |||
| Measures, Weight | Ounce, pound, gram, kilogram | Ton | Metric ton | |||
| Mental math | In addition, subtraction, multiplication, division | |||||
| Metric/ English conversion | introduced | |||||
| Mortgage loans/land contracts | introduced | |||||
| Missing numbers, finding | addend, minuend, subtrahend, factor, divisor, dividend | |||||
| Mixed computation | Addition, subtraction, multiplication | division | ||||
| Mixed numbers | recognizing | Adding/ subtracting; changing mixed numbers to improper fractions; multiplying mixed numbers | Dividing; rounding | |||
| Money | Penny, nickle, dime, quarter, half dollar, dollar, $1, $2; writing money amounts; adding/ subtracting money amounts; making change for 25¢, 50¢, $1.00 | $5, $10, $20, $50, $100 bills; making change for $1 to $100 | ||||
| Multiples | Common; least common | |||||
| Multiplication | Meaning of; families 1-10; writing multiplication facts; terms; factor/product; table numbers; multiplying with 4-digit multiplicands; multiplying by zeros; checking by addition/division; multiplying money numbers; choosing multiplication/division; choosing the right product | Terms: multiplier/ multiplicand; multiplying 7-digit numbers with one digit multipliers; families 11 and 12; multiplying by powers of 10; two digit multipliers | 3-digit multipliers; 6-digit and more multiplicands; partial products; multiplicands ending with zeros; fractions; mixed numbers; mixed measures; decimal factors; decimals by powers of 10 | 4-digit and larger multipliers; zeros in multiplier; decimals in multiplier and multiplicand | 15 family | 16 family |
| Number words | To 5 digit numbers | 7 digits and more | With mixed decimals | |||
| Ordinal numbers | To twenty | To one hundred | ||||
| Original numbers | Finding | Finding orignal amount/ purchase price | ||||
| Payments/ installments | Yearly | Quarterly, semiannually | ||||
| Percents | Meaning of; percent/decimal/fraction equivalents; more than 100% | Less than 1%; changing uneven percents to decimals; using percents in Type I, II, III problems | ||||
| Perimeters | Triangles, rectangles, squares | Formulas for finding perimeters | Using unlike measures | |||
| Place value | To ten thousands | To millions | To hundred billions: periods to billions; taking numbers apart; decimals to thousandths | To hundred trillions; trillion's period; decimals to ten thousandths | Decimals to hundred trillions | |
| Positive/negative numbers | introduced | Adding | See Signed Numbers | |||
| Prefixes, metric | introduced | Mega, micro | ||||
| Principle | Finding | |||||
| Prime and composite numbers | introduced | Factors of composite numbers | ||||
| Process order | With multiplication/ division | With parenthesis | Parenthesis within a parenthesis | |||
| Proper/improper fractions | Recognizing; changing improper fractions to whole/mixed numbers | |||||
| Proportions | Meaning of; cross multiplication | using | Terms; antecedent, consequent; using proportions to solve ratio problems; using proportions as percents; inverse/direct ratio problems; using proportions as percents; inverse/direct | |||
| Protractor | using | |||||
| Rate of, finding | Discount; increase/decrease | |||||
| Ratios | Using to compare; writing/reading | Ratio factors; also see Proportions | ||||
| Record Keeping | introduced | With double entries | ||||
| Reference measures | Handspan, finger inch, arm spread | Shoe foot | ||||
| Roman Numerals | To 100 | To 500 | To 1000 | Using a dash for larger numbers | Using more than one dash for larger numbers | |
| Rounding Numbers | To tens, hundreds | To nearest dollar | To billions | Mixed numbers; decimals to hundredths | To thousandths and more; percents | |
| Scale drawing | Reading scale drawings | Drawing scales | ||||
| Sequence patterns | introduced | |||||
| Signed Numbers | Adding/ subtracting with number line | Adding, subtracting, multiplying, dividing | ||||
| Square Measures | Centimeters, inch, foot, yard, mile | Meter, kilometer | ||||
| Square Root | Meaning of; finding by trial and error method | Extracting the square root | ||||
| Story Problems | Using addition; subtraction; multiplication; division; tricky words; making addition/ subtraction story problems; 2-step problems | Making multiplication/ division story problem; choosing which kind of division used in story problems | 3-step; stories without numbers | Fraction and decimal Type I, II, III | Percent Type I, II, III | |
| Subtraction | Meaning of; terms; facts; borrowing from tens, hundreds, thousands; finding differences; checking by addition; working with zeros in borrowing; choosing the right remainder | Borrowing from millions; subtracting like fractions | Subtracting mixed numbers; unlike fractions, fractions from whole numbers, like/unlike fractions, mixed measures; borrowing in mixed numbers | Subtracting mixed numbers | ||
| Symbols | Greater than, less than, equal; feet, inch, degrees | Angle; triangle; pi | ||||
| Tally Marks | introduced | |||||
| Taxes | General | Property; income | ||||
| Telling time | To the hour, half hour, quarter past/till, 5 minutes, minute | Time zones | ||||
| Temperature | Fahrenheit freezing/boiling point; reading thermometers | Negative temperatures; Celsius freezing/boiling point | Fahrenheit/Celsius normal body temperature | |||
| Total surface area | Cone, cube, cylinder, pyramid, rectangular prism, triangular prism, sphere | |||||
| Triangle | Sum of degrees; drawing | Right, acute, obtuse, equilateral, isosceles, scalene, copying | ||||
| Type of | Type I, II, III fraction problems, decimal problems | Percent Type I, II, III | ||||
| Volume | Cube; rectangular prism; cylinder, pyramid | Triangular prism, trapezoidal prism, cone, sphere, hemisphere | ||||
| Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8 | |