Concepts Taught in Study Time Arithmetic

Concepts are introduced in the grade specified, and reviewed in subsequent grades.

 Grade 3Grade 4Grade 5Grade 6Grade 7Grade 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 3Grade 4Grade 5Grade 6Grade 7Grade 8