Many people request a Scope & Sequence for Mastering Mathematics. Unlike other math programs, children move at their own pace through Mastering Mathematics. That makes it more difficult to say where an individual child will be each year.

To encourage this individualization, we include a Grade-Page Scope & Sequence chart in our manual. This chart lists page numbers which show the ** minimum** a child should cover according to the California Achievement Test (ex: Grade 1 - Addition - student should cover pgs. 1-43; 55-56; 60 and the Parent's Manual suggestions on counting, money, time, and measurement). Here is the chart in words, with approximate grade level equivalents, according to the C.A.T.:

*Grade 1* - Many children are finished with this work by February and begin their 2nd grade work early.

**Counting** - sequencing; ordinal numbers (first, second, etc.); by 2s, 5s, and 10s

**Number recognition** - using Number Cubes through 999

**Addition/ Subtraction** - memorization of all addition and subtraction facts 0-9s; computation up to 6 places, with regrouping (carrying) in addition, but no regrouping (borrowing) in subtraction; Counting Strips manipulative and Number Cubes for fact practice

**Pictographs**

**Money** - counting change, at least to 25 cents; coin recognition; reading/writing amounts with both cents and dollar signs

**Time** - days, months, seasons; clocks (digital and analog); "telling time" at least learning hours and half hours; counting by 5s; simple calendars

**Measurement** - inches on rulers; linear equivalents through Equivalents games (ex: 3 feet = yard = yd. = 36 inches)

**Temperature** - minimal introduction to reading a thermometer; counting by 2s

**Fractions** - recognizing common fractions of half, quarter (fourths), thirds and eighths; seeing equivalents using Fraction Picture Proofs' manipulative and "Sandwich Math" suggestions in Parent's Manual

**Place Value** - ones and tens (optional) using Go to the Bank manipulative

**Shape recognition** - circle, square, triangle, etc., using Geometry Equivalents cards

*Grade 2* - any review of previous grade's materials/facts as necessary (use placement test to see if anything was forgotten and work starred pages in workbook/play fact and Equivalents games to catch up)

**Money** - counting change at least to $1.00; making change/cashier practice

**Temperature** - emphasizing reading thermometers and appropriate clothing, seasons, etc.

**Addition** - learn to add more than 2 numbers together (ex: 234+365+480)

**Subtraction** - learn to regroup one time (borrow)

**Time** - "quarter after" and "quarter 'till" should be emphasized, if it wasn't mastered last year

**Place value** - hundreds place (optional)

**Measurement** - simple liquid measurement equivalents (ex: 2 cups = 1 pint = pt. = 16 oz.); metric included in complete program (optional)

**Fractions/Geometry** - recognizing shaded parts of common shapes (no computation)

*Grade 3* - any review of previous grade's materials necessary

**Addition and Subtraction** - continued skill development with longer problems (if child has not mastered this) - Addition book should be completed this year

**Multiplication** - one place multiplier; learn all facts 0-9s; regrouping over zeros emphasized

**Division** - simple 1 place divisors; simple whole number remainders

**Measurement** - linear and liquid (Equivalents game); perimeter (Addition workbook)

**Counting** - odds and evens (taught with Number Cubes); reading numbers through 9,999

**Money** - counting change above $1.00

**Place Value** - thousands (optional)

**Fractions** - more shaded parts of irregular shapes (no computation); cooking measurements; mixed numbers

*Grade 4* - any review of previous grade's materials necessary

**Subtraction** - regrouping many times; Biblical time lines; computing BC to AD dates; simple Roman numerals

**Multiplication** - review facts and skills of one place multipliers

**Division** - long division introduced using one place divisors and whole number remainders

**Place Value** - whole numbers through thousands and decimal places of tenths

**Decimals** - addition and subtraction using decimal numbers

**Fractions** - adding and subtracting fractions with common denominators; no reducing to lowest terms; simple equivalents

**Time** - 'till the hour emphasized; "What time is it?" several hours after a given time

**Numbers written as words**

**Estimating** - rounding to the nearest ten or hundred

**Geometry** - identifying solids (cone, sphere, cylinder, prisms); line/ray/segments; intersections; right angles

*Grade 5* - any review of previous grade's materials necessary - same computation as listed above, only 1 place longer

**Subtraction** - borrowing a foot's worth of inches, and hour's worth of minutes, etc.

**Multiplication** - 1 and 2 place multipliers; money problems; "multiplying by zeros" shortcut

**Division** - 2 place divisors; rounding

**Roman Numerals**

**Decimals** - to the thousandths place; addition, subtraction and multiplication

**Fractions** - computation now includes mixed numbers; finding the lowest common denominator; whole number times a fraction

**Time** - so many hours before a given time

**Geometry** - congruent shapes; line of symmetry; pyramids; parallel lines; radius

*Grade 6* - any review of previous grade's materials necessary

**Multiplication** - 1, 2, and 3 place multipliers; finding area of squares and rectangles

**Division** - 3 place divisors; rounding to the nearest whole; determining which is the better buy by figuring price per ounce/item, etc.

**Decimals** - rounding to the nearest whole; writing decimals as fractions

**Place Value** - through hundred thousands in wholes and thousandths in decimals

**Fractions** - addition, subtraction, multiplication, division; reducing to lowest terms; finding area of right triangles

**Time** - 4:42 = ? min. to 5

**Geometry** - diameter/formula; identifying acute and obtuse angles; volume

*Grade 7 & 8* - any review of previous grade's materials necessary, while solidifying all basic skills in readiness for pre-algebra

**Checking** - writing checks and deposit slips; keeping a check register; reading bank statements

**Multiplication** - exponents

**Division** - pre-algebra variables with equations; reading more complex graphs

**Decimals** - solidifying skills in addition, subtraction, multiplication and division of decimals; converting decimals to percentages and percentages to decimals

**Fractions** - solidifying skills in addition, subtraction, multiplication and division of fractions; converting to decimals; metric conversions

**Geometry** - identifying different types of triangles (isosceles, right, equilateral, scalene); diameter, radius, center point of circle; hypotenuse; volume of a cone and formula

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