PRE-ALGEBRA SUMMARY WHOLE NUMBERS

Size: px
Start display at page:

Download "PRE-ALGEBRA SUMMARY WHOLE NUMBERS"

Transcription

1 PRE-ALGEBRA SUMMARY WHOLE NUMBERS Introduction to Whole Numbers and Place Value Digits Digits are the basic symbols of the system 0,,,, 4,, 6, 7, 8, and 9 are digits Place Value The value of a digit in a number depends on its position or place. 7,,89 Ones Tens Hundreds Thousands Ten thousands Hundred thousands Millions The value of a number is the sum of each digit multiplied by its place value.,4 = (,000) + ( 00) + (4 0) + ( ) Addition of Whole Numbers Addends The numbers that are being added. Sum The result of the addition. + 8 Addends Sum The Properties of Addition The Commutative Property The order in which you add two whole numbers does not affect the sum. The Associative Property The way in which you group whole numbers in addition does not affect the final sum. The Additive Identity The sum of 0 and any whole number is just that whole number. Measuring Perimeter The perimeter is the total distance around the outside edge of a shape. The perimeter of a rectangle is P = L + W + L + W (which can be written as P = L + W). ft + 4 = 4 + ( + 7) + 8 = + (7 + 8) 6 ft 6 ft = = 6 ft P = L + W + L + W = 6 ft + ft + 6 ft + ft = 6 ft Subtraction of Whole Numbers Minuend The number we are subtracting from. Subtrahend The number that is being subtracted. Difference The result of the subtraction. Minuend + 8 Subtrahend Difference 00 McGraw-Hill Companies

2 PRE-ALGEBRA SUMMARY WHOLE NUMBERS Rounding, Estimation, and Ordering of Whole Numbers Step To round a whole number to a certain decimal place, look at the digit to the right of that place. Step a. If that digit is or more, that digit and all digits to the right become 0. The digit in the place you are rounding to is increased by. b. If that digit is less than, that digit and all digits to the right become 0. The digit in the place your are rounding to remains the same. Order on the Whole Numbers For the numbers a and b, we can write. a < b (read a is less than b ) when a is to the left of b on the number line. To the nearest hundred, 4,78 is rounded to 4,600. To the nearest thousand, 7, is rounded to 7, <. a > b (read a is greater than b ) when a is to the right of b on the number line. > Multiplication of Whole Numbers Factors The numbers being multiplied. Product The result of the multiplication. The Properties of Multiplication The Commutative Property Multiplication, like addition, is a commutative operation. The order in which you multiply two whole numbers does not affect the product. The Distributive Property To multiply a factor by a sum of numbers, multiply the factor by each number inside the parentheses. Then add the products. Multiplicative Property of Zero The product of zero and any number is zero. Multiplicative Identity Property The product of one and any number is that number. The Associative Property Multiplication is an associative operation. The way in which you group numbers in multiplication does not affect the final product. 7 9 = 6 Product Factors 7 9 = 9 7 ( + 7) = ( ) + ( 7) 0 = 0 = 0 = = ( ) 6 = ( 6) Finding the Area of a Rectangle The area of a rectangle is found using the formula A = L W. 6 ft ft A = L W = 6 ft ft = ft 00 McGraw-Hill Companies

3 PRE-ALGEBRA SUMMARY WHOLE NUMBERS Division of Whole Numbers Divisor The number we are dividing by. Dividend The number being divided. Quotient The result of the division. Remainder The number left over after the division. Divisor 7 8 Quotient Dividend Remainder Dividend = divisor quotient + remainder 8 = 7 + The Role of 0 in Division Zero divided by any whole number (except 0) is = 0 Division by 0 is undefined. 7 0 = undefined. Exponents and Whole Numbers Using Exponents Base The number that is raised to a power. Exponent The exponent is written to the right and above the base. The exponent tells the number of times the base is to be used as a factor. Base Exponent = = Three Factors This is read to the third power or cubed Grouping Symbols and the Order of Operations The Order of Operations Mixed operations in an expression should be done in the following order: Step Do any operations inside parenthesis. Step Evaluate any exponents. Step Do all multiplication and division in order from left to right. Step 4 Do all addition and subtraction in order from left to right. Remember Please Excuse My Dear Aunt Sally. 4 ( + ) 7 = 4 7 = 4 7 = 00 7 = 9 An Introduction to Equations An expression is a number or a meaningful collection of operations (+,,, ) and numbers. An equation is two expressions connected by an equal sign. An equation can be true or false = = 8 is true 4 = is false 00 McGraw-Hill Companies

4 PRE-ALGEBRA SUMMARY INTEGERS AND INTRODUCTION TO ALGEBRA Introduction to Integers Positive Integers Integers used to name whole numbers to the right of the origin on the number line. Negative Integers Integers used to name the opposites of whole numbers. Negatives are found to the left of the origin on the number line. Integers Whole numbers and their opposites. The integers are {, -, -, -, 0,,,, } Absolute Value The distance (on the number line) between the point named by a signed number and the origin. The absolute value of x is written x. The origin Negative Integers 7 = 7 0 = 0 Positive Integers Addition of Integers Adding Integers. If two integers have the same sign, add their absolute values. Give the result the sign of the original integers.. If two integers have different signs, subtract their absolute values, the smaller from the larger. Give the result the sign of the integer with the larger absolute value = 6 (-9) + (-7) = -6 + (-0) = (-) + 9 = - Subtraction of Integers Subtracting Integers. Rewrite the subtraction problem as an addition problem by: a. Changing the subtraction symbol to an addition symbol b. Replacing the integer being subtracted with its opposite. Add the resulting integers as before. 6 8 = 6 + (-8) = 8 8 = 8 + (-) = -7-9 (-7) = = - Multiplication of Integers Multiplying Integers Multiply the absolute values of the two integers.. If the integers have different signs, the product is negative.. If the integers have the same sign, the product is positive. (-7) = - (-0)(9) = = 6 (-9)(-8) = 7 (-) = (-)(-) = 4 - = -( ) = McGraw-Hill Companies 4

5 PRE-ALGEBRA SUMMARY INTEGERS AND INTRODUCTION TO ALGEBRA Division of Integers Dividing Integers Divide the absolute values of the two integers.. If the integers have different signs, the quotient is negative.. If the integers have the same sign, the quotient is positive Introduction to Algebra: Variables and Expressions Multiplication x y (x)(y) xy These all mean the product of x and y or x times y The product of m and n is mn. The product of and the sum of a and b is (a + b) Evaluating Algebraic Expressions Evaluating Algebraic Expressions To evaluate an algebraic expression:. Replace each variable or letter with its value.. Do the necessary arithmetic, following the rules for order of operations. Evaluate x + y if x = and y = -. x + y = () + (-) = 0 + (-6) = 4 Simplifying Algebraic Expressions Term A number or the product of a number and one or more variables xy is a term Combining Like Terms To combine like terms:. Add or subtract the coefficients (the numbers multiplying the variables). Attach the common variable. x + x = 7x 8a a = a Introduction to Linear Equations Equation A statement that two expressions are equal Solution A value for a variable that makes an equation a true statement. x = is an equation 4 is a solution for the above equation because (4) = The Addition Property of Equality Equivalent Equations Equations that have exactly the same solutions. x = and x = 4 are equivalent equations The Addition Property of Equality If a = b, then a + c = b + c If x = = 7, then x + = McGraw-Hill Companies

6 PRE-ALGEBRA SUMMARY FRACTIONS AND EQUATIONS Introduction to Fractions Fraction Fractions name a number of equal parts of a unit or whole. A fraction is written in the form b a, in which a is an integer and b is a natural number. is a fraction. 8 Numerator The number of parts of the whole that are being considered. Denominator The number of equal parts into which the whole is divided. 8 Numerator Denominator Proper Fraction A fraction whose numerator is less than its denominator. It names a number less than. Improper Fraction A fraction whose numerator is greater than or equal to its denominator. It names a number greater than or equal to. and are proper fractions. 7, 0 and 8 8 are improper fractions. Prime Numbers and Factorization Prime Number Any natural number greater than that has exactly two factors, and itself. Composite Number Any natural number greater than that is not prime. Prime Factorization To find the prime factorization of a number, divide the number by a series of primes until the final quotient is a prime number. The prime factors include each prime divisor and the final quotient. 7,, 9, and 7 are prime numbers. 8,, 4, and 6 are composite numbers. 60 = 7 Greatest Common Factor (GCF) The GCF is the largest number that is a factor of each of a group of numbers. To Find the GCF Step Write the prime factorization for each of the numbers in the group. Step Locate the prime factors that are common to all the numbers. Step The greatest common factor (GCF) will be the product of all the common prime factors. If there are no common prime factors, the GCF is. To find the GCF of 4, 0, and 6: The GCF is = 6 00 McGraw-Hill Companies 6

7 PRE-ALGEBRA SUMMARY FRACTIONS AND EQUATIONS Equivalent Fractions The Fundamental Principal of Fractions For the fraction b a, and any nonzero number c, a a c b b c In words: We can divide the numerator and denominator of a fraction by the same nonzero number. This is used to simply (or reduce) a fraction. Equivalent Fractions The fundamental principal can also be written as a a c c 0 b b c This is used to build up an equivalent fraction and are equivalent fractions. 0 Multiplication and Division of Fractions To Multiply Two Fractions. Multiply numerator by numerator. This gives the numerator of the product.. Multiply denominator by denominator. This gives the denominator of the product.. Simplify the resulting fraction if possible. In simplifying fractions, it is usually easiest to divide by any common factors in the numerator and denominator before multiplying. To Divide Two Fractions Replace the divisor by its reciprocal and multiply Linear Equations in One Variable Solving Linear Equations The steps for solving a linear equation are as follows:. Use the distributive property to remove any grouping symbols. Then simply by combining like terms.. Add or subtract the same term on both sides of the equation until the variable term is on one side and a number is on the other.. Multiply or divide both sides of the equation by the same nonzero number so that the variable is alone on one side of the equation 4. Check the solution in the original equation. Solve: (x ) + 4x = x + 4 x 6 + 4x = x + 4 7x 6 = x = + 6 7x = x + 0 -x = -x 4x = 0 4x x = 00 McGraw-Hill Companies 7

8 PRE-ALGEBRA SUMMARY APPLICATIONS OF FRACTIONS AND EQUATIONS Addition and Subtraction of Fractions To Add (Subtract) Like Fractions. Add (subtract) the numerators.. Place the sum (difference) over the common denominator.. Simplify the resulting fraction if necessary Least Common Multiple (LCM) The LCM is the smallest number that is a multiple of each of a group of numbers. To Find the LCD of a Group of Fractions. Write the prime factorization for each of the denominators.. Find all the prime factors that appear in any one of the prime factorizations.. Form the product of those prime factors, using each factor the greatest number of times it occurs in any one factorization. To find the LCD of fractions with denominators 4, 6, and : 4 = 6 = = The LCD =, or 60 To Add or Subtract Unlike Fractions. Find the LCD of the fractions. 7. Change each fraction to an equivalent fraction with the LCD as a common denominator. 9. Add (subtract) the resulting like fractions as before. 0 Operations on Mixed Numbers 4 0 Mixed Number The sum of a whole number and a proper fraction To Change an Improper Fraction into a Mixed Number. Divide the numerator by the denominator. The quotient is the wholenumber portion of the mixed number.. If there is a remainder, write the remainder over the original denominator. This gives the fractional portion of the mixed number. and 7 are mixed numbers. 8 Note that means 4. 4 Quotient 0 Remainder To Change a Mixed Number to an Improper Fraction. Multiply the denominator of the fraction by the whole-number portion of the mixed number.. Add the numerator of the fraction to that product.. Write the sum over the original denominator to form the improper fraction. Denominator Whole Number Numerator (4) Denominator 00 McGraw-Hill Companies 8

9 PRE-ALGEBRA SUMMARY APPLICATIONS OF FRACTIONS AND EQUATIONS Addition and Subtraction of Fractions Multiplying or Dividing Mixed Numbers 4 Convert any mixed or whole numbers to improper fractions Then multiply or divide the fractions as before. To Add or Subtract Mixed Numbers. Rewrite as improper fractions.. Add or subtract the fractions.. Rewrite the results as a mixed number if required Equations Containing Fractions To Solve an equation containing one or more fractions. Find the LCD of the denominators.. Multiply every term by the LCD.. Solve the resulting equation as before. x To solve ;. The LCD is 0. x. 0( ) 0( ). x + 0 = x = - x Applications of Linear Equations in One Variable To Use an Equation to Solve a Word Problem. Read the problem carefully to decide what you are asked to find.. Choose a letter to represent one of the unknowns. Then represent all other unknowns with expressions using that same letter.. Translate the problem to algebra to form an equation. 4. Solve the equation and answer the original question.. Check your solution by returning to the original problem. Consecutive Integers If x is an integer, then x + is the next consecutive integer, x + is the next, and so on. If 0 is an integer, 0 + = is the next consecutive integer. Complex Fractions A complex fraction has a fraction in its numerator or denominator (or both) To simplify a complex fraction, multiply the numerator and denominator by the LCD of the fractions within the complex fraction. is a complex fraction McGraw-Hill Companies 9

10 PRE-ALGEBRA SUMMARY DECIMALS Introduction to Decimals, Place Value, and Rounding Decimal Fraction A fraction whose denominator is a power of 0. We call decimal fractions decimals and are decimal fractions Decimal Place Each position for a digit to the right of the decimal point. Each decimal place has a place value that is one-tenth the value of the place to its left..46 Ten thousandths Thousandths Hundredths Tenths Reading and Writing Decimals in Words. Read the digits to the left of the decimal point as a whole number.. Read the decimal point as the word and.. Read the digits to the right of the decimal point as a whole number followed by the place value of the rightmost digit. Rounding Decimals. Find the place to which the decimal is to be rounded.. If the next digit to the right is or more, increase the digit in the place you are rounding by. Discard any remaining digits to the right.. If the next digit to the right is less than, just discard that digit and any remaining digits to the right. Hundredths 8. is read eight and fifteen hundredths. To round.87 to the nearest tenth:.87 is rounded to.9 To round.44 to the nearest thousandth:.44 is rounded to.4 Addition and Subtraction of Decimals To Add or Subtract Decimals. Write the numbers being added (or subtracted) in column form with their decimal points in a vertical line. You may have to place zeros to the right of the existing digits.. Add (or subtract) just as you would with whole numbers.. Place the decimal point of the sum (or difference) in line with the decimal points. To subtract.87 from 8.: Multiplication of Decimals To Multiply Decimals. Multiply the decimals as though they were whole numbers.. Add the number of decimal places in the factors.. Place the decimal point in the product so that the number of decimal places in the product is the sum of the number of decimal places in the factors. Multiplying by Powers of 0 Move the decimal point to the right the same number of places as there are zeros in the power of 0. To multiply :.8 Two places x 0.04 Three places Five places.7 0 = ,000 = McGraw-Hill Companies 0

11 PRE-ALGEBRA SUMMARY DECIMALS Division of Decimals To Divide by a Decimal. Move the decimal point to the right, making the divisor a whole number.. Move the decimal point in the dividend to the right the same number of places. Add zeros if necessary.. Place the decimal point in the quotient directly above the decimal point in the dividend. 4. Divide as you would with whole numbers To Divide by a Power of 0 Move the decimal point to the left the same number of places as there are zeros in the power of 0. To divide 6. by., move the decimal points: = ^.8=.8 Fractions and Decimals To Convert a Common Fraction to a Decimal. Divide the numerator of the common fraction by its denominator.. The quotient is the decimal equivalent of the common fraction. To Convert a Terminating Decimal Less Than to a Common Fraction. Write the digits of the decimal without the decimal point. This will be the numerator of the common fraction.. The denominator of the fraction is a followed by as many zeros as there are places in the decimal. To convert to a decimal: To convert 0.7 to a common fraction: Equations Containing Decimals To solve an equation that contains decimals, use the same procedure used for solving other linear equations..x +.9x =.7x..x =.7x..4x = -.. x =.4 x =. Square Roots and the Pythagorean Theorem The square root of a number is a value that, when squared, gives us that number. The length of the three sides of a right triangle will form a perfect triple = The Pythagorean theorem is usually written as c = a + b a b c 00 McGraw-Hill Companies

12 PRE-ALGEBRA SUMMARY RATIO, RATE, AND PROPORTION Ratios Ratio A means of comparing two numbers or quantities. A ratio can be written as a fraction. 4 can be thought of a the ratio of 4 to 7. 7 Rates Rate A fraction involving two denominate numbers with different units. Unit Price The cost per unit. 0home runs home run 0games games $ rolls $0.40per roll Proportions Proportion A statement that two ratios or rates are equal. 6 is a proportion that reads, three is 0 to five as six is to ten. The Proportion Rule If a c 6, then a d = b c If, then 6 = 0 b d 0 To Solve a Proportion. Use the proportion rule to write the equivalent equation a d = b c.. Divide both terms of the equation by the coefficient of the variable.. Use the value found to replace the unknown in the original proportion. Check that the ratios or rates are proportional. To solve: x 6 0 0x 6 0x 80 0 x 0 x Similar Triangles and Proportions A triangle in which two of the sides are perpendicular is called a right triangle. is a right triangle. Two right triangles are similar if their corresponding sides are proportional. 6 are proportional. 0 If we know that two triangles are similar, we can use a proportion to find the length of a missing side. 8 8 x x 8 x 4 x x 00 McGraw-Hill Companies

13 PRE-ALGEBRA SUMMARY RATIO, RATE, AND PROPORTION Linear Measurement and Conversion The English system of measurement is in common use in the United States. English Units of Measurement and Equivalents Length Weight foot (ft) = inches (in.) pound (lb) =6 ounces (oz) yard (yd) = ft ton =,000 lb mile (mi) =,80 ft Capacity pint (pt) = 6 fluid ounces (fl oz) quart (qt) = pt gallon (gal) = 4 qt Units fractions A fraction whose value is. Units fractions can be used to convert units. To Add Like Units of Length. Arrange the numbers so that the like units are in the same column.. Add in each column.. Simply if necessary. To Subtract Like Units of Length. Arrange the numbers so that the like units are in the same column.. Subtract in each column. You may have to borrow from the larger unit at this point.. Simplify if necessary. To Multiply or Divide Units by Abstract Numbers. Multiply or divide each part of the measurement by the abstract number.. Simplify if necessary. in. ft and are unit fractions. ft yd To add 4 ft 7 in. and ft 0 in.: To subtract: 4 ft 7 in. + ft 0 in. 9 ft 7 in. = 0 ft in. 4 ft 7 in. ft 9 in. Borrow and rename: ft 9 in. ft 9 in. ft 0 in. ( yd ft) = 6 yd 4 ft, or 7 yd ft Metric Units of Length The metric system of measurement is used throughout most of the world. Common metric units of length are the meter (m), centimeter (cm), millimeter (mm), and kilometer (km). Basic Metric Prefixes milli* means,000 centi* means 00 deci means 0 kilo* means,000 hecto means 00 deka means 0 * These are the most commonly used and should be memorized. 00 McGraw-Hill Companies

14 PRE-ALGEBRA SUMMARY PERCENT Percents, Decimals, and Fractions Percent Another way of naming parts of a whole. Percent means per hundred.. To convert a percent to a fraction, divide by 00.. To convert a percent to a decimal, remove the percent symbol and move the decimal point two places to the left.. To convert a decimal to a percent, move the decimal point two places to the right and attach the percent symbol. 4. To convert a fraction to a percent, write the decimal equivalent of the fraction and then change that decimal to a percent. Fractions and decimals are other ways of naming parts of a whole. % % % = = 8% % Solving Percent Problems Using Proportions Every percent problem has the following three parts:. The base. This is the whole in the problem. It is the standard used for comparison. Label the base B.. The amount This is the part of the whole being compared to the base. Label the amount A.. The rate. This is the ratio of the amount to the base. The rate is written as r a percent. Label the rate or R is 0% of 0 A R B Using the Percent Proportion The percent proportion is A B r 00 To solve a percent problem using this proportion:. Substitute the two known values into the proportion.. Solve the proportion to find the unknown value. What is 4% of 00? A A = 7,00 A = 7 00 McGraw-Hill Companies 4

15 PRE-ALGEBRA SUMMARY PERCENT Solving Percent Applications Using Equations Translating a question into an equation: What is r% of B? r A B 00 What is % of 00? A A = A = 69 Sales tax, commissions, and discounts are all rates. Applications can be solved by the percent proportion or by translating the question into an equation. If a % commission is $,000, what is the total?,000 B 00 B = 00,000 B = $,000 Applications: Simple and Compound Interest Simple interest is a rate. Compound interest is interest on an amount that includes previous interest. 00 McGraw-Hill Companies

16 PRE-ALGEBRA SUMMARY GEOMETRY Lines and Angles Line A series of points that goes on forever. Line segment A piece of a line that has two endpoints. Angle A geometric figure consisting of two line segments that share a common endpoint. Perpendicular lines Lines are perpendicular if they intersect to form four equal angles. A A O B B C D Parallel lines Lines are parallel if they never intersect. Right angles have a measure of 90 o. Acute angles have a measure less than 90 o. Obtuse angles have a measure between 90 o and 80 o. O A B C E F 00 McGraw-Hill Companies 6

17 PRE-ALGEBRA SUMMARY GEOMETRY Perimeter and Circumference A polygon is a closed figure with three or more sides. Each side is a line segment. Triangle Square The perimeter is the sum of the lengths of its sides: Rectangle Circumference Circle P = a + b + c P = 4s P = L + W C = πr Find the perimeter of the figure: P cm.6 cm = L + W = (.6 cm) + ( cm) =. cm + 0 cm =. cm Area and Volume The area of an object is the number of unit squares needed to cover its surface. Square A = s Rectangle A = L W Triangle A b h Parallelogram A = b h Circle A = πr Some common volume formulas: Cube V = s Rectangular solid V = L W H Sphere V = 4 r Cylinder V = πr h Find the area of the figure: A (6 in.)(.4 in.) = ( in.)(.4 in) = 7. in. Find the area of the figure:.4 in. 6 in. h =4 cm r = cm V = πr h = π( cm) (4 cm) = 6π cm =. cm 00 McGraw-Hill Companies 7

18 PRE-ALGEBRA SUMMARY GRAPHING AND INTRODUCTION TO STATISTICS Tables and Graphs of Data A table is a display of information in parallel columns or rows. A graph is a diagram that relates two different pieces of information. One of the most common graphs is the bar graph. Amount 4 Day In line graphs, one of the axes is usually related to time. The Rectangular Coordinate System The Rectangular Coordinate system The rectangular coordinate system is a system formed by two perpendicular axes that intersect at a point called the origin. The horizontal line is called the x-axis. The vertical line is called the y-axis. Graphing Points from Ordered Pairs The coordinates of an ordered pair allow you to associate a point in the plain with every ordered pair. To graph a point in the plane, Step Start at the origin. Step Move right or left according to the value of the x-coordinate: to the right if x is positive or to the left if x is negative. Step Then move up or down according to the value of the y-coordinate: up if y is positive and down if y is negative. To graph the point corresponding to (, ) y (, ) units x units Linear Equations in Two Variables Solutions of Linear Equations A pair of values that satisfies the equation. Solutions for linear equations in two variables are written as ordered pairs. An ordered pair has the form If x y = 0, (6, ) is a solution for the equation, because substituting 6 for x and for y gives a true statement. (x, y) x-coordinate y-coordinate Linear Equations in Two Variables 00 McGraw-Hill Companies 8

19 PRE-ALGEBRA SUMMARY GRAPHING AND INTRODUCTION TO STATISTICS Linear Equation An equation that can be written in the form Ax + By = C in which A and B are not both 0. x y = 4 is a linear equation. Graphing Linear Equations Step Find at least three solutions for the equation and put your results in tabular form. Step Graph the solutions found in step. Step Draw a straight line through the points determined in step to form the graph of the equation. x - y = 6 (6, 0) (, -) (0, -6) Mean, Median, and Mode Finding the Mean To find the mean for a group of numbers follow these two steps: Step Add all the numbers in the group. Step Divide that sum by the number of items in the group. Given the numbers 4, 8, 7, = Mean = 4 Finding the Median The median is the number for which there are as many instances that are to the right of that number as there are instances to the left of it. To find the median follow these steps: Step Rewrite the numbers in order from smallest to largest. Step Count from both ends to find the number in the middle. Step If there are two numbers in the middle, add them together and find their mean. Given the numbers 9,,,, 7, Rewrite them:,,, 7, 9, The middle numbers are and Median = 6 Finding the Mode The mode is the number that occurs most frequently in a set of numbers. Given the numbers,,,,,, 7, 7, 9,. The mode is. 00 McGraw-Hill Companies 9

20 PRE-ALGEBRA SUMMARY POLYNOMIALS Properties of Exponents. a m a n = a m+n. (a m ) n = a mn. (ab) m =a m b m m a mn 4. a ( a 0) n a m a m a. ( ) ( b 0) b m b x x = x (x ) = x 6 (4x) =4 x =64x x x 7 x ( ) y x x y Introduction to Polynomials Term A term is a number or the product of a number and variables. Polynomial A polynomial is an algebraic expression made up of terms in which the exponents are whole numbers. These terms are connected by plus or minus signs. Each sign (+ or -) is attached to the term following that sign. Coefficient In each term of a polynomial, the number in front of the variable is called the numerical coefficient or, more simply, the coefficient of that term. Types of Polynomials A polynomial can be classified according to the number of terms it has. A monomial has one term. A binomial has two terms. A trinomial has three terms. 4x x + x is a polynomial. The terms of 4x x + x are 4x, -x, and x. The coefficients of 4x x are 4 and -. x is a monomial. x 7x is a binomial. x x + is a trinomial. Addition and Subtraction of Polynomials Removing Signs of Grouping. If a plus sign (+) or no sign at all appears in front of parentheses, just remove the parentheses. No other changes are necessary.. If a minus sign (-) appears in front of parentheses, the parentheses can be removed by changing the sign of each term inside the parentheses. Adding Polynomials Remove the signs of grouping. Then collect and combine any like terms. Subtracting Polynomials Remove the signs of grouping by changing the sign of each term in the polynomial being subtracted. Then combine any like terms. x + (x ) = x + x x (x 4) = x x + 4 (x +) + (x ) = x + + x = x (x + x) (x + x ) = x + x x -x + Signs change = x x + x x + = x x + 00 McGraw-Hill Companies 0

21 PRE-ALGEBRA SUMMARY POLYNOMIALS Multiplying Polynomials To Multiply a Polynomial by a Monomial Multiply each term of the polynomial by the monomial and simplify the results. x(x + ) = x x + x = 6x + 9x To Multiply a Binomial by a Binomial Use the FOIL method: F O I L (a + b)(c + d) = a c + a d + b c + b d To Multiply a Polynomial by a Polynomial Arrange the polynomials vertically. Multiply each term of the upper polynomial by each term of the lower polynomial and add the results. (x )(x + ) = 6x + 0x 9x F O I L = 6x + x x x + x -x + 9x x 6x +0x x 9x +9x Introduction to Factoring Polynomials Common Monomial Factor A common monomial factor is a single term that is a factor of every term of the polynomial. The greatest common factor (GCF) of a polynomial is the common monomial factor that has the largest possible numerical coefficient and the largest possible exponents. Factoring a Monomial from a Polynomial. Determine the GCF for all terms.. Factor the GCF from each term and then apply the distributive property in the form ab + ac = a(b + c) The greatest common factor. Mentally check by multiplication 4x is the greatest common factor of 8x 4 x + 6x. 8x 4 x + 6x = 4x (x x +4) 00 McGraw-Hill Companies

Glossary. Glossary 981. Hawkes Learning Systems. All rights reserved.

Glossary. Glossary 981. Hawkes Learning Systems. All rights reserved. A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Addends The numbers being added in an addition problem Addition principle

More information

Geometric Formulas (page 474) Name

Geometric Formulas (page 474) Name LESSON 91 Geometric Formulas (page 474) Name Figure Perimeter Area Square P = 4s A = s 2 Rectangle P = 2I + 2w A = Iw Parallelogram P = 2b + 2s A = bh Triangle P = s 1 + s 2 + s 3 A = 1_ 2 bh Teacher Note:

More information

Decimal Addition: Remember to line up the decimals before adding. Bring the decimal straight down in your answer.

Decimal Addition: Remember to line up the decimals before adding. Bring the decimal straight down in your answer. Summer Packet th into 6 th grade Name Addition Find the sum of the two numbers in each problem. Show all work.. 62 2. 20. 726 + + 2 + 26 + 6 6 Decimal Addition: Remember to line up the decimals before

More information

Basic Math. Curriculum (358 topics additional topics)

Basic Math. Curriculum (358 topics additional topics) Basic Math This course covers the topics outlined below and is available for use with integrated, interactive ebooks. You can customize the scope and sequence of this course to meet your curricular needs.

More information

Glossary. Glossary Hawkes Learning Systems. All rights reserved.

Glossary. Glossary Hawkes Learning Systems. All rights reserved. A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Acute triangle A triangle in which all three angles are acute Addends The

More information

Prep for the CSU ELM

Prep for the CSU ELM Prep for the CSU ELM This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

More information

High School Preparation for Algebra 1

High School Preparation for Algebra 1 High School Preparation for Algebra 1 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence

More information

Alaska Mathematics Standards Vocabulary Word List Grade 4

Alaska Mathematics Standards Vocabulary Word List Grade 4 1 add addend additive comparison area area model common factor common multiple compatible numbers compose composite number counting number decompose difference digit divide dividend divisible divisor equal

More information

Pre Algebra. Curriculum (634 topics)

Pre Algebra. Curriculum (634 topics) Pre Algebra This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.

More information

Pre Algebra and Introductory Algebra

Pre Algebra and Introductory Algebra Pre Algebra and Introductory Algebra This course covers the topics outlined below and is available for use with integrated, interactive ebooks. You can customize the scope and sequence of this course to

More information

California 5 th Grade Standards / Excel Math Correlation by Lesson Number

California 5 th Grade Standards / Excel Math Correlation by Lesson Number (Activity) L1 L2 L3 Excel Math Objective Recognizing numbers less than a million given in words or place value; recognizing addition and subtraction fact families; subtracting 2 threedigit numbers with

More information

Math 75 Mini-Mod Due Dates Spring 2016

Math 75 Mini-Mod Due Dates Spring 2016 Mini-Mod 1 Whole Numbers Due: 4/3 1.1 Whole Numbers 1.2 Rounding 1.3 Adding Whole Numbers; Estimation 1.4 Subtracting Whole Numbers 1.5 Basic Problem Solving 1.6 Multiplying Whole Numbers 1.7 Dividing

More information

HW: page 168 (12-24 evens, 25-28) Extra Credit # 29 & 31

HW: page 168 (12-24 evens, 25-28) Extra Credit # 29 & 31 Lesson 5-1 Rational Numbers pages 166-168 Review our number system and real numbers. Our Number System Real Complex Rational Irrational # Integers # Whole # Natural Rational Numbers the word "rational"

More information

Foundations of High School Math

Foundations of High School Math Foundations of High School Math This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to

More information

Part 1 - Pre-Algebra Summary Page 1 of 22 1/19/12

Part 1 - Pre-Algebra Summary Page 1 of 22 1/19/12 Part 1 - Pre-Algebra Summary Page 1 of 1/19/1 Table of Contents 1. Numbers... 1.1. NAMES FOR NUMBERS... 1.. PLACE VALUES... 3 1.3. INEQUALITIES... 4 1.4. ROUNDING... 4 1.5. DIVISIBILITY TESTS... 5 1.6.

More information

ACT MATH MUST-KNOWS Pre-Algebra and Elementary Algebra: 24 questions

ACT MATH MUST-KNOWS Pre-Algebra and Elementary Algebra: 24 questions Pre-Algebra and Elementary Algebra: 24 questions Basic operations using whole numbers, integers, fractions, decimals and percents Natural (Counting) Numbers: 1, 2, 3 Whole Numbers: 0, 1, 2, 3 Integers:

More information

Reference Page Math Symbols- + add - subtract x multiply divide = equal % percent $ dollar cent # at degree.

Reference Page Math Symbols- + add - subtract x multiply divide = equal % percent $ dollar cent # at degree. Reference Page Math Symbols- + add - subtract x multiply divide = equal % percent $ dollar cent # number/pound @ at degree. decimal point pi Roman Numerals Conversion I = 1 C = 100 V = 5 D = 500 X = 10

More information

6th Grade Mathematics

6th Grade Mathematics Standard 1: Number & Operation and use numbers and use numbers 27-31% and use numbers 6.M.1.1.1 Compare magnitudes and relative magnitudes of positive rational numbers, including whole numbers through

More information

Destination Math. Scope & Sequence. Grades K 12 solutions

Destination Math. Scope & Sequence. Grades K 12 solutions Destination Math Scope & Sequence Grades K 12 solutions Table of Contents Destination Math Mastering Skills & Concepts I: Pre-Primary Mathematics, Grades K-1... 3 Destination Math Mastering Skills & Concepts

More information

Fifth Grade Mathematics Mathematics Course Outline

Fifth Grade Mathematics Mathematics Course Outline Crossings Christian School Academic Guide Middle School Division Grades 5-8 Fifth Grade Mathematics Place Value, Adding, Subtracting, Multiplying, and Dividing s will read and write whole numbers and decimals.

More information

Math Glossary. Version September 1, Next release: On or before September 30, for the latest version.

Math Glossary. Version September 1, Next release: On or before September 30, for the latest version. Math Glossary Version 0.1.1 September 1, 2003 Next release: On or before September 30, 2003. E-mail edu@ezlink.com for the latest version. Copyright 2003 by Brad Jolly All Rights Reserved Types of Numbers

More information

Middle School Math Course 2

Middle School Math Course 2 Middle School Math Course 2 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet

More information

Middle School Math Course 3

Middle School Math Course 3 Middle School Math Course 3 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet

More information

Algebra Readiness. Curriculum (445 topics additional topics)

Algebra Readiness. Curriculum (445 topics additional topics) Algebra Readiness This course covers the topics shown below; new topics have been highlighted. Students navigate learning paths based on their level of readiness. Institutional users may customize the

More information

Florida Math 0022 Correlation of the ALEKS course Florida Math 0022 to the Florida Mathematics Competencies - Lower and Upper

Florida Math 0022 Correlation of the ALEKS course Florida Math 0022 to the Florida Mathematics Competencies - Lower and Upper Florida Math 0022 Correlation of the ALEKS course Florida Math 0022 to the Florida Mathematics Competencies - Lower and Upper Whole Numbers MDECL1: Perform operations on whole numbers (with applications,

More information

Study Guide for Math 095

Study Guide for Math 095 Study Guide for Math 095 David G. Radcliffe November 7, 1994 1 The Real Number System Writing a fraction in lowest terms. 1. Find the largest number that will divide into both the numerator and the denominator.

More information

Harbor Creek School District

Harbor Creek School District Numeration Unit of Study Big Ideas Algebraic Concepts How do I match a story or equation to different symbols? How do I determine a missing symbol in an equation? How does understanding place value help

More information

Customary Units of Measurement

Customary Units of Measurement Customary Units of Measurement What would it be like to have no system of measurement? If we are to measure something, we need a unit of measure. standard unit of measure: one that people have agreed to

More information

Florida Math Curriculum (433 topics)

Florida Math Curriculum (433 topics) Florida Math 0028 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

More information

Vocabulary Cards and Word Walls Revised: June 29, 2011

Vocabulary Cards and Word Walls Revised: June 29, 2011 Vocabulary Cards and Word Walls Revised: June 29, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,

More information

Pre Algebra. Curriculum (634 topics additional topics)

Pre Algebra. Curriculum (634 topics additional topics) Pre Algebra This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.

More information

Destination Math California Intervention

Destination Math California Intervention Destination Math California Intervention correlated to the California Intervention 4 7 s McDougal Littell Riverdeep STANDARDS MAPS for a Mathematics Intervention Program (Grades 4-7) The standards maps

More information

Mathematics Tutorials. Arithmetic Tutorials Algebra I Tutorials Algebra II Tutorials Word Problems

Mathematics Tutorials. Arithmetic Tutorials Algebra I Tutorials Algebra II Tutorials Word Problems Mathematics Tutorials These pages are intended to aide in the preparation for the Mathematics Placement test. They are not intended to be a substitute for any mathematics course. Arithmetic Tutorials Algebra

More information

Eleven reference pages that conveniently fit a standard composition book!

Eleven reference pages that conveniently fit a standard composition book! Eleven reference pages that conveniently fit a standard composition book! By: Deborah Kirkendall 2013 http://www.teacherspayteachers.com/store/deborah-kirkendall Operation Words to Describe Add + Subtract

More information

Arithmetic with Whole Numbers and Money Variables and Evaluation (page 6)

Arithmetic with Whole Numbers and Money Variables and Evaluation (page 6) LESSON Name 1 Arithmetic with Whole Numbers and Money Variables and Evaluation (page 6) Counting numbers or natural numbers are the numbers we use to count: {1, 2, 3, 4, 5, ) Whole numbers are the counting

More information

Course Readiness and Skills Review Handbook (Topics 1-10, 17) (240 topics, due. on 09/11/2015) Course Readiness (55 topics)

Course Readiness and Skills Review Handbook (Topics 1-10, 17) (240 topics, due. on 09/11/2015) Course Readiness (55 topics) Course Name: Gr. 8 Fall 2015 Course Code: C6HNH-TEK9E ALEKS Course: Middle School Math Course 3 Instructor: Mr. Fernando Course Dates: Begin: 08/31/2015 End: 06/17/2016 Course Content: 642 Topics (637

More information

St. Ann s Academy - Mathematics

St. Ann s Academy - Mathematics St. Ann s Academy - Mathematics Students at St. Ann s Academy will be able to reason abstractly and quantitatively. Students will define, explain, and understand different types of word problems (simple

More information

Term Definition Example. 3-D shapes or (3 dimensional) acute angle. addend. algorithm. area of a rectangle. array

Term Definition Example. 3-D shapes or (3 dimensional) acute angle. addend. algorithm. area of a rectangle. array Term Definition Example 3-D shapes or (3 dimensional) an object that has height, width, and depth, like any object in the real world. acute angle an angle that is less than 90 addend a number that is added

More information

Essentials of Mathematics Lesson Objectives

Essentials of Mathematics Lesson Objectives Essentials of Mathematics Lesson Unit 1: NUMBER SENSE Reviewing Rational Numbers Practice adding, subtracting, multiplying, and dividing whole numbers, fractions, and decimals. Practice evaluating exponents.

More information

Achievement Level Descriptors Mathematics

Achievement Level Descriptors Mathematics Achievement Level Descriptors Mathematics Achievement Level Descriptors (ALD) look at each Target within a Claim and outline what students should know and be able to do at different levels of understanding.

More information

Algebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher

Algebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher Algebra 1 S1 Lesson Summaries For every lesson, you need to: Read through the LESSON REVIEW which is located below or on the last page of the lesson and 3-hole punch into your MATH BINDER. Read and work

More information

Teacher: CORE Math Grade 7 Year: Greatest Common Factor (GCF) Factor 'T' Chart

Teacher: CORE Math Grade 7 Year: Greatest Common Factor (GCF) Factor 'T' Chart Teacher: CORE Math Grade 7 Year: 2010-11 Course: Math Grade 7 Month: All Months S e p t e m b e r NUMBER SENSE AND OPERATIONS Place Value Greatest Common Factor Identify whole Decimal number place Notation

More information

addend angle composite number capacity Vocabulary Flash Cards Review Review Review Review Review Review

addend angle composite number capacity Vocabulary Flash Cards Review Review Review Review Review Review addend angle area bar graph capacity composite number cubic units difference A figure formed by two rays with the same endpoint A number to be added to another number. 2 or 3 in the sum 2 + 3. A graph

More information

4R & 4A Math Pacing Guides

4R & 4A Math Pacing Guides GRADING PERIOD: 1st Nine Weeks Getting to Know You - Community Building 4.14- Data a. Collect data, using observations, surveys, measurement, polls, or questionnaires. b. Organize data into a chart or

More information

OBJECTIVES UNIT 1. Lesson 1.0

OBJECTIVES UNIT 1. Lesson 1.0 OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint

More information

Summer Math Packet for Students Entering 6th Grade. Please have your student complete this packet and return it to school on Tuesday, September 4.

Summer Math Packet for Students Entering 6th Grade. Please have your student complete this packet and return it to school on Tuesday, September 4. Summer Math Packet for Students Entering 6th Grade Please have your student complete this packet and return it to school on Tuesday, September. Work on your packet gradually. Complete one to two pages

More information

Prealgebra and Elementary Algebra

Prealgebra and Elementary Algebra Prealgebra and Elementary Algebra 978-1-63545-089-7 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Lynn Marecek, Santa

More information

My Math Plan Assessment #1 Study Guide

My Math Plan Assessment #1 Study Guide My Math Plan Assessment #1 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4. Use factoring to solve the quadratic equation. x + 9x + 1 = 17. Find the difference.

More information

Chapter 1: Fundamentals of Algebra Lecture notes Math 1010

Chapter 1: Fundamentals of Algebra Lecture notes Math 1010 Section 1.1: The Real Number System Definition of set and subset A set is a collection of objects and its objects are called members. If all the members of a set A are also members of a set B, then A is

More information

Corequisite Support for Liberal Arts Mathematics/Quantitative Reasoning

Corequisite Support for Liberal Arts Mathematics/Quantitative Reasoning Corequisite Support for Liberal Arts Mathematics/Quantitative Reasoning This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users

More information

Foundations of Mathematics

Foundations of Mathematics Foundations of Mathematics 978-1-63545-087-3 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Lynn Marecek, Santa Ana College

More information

ARITHMETIC AND BASIC ALGEBRA

ARITHMETIC AND BASIC ALGEBRA C O M P E T E N C Y ARITHMETIC AND BASIC ALGEBRA. Add, subtract, multiply and divide rational numbers expressed in various forms Addition can be indicated by the expressions sum, greater than, and, more

More information

WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5

WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5 May 06 VIRGINIA MATHEMATICS STANDARDS OF LEARNING CORRELATED TO MOVING WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5 NUMBER AND NUMBER SENSE 5.1 The student will a. read, write, and identify the place values

More information

Algebra I Part B. Help Pages & Who Knows

Algebra I Part B. Help Pages & Who Knows Algebra I Part B & Who Knows 83 Vocabulary General Absolute Value the distance between a number,, and zero on a number line; written as. Eample: 5 = 5 reads The absolute value of 5 is 5. -7 = 7 reads The

More information

Grade Demonstrate mastery of the multiplication tables for numbers between 1 and 10 and of the corresponding division facts.

Grade Demonstrate mastery of the multiplication tables for numbers between 1 and 10 and of the corresponding division facts. Unit 1 Number Theory 1 a B Find the prime factorization of numbers (Lesson 1.9) 5.1.6 Describe and identify prime and composite numbers. ISTEP+ T1 Pt 1 #11-14 1b BD Rename numbers written in exponential

More information

Check boxes of Edited Copy of Sp Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and

Check boxes of Edited Copy of Sp Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and Check boxes of Edited Copy of 10021 Sp 11 152 Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and Additional Topics Appendix Course Readiness Multiplication

More information

Using Proportions to Solve Percent Problems (page 562)

Using Proportions to Solve Percent Problems (page 562) LESSON Name 81 Using Proportions to Solve Percent Problems (page 562) Percent problems can be solved using proportions. Make and complete a percent box. (The total is always 100.) 1. Write in the known

More information

Evaluate algebraic expressions for given values of the variables.

Evaluate algebraic expressions for given values of the variables. Algebra I Unit Lesson Title Lesson Objectives 1 FOUNDATIONS OF ALGEBRA Variables and Expressions Exponents and Order of Operations Identify a variable expression and its components: variable, coefficient,

More information

Math Literacy. Curriculum (457 topics additional topics)

Math Literacy. Curriculum (457 topics additional topics) Math Literacy This course covers the topics outlined below, and can be used to support a non STEM pathways course. You can customize the scope and sequence of this course to meet your curricular needs.

More information

Study Guide. Summer Packet 06/03/2014 Area of Triangle - B

Study Guide. Summer Packet 06/03/2014 Area of Triangle - B Study Guide Summer Packet 06/03/2014 Area of Triangle - B This skill requires the student to find the area of a triangle, which is one half the area of a rectangle that has the same base and height. The

More information

Finding a Percent of a Number (page 216)

Finding a Percent of a Number (page 216) LESSON Name 1 Finding a Percent of a Number (page 216) You already know how to change a percent to a fraction. Rewrite the percent as a fraction with a denominator of 100 and reduce. 25% = 25 100 = 1 5%

More information

Foundations 5 Curriculum Guide

Foundations 5 Curriculum Guide 1. Review: Natural Numbers...3 2. Reading and Writing Natural Numbers...6 3. Lines, Rays, and Line Segments...8 4. Comparing Natural Numbers... 12 5. Rounding Numbers... 15 6. Adding Natural Numbers...

More information

Math Literacy. Curriculum (457 topics)

Math Literacy. Curriculum (457 topics) Math Literacy This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

More information

Accessible Topic - Topics accessible to visually impaired students using a screen reader.

Accessible Topic - Topics accessible to visually impaired students using a screen reader. Course Name: Winter 2018 Math 95 - Course Code: ALEKS Course: Developmental Math Instructor: Course Dates: Begin: 01/07/2018 End: 03/23/2018 Course Content: 390 Topics (172 goal + 218 prerequisite) / 334

More information

Parallelograms (page 368)

Parallelograms (page 368) LESSON 71 Parallelograms (page 368) Name A parallelogram has two pairs of opposite, parallel sides. The opposite angles of a parallelogram have equal measures. The adjacent angles of a parallelogram are

More information

Grade 5 6 Summer Homework Math Package

Grade 5 6 Summer Homework Math Package Grade Homework Math Package It is important that you keep practicing your mathematical Knowledge over the summer to be ready for 6 th grade. In this Package you will find a calendar of activities for the

More information

MHCA Math Summer Packet

MHCA Math Summer Packet Name: Score: MHCA Math Summer Packet For students entering Algebra I CP The Summer Packet is broken into 10 different sections labeled weeks with 10 questions in each section. If you do one section a week,

More information

Level Unit Chapter Lesson ChapterTitle LessonTitle Introduction Introduction How to take the placement tests How to take the

Level Unit Chapter Lesson ChapterTitle LessonTitle Introduction Introduction How to take the placement tests How to take the Level Unit Chapter Lesson ChapterTitle LessonTitle 0 0 1 1 Introduction Introduction 0 0 2 1 How to take the placement tests How to take the placement tests 0 0 3 0 Placement Test I 0 0 4 0 Placement Test

More information

California 3 rd Grade Standards / Excel Math Correlation by Lesson Number

California 3 rd Grade Standards / Excel Math Correlation by Lesson Number California 3 rd Grade Standards / Lesson (Activity) L1 L2 L3 L4 L5 L6 L7 L8 Excel Math Lesson Objective Learning about the tens place and the ones place; adding and subtracting two-digit numbers; learning

More information

HSED Math Course Outcome Summary

HSED Math Course Outcome Summary Wisconsin Technical College System HSED 5.09 - Math Course Outcome Summary Course Information Description Learners will apply math concepts in real-world context including financial literacy consumer applications.

More information

Simple Solutions Mathematics. Part A. Algebra I Part A. Help Pages & Who Knows

Simple Solutions Mathematics. Part A. Algebra I Part A. Help Pages & Who Knows Simple Solutions Mathematics Algebra I Part A & Who Knows 83 Vocabulary General Absolute Value the distance between a number, x, and zero on a number line; written as x. Example: 5 = 5 reads The absolute

More information

Granite School District Parent Guides Utah Core State Standards for Mathematics Grades K-6

Granite School District Parent Guides Utah Core State Standards for Mathematics Grades K-6 Granite School District Parent Guides Grades K-6 GSD Parents Guide for Kindergarten The addresses Standards for Mathematical Practice and Standards for Mathematical Content. The standards stress not only

More information

8 th Grade Intensive Math

8 th Grade Intensive Math 8 th Grade Intensive Math Ready Florida MAFS Student Edition August-September 2014 Lesson 1 Part 1: Introduction Properties of Integer Exponents Develop Skills and Strategies MAFS 8.EE.1.1 In the past,

More information

Mississippi College and Career Readiness Standards for Mathematics Scaffolding Document. Grade 6

Mississippi College and Career Readiness Standards for Mathematics Scaffolding Document. Grade 6 Mississippi College and Career Readiness Standards for Mathematics Scaffolding Document Grade 6 Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems

More information

California Algebra 1

California Algebra 1 California Algebra 1 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

More information

Course Readiness and Skills Review Handbook (83 topics) Course Readiness (21 topics) Course Name: Algebra Course Code: UY6JA-RATXM

Course Readiness and Skills Review Handbook (83 topics) Course Readiness (21 topics) Course Name: Algebra Course Code: UY6JA-RATXM Course Name: Algebra 1 2014-15 Course Code: UY6JA-RATXM ALEKS Course: Algebra 1A Instructor: Ms. Dalton Course Dates: Begin: 11/18/2014 End: 06/18/2015 Course Content: 335 Topics (334 goal + 1 prerequisite)

More information

K-8 CCSS Vocabulary Word List Revised: 5/5/14

K-8 CCSS Vocabulary Word List Revised: 5/5/14 AA (angle-angle criterion) a.m. above absolute value acute angle acute triangle add addend Addition Property of Equality additive comparison additive inverse Additive Identity Property of 0 adjacent angle

More information

Dividing in Scientific Notation Name (page 778)

Dividing in Scientific Notation Name (page 778) LESSON 111 Dividing in Scientific Notation Name (page 778) To divide powers of 10, subtract the exponents. 10 7 10 4 = 10 7 4 = 10 3 To divide numbers in scientific notation: 1. Divide the decimal or whole

More information

Copyright 2012 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/6

Copyright 2012 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/6 Course Name: MTH099 Fall 2012 Prov Course Code: ADPNR-EADAW ALEKS Course: Beginning and Intermediate Algebra Combined Instructor: Lynd Course Dates: Begin: 08/23/2012 End: 01/20/2013 Course Content: 210

More information

A Correlation of. Pearson. Mathematical Ideas. to the. TSI Topics

A Correlation of. Pearson. Mathematical Ideas. to the. TSI Topics A Correlation of Pearson 2016 to the A Correlation of 2016 Table of Contents Module M1. Linear Equations, Inequalities, and Systems... 1 Module M2. Algebraic Expressions and Equations (Other Than Linear)...

More information

Visit us at: for a wealth of information about college mathematics placement testing!

Visit us at:   for a wealth of information about college mathematics placement testing! North Carolina Early Mathematics Placement Testing Program, 9--4. Multiply: A. 9 B. C. 9 9 9 D. 9 E. 9 Solution and Answer to Question # will be provided net Monday, 9-8-4 North Carolina Early Mathematics

More information

Vocabulary Cards and Word Walls

Vocabulary Cards and Word Walls Vocabulary Cards and Word Walls Revised: September 9, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the mathematics learning standards adopted by the Washington

More information

Answers. Chapter thirteen thousand, one hundred twenty-six 14. one thousand, eight hundred eightythree

Answers. Chapter thirteen thousand, one hundred twenty-six 14. one thousand, eight hundred eightythree Copyright 008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter.. words. standard form. expanded form. period. place value. whole. ten 8. thousand 9. ten thousand 0. four hundred three.

More information

Purposeful Design Publications. Intermediate Mathematics Series Scope and Sequence

Purposeful Design Publications. Intermediate Mathematics Series Scope and Sequence Purposeful Design Publications Intermediate Mathematics Series Scope and Sequence All rights reserved, 2004 PO Box 35097 Colorado Springs, CO 80935-3509 800.367.0798 www.purposefuldesign.com I. NUMBER

More information

= ( 17) = (-4) + (-6) = (-3) + (- 14) + 20

= ( 17) = (-4) + (-6) = (-3) + (- 14) + 20 Integer Operations Adding Integers If the signs are the same, add the numbers and keep the sign. If the signs are different, find the difference and use the sign of the number with the greatest absolute

More information

ABE Math Review Package

ABE Math Review Package P a g e ABE Math Review Package This material is intended as a review of skills you once learned and wish to review before your assessment. Before studying Algebra, you should be familiar with all of the

More information

Next Generation Sunshine State Standards Grade K

Next Generation Sunshine State Standards Grade K Next Generation Sunshine State Standards Grade K Benchmark Level B Level C Big Idea 1: Represent, compare, and order whole numbers, and join and separate sets. MA.K.A.1.1 Represent quantities with numbers

More information

Math 6, Unit 9 Notes: Measurement and Geometry

Math 6, Unit 9 Notes: Measurement and Geometry Math 6, Unit 9 Notes: Measurement and Geometry Customary and Metric Units of Measure Objective: (6.3)The student will estimate corresponding units of measure between customary and metric systems for temperature,

More information

GTPS Curriculum 6 th Grade Math. Topic: Topic 1- Numeration

GTPS Curriculum 6 th Grade Math. Topic: Topic 1- Numeration 9 days / September Compute fluently with multi-digit numbers and find common factors and multiples. 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm

More information

MATHEMATICS Grade 5 Standard: Number, Number Sense and Operations. Organizing Topic Benchmark Indicator

MATHEMATICS Grade 5 Standard: Number, Number Sense and Operations. Organizing Topic Benchmark Indicator Standard: Number, Number Sense and Operations Number and A. Represent and compare numbers less than 0 through 6. Construct and compare numbers greater than and less Number Systems familiar applications

More information

6 th Grade Math. Full Curriculum Book. Sample file. A+ Interactive Math (by A+ TutorSoft, Inc.)

6 th Grade Math. Full Curriculum Book. Sample file. A+ Interactive Math (by A+ TutorSoft, Inc.) 6 th Grade Math Full Curriculum Book Release 7 A+ Interactive Math (by A+ TutorSoft, Inc.) Email: info@aplustutorsoft.com www.aplustutorsoft.com Page 3 of 518 Copyright 2014 A+ TutorSoft Inc., All Rights

More information

Ready To Go On? Skills Intervention 7-1 Integer Exponents

Ready To Go On? Skills Intervention 7-1 Integer Exponents 7A Evaluating Expressions with Zero and Negative Exponents Zero Exponent: Any nonzero number raised to the zero power is. 4 0 Ready To Go On? Skills Intervention 7-1 Integer Exponents Negative Exponent:

More information

MATH Spring 2010 Topics per Section

MATH Spring 2010 Topics per Section MATH 101 - Spring 2010 Topics per Section Chapter 1 : These are the topics in ALEKS covered by each Section of the book. Section 1.1 : Section 1.2 : Ordering integers Plotting integers on a number line

More information

Prep for College Algebra

Prep for College Algebra Prep for College Algebra This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (219 topics + 85 additional topics)

More information

Variables and Expressions

Variables and Expressions Variables and Expressions A variable is a letter that represents a value that can change. A constant is a value that does not change. A numerical expression contains only constants and operations. An algebraic

More information

1 1. Basic Math Whole numbers Fractions Decimals Advanced Math

1 1. Basic Math Whole numbers Fractions Decimals Advanced Math Unit. Mathematics. Basic Math... 00. Whole numbers... 00. Fractions... 3 003. Decimals... 7. Advanced Math... 6 004. Ratios... 6 005. Proportion... 9 006. Positive and negative numbers... 9 007. Powers

More information

Part 2 - Beginning Algebra Summary

Part 2 - Beginning Algebra Summary Part - Beginning Algebra Summary Page 1 of 4 1/1/01 1. Numbers... 1.1. Number Lines... 1.. Interval Notation.... Inequalities... 4.1. Linear with 1 Variable... 4. Linear Equations... 5.1. The Cartesian

More information

Prep for College Algebra with Trigonometry

Prep for College Algebra with Trigonometry Prep for College Algebra with Trigonometry This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (246 topics +

More information

REPUBLIC OF THE MARSHALL ISLANDS PUBLIC SCHOOL SYSTEM CONTENT STANDARDS AND PERFORMACE INDICATORS

REPUBLIC OF THE MARSHALL ISLANDS PUBLIC SCHOOL SYSTEM CONTENT STANDARDS AND PERFORMACE INDICATORS Page 1 Kindergarten STANDARD 1 Number Sense, Operations, Mental Computation and Estimation - Students will develop number sense and an understanding of numbers and operations By the end of Kindergarten

More information

Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression

Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression 1 Words to Review Give an example of the vocabulary word. Numerical expression 5 12 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression

More information