# ACE Grade 6 Math PACEs

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (torn out from the center), to measure understanding.

This set includes Math Grade 6 PACEs 1061-1072, which cover:

• Learns the properties of addition and multiplication-commutative, associative, identity, and zero.
• Works with exponents and is introduced to expanded notation using exponents.
• Rounds and estimates large numbers and works mental estimation problems.
• Learns factoring rules (divisibility rules); identifies prime numbers and composite numbers.
• Reviews fractions and fraction terms; adds, subtracts, multiplies, and divides fractions; changesfractions to decimals using long division; and converts fractions to percents.
• Reviews decimals; adds, subtracts, multiplies, and divides decimals; defines repeating andterminating decimals; and changes decimals to percents.
• Relates percents and decimals to fractions, learns common percents, changes percents to decimals,and finds percent of a number.
• Is introduced to integers.
• Learns order of operation.
• Learns the terms equations and inequalities when comparing number sentences (<, >, =).
• Defines a variable and solves equations (one variable) using inverse operations.
• Works with ratios and proportions, and uses proportions to solve problems.
• Finds the probability of an event, and expresses probability as a ratio.
• Uses critical thinking skills to solve word problems.
• Defines and interprets circle, line, bar, and double-line graphs.
• Builds geometric knowledge; measures angles; finds the perimeter, area, and volume; and defines theparts of a circle.
• Rounds money to find estimated costs and solves money problems.
• Compares English and metric measurements, and carries out conversions.

A variety of exercises help with review and retention. 49 pages each, paperback booklets. Grade 6. PACE 1061-1072.

Answers are not included, but are available in the sold-separately PACE Score Key Set.

• This answer key set includes four PACE SCORE keys that cover Math PACEs 1061-1063. Keys are three-hole-punched, and have each page and question number clearly labeled; answers are overlaid on reproduced student pages. Test and workbook exercises included. 12 booklets. Grade 6.

ACE's Math PACE 1061 covers: knowing place value through the hundred millions' place; reviewing adding and subtracting 3-, 4-, and 5-digit numbers; using number sentences to show commutative and associative properties of addition; learning about inverse operations; reviewing how to multiply 2- and 3-digit numbers; reviewing how to divide by 1-digit divisors and by multiples of 10; reviewing rules for finding factor of numbers; identifying prime and composite numbers; reviewing the basic concept of fractions, equivalent fractions, and fractions with like denominators; and solving word problems.

A variety of exercises help with review and retention. Full-color pictures. 49 pages, paperback booklet. Grade 6. PACE 1061. Answers are in the sold-separate PACE SCORE Key booklet.

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (removed from the center) to measure understanding.

ACE's Math PACE 1062 covers: writing number words through hundred millions; changing the value of a large number by increasing or decreasing one of the digits by a multiple of 10; multiplying 4-digit numbers by 3-digit numbers; rounding numbers to the nearest multiple of 1,000; dividing by 2-digit divisors; learning about commutative and associative properties of addition and multiplication; learning identity properties of addition and multiplication; finding common factors and determining the GCF; writing fractions in simplest form; identifying proper, improper, and equivalent fractions; changing improper fractions to whole or mixed numbers; adding and subtracting mixed numbers with like fractions and writing the answers in simplest form; making and interpreting bar graphs; and solving word problems.

A variety of exercises help with review and retention. Full-color pictures. 49 pages, paperback booklet. Grade 6. PACE 1062. Answers are in the sold-separate PACE SCORE Key booklet.

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (removed from the center) to measure understanding.

ACE's Math PACE 1063 covers: writing numbers in expanded notation; writing numbers in standard notation from expanded notation; multiplying with multiples of 10, 100, and 1,000 mentally; reviewing commutative, associative, and identity properties; dividing by 2-digit divisors with larger dividends and quotients and begin dividing with 3-digit divisors; finding averages; learning about equations and inequalities; using borrowing to subtract fractions from whole or mixed numbers; reviewing finding equivalent fractions; using cross products in determining equivalent fractions; finding the least common denominator; adding and subtracting mixed numbers with unlike fractions; using borrowing to subtract mixed numbers with unlike fractions; learning about decimals through the thousandths' place; learning about equivalent decimals; comparing decimals by place value through the thousandths' place; adding and subtracting decimals through the thousandths' place; and solving word problems.

A variety of exercises help with review and retention. Full-color pictures. 49 pages, paperback booklet. Grade 6. PACE 1063. Answers are in the sold-separate PACE SCORE Key booklet.

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (removed from the center) to measure understanding.

This single ACE "PACE" score key includes the answers for the sold-separately Math PACEs 1061, 1062, and 1063. Test and workbook exercises included; answers are overlaid on reproduced student pages. This key is three-hole-punched. Grade 6.

ACE's Math PACE 1064 covers: defining and working with exponents; writing powers of 10 as exponents; learning more about rounding to the nearest 10, 100, and 1000; estimating products by rounding the factors; learning more about dividing with 3-digit divisors; finding the least common multiple; reviewing how to add and subtract mixed numbers with unlike fractions; applying the commutative, associative, and identity properties of addition to fractions; learning more about ratios; multiplying fractions with fractions and fractions with whole numbers using cancellation; multiplying fractions and mixed numbers using cancellation; writing decimals as fractions in simplest form; learning about decimals through the ten-thousandths' place; adding and subtracting decimals through the ten-thousandths' place; and solving word problems.

A variety of exercises help with review and retention. Full-color pictures. 49 pages, paperback booklet. Grade 6. PACE 1064. Answers are in the sold-separate PACE SCORE Key booklet.

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (removed from the center) to measure understanding.

ACE's Math PACE 1065 covers: reviewing exponents; multiplying numbers times powers of 10 using exponents; comparing large numbers by place value; rounding large numbers; estimating sums and differences by rounding large numbers; determining the function rule by patterns in function tables; using multiplication to check division; learning about the "mean"; finding the least common multiple of three numbers; finding the least common denominator of three fractions and add them; reviewing how to multiply fractions; multiplying mixed numbers with whole numbers and mixed numbers with mixed numbers; learning about ratio and probability; comparing decimals by place value through the ten-thousandths' place; multiplying decimals through the ten-thousandths' place; finding area, using decimals as the length and width; studying and comparing line graphs and bar graphs; and solving word problems.

A variety of exercises help with review and retention. Full-color pictures. 49 pages, paperback booklet. Grade 6. PACE 1065. Answers are in the sold-separate PACE SCORE Key booklet.

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (removed from the center) to measure understanding.

ACE's Math PACE 1066 covers: using the order of operations in evaluating expressions; substituting numbers for variables in evaluating expressions; using a formula to determine the area of a rectangle; working long division problems with zero in the quotient; rounding whole numbers to the place of greatest value; learning to use the divisibility rules; using the GCF to solve problems; reviewing how to multiply fractions; dividing whole numbers by fractions and fractions by fractions; adding and subtracting whole numbers and decimals; reviewing how to multiply decimals; rounding decimals to the nearest whole number; rounding decimals to the nearest tenth, hundredth, and thousandth; defining and learning about percents; and solving word problems.

A variety of exercises help with review and retention. Full-color pictures. 49 pages, paperback booklet. Grade 6. PACE 1066. Answers are in the sold-separate PACE SCORE Key booklet.

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (removed from the center) to measure understanding.

This single ACE "PACE" score key includes the answers for the sold-separately Math PACEs 1064, 1065, and 1066. Test and workbook exercises included; answers are overlaid on reproduced student pages. This key is three-hole-punched. Grade 6.

ACE's Math PACE 1067 covers: studying the pattern of a sequence in order to determine the next term of the sequence; studying the pattern for all the pairs of numbers of a function table in order to write the function rule as an equation; using inverse operations to solve for the missing number in addition and subtraction equations; comparing unlike fractions by finding the least common denominator (LCD); reviewing how to divide fractions by fractions and whole numbers by fractions; dividing fractions by whole numbers or mixed numbers; dividing decimals by whole numbers; multiplying and dividing decimals by powers of ten by moving the decimal point; changing decimals to percents and percents to decimals by moving the decimal point; learning about circle graphs; and solving word problems.

A variety of exercises help with review and retention. Full-color pictures. 49 pages, paperback booklet. Grade 6. PACE 1067. Answers are in the sold-separate PACE SCORE Key booklet.

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (removed from the center) to measure understanding.

ACE's Math PACE 1068 covers: knowing place value through the hundred billions' place; reading and writing number words through hundred billions; writing in expanded notation through hundred billions by using exponents; using inverse operations to solve for the missing numbers in multiplication and division equations; determining if two ratios are equivalent by using cross products; defining proportions; comparing unlike fractions by using cross products; dividing mixed numbers; dividing by decimal divisors; dividing and expressing remainders as decimals; and solving word problems.

A variety of exercises help with review and retention. Full-color pictures. 49 pages, paperback booklet. Grade 6. PACE 1068. Answers are in the sold-separate PACE SCORE Key booklet.

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (removed from the center) to measure understanding.

ACE's Math PACE 1069 covers: reviewing place value and expanded notation through the hundred billions' place; reviewing the order of operations; reviewing how to solve for the missing number using inverse operations; learning about positive and negative numbers using the number line and the thermometer; reviewing how to add, subtract, multiply, and divide fractions; multiplying three fractions using cancellation; learning more about taking a fraction of a whole number; solving for the missing number in a proportion; reviewing how to divide by a decimal; dividing whole numbers when the divisor is greater than the dividend; changing a fraction to a decimal by dividing the numerator by the denominator; reviewing the relationship between fractions, decimals, and percents; changing a fraction to a percent and a percent to a fraction; and solving word problems.

A variety of exercises help with review and retention. Full-color pictures. 49 pages, paperback booklet. Grade 6. PACE 1069. Answers are in the sold-separate PACE SCORE Key booklet.

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (removed from the center) to measure understanding.

This single ACE "PACE" score key includes the answers for the sold-separately Math PACEs 1067, 1068, and 1069. Test and workbook exercises included; answers are overlaid on reproduced student pages. This key is three-hole-punched. Grade 6.

ACE's Math PACE 1070 covers: reviewing positive and negative numbers; writing positive and negative numbers in order from least to greatest; rounding numbers and finding the closest estimate; finding the best equation to use to mentally estimate an answer; reviewing how to add, subtract, multiply, and divide fractions; learning more about multiplying three fractions using cancellation; reviewing how to add, subtract, multiply, and divide decimals; learning about terminating and repeating decimals; changing fractions to terminating or repeating decimals; finding decimal equivalents for mixed numbers and mixed number equivalents for decimals; comparing decimals, fractions, and percents; using decimal equivalents to find the percent of a number; using proportions to find the percent of a number; using proportions to write ratios as percents; finding what percent on number is of another; and solving word problems.

A variety of exercises help with review and retention. Full-color pictures. 49 pages, paperback booklet. Grade 6. PACE 1070. Answers are in the sold-separate PACE SCORE Key booklet.

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (removed from the center) to measure understanding.

ACE's Math PACE 1071 covers: learning more about point, lines, line segments, and rays; naming perpendicular and parallel lines and line segments using symbols; naming angles in three ways using symbols; identifying and comparing kinds of angles; using a protractor to measure angles; using a protractor to construct angles to a given measure; naming congruent line segments and angles using symbols; classifying polygons by the number of sides or angles; recognizing regular polygons; comparing congruent and similar polygons; learning about lines of symmetry; identifying and comparing quadrilaterals; naming parallel and congruent sides of quadrilaterals; recognizing kinds of angles in quadrilaterals; plotting points for ordered pairs on a grid; and connecting the points of ordered pairs to form polygons.

A variety of exercises help with review and retention. Full-color pictures. 49 pages, paperback booklet. Grade 6. PACE 1071. Answers are in the sold-separate PACE SCORE Key booklet.

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (removed from the center) to measure understanding.

ACE's Math PACE 1072 covers: finding the perimeter of a polygon; finding the length of each side of a regular polygon; using a formula to find the area of a rectangle; using a formula to find the area of a parallelogram; classifying triangles by the kinds of angles and by the number of degrees in each angle; using inverse operations to solve for the missing angle measure of a triangle; describing and identifying the parts of a circle; learning about the relationship between the parts of a circle; describing and identifying solid figures; comparing plane figures and solid figures; learning about volume and cubic units; using a formula to find the volume of a rectangular prism; determining whether a given situation is calling for perimeter, area, or volume measure; and solving word problems.

A variety of exercises help with review and retention. Full-color pictures. 49 pages, paperback booklet. Grade 6. PACE 1072. Answers are in the sold-separate PACE SCORE Key booklet.

Accelerated Christian Education (ACE) curriculum has Scripture as its foundation, fully integrating biblical principles, wisdom, and character-building concepts into education. Students move at their own speed through the self-instructional "PACE" workbooks. Following the mastery approach, PACEs are formatted for students to complete the exercises found throughout the workbook, take a practice "self test," and conclude with a "final test" (removed from the center) to measure understanding.

This single ACE "PACE" score key includes the answers for the sold-separately Math PACEs 1070, 1071, and 1072. Test and workbook exercises included; answers are overlaid on reproduced student pages. This key is three-hole-punched. Grade 6.