MATHEMATICS

MATH PACE's 1001 – 1012
1001 Character objective: Appreciative
Counting 1-5 (Groups of how many); Number 1-5 (write; how many)
1002 Character objective: Concerned
Counting 1-9 (Groups of how many); Numbers 6-9 (write; how many
1003 Character objective: Cooperative
Addition 1-5 (More; Facts; Vertical Addition; Word problems)
1004 Character objective: Dependable
Addition 6-9 (More; Facts; Vertical Addition; Word problems)
1005 Character objective: Efficient
Subtraction 1-5 (Take away; Facts; Vertical subtraction; Word problems)
1006 Character objective: Flexible
Subtraction 6-9 (Take away; Facts; Vertical subtraction; Word problems
1007 Character objective: Honest
Write 0; Addition of zero; Group of ten (Names for ten); Numbers 1-20 (Count, Write)
1008 Character objective: Generous
Group of ten (Names for tens; Tens and ones); Addition (Sums from 10-18); Numbers 1-30 (Count, Write)
1009 Character objective: Joyful
Numbers 1-100 (Count, Write); Subtraction (Differences 0-9)
1010NZ Character Objective: Submissive
Money – to add 5, 10, and 20 pieces; length – comparing (longer, shorter); time – clock (hours)
1011NZ Character Objective: Friendly
Number words – match symbols; with word, match word with how many liquids – cups,
litres, name how many recognize shapes – circle, square, triangle, rectangle
1012 Character objective: Thrifty
Contrasting Numbers (The same, not the same, more than, less than); Order of numbers (before, between, after); Number lines (addition, subtraction)

MATH PACE’s 1013 – 1024
1013 Character objective: Attentive
Count and write from 1-100 (also dot-to-dot); Count and write by 10s to 100, 2s to 20; Work addition facts, sum 2-18. vertically/horizontally; Work subtraction facts, differences 0-9, vertically/horizontally; Work word problems with addition/subtraction facts; Recognize a circle, square, rectangle, triangle, and cone. Write from 1-10 and 10-1. Relate numbers to number words for 1-10. Write the number that comes before or after. Recognize symbols +, -, and =
1014 Character objective: Confident
Count and write by 1s, 2s, 5s, and 10s. Work addition facts, sums 2-18 vertically/horizontally. Add 3, 1-digit addends vertically/horizontally. Work word problems with 3 addends. Add 1 digit to multiple of 10. Work subtraction facts, differences 0-9, vertically/horizontally. Complete patterns of geometric shapes. Recognize a circle, square, rectangle, triangle, and cone. Write the numbers for number words 1-10. Write the number that comes before, after or between.
1015 Character objective: Courageous
Count and write from 1-100, 101-200. Count and write by 2s, 5s, and 10s. Add 3, 1-digit addends vertically/horizontally. Add/subtract multiples of 10. Work word problems, adding/subtracting multiples of 10. Add 1 digit to multiple of 10. Work word problems, adding 1 digit to multiples of 10. Add/subtract 2 digits plus/minus 1 digit. Work word problems with 2 digits plus/minus 1 digit. Write the number that comes before, between or after. Write and recognize even and odd numbers. Write numbers in place value – 1s and 10s.
1016 Character objective: Determined
Count (using dot-to-dot) and write from 201 to 300. Count and write by 2s and 5s. Add/subtract multiples of 10. Add 1 digit to multiples of 10. Add/subtract 2 digits plus/minus 1 or 2 digits. Work word problems with 2 digits plus/minus 2 digits. Time addition/subtraction facts (oral). Add/subtract 2 digits plus 2 digits as place value – 1s and 10s. Complete patterns of geometric shapes. Circle word for which one (first-tenth). Find circles, squares, rectangles, triangles, and cones in a picture. Write even/odd numbers. Write numbers in place value – 1s and 10s. Write the number that comes before, after or between. Write numbers for number words – 1-10. Write missing numbers in number sequence.
1017 Character objective: Equitable
Count (using dot-to-dot) and write from 301-400. Add/subtract 2 digits plus 2 digits. Time addition/subtraction facts (oral). Add/subtract multiples of 100 as 1s, 10s, and 100s. Add/subtract 3 digits plus/minus 3 digits as 1s, 10s, and 100s. Work word problems with 3 digits plus/minus 3 digits. Work word problems with 2 digits plus/minus 2 digits. Circle the number that is greater/less than. Complete the pattern of geometric shapes. Match which one (first-tenth). Write the missing numbers on a 100s number chart. Write even/odd numbers. Write numbers in place value – 1s, 10s and 100s.
1018 Character objective: Forgiving
Count and write from 401-500 (also dot-to-dot). Count and write by 2s, 5s and 10s. Work addition/subtraction facts vertically/horizontally. Add 3, 1-digit addends. Add/subtract 2 digits plus/minus 1 or 2 digits. Work word problems with 2 digits plus/minus 1 or 2 digits. Add/subtract 3 digits plus/minus 3 digits. Work word problems with 3 digits plus/minus 3 digits. Add and “carry” 2 digits plus 1 digit. Work word problems with add and “carry” 2 digits plus 1 digit. Circle the number that is greater/less than. Complete the pattern of geometric shapes. Write which one (first-tenth). Write even/odd numbers. Write numbers in place value – 1s and 10s.
1019 Character objective: Humble
Count from 401-500, using dot-to-dot. Count and write by 2s, 5s and 10s. Add/subtract 2 digits plus/minus 2 digits. Work addition/subtraction facts vertically/horizontally. Add and “carry” 2 digits plus 1 digit. Work word problems with add and “carry” 2 digits plus 1 digit. Compare addition to subtraction. Compare the answers to addition problems when increasing the second addend by 1. Compare the answers to subtraction problems when increasing the minuend by 1. Answer questions from pictograph; add/subtract. Work word problems with subtraction facts. Complete the pattern of geometric shapes. Choose the number that is greater/less than. Match place value – 1s and 10s – to number. Match number to its number word (1-10). Write the number that comes before, after, or between. Write even/odd numbers.
1020 Character objective: Merciful
Count (using dot-to-dot) from 1-50 and one-twenty. Count and write by 2s, 5s, and 10s. Add 3 addends. Add/subtract multiples of 10. Add/subtract 2 digits plus/minus 2 digits. Add/subtract 3 digits plus/minus 3 digits. Add and “carry” 2 digits plus 1 digit. Work word problems with add and “carry” 2 digits plus 1 digit. Work addition/subtraction facts. Time addition/subtraction facts (oral). Write in the missing addend/subtrahend. “Borrow” and subtract 2 digits minus 1 digit. Work word problems with “borrow” and subtract 2 digits minus 1 digit. Complete the pattern of geometric shapes. Match number (1-20) to its number word. Write even/odd numbers. Write numbers and circle wrong numbers on a calendar. Write the numbers that come before, after, and between.
1021 Character objective: Perseverant
Count by and write 2s, 3s, 5s, and 10s. Work addition/subtraction facts. Add and “carry” 2 digits plus 1 or 2 digits. Work word problems with add and “carry” 2 digits plus 1 or 2 digits. Add and “carry” to 10s – 3 digits plus 2 digits. Work word problems with add and “carry” to 10s – 3 digits plus 2 digits. “Borrow” and subtract 2 digits minus 1 digit. Work word problems with “borrow” and subtract 2 digits minus 1 digit. Use subtraction fact answers related to letters to decipher a secret Scripture message. Write the number for the number word and vice versa. Write the number word for which one.
1022NZ Character Objective: Responsible
Money – 5, 10, 20, 50: counting coins: addition and subtraction of cents; order or numbers – before–between–after; counting on number line
1023 Character objective: Submissive
Add/subtract 2 digits plus/minus 1 or 2 digits. Add/subtract 3 digits plus/minus 1, 2, or 3 digits. Add 3 or 4 addends. “Borrow” and subtract 2 digits minus 1 or 2 digits. “Borrow” and subtract from 10s – 3 digits minus 1, 2, or 3 digits. Work word problems with “borrow” and subtract 2 or 3 digits minus 2 digits. Relate multiplication to addition – 2 x 1 digit. Use the concept of a point to draw a line, curve, circle, square, triangle, and rectangle between points. Tell time on the hour, half-hour, and quarter-hour. Divide clock into 5-minute increments.
1024NZ Character Objective: Tolerant
Length – how long; compare cups, litres, 2 litres and other containers; numbers – 1’s,
10’s, 100’s

MATH PACE’s 1025 – 1036
1025 Character objective: Available
Count from 201-300, using dot-to-dot. Count and write by 2s, 3s, 4s, 5s, 10s, and 100s. Compare 2 sets of addends having the same sum. Time/subtraction addition facts (oral). Work addition/subtraction facts. Add – show commutative aspect of addition. Add 3 or 4, 1-digit addends vertically/horizontally. Add 2 digits plus 1 or 2 digits. Work word problems with 2 digits plus/minus 2 digits. Add 3 digits plus 1, 2, or 3 digits. Work word problems with 3 digits plus/minus 1, 2, or 3 digits. Add and “carry” 2 digits plus 1 or 2 digits. Work word problems with add and “carry” 2 digits plus 1 digit. Add and “carry” to 10s – 3 digits plus 3 digits. Subtract 2 digits minus 1 or 2 digits. Subtract multiples of 10. Work word problems, subtracting multiples of 10. “Borrow” and subtract 2 digits minus 1 or 2 digits. “Borrow” and subtract from 10s – 3 digits minus 2 digits. Work word problems with “borrow” and subtract from 10s – 3 digits minus 2 digits. Compare addition to multiplication. Relate multiplication to addition – 2 and 4 x 1 digit. Circle the even/odd numbers. Complete the pattern of geometric shapes. Tell time on the hour, half-hour, quarter-hour, and in 5-minute increments. Write the missing numbers that come before, after, or between. Write numbers in place value – 1s, 10s, or 100s.
1026 Character objective: Considerate
Count and write from 501-600 (also dot-to-dot). Count and write by 1s, 2s, 3s, 4s, 5s, 10s, and 100s. Add 3 or 4, 1-digit addends. Add 2 digits plus 2 digits. Work addition/subtraction problems with data from table. Add and “carry” 2 digits plus 1 or 2 digits. Add and “carry” to 10s – 3 digits plus 3 digits. Subtract 3 digits minus 2 digits. “Borrow” and subtract 2 digits minus 1 or 2 digits. Work word problems with “borrow” and subtract 2 digits minus 1 or 2 digits. “Borrow” and subtract from 10s – 3 digits minus 3 digits. Compare addition to multiplication. Multiple 2 by 1-9. Time multiply 2s (written). Complete the pattern of geometric shapes. Match the ordinal word (first-tenth) with its symbol. Tell time on the hour, half-hour, or quarter-hour. Write/circle even/odd numbers. Write the missing numbers in number sequence.
1027 Character objective: Creative
Count and write from 601-700 (also dot-to-dot). Count and write by 1s, 2s, 3s, 4s, and 5s, 10s, 100s, and 1000s. Count and write by 2s and 10s, forward/backward. Add 3, 4, or 12, 1-digit addends. Add 3 digits plus 3 digits, 4 digits plus 4-digits. Add and “carry” to 10s – 2 digits plus 2 digits, 3 digits plus 2 or 3 digits. Work word problems with add and “carry” to 10s – 2 digits plus 2 digits, 3 digits plus 2 or 3 digits. Subtract 3 digits minus 3 digits, 4 digits minus 4 digits. “Borrow” and subtract from 10s – 2 digits minus 1 digit, 3 digits minus 2 or 3 digits. Work word problems from 10s – 2 digits minus 2 digits, 3 digits minus 2 digits or 3 digits. Compare multiplication to addition. Multiply 0s, 1s, and 2s. Work word problems, multiplying 2s. Time multiply 0s, 1s, and 2s (written). Match the ordinal word (first – tenth) to its
symbol. Use comma to separate thousands from hundreds. Write number as place value – 1s, 10s, 100s, and 1000s. Write first ten even/odd numbers. Write missing number in add/subtract number sentence.
1028 Character objective: Diligent
Count and write from 701-800 (also dot-to-dot). Count and write by 1s, 2s, 3s, 4s, 5s, 10s, 100s, and 1000s. Add and “carry” to 10s – 3 digits plus 3 digits. Work word problems with add and “carry” to 10s -- 3 digits plus 3 digits. Add and “carry” to 100s – 3 digits plus 2 or 3 digits. Work word problems with add and “carry” to 100s – 3 digits plus 2 or 3 digits. Subtract 3 digits minus 2 or 3 digits, 4 digits minus 3 or 4 digits. “Borrow” and subtract 2 digits minus 1 or 2 digits. Work word problems with “borrow” and subtract 2 digits minus 1 or 2 digits. “Borrow” and subtract from 10s – 3 digits minus 2 or 3 digits. Work problems with “borrow” and subtract from 10s – 3 digits minus 2 or 3 digits. Multiply 3 by 1-9. Work word problems, multiplying 2s. Time multiply 3s (written). Multiply 0s – 2s. Draw a line through a maze. Use comma to separate thousands from hundreds.
1029 Character objective: Fair
Count and write from 801-900 (also dot-to-dot). Alternate working addition with subtraction facts. Alternate working 2 digits plus 2 digits with 2 digits minus 2 digits. Alternate working 3 digits plus 3 digits with 3 digits minus 3 digits. Alternate working 4 digits plus 4 digits with 4 digits minus 4 digits. Add and “carry” 2 digits plus 1 or 2 digits. Add and “carry” to 10s – 3 digits plus 3 digits. Add and “carry” to 100s – 3 digits plus 2 or 3 digits. Work add/subtract problems with data from table. “Borrow” and subtract from 10s – 3 digits minus 2 or 3 digits. Work word problems with “borrow” and subtract from 10s – 3 digits minus 2 or 3 digits. Multiply 4 by 1-9. Work word problems, multiplying 4s. Multiply 0-3. Time multiply 4s (written). Circle objects in groups of 2 or 5 (division). Color a picture in designated colors. Draw a line through a maze.
1030 Character objective: Friendly
Count and write from 901-1000 (also dot-to-dot). Count and write by 1s, 2s, 3s, 4s, and 5s. Add 4, 1-digit addends, 4, 2-digit addends. Add 3, 1-digit addends, 3, 2-digit addends vertically/horizontally. Match addition/subtraction word sentence with its number sentence. “Borrow” and subtract from 100s – 3 digits minus 2 or 3 digits. Multiply 0s – 4s. Multiply 5 by 1-9. Time multiply 5s (written), 0s – 5s (written). Work word problems, multiplying 2s – 5s. Multiply 2 or 3 digits times 1 digit. Divide objects into groups of 2, 3, 4, 5, 6, or 7. Color a picture in designated colors. Write numbers for number words to the thousands.
1031 Character objective: Joyful
Count and write by 1s, 2s, 3s, 4s, 5s, and 6s; add and “carry” to 10s and 100s—3 digits plus 2 or 3 digits; work word problems with “borrow” and subtract from 10s and 100s—3 digits minus 2 or 3 digits; multiply 0s-5s; multiply 6 by 1-9; time multiply 6x (written); multiply 2 or 3 digits times 1 digit; answer questions from a bar graph/chart; write in missing +, --, or = sign for number sentences; write missing numbers in number sequences
1032 Character objective: Observant
Count and write by 7s; add doubles; e.g., 4 + 4; multiply 0s-6s; multiply 7 by 1-9; time multiply 7s (written); multiply 2 digits times 1 digit; choose open/closed shapes; choose the inside/outside of a shape; circle the greater set; circle the numbers or number of objects that are greater/less than; find squares, circles, triangles, and rectangles in everyday shapes; write ordinals first-tenth; write the number of objects in a set
1033 Character objective: Persuasive
Count and write by 8s; add and “carry” to 10s—2 digits plus 1 or 2 digits, 3 digits plus 3 digits; add and “carry” to 100s—3 digits plus 2 or 3 digits; add and “carry” to 10s and 100s—3 digits plus 2 or 3 digits
1034 Character objective: Respectful
Count and write by 9s; add 4, 1-digit or 2-digit addends; work word problems with 4, 2-digit addends; add and “carry” to 10s—4, 2-digit or 3-digit addends; work word problems with add and “carry” 4, 2-digit addends; “borrow” and subtract from 10s—2 digits minus 1 or 2 digits; “borrow” and subtract from 10s and/or 100s—3 digits minus 2 or 3 digits; work commutative multiplication problems; multiply 9 by 1-9; time multiply 9s (written); work word problems multiplying 9s; multiply 2 or 3 digits times 1 digit; circle objects to divide into groups of 3; divide by 3
1035 Character objective: Tactful
Count and write by 1s-9s; add/subtract on a number line; add and “carry” to 10s and/or 100s—3 digits plus 1, 2, or 3 digits; work word problems with add and “carry” to 10s and/or 100s—3 digits plus 1, 2, or 3 digits; “borrow” and subtract from 10s and/or 100s—3 digits minus 1, 2, or 3 digits; work word problems with “borrow” and subtract from 10s and/or 100s—3 digits minus 1, 2, or 3 digits; multiply 0s-9s; work word problems multiplying 0s-9s; multiply 3 digits times 1 digit; use a number line to divide by 2, 3, 5, and 6; divide objects or sets of objects into halves (1/2); tell time on hour or half-hour; divide clock into minutes and tell time to 5-minute intervals (2:35, 6:10, …); convert time from “past the hour” to “to the hour”; e.g., 35 minutes past 2 is 25 minutes to 3; write the missing number on the blank, counting by 1s-10s; write even/odd numbers
1036NZ Character Objective: Respectful
Coins & Amount
5, 10, 20 50 cents; Cents – addition, subtraction. Addition with carrying, Subtraction with borrowing; How many 5 cents; Number of items which can be purchased; Word problems.

Math PACE’s 1037-1048
1037 Character objective: Committed
Count from 1-100, using dot-to-dot; count and write by 1s-9s; compare addition with multiplication; add 3, 1-digit, 2-digit, or 3-digit addends; work word problems with 3, 2-digit addends; time addition facts (oral); add and “carry” 2 digits plus 1 digit; “borrow” and subtract 2 digits minus 1 digit; work subtraction facts and check by addition; multiply 0s-9s; learn numbering trick for knowing 1 digit x 9; time multiplication facts (written); multiply 2 or 3 digits times 1 digit; multiply a number times 10 (add 0 to end of number); work word problems, including addition, subtraction, and multiplication; color a picture in designated colors, use a pictograph to answer questions; write time as “minutes after” or “minutes to;” compare numbers as greater/less than; complete the pattern of geometric shapes
1038 Character objective: Consistent
Count from 101-200, using dot-to-dot; count and write by 11s; add and “carry” 2 digits plus 2 digits; work word problems with add and “carry” 2 digits plus 2 digits; write 3-digit numbers in expanded form; add “borrow” and subtract 2 digits minus 2 digits; work word problems with “borrow” and subtract 2 digits minus 2 digits; time subtraction facts (oral); multiply 0s-9s; work word problems with multiplication facts; multiply 11s; multiply 2 or 3 digits times 1 digit; circle objects in groups of 2; use a number line to divide by 2; divide by 2; circle objective
1039 Character objective: Decisive
Count and write by 4s-11s; add 4, 1-digit, 2-digit, or 3-digit addends; work word problems with 4, 2-digit addends; add and “carry” to 10s—3 digits plus 3 digits; “borrow” and subtract from 10s---3 digits minus 2 digits or 3 digits; work word problems with “borrow” and subtract from 10s—3 digits minus 3 digits; multiply 0s-11s; work word problems with multiplication facts; multiply 2 or 3 digits times 1 digit; time multiplication facts (written); write the missing factor (N) in multiplication facts; write even/odd numbers; multiply 5 by even/odd numbers to get answer ending in 0 or 5; divide by 1,2, or 3, using multiplication to find quotient; divide by 1, 2, or 3 and check by multiplication; round numbers on a number line to the nearest 10
1040 Character objective: Discerning
Count from 401-500, using dot-to dot; alternate adding 2 digits plus 2 digits with subtracting 2 digits minus 2 digits; work word problems, alternating adding 2 digits plus 2 digits with subtracting 2 digits minus 2 digits; alternate adding 3 digits plus 3 digits with subtracting 3 digits minus 3 digits; work word problems, alternating adding 3 digits plus 3 digits with subtracting 3 digits minus 3 digits; alternate adding 4 digits plus 4 digits with subtracting 4 digits minus 4 digits; work word problems, alternating adding 4 digits plus 4 digits with subtracting 4 digits minus 4 digits; add and “carry” to 100s—3 digits plus 2 digits; “borrow” and subtract from 100s—3 digits minus 2 digits; multiply 0s-11s; time multiply 0s-11s; write answers in multiplication table; compare multiplication facts as greater/less than; work word problems with multiplication facts; multiply and “carry” 2 digits times 1 digit; work word problems with multiply and “carry” 2 digits times 1 digit; divide by 1, 2, 3, or 4 and check by multiplication; divide by 4, using multiplication to find quotient; answer questions, referencing a bar graph; round numbers on a number line to the nearest 5 or 10; write the missing number in the box for addition, subtraction, and multiplication facts; write 3-digit numbers in expanded form
1041 Character objective: Faithful
Count from 501-600, using dot-to-dot; add and “carry” to 100s—3 digits plus 3 digits; write numbers to complete addition square; “borrow” and subtract from 100s—3 digits minus 3 digits; multiply 0s-9s; work word problems with multiplication facts; multiply 2 digits times 1 digit, 2 digits times 2 digits; work word problems, multiplying 2 digits times 2 digits; multiply and “carry” 2 digits times 1 digit; work word problems with multiply and “carry” 2 digits times 1 digit; write answers in multiplication table; use multiplication table to work division facts; divide by 1-4 and check by multiplication; divide by 5, using the multiplication table; divide by 5 and check by multiplication; time divide by 1-5 (written); compare numbers as greater/less than; complete the pattern of geometric shapes; write Roman numerals 1-10; 11-50; work word problems with Roman numerals converted to numerals and subtracted or placed as time on clock; write same time as “minutes past” and “minutes to”
1042 Character objective: Generous
Time addition/subtraction facts; add and “carry” to 10s and 100—3 digits plus 2 digits; work word problems with add and “carry” to 10s and 100—3 digits plus 2 digits; write answers to complete addition square; “borrow” and subtract from 10s and 100s—3 digits minus 2 digits; work word problems with “borrow” and subtract from 10s and 100s—3 digits minus 2 digits; work word problems with multiplication facts; time multiplication facts (written); multiply 2 digits times 1 or 2 digits; multiply and “carry” 2 digits times 1 or 2 digits; work word problems with multiply and “carry” 2 digits times 2 digits; divide by 6, using the multiplication table; divide by 1-6 and check by multiplication; write division problems, using divide signs; work word problems, dividing by 3-6; divide by 6 and check by multiplication; work problems, showing how multiplication and division work together (4 x 2 + 8, so 8 divided by 2 = 4 and 8 divided by 4 = 2); answer questions, referencing a bar graph
1043 Character objective: Kind
Count from 601-700, using dot-to-dot; add 3, 1-digit or 2-digit addends; add and “carry” to 10s—3 digits plus 1 or 2 digits; add and “carry” to 10s and 100s—3 digits plus 3 digits; work word problems with add and “carry” to 10s and 100s—3 digits plus 3 digits; add and “carry” to 10s and 100s—3 digits plus 3 digits, and check by subtraction; “borrow” and subtract from 10s and 100s—3 digits minus 3 digits, and check by addition; work multiplication facts; time multiplication facts (written); multiply and “carry” 2 digits times 1 or 2 digits; work word problems with multiply and “carry” 2 digits times 1 or 2 digits; write answers in multiplication table; divide by 2-6 and check by multiplication; divide by 7, using multiplication table; divide by 7 and check by multiplication work word problems, dividing by 7; divide by 2-7 with remainders; break down a division problem into its division, multiplication, and subtraction components and answer each part separately; answer questions, referencing a bar graph; round numbers on number line to the nearest 5 or 10; write number words in expanded form and as numbers
1044 Character objective: Optimistic
Count from 701-800, using dot-to-dot; count from 801-900, using dot-to-dot; count and write by 2s and 4s—forward/backward; add 3, 1-digit or 2-digit addends; add and “carry” to 10s and 100s—3 digits plus 2 or 3 digits; time addition facts (written); add and “carry” to 10s and 100s—3 digits plus 2 or 3 digits; “borrow” and subtract 2 digits minus 1 or 2 digits; “borrow” and subtract from 10s—3 digits minus 1 digit, from 10s and 100s—3 digits minus 2 or 3 digits; time subtraction facts; “borrow” and subtract 3 digits minus 2 or 3 digits, and check by addition; work multiplication facts; time multiplication facts (written); work word problems with multiplication facts; multiply and “carry” 2 digits times 1 or 2 digits; multiply and “carry” to 10s and 100s—3 digits times 1 digit; divide by 1-7 and check by multiplication; divide by 8, using the multiplication table; divide by 8 and check by multiplication; divide by 2-7 with remainders; divide by 8 with remainders; work a mix of addition, subtraction, multiplication, and division facts, having a number in common; work word problems with dividing by 3-8; match the words addends, sum, minuend, subtrahend, difference, multiplier, multiplicand, and product to the correct numbers in problems; write numbers in place value and expanded form; write the missing number in the sequence; work elapsed-time problems
1045 Character objective: Prudent
Count from 901-1000, using dot-to-dot; count and write by 1s-9s; add and “carry” 2 digits plus 1 or 2 digits; add and “carry” to 10s—3 digits plus 3 digits; add and “carry” to 100s-3 digits plus 2 or 3 digits; add and “carry” to 10s and 100s—3 digits plus 2 or 3 digits; “borrow” and subtract from 10s—2 digits minus 1 or 2 digits, 3 digits minus 2 or 3 digits; “borrow” and subtract from 100s—3 digits minus 2 or 3 digits; “borrow” and subtract from 10s and 100s—3 digits minus 2 or 3 digits; match addition problem with multiplication problem; work multiplication facts; work word problems with multiplication problem; work multiplication facts; work word problems with multiplication facts; multiply and “carry” 2 digits times 1 or 2 digits, 3 digits times 1 digit; multiply and “carry” multiples of 10 times 2 digits; work word problems with multiply and “carry” 2 digits times 2 digits; divide by 2-8 and check by multiplication; divide by 9, using fill in the blank multiplication and multiplication table; work word problems, dividing by 9; divide by 2-8 with remainders; divide by 9 with remainders; match division problem with its multiplication counterpart; complete the pattern of geometric shapes; identify addends, sum, minuend, subtrahend, difference, multiplier, multiplicand, and product; write numbers in place value and expanded form; write how many sides are found in a circle, square, rectangle, triangle, and pentagon; work elapsed-time word problems
1046NZ Character Objective: Secure
Numbers – more or less; coins & amount – 5, 10, 20, 50 cents, dollar; cents – addition, subtraction; multiplication; dollars and cents – addition with and without carrying; subtraction with and without borrowing, word problems; counting change – word problems; number words – ones, ones and tens, tens, two words, how many.
1047NZ Character Objective: Punctual
Measurement of time; measurement of length – centimetres, ½ centimetres, metre; measurement of weight; measurement of liquids – cup, litre, 2 litres, 4 litres, same measures of volume; multiplication – carrying to hundreds – 3 digit x 1 digit =, 3 and 4 digits, carrying to tens and hundreds – 3 digit x 1 digit = 3 and 4 digits; ordinal numbers - first through twentieth.
1048 Character objective: Virtuous
Count pennies, nickels, and dimes; learn dollar as equal to 100 pennies, 20 nickels, 10 dimes, or 4 quarters; add/combine coins to equal a dollar or more; use $ with decimal point in dollars and cents; add 2 digits plus 2 digits with $ and decimal; add 3 digits plus 3 digits with $ and decimal; add and “carry” to 10s and/or 100s—3 digits plus 3 digits with $ and decimal; subtract 2 digits minus 2 digits with $ and decimal; subtract 3 digits minus 3 digits with $ and decimal; match amount to price of item; match amounts that are the same; determine change after purchase, using picture of coins; work multiplication facts in cents; multiply and “carry” to 10s and/or 100s—3 digits times 1 digit; divide by 2-9 and check by multiplication; divide by 2-9 with remainders; color a picture in designated colors; measure objects in inches and centimetres; convert inches to feet, feet to yards, inches to yards; add/subtract like fractions; read scale in pounds; convert cups to pints, pints to quarts, quarts to gallons

MATH PACE’s 1049 - 1060
1049 Character objective: Compassionate
Count and write by 1’s 10’s and/or 100’s and 1000’s. Add and carry to 10’s, 100’s, and 1000’s. Work addition facts. Add 3 or 4, 3-digit addends. Borrow and subtract from 10’s 100’s write numbers in expanded form to thousands. Work multiplication facts, time multiplication facts. Multiply tens by adding 0 to numbers. Work word problems with multiplication. Work division facts and check with multiplication. Divide by 2 -5 with remainders. Write fractions using shaded shapes. Match 4 – digit numbers with number words.
1050 Character objective: Content
Addition; 3 and 4 digits with checking; subtraction; 3 and 4 digits with checking; multiplication; basic facts 0-10; division; by 1-3 with checking; by 2 with remainders; multiplication; 2 digits with carrying. Fraction work, using shaded shapes. Recognizing the numerator and denominator. Writing number words.
1051 Character objective: Deferent
Addition; 4 digits with checking; subtraction; 4 digits with checking; multiplication; 2 digits; division by 1-4 with checking; by 2 and 3 with remainders. Factoring with fractions. Learning fraction vocabulary
1052 Character objective: Discreet
Addition; basic facts timed test; 4 digits with checking; subtraction; basic facts timed test; 4 digits with checking; multiplication; basic facts timed test; 2 digits; division by 1-5 with checking; by 2-4 with remainders. Reducing and adding like fractions.
1053 Character objective: Fearless
Addition with carrying 3 digits and checking; subtraction with borrowing; 4 digits with carrying; multiplication; 2 and 3 digits; division by 1-6 with checking; by 2-5 with remainders. Subtract like fractions. Rounding with estimation. Write even odd numbers
1054 Character objective: Gentle
Addition with carrying; 3 digits with checking; subtraction with borrowing; 3 digits with checking; multiplication; 3 digits; division by 1-7 with checking; by 2-6 with remainders. Add/subtract like fractions. Write numbers for number words. Find the perimeter of shapes. Estimate and add or multiply numbers.
1055 Character objective: Loyal
Addition with carrying; 3 and 4 digits with checking; subtraction with borrowing; 3 and 4 digits with checking; multiplication; 2 and 3 digits; division by 1-8 with checking; by 2-7 with remainders. Multiply fractions by cancellation. Roman numerals 1- 20. Drawing line of symmetry on objects. Recognizing geometry shapes.
1056 Character objective: Patient
Addition with carrying; subtraction with borrowing; 3 and 4 digits with checking; multiplication; 2, 3, and 4 digits; division by 1-9 with checking; by 2-9 with remainders. Add/subtract fractions. Write proper improper fractions. Subtract mixed numbers. Determining intersecting and parallel lines. Write number from expanded form. Write Roman numerals to 375
1057 Character objective: Purposeful
Addition; basic facts times test; subtraction; basic facts timed test; subtraction; basic facts timed test; division by 1-11 with checking; by 2-9 with remainders; Divide fractions by fractions. Fractions and mixed numbers
1058 Character objective: Self-controlled
Addition; 4 digits; subtraction; 4 digits; multiplication; 4 digits; division by 1-12 with checking; by 2-11 with remainders. Find LCD of 3 fractions; add. Divided whole numbers by fractions. Roman numerals
1059 Character objective: Thorough
Addition; 4 digits; subtraction; 4 digits; multiplication; 4 digits; division by 1-12 with checking; by 2-12 with remainders; greater than > and less than <; Using clocks and calendars.
1060NZ Character Objective: Appreciative
Count dollars and cents; to study the metric system of measurements of length, weight, and liquid volume.

MATH PACE's 1061-1072
1061 Character objective: Concerned
Division by 1-12 with checking; multiplication; 3 and 4 digits with checking; subtraction; 4 digits with borrowing; addition; 4 digits with carrying; Find the LCD of 2 or 3 unlike fractions. Write Roman numerals for numbers. Referencing bar graph.
1062 Character objective: Cooperative
Whole numbers; addition; subtraction; multiplication; division (divisors up to 99); Add/subtract like/unlike fractions or mixed numbers. Change improper fractions to whole or mixed numbers. Add/ subtract decimals. Write decimals as proper fractions
1063 Character objective: Dependable
Whole numbers; addition; subtraction; multiplication; division (divisors up to 999); Multiply/ divide fractions or mixed numbers. Draw line segments, lines or intersecting and parallel lines. Draw lines of symmetry and geometry shapes. Draw angles.
1064 Character objective: Efficient
Whole numbers and fractions; addition; subtraction; multiplication; division; read and write numbers correctly; word problems Multiply/divide decimals. Angles with protractor. Parallel and perpendicular lines
1065 Character objective: Flexible
Whole numbers and fractions; addition subtraction; multiplication; division. Writing decimals; rounding numbers. Drawing angles with protractor. Find the measure of third angle of a triangle
1066 Character objective: Honesty
Add and carry 6 3 –digit addends; find the missing addend borrow and subtract multiply and divide 3-4 digits; Borrow and subtract mixed numbers. Compare decimals and fractions. Rounding numbers to nearest 10, 100, 1000 or 10 000; Find the perimeter/area of geometric objects.
1067 Character objective: Meek
Add/subtract/multiply fractions or mixed numbers. Work word problems with fractions; add/subtract decimals. Multiply decimals; divide decimals; change decimals to fractions; referencing line/ bar graph. Compute circumference of a circle
1068 Character objective: Peaceful
Review of fractions; addition; subtraction; multiplication; division; review of decimals; addition; subtraction
1069 Character objective: Resourceful
Mixed numbers; addition; subtraction; multiplication; division; decimals; addition; subtraction; multiplication; roman numerals through one thousand
1070 Character objective: Sincere
Decimals; addition; subtraction; multiplication; review of fractions; addition; subtraction; multiplication; division; division of decimals. Review of roman Numerals
1071 Character objective: Thrifty
Review of decimals and mixed numbers; addition; subtraction; multiplication; division; metric system of measurement; length, weight, volume. Write ratios and proportions, change fractions to percents; multiply/divide percent times whole number
1072NZ Character Objective: Attentive
Equate dollar to pennies, nickels, dimes or quarters. Give change. Convert meters to centimeters millimeters, or kilometers. Using 20, 50 and 100 dollar notes.

MATH PACE’s 1073 – 1084
1073 Character objective: Confident
Whole numbers, mixed numbers and common fractions. Mathematical vocabulary: minuend, quotient, numerator, denominator
1074 Character objective: Courageous
Decimals and fractions; change decimals to fractions; multiply and divide fractions; reduce answers to lowest terms; proper mathematical vocabulary—dividend, multiplicand, product; simplify
1075 Character objective: Determined
Ratio; proportions; percent; change fractions to decimals; find the number when a percent is known;
1076 Character objective: Equitable
Data and graphs; mean, mode, median, range, rank, and read; translation of Roman numerals into Arabic numbers
1077 Character objective: Forgiving
Arithmetic in business; profit and loss; commission; discount; successive discounts; bills and receipts; invoices with discounts; word problems
1078 Character objective: Humble
Business methods at home; financial freedom; keeping cash accounts; keeping household accounts; budgets; insurance (fire); reading gas and electric meters
1079 Character objective: Merciful
Money; banks; savings accounts; checking accounts; deposits; interest; loans;
1080 Character objective: Perseverant
Using metric measures: length mass, volume, temperature
1081 Character objective: Reverent
Basic geometry; points, lines, rays, angles, etc.; use of protractor; measure angles; construct angles; add and subtract angles; geometric symbols
1082 Character objective: Submissive
Geometric vocabulary; use of compass and straightedge; geometric constructions; bisect angles; parallel lines; right angles; triangles; polygons; finding perimeter
1083 Character objective: Tolerant
Perimeter and area; polygons; circles; solids; surface area; volume; vocabulary and symbols
1084 Character objective: Available
Introduction to equations; one variable; sets; set notation; vocabulary and symbols;

Math PACE’s 1085 – 1096 (Maths Overview) 1 Credit
1085 Character objective: Considerate
Tables and graphs; preparation; use; rate, time, and distance
1086 Character objective: Creative
Equation solving; one step; two step; opposite operations with fractions; fractions; addition; subtraction; multiplication; division
1087 Character objective: Diligent
Equations from written problems; formula equations in problem solving; new formulas from old formulas; percentage problems solved by equations
1088 Character objective: Fair
Volume and surface area formulas; prism; cylinder; pyramid; cone; sphere
1089 Character objective: Friendly
Identifying proper and improper fractions and mixed numbers; calculating prime factors; simplifying and comparing fractions; multiplying fractions and decimals; dividing fractions and decimals; dividing fractions and decimals; identifying decimals to millionths
1090 Character objective: Joyful
Use of Pythagorean Theorem; use of right triangles to find height and distance; finding hypotenuse of a right triangle; square root
1091 Character objective: Observant
Banks; interest; discounts; savings; deposits; simple interest; compound interest; financial freedom
1092 Character objective: Persuasive
Mortgages; investments; real estate (land and buildings); stocks and bonds; Biblical implications
1093 Character objective: Responsible
Taxes; Federal taxes, income taxes; F.I.C.A.; property taxes; sales taxes finding tax rates
1094 Character objective: Tactful
Insurance; premiums; policies; life; fire; car
1095 Character objective: Truthful
Use metric system to solve problems; length, weight, volume; Solve problems in area using metric system, solve problems in solid and fluid volume using the Metric system
1096 Character objective: Committed
Positive and negative numbers; line graphs with + and – numbers plotted; adding and subtracting; positive to a negative; negative to a positive; positive to a larger negative; positive to a smaller negative

Math PACE’s 1097 – 1108 (Algebra I) 1 Credit
1097 Character objective: Consistent
Definitions of algebra, signs of operation; algebraic expressions; exponents, radical signs, powers, and roots; order of operations for combining terms; positive and negative numbers; adding; subtracting; multiplying; dividing; starting numerical relationships
1098 Character objective: Decisive
Solving and providing algebraic equations; equations with one variable; axioms for solving algebraic equations; transposing terms in algebraic equations; cancelling terms in algebraic equations; simplifying equations by multiplying or dividing; equations with parenthesis; word problems
1099 Character objective: Discerning
Review of monomials; addition—subtraction; multiplication—division; polynomials in proper order; addition—subtraction; multiplication—division Review of basic math and algebra
1100 Character objective: Faithful
Using parenthesis, brackets, and braces in algebra; multiplying binomials horizontally; recognizing the difference of two squares; factoring the difference of two squares; recognizing a perfect square trinomial; factoring a perfect square trinomial; factoring polynomials
1101 Character objective: Generous
Algebraic fractions; reducing—simplifying; addition—subtraction; multiplication—division; simplifying complex fractions; substituting numerical values and simplifying; solving and proving fractional equations; word problems
1102 Character objective: Kind
Simple simultaneous equations; addition and substitution; algebraic graphs; linear equations; consistent, inconsistent, and dependent equations; word problems
1103 Character objective: Optimistic
Recognizing sets and subsets; stating the union and intersection of sets; using Venn diagrams; inequalities with one unknown; recognizing; solving; graphing; conjunctions and disjunctions; solving; graphing; inequalities with two unknowns; solving; graphing
1104 Character objective: Prudent
Reviewing multiplying and dividing terms with exponents; reviewing the rule for zero exponents; changing terms with negative exponents to terms with positive exponents; finding roots and powers of expressions; using fractional exponents; simplifying radical terms; finding square roots; using the Pythagorean Theorem
1105 Character objective: Secure
Radical equations; incomplete quadratic equations; simplifying radical solutions; quadratic equations; factoring; completing the square; quadratic formula; word problems
1106 Character objective: Temperate
Translating word problems to algebraic equations; solve and check averages, percent, and interest; area and volume; numbers and quantities; monetary value
1107 Character objective: Virtuous
Ration and proportion; evaluating formulas; relationship between variables in formulas; stating and solving problems about work, about money, about mixtures
1108 Character objective: Compassionate
Review of concepts taught in Algebra PACE’s 1097-1104; comprehensive final test

MATH PACE’s 1109 -1120 (Geometry) 1 Credit
1109 Getting acquainted with geometry; section one points, lines, and circles; basic constructions; section two angles (with constructions); properties on equality; section three; triangles (SSS, SAS, ASA, Postulates)
1110 Introduction to proofs; section one; deductive reasoning; introduction to formal proofs; section two; congruent triangles; section three; congruent right triangles
1111 Parallel lines and constructions; section one; parallel lines (basic proofs); transversals intersecting parallel lines; section two; proving converse of theorem; angles of a triangle; section three; construction theorems
1112 Polygons and quadrilaterals
Section one; types of polygons; angles of polygons; types of quadrilaterals; section two; theorems concerning parallelograms; section three; rectangles, rhombuses, squares, and trapezoids
1113 Loci and circles
Section one; locus; section two; circumference and area of circles; central angles and arcs; arcs and chords; section three; tangents; theorems of tangency
1114 Measurements of angles in a circle; section one; inscribed and circumscribed polygons; an inscribed angle and its measure; section two; angles formed by a tangent and a secant; angle between two secants intersecting within a circle; angles formed by two secants, two tangents, or a tangent and a secant; section three; circle constructions
1115 Inequalities
Section one; exterior angle theorem; triangle inequality corollary; hinge theorem; converse of the hinge theorem; section three inequalities in circles
1116 Ratios and proportions
Section one; ratios; proportions and properties of proportions; similar polygons (continued); segment proportionality; constructing proportional segments; section three; angle bisection and proportionality
1117 Similar polygons
section one; similar polygons; angles equal; lines proportional; section two; similar polygons; 3. sides proportional; section three; similar polygons
1118 Areas of polygons; section one; rectangle, parallelogram, triangle, equilateral triangle; section two; rhombus, trapezoid, irregular polygons, similar triangles, similar polygons, triangles, Pythagorean theorem; section three; pyramid, cone, cylinder, prism, sphere
1119 Regular polygons and measurement of the circle; section one; inscribed and circumscribed circles; theorems about regular polygons; section two; constructions: inscribe as square, regular hexagon, equilateral triangle, other regular polygons; theorems about regular polygons; section three; measurement of the circle
1120 Transformations; section one; reflections; reflections across a point; isometries; applications of reflections; section two; translations; rotations; glide reflections; section three; symmetry; dilations; properties of dilations

MATH PACE’s 1121 -1132 (Algebra II) 1 Credit
1121 A review of set theory and an introduction to real number axioms and applications
1122 Arithmetic and geometric sequences and series and sentences with one variable
1123 A study of linear equations and graphs—solving by linear combinations and substitutions
1124 A study of multiplying polynomials and factoring—factoring monomials, squares, groups, and open sentences
1125 A study of fractions and operations, fractions and equations, and rational numbers as decimals
1126 A study of first and second degree functions
1127 A study of radicals and operating with radicals and a study of complex numbers
1128 A study of quadratic equations, quadratic solutions, and polynomial functions
1129 A study of quadratic relations, conic sections (parabolas and hyperbolas), and quadratic systems
1130 A study of computations, exponential functions, logarithms, and antilogarithms
1131 A study of permutations, combinations, binomial expansions, and a probability
1132 A study of matrices and their properties, determinants of equations, and systems of equations

BUSINESS MATH 1 Credit
A course designed to review, addition, subtraction, multiplication, and division of whole numbers: fractions, decimals, and percents; and applies math skills to various practical situations, in the home and business world.
109 A review of the addition of whole numbers, common fractions, and decimals
110 A review of the subtraction of whole numbers, common fractions, and decimals
111 A review of the multiplication of whole numbers, common fractions, and decimals
112 A review of the division of whole numbers, common fraction, and decimals
113 A study of percentages
114 An application of arithmetic to the hourly wage system, the salary, and the commission
115 A study of figuring checking accounts and savings accounts , budgets, and home and auto ownership
116 A study of figuring taxes: local, state, and federal
117 A study of insurance and its mathematical problems
118 A study of discounts: trade, cash, banks, and retail
119 A study of purchasing and pricing goods and profit
120 A study of mathematics of the wholesaler and the manufacturer

ACCOUNTING 1 Credit
For above-average students. This course is designed to acquaint the students with the nature, scope, vocabulary, and techniques of accounting.
121 Introduction to the concepts of accounting, the business transactions, and the balance sheet.
122 A study of accounts, the process of journalizing, and making a trial balance.
123 A study of the accounting period, adjusting the accounts, and completing the accounting process
124 A study of accounting for revenue gained by sales and lost purchases
125 A study of the elements of the manual accounting system: journals, ledgers, and special records.
126 A study of assets: their nature, fixed assets, depreciation, amortization, and depletion
127 A study of cash, notes receivable, and accounts receivable
128 A study of inventory and its special problems
129 A study of liabilities (current and long-term) and working capital utilization
130 A study of accounting for taxes and handling the payroll
131 A study of partnership
132 A study of corporations

TRIGONEMETRY  1133-1138

1133 To review properties of angles and triangles. Learn definitions of the six trigonometric functions for acute angles.  Find the values of the trigonometric functions using a graphing calculator.  Establish and use basic trigonometric identities. 

Show that the values of the trigonometric functions depend only on the angle. Solve problems involving right triangles Begin a study notebook for trigonometry.   Study the eternal nature of God and His plan for mankind. Memorise Revelation 1:8; 2 Corinthians 4:18 and Hebrews 5:9.

1134  Review properties of the Cartesian coordinate plane.  Measure angles in both degrees and radians.  Define the six trigonometric functions for any angle. Understand the trig functions are well defined. Find reference angles and know how to use them. Use the unit circle to find values of the trig functions. Use identities and quadrants to find missing trig values. Study the well-defined plan of God for all mankind. Memorise Hosea 2:23; Acts 10:45 and Isaiah 45:22.

1135 Convert among speeds associated with a tire.

Express intervals of real numbers in interval notation. Graph the sine and cosine functions by

plotting points. Graph all six trig functions using a graphing calculator. Find the domain, range and

period of a trig function. Determine the amplitude of a sine or cosine function. Identify special points

on a graph using a graphing calculator.  Study how God’s dependability is evident in His Creation. Memorise Ecclesiastes 1:5, Ecclesiastes 1:9 and Hebrews 13:8.

1136  Convert data to a more convenient form. Create a scatter plot for a set of bivariate data.  Use sinusoidal regression to model data.  Verify trigonometric identities. Learn several more important sets of identities. Define the inverse functions for sine, cosine and tangent.  Find angle measures for the length of the sides of a triangle. Study the relationship between man’s plans and God’s sovereignty. Memorise Luke 14:28, Luke 12:20 and Ecclesiastes 1:15.

1137 Solve trig equations graphically. Solve trig equations algebraically using the unit circle. Solve trig equations algebraically using the inverse trig functions. To find missing lengths and angle measures using the Law of Sines. To find missing lengths and angle measures using the Law of Cosines. Distinguish among AAS, ASA, SAS, SSS, and the Ambiguous Case. Find the areas of triangles using trigonometry. Study God’s solutions to man’s problems. To memorise 1 Corinthians 10:13, Deuteronomy 31:8, and John 19:30.

1138 Conclude our study of triangles. Model simple harmonic motion. Learn the polar coordinate system and graph equations in the polar plane. Convert equations and points between rectangular and polar coordinates. Review complex numbers and complex number arithmetic.  Graph complex numbers as points in a plane.  Multiply complex numbers in polar form and find powers and roots of complex numbers. Realise our in-complete understanding of God. Memorise 1 Corinthians 2:7, 1 Corinthians 13:12, and 1 Timothy 3:16.

SENIOR MODERN MATH I 1-10

1  The graphic calculator.

2  Variation. Ratios and rates, direct variations, inversevariations, joint variations, part variations

3  Application of Trigonometry Ratios. Directions, bearings, contour lines and maps. Geometrical facts, angles of elevation and depression, directions and bearings, contour lines and maps, and average slope. Three-dimensional problems.

4  Arithmetic and Geometric Progressions. Study of arithmetic and geometric mean and means, series, the sum of numberical terms and sequence models, recurring decimals.

5  Univariate Data. Variables, collection of data, categorical data and numerical data. Line plots, pie charts, bar graphs, line graphs, useful processes to be interpolated and extrapolated, stem-leaf plots. Outliers, stem plots with multiple digits, frequency distributions, frequency density, histograms, frequency polygons, distributions and cumulative frequency curve. Locations, percentiles, quartiles, median, box plots and outliers and their effects. parity, complementary, periodicity and phase properties. Trigonometric graphs by transformations including translations, dilations and reflections. Amplitude, periods, domains and range from graphs.

6  Indices and Logarithmic Functions. Incorporate the index form, rational indices, exponential functions and indicial equations. Definition and laws of logarithms. Solve indicial equations which contain exponents.

7 Growth and Decay of Money. Compound interest, investment models. Interest periods, growth

adjustments, contrast investments. Depreciation, flat rate depreciation, reducing balance depreciation, unit cost depreciation. inflation rates and radioactive decay.

8  Data Descriptors. Grouped and ungrouped data. Mean using classic intervals. Mean and standard deviation. Median, mode and skewed data. Study population, samples and parameters. Effect of change of origin and scale and weighted averages.

9  Relations and Functions. Describe function relations. Define table values, domain, and odd and even functions. Sketch various graphs to test and model. Permissible x and y functions and relationships including straight lines, parabolas, exponentials and hyperbolas. Linear functions. Recognizing graphs. Reflection, dilation, translation.

10 Periodic Functions. Radian measure. Geometrical definitions of tangent functions, specific periodic functions, reciprocal trigonometric functions and special angles.

11 Introduction to Differentiation. Tangents and secants, limits and continuity. theorems and points of discontinuity. Derivative of a function and differentiation. Differentiation rules relating to a constant, a power, a constant times a function, the sum of two functions, and the difference of two functions.

SENIOR MODERN MATH II 12-20

12 Algebraic Graphs. Domains, ranges; sketch graphs of various polynomial functions. Rational functions, reciprocal functions, absolute values of functions, inverse of functions. Asymptotes, applications and families of polynomials.

13 Trigonometric Graphs. Circular functions such as quadrants, symmetry properties of circular functions and their signs. Graph sine, cosine and tangent. Pythagorean, parity, complementary, periodicity and phase properties. Trigonometric graphs by transformations including translations, dilations and reflections. Amplitude, periods, domains and range from graphs.

14 Application of Derivatives. Algebraic and geometric derivatives. derivative notion and the second higher derivatives. Rate of change of a function due to time. Velocity and acceleration.

15 Anti-differentiation. Properties of integration, application of anti-differentiation, families of curves, approximate integration and approximation integration.

16 Differentiation Rules. Concepts of continuity limits. The chain rule, product rule, quotient rule.

17 Discrete Probability Distribution. Random variable, secret probability distributions and functions. Expected value, expectation theorems, applications, variance of a random variable, standard deviation, application of standard deviation, quality control. Binomial probability distribution, Bernoulli trials, application of binomial distributions, effect of parameters, the mean and variance of binomial distributions and binomial theorem.

18 The Normal Distribution. Parameters of the normal distribution, properties of its curve. Properties of standard normal curve, cumulative normal distribution table, approximation of binomial distribution. Confidence limits.

19 Circular, Exponential and Logarithmic Functions. Derivatives of circular functions, integrals of

exponential and logarithmic functions. Practice and application of rules.

20 Applications of the Integral. Numerical integration, midpoint and trapezium rules. Infinite integrals and reduction formulas.

Area between two curves, solid resolutions and related rates.

21 Hypothesis Testing.

Assessing data consistency, within given parameters, Binomial and normal distribution tables.

COLLEGE MATHS 1-10

An introduction to various mathematical concepts. This course covers such topics as sets, logic, functions, and mathematical systems.

1 A study of sets, symbols, roster and set builder notation in defining sets, with emphasis on identifying sets.

2 A further study of sets: power sets, disjoint sets, intersection and union, relative complements of a set, and unary and binary operations.

3 A completion of sets: (infinite sets) and an introduction to logic, defining statements, and quantifiers.

4 A further study in logic: defining the truth as a statement, using a Venn diagram, identifying logically true statements, and logically false statements.

5 Another study of logical reasoning: conditional statements, bi-conditionals, variations on the conditional, and tautologies.

6 An introduction to deductive reasoning: the validity of arguments, theorems, indirect proofs, and invalid arguments.

7 A study in relations and functions, with ways of representing functions, inverses, and special functions.

8 A study of the composition of functions and binary operations.

9 A study of groups: definitions, proving theorems about groups, subgroups, and group generators.

10 A further study of the isomorphisms of groups, rings and subrings, and integral domains and fields.

COLLEGE MATHS (Pre-calculus) 11-20

This course is designed to ready the student for college-Grade calculus. The material covers the entire scope of trigonometry: the functions, inverse functions, combination functions, coordinates, and the function laws.

11 An introduction to pre-calculus, relations, and functions.

12 A study of special functions: linear, second degree, greatest integer, exponential, and logarithmic.

13 A study of the trigonometric functions.

14 A study of the radian measure, and circular functions and their graphs.

15 A study of the properties of circular functions.

16 A study of additional sum and difference formulas, double and half-angle formulas, and trigonometric equations.

17 A study of trigonometric functions of any angle, the law of cosines and sines, and applications problems.

18 A study of the inverse trigonometric functions and graphs.

19 A study of polar coordinates and equations and their graphs.

20 A study of algebraic and trigonometric functions, logarithmic and exponential functions, trigonometric series and equations, and special applications.

CALCULUS 1-10

1 Limits; differentiation and higher derivatives

2 Tangents and normal to curves; stationary points

3 Anti-differentiation; application of the anti-derivative to motion in a straight line

4 Area under a straight line; area under a curve; numerical integration

5 Continuity and limits; gradients; derivatives; rules for differentiation

6 Composite functions and their derivatives; inverse functions and their derivatives; implicit relations and their derivatives; reverse differentiation

7 The derivative of ex; logarithmic functions; integration of exponential functions; the derivative of

sin x and cos x; integration of sin x and cos x

8 Plotting nth degree polynomials; n3; plotting relational functions

9 Integration of special quotients; integration of substitution; integration by parts; areas and solids of

revolution

10 The differential; differential equations of the form dy = k.y; differential equations of the form dy = a.y+c dxdx

APPROVED NON ACE MATH

NZ MATHEMATICS YEAR 7

7-01 Whole Numbers, History of number, How many? The language of number. A numbered world, The number system, Zero, Rounding numbers, Estimation and Approximation, Place value, Number line, Number puzzles.

7-02 Two Dimensional Geometry, Points and Lines, Planes and Polygons, Angles, Perpendicular lines, Triangles and Quadrilaterals Circles.

7-03 Number Facts, Addition and Subtraction, Multiplication & Division by powers of 10, Calculator use, Multiplication and Division, Order of operations, Operations machines (extension), Factors of natural numbers, Prime factors, Multiples of natural numbers.

7-04 Measurement, Units of measure, Perimeter, Area, Metric area units, Area of a rectangle, Volume and Capacity, Calculation volumes and capacities.

7-05 Fractions, Fractions, Representation of fractions, Fractions of regular shapes, Fractions of quantities, Finding the whole from a fraction, Ordering of fractions, Equivalent fractions, Comparing fraction sizes, Problem solving with fractions.

7-06 Decimals, Representing decimals, Using a number line, Using place value blocks, Place value

Value of money, Adding decimal numbers, Subtracting decimal numbers, Multiplying & dividing by powers of 10, Converting fractions to decimals, Percentage, Multiplication with whole numbers

Division by whole numbers, Problem solving.

7-07 Location, Scales, Grids, Maps, Direction, Plans, Coordinates, Locus.

7-08 Solids, Polyhedra, Drawing solids, Making solids from nets, Different views of objects, Intersection of solids and planes.

7-09 Statistics, Charts & Graphs, Sampling, Organizing data, Displaying data, Interpreting data, Measuring the ‘middle’ of a data set.

7-10 Time, Time lines, Units of time, A date with a calendar, Reading clocks and watches, Clockwise direction, Time tables.

7-11 Algebra, Number patterns (sequences), Dot patterns, Matchstick patterns, Rules and problem solving, Graphing patterns, Using word formulae, Converting words to symbols, Using a spreadsheet

Algebraic expressions.

7-12 Geometry, The language of transformations, Translations, Reflections, Rotations, Enlargements and reductions, Tessellations.

7-13 Chance, Describing chance, All possible results, Probability, Statistics and probability, (extension), Life insurance tables (extension).

NZ MATHEMATICS YEAR 8

8-01 Whole Numbers, The number system, Maori numbers, Rounding numbers, Operations with whole numbers, Estimation and Approximation, Place value, How big is one million?, Numbers beyond one million, A numbers game, History of number.

8-02 Algebra, Geometric patterns, Number patterns, Formulae and variables, Discovering formulae

Practical problems using formulae, Solving equations, Graphs of real life situations.

8-03 Number properties, Operation with numbers, Order of operations, Number line, Factors of natural numbers, Multiples of natural numbers, Square numbers, Divisibility rules, Powers or index numbers, Powers with base 10 Roman X–word.

8-04 Fractions, Fractions are everywhere, Representation of fractions, Fractions of regular shapes

Equal (equivalent) fractions, Simplest form, Fractions of quantities, Finding the whole from a fraction, Ordering of fractions, Comparing fraction sizes, Problem solving, Activities with fractions.

8-05 Angles, Angles, Using a protractor, Angles of a triangle, Circles, Constructing a triangle, Bisecting and constructing angles, Bearings and directions, Loci

8-06 Decimals, Representing decimals, Fractions as decimals, Place value Ordering decimals Addition and subtraction of decimals, Multiplying and dividing by powers of 10, Multiplying decimal numbers, Decimal approximations, Division of decimals by whole numbers, Large decimal numbers

Terminating and recurring decimals, Converting decimals to fractions.

8-07 Geometry, Transformations, Lines, Polygons, Triangles and quadrilaterals, Euler’s rule, Solids, Nets of solids, Drawing solids, Plans, Number planes

8-08 Percentage, Percentage, Fractions to percentages, Plotting numbers on a number line, Representing percentages, Percentages are all around us, Converting percentages, Geometric representation, One quantity as a percentage of another, Finding percentages of quantities,, Percentages and money, Goods and services tax (GST), Discount, Simple interest.

8-09 Measurement, Units of measurement, Reading scales, Length conversions, Perimeter, The circle, Scale diagrams, Mass, Qualitative data, Speed, Problem solving.

8-10 Time, Time lines, Units of time, Differences in time, Reading clocks and watches, Timetables, Time zones.

8-11 Statistics, Samples and populations, Dot plots, Frequency tables, Bar graphs, Mean, mode and median, Stem-and-leaf plots, Pie charts, Line graphs and time series.

8-12 Chance, Describing chance, Assigning numbers to chance, Defining probability, Tree diagrams.

8-13 Area and Volume, Area units, Area of a rectangle, Area of a triangle, Volume of capacity, Volume, Capacity, Problem solving.

NZ MATHEMATICS YEAR 9

9-01 Geometry (Objects and Drawings), Measuring angles, Classifying and naming angles

Complementary and supplementary angles, Angles in a revolution, Bisecting angles, Constructing 90 angles to a line, Plane shapes, Points and lines, Solids, Nets of solids, Drawing solids, Plans, Paper modelling, Locus.

9-02 Whole numbers, The Maori number system, The number system, Rounding and estimation, Operating with numbers, Divisibility rules, Factors of natural numbers, Exponent (index) notation, Square numbers and square roots, Multiples of natural numbers, Number patterns, Order of operations.

9-03 Integers, Opposites, Integers and the number line, Using a number line to add and subtract

Rules for adding and subtracting, Multiplication of integers, Combined operations, Using your calculator.

9-04 Algebra: Patterns and Models, Geometric patterns, Symbols in algebra, Number crunching machines, Substitution into formulae, Using patterns, Building shapes and things, Expressions with two variables, Algebraic products, Evaluation of algebraic expressions, The distributive law

Factorisation.

9-05 Fractions, Representations of fractions, Improper fractions and mixed numbers, Placing fractions on a number line, Equivalent fractions, Comparing fraction sixes, Adding fractions, Subtracting, fractions, Multiplying fractions, Reciprocals, Division of fractions, Problem solving, Rational numbers, Algebraic fractions.

9-06 Decimals, Place value, Ordering decimal numbers, Addition and subtraction of decimals

Multiplying and dividing by powers of 10, Decimal approximations, Dividing decimal numbers, Multiplying decimal numbers, Solving decimal problems, Terminating and recurring decimals.

9-07 Percentages, Understanding percentages, Interchanging number forms, One quantity as a, percentage of another, Finding percentages of quantities, The unitary method in percentage, Percentage increase or decrease, Finding the percentage change, Business applications of percentage.

9-08 Coordinates and Graphs, Map references, Bearings, Number grids, Interpreting points on a graph, Interpreting line graphs, Constructing graphs, The number plane, Graphing linear relationships

Equations of lines.

9-09 Measurement, Length, Perimeter, Circumference, Areas of polygons, Areas of circles, Volume, Capacity, Mass, Time, 24-hour time.

9-10 Ratio, Proportion and Rate, Ratio, Equal ratios, Equal ratios and proportion, Using ratios to divide quantities, Application of ratios – scale diagrams, Slope, an application of ratios, Rates, Converting rates.

9-11 Equations, Algebraic expressions and equations, Writing equations using symbols, Maintaining, balance, Inverse operations, Building and undoing expressions, Equations with two or more operations, The unknown occurring more than once, The unknown occurring on both sides,, Miscellaneous equations, Problem solving, Inequalities.

9-12 Geometry (Lines, Shapes and Solids), Plane figures, Line pairs, Construction perpendiculars

Classifying triangles, Constructing and drawing triangles, Angles of a triangle, Constructing a 60 angle, Exterior angles of triangles, Quadrilaterals, Angles of a quadrilateral, Interior angles of polygons.

9-13 Statistics, Statistical enquiries (investigations), Populations and samples, Categorical data, Numeric data, Analysing data, Discussion and report writing.

9-14 Chance/Probability, Describing chance, Assigning numbers to chance, The statistics-probability connection, Listing possible outcomes, Tree diagrams, Calculating probabilities, Tree diagrams and probability, Making probability generators.

9-15 Transformation Geometry, Reflection, Rotation, Translation, Enlargement, Properties of transformations.

NZ MATHEMATICS YEAR 10

10-01 Numbers, Integers and order of operations Rational numbers (fractions), Decimal Numbers,, Percentage, Ratio, Rates, Standard form (scientific notation), Significant figures.

10-02 Algebra, The language of mathematics, Changing words to symbols, Evaluation, Collecting like terms, Adding and subtracting algebraic fractions, Multiplying and dividing algebraic fractions, Algebraic simplification and index form, Index laws, Zero indices, Number patterns and rules

10-03 Pythagoras’ Rule, Square roots, Solving equations of the form x2=k, The rule of Pythagoras

The converse of the Pythagorean Rule, Pythagorean triples, Problem solving using Pythagoras

10-04 Percentage and Business Applications, Percentage, The unitary method in percentage, Finding a percentage of a quantity, Percentage increase and decrease, Percentage change using a multiplier

Simple interest, Interpreting graphs and charts.

10-05 Similarity, Trigonometry and Vectors, Similarity, Using scale diagrams in geometry, Trigonometry, The trigonometric ratios, Problem solving with trigonometry, Vectors, Practical problems.

10-06 Measurement, Lengths and perimeters, Area, Surface area, Volume, Capacity, Problem solving

Qualitative data.

10-07 Coordinate Geometry (2-D Graphs), Two dimensional graphs, Plotting points, Linear relationships, Plotting linear graphs, The equation of a line, The slope (gradient) of lines, Graphing lines form equations, Other line forms, Travel graphs.

10-08 Linear Equations and Inequalities, Solution by inspection or trial and error, Maintaining balance

Building expressions and isolating the unknown, Formal solution of linear equations, Equations with a repeated unknown, Fractional equations, Converting into algebraic form, Forming equations, Problem solving using linear equations, Finding an unknown from a formula, Linear inequalities.

10-09 Geometry, (Polygons, Circles & Isometric Drawings), Review of geometrical facts, Triangles, Quadrilaterals and other polygons, Circle Geometry, Drawing solids.

10-10 Statistics, Review, Comparing categorical data, Quantitative (numerical) data, Grouped discrete data, Continuous data, Measuring the centre, Measuring the spread of data, Box-and-whisker plots, Statistics from a graphics calculator, Statistics from a computer package, Comparing and reporting, data, Data collection and misleading graphs, Time series data.

10-11 Algebra, (Expansion, Factorisation & Quadratic Theory), Algebraic expansion, Expanding products of linears, Factorising with common factors, Factorising quadratics, Difference of two squares factorising, Perfect square factorisation, Quadratic equations, Problem solving with quadratics.

10-12 Constructions, Constructing a triangle given its sides, Bisecting angles, Constructing perpendiculars, Angle construction, Finding a circle’s centre, Constructing parallel lines, Regular polygon construction.

10-13 Probability, Probability by experiment, Chance investigations, Sample space, Theoretical probability, Using grids to find probabilities, Multiplying probabilities, Using tree diagrams, Sampling with and without replacement, Expectation, Odds, Further simulation.

10-14 Transformations and Locus, Translations Rotations, Reflections, Enlargements and reductions, Tessellations, Locus.

10-15 NCEA Type Tests for Grade 5, Assessment for achievement standard 1.1, Assessment for achievement standard 1.2, Assessment for achievement standard 1.3, Assessment for achievement standard 1.4, Assessment for achievement standard 1.5, Assessment for achievement standard 1.6

Assessment for achievement standard 1.7, Assessment for achievement standard 1.8, Assessment for achievement standard 1.9.

10-16 Extension Algebra, Adding and subtracting algebraic fractions, Solving fractional equations

Converting into algebraic form, Forming equations, Problem solving using linear equations, Finding an unknown from a formula, Expansions using the distributive law, Factorising involving common factors

Factorising (difference of two squares), Factorising perfect squares Factorising expressions with four terms, Miscellaneous factorising, Problem solving with quadratics, Expansion laws.

NZ MATHEMATICS YEAR 11

11-01 Review of Number Skills, Decimal Approximations, Estimation, Standard form (Scientific notation), Integers, Fractions, Squares and square roots, Order of operations Ratio.

11-02 Percentages and money matters, Review of basic skills, Earning an income, Percentage, change using a multiplier, Appreciation, Compound interest, Depreciation, Borrowing.

11-03 Measurement, Length and perimeter, Area, Surface area, Volume and capacity, Mass and density, Rate, 24-hour time, Accuracy of measurements, Qualitative data.

11-04 Constructions and Loci, Review of key constructions, Triangle properties, Locus, Applications of locus.

11-05 Transformation Geometry, Translations, rotations and reflections, Symmetry, Coordinates in transformations, Enlargements and reductions, Combined transformations.

11-06 Geometry, Review of facts and theorems, Polygons, Circle theorems, Further circle theorems, Cyclic quadrilaterals, Geometric proof, Congruence of triangles, Similar triangles, Problem solving with similar triangles.

11-07 Pythagoras’ Theorem, Pythagoras’ theorem, The converse of Pythagoras’ theorem, Problem solving with Pythagoras, Application of Pythagoras, Three-dimensional problems.

11-08 Trigonometry, Using scale diagrams, Labelling triangles, The trigonometric problem solving, 3-dimensional problem solving, Trigonometric graphs, Areas of triangles, The sine rule, The cosine rule, Problem solving with sine and cosine rules.

11-09 Vectors and Bearings, Vectors, Operating with vectors, Multiplying vectors by a number, Vector subtraction, Length of vectors, Compass bearings, Direction of a vector, Problems solving with vectors and bearings.

11-10 Linear Equations, Inequations & Simultaneous, Equations, Linear equations, Fractional equations, Linear inequalities, Problem solving, Money/investment problems, Motion problems, Mixture problems, Linear simultaneous equations, Problem solving

11-11 Patterns and Algebra (Formulae), Algebraic notation, Simplifying by combining like terms, Algebraic substitution, Formula substitution, Formula rearrangement, Substitution after rearrangement, Formula construction, Formulae by pattern (induction).

11-12 Linear Graphs, Understanding graphs, Distance and displacement graphs, Gradient, Using gradients, Graphing y = mx + c, Vertical and horizontal lines, Equations from graphs, Graphing lines not given in the form y = mx + c, Applications Finding the equation of a line Points on lines, Where lines meet.

11-13 Expanding, Factorising and Solving Quadratic, Equations, Products and expansions, The product (a+ b)(c+ d), Difference of two squares, Perfect squares expansion, Factorisation of quadratic expressions.