Our classes begin with kindergarten (open to 4 1/2 year olds) and currently continue through 8th grade. We add an additional grade each year. Each grade is divided into two semester-long (18 lesson) classes. Classes with A in their title (e.g., KA or 6A) are the first semester of that grade. Classes with B in their title (e.g., KB or 6B) are the second semester of that grade. Both the first and the second semester classes of each grade are taught in the fall and spring semesters, when there is sufficient enrollment.

Accelerated Classes
For grades 1 to 5, we also offer accelerated classes (1A+ to 5B+). Our accelerated classes cover the same material as our regular classes, but do so 50% faster. They allow strong students to complete three semesters of material each academic year rather than the usual two. Accelerated classes also allow struggling students to acquire the skills and understanding they missed in their regular school, while gradually working back up to grade level (and beyond).

Class Descriptions
To learn more about a class, select it from the table below.

	First	Second
Grade	Semester	Semester
Kindergarten	KA	KB
First grade	1A, 1A+	1B, 1B+
Second grade	2A, 2A+	2B, 2B+
Third grade	3A, 3A+	3B, 3B+
Fourth grade	4A, 4A+	4B, 4B+
Fifth grade	5A, 5A+	5B, 5B+
Sixth grade	6A	6B
Seventh grade	7A	7B
Eighth grade	8A	8B

Class Schedules
Visit the Fall 2010 Classes page for a lists of open enrollment fall classes and their times.

Placement Evaluations
Not sure which class your child belongs in? Visit the Placement Evaluations page and to access placement exams for all classes.

KA Classes

Overview: This is the first semester of our kindergarten course. It is open to children ages 4 1/2 and older. Sample problems (pdf)

Meets: Once a week for 1 hour.
Note: Classes may be longer and/or meet more frequently during the summer.

Topics:

• Capacity
• Count to 5
• Different
• Equal Sets
• Length
• Less
• More
• Number Order
• Numbers to 5
• Numbers to 10
• Patterns
• Same / Different
• Sets
• Shapes
• Size
• Weight

KB Classes

Overview: This is the second semester of our kindergarten course. It is open to children ages 4 1/2 and older.

Meets: Once a week for 1 hour.
Note: Classes may be longer and/or meet more frequently during the summer.

Topics:

• Addition
• Comparing Numbers
• Counting On
• Counting Back
• Fact Families
• Making 10
• Number Bonds
• Numbers to 20
• Ordering
• Ordinal Numbers
• Parts and Whole
• Part-Whole Models
• Subtraction
• Ten and Ones
• Writing addition sentences
• Writing subtraction sentences
• Word Problems
• Comparison Models

1A and 1A+ Classes

Overview: This is the first semester of our first grade course.  1A and 1A+ cover the same material. 1A is a normal paced class. It covers the material in 18 lessons. 1A+ is an accelerated class. It covers the material in 12 lessons.

Meets: 1A meets once a week for 1.5 hours; 1A+ meets once a week for 1.75 hours.
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: This class is open to 6-year-olds. Younger children who have sussessfully completed our K-B class or who are proficient at addition and subtraction with single-digit numbers, may also take this class.

Topics:

• Reading and writing numbers up to 10 – To read and write the numerals and number words within 10, understand what they mean, and count up to 10 objects.

• Comparing numbers up to 10 – To compare two or more sets of objects within 10 and understand the meaning of “more than”, “less than” and “same as”.

• Sequencing numbers up to 10 – To understand the relative value of numbers within ten and use that understanding to arrange numbers in ascending or descending order and complete number sequences.

• Challenging problems with numbers up to 10 – To apply knowledge of numbers up to 10 to solve word and other challenging problems.

• Number Bonds – Identify parts in a whole. Make up number stories to illustrate number bonds within 10. Write number bonds for a given number within 10. Find number pairs that make 2, 3, 4, 5, 6, 6, 7, 9, or 10. Find the missing part of a number bond. Review ways to make 10. Review all number bonds.

• Making Number Stories – Understand the meaning of addition. Associate addition with the whole-part concept. Write addition sentences using “+” and “=”.

• Addition with Number Bonds – Relate number bonds and addition sentences. Write two addition facts for a number bond. Relate addition facts within 10 to number bonds.

• Other Methods of Addition (1, 2 or 3 more; counting on) – Use the “count on” strategy to add 1, 2 or 3 to a number within 10. Review number pairs that make 10.

• Making Subtraction Stories – Understand the meaning of subtraction. Associate subtraction with the whole-part concept. Make number stories for subtraction. Compare addition to subtraction. Write addition sentences using  “-” and “=”. Find the missing part of a set using subtraction.

• Methods of Subtraction – Use “taking-away” as a method of subtraction. Relate subtraction within 10 to number bonds. Write a family of 4 addition and 4 subtraction facts for given number bonds. Recall subtraction facts within 5. Use counting back to subtract 1, 2, or 3 from a number within 10. Recognize numbers that differ by 1 or two. Review number pairs that make 10. Determine whether a problem is a subtraction or addition problem.

• Ordinal Numbers – Name a position using ordinal numbers. Compare ordinal numbers to numbers. Find an ordinal position from the left or the right.

• Numbers to 20 – Count to 20 by building up from 10. Relate numbers 11 to 20 to a ten plus ones. Read and write numerals and number words 11 to 20. Count from 20 to 10. Order numbers within 20.

• Addition within 20 – Add two 1-digit numbers using the “make 10″ strategy. Add a 2-digit number within 20 to a 1-digit number.

• Subtraction within 20 – Subtract a 1-digit number form a 2-digit number within 20 when there are enough ones. Subtract a 1-digit number form a 2-digit number within 20 when there are not enough ones by subtracting from the ten. Subtract 1, 2, or 3 from a number by counting back.

• Modeling Word Problems with Whole-Part Models – Review concepts of parts and wholes. Review number bond models. Learn names for terms in addition and subtraction sentences and relate them to parts and wholes. Learn to read and draw part-whole bar models for addition and subtraction. Use whole-part bar models to help solve addition and subtraction word problems.

• Modeling Word Problems with Comparison Models – Learn to read and draw comparison bar models for addition and subtraction. Use comparison bar models to help solve addition and subtraction word problems.

• Word Problems within 20 – Solve word problems involving the addition or subtraction of a 1-digit number within 20.

• Shapes and Patterns – Recognize and name basic shapes. Sort and classify 2-dimensional shapes by shape, size or color. Describe or continue a pattern according to one or two attributes such as shape, size or color. Fit matching pieces together to form a basic shape.

• Length – Compare the lengths of two or more objects. Estimate and measure length in non-standard units.

• Weight – Compare the weights of two or more objects. Estimate and measure weight in non-standard units.

• End-of-Semester Review – Cumulative review of topics covered in 1A

1B and 1B+ Classes

Overview: This is the second semester of our first grade course. 1B and 1B+ cover the same material. 1B is a normal paced class. It covers the material in 18 lessons. 1B+ is an accelerated class. It covers the material in 12 lessons.

Meets: 1B meets once a week for 1.5 hours. 1B+ meets once a week for 1.75 hours.
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the Placement Page.

Topics:

• Comparing Numbers – Use terms “more than” and “less than”. Understand “1 more” as adding on and “1 less” as taking away. Compare two sets of objects by subtraction. Solve picture problems that involve comparison by subtraction.

• Picture Graphs – Read and interpret picture graphs. Create picture graphs from given data using one-to-one representation. Create picture graphs from self-generated data using one-to-one representation.

• Numbers to 40: Counting – Count within 30. Count within 40. Count within 40 by making tens first. Count on by ones. Count back by ones. Determine missing numbers in a sequence, up to 40. Compare and order numbers within 40.

• Numbers to 40: Tens and Ones – Interpret 2-digit numbers within 40 in terms of tens and ones. Find a number which is 1 or 10 more, or less, than a number within 40.

• Numbers to 40: Adding and Subtracting Ones and Tens, within 40 – Without renaming: add a 1-digit number to, or subtract a 1-digit number from, a 2-digit number within 40.  Add ten to, or subtract ten from, a two-digit number, within 40.

• Addition Within 40 – Add or subtract 1, 2, or 3 to a number within 40 by counting on or back. Add a 1-digit number to a 2-digit number within 40, using the make-ten strategy.

• Addition within 40: Word Problems – Solve word problem involving the addition of a 1-digit number to a 2-digit number within 40.

• Subtraction Within 40 – With renaming, subtract a 1-digit number from a 2-digit number within 40, using the subtract-from-ten strategy.

• Subtraction within 40: Word Problems – Solve word problems involving subtracting a 1-digit number from a 2-digit number within 40, using the subtract-from-ten strategy.

• Adding Three One-Digit Numbers – Add three one-digit numbers.

• Multiplication within 40 – Recognize equal groups. Find the total number in a collection of equal groups, using repeated addition. Use mathematical language such as “4 sixes” or “4 groups of six” to describe equal groups. Write multiplication sentences using “x” and “=” for situations that involve multiplication. Make up number stories that involve multiplication. Interpret multiplication sentences with objects or pictures.

• Division within 40 – Sharing and Grouping – Understand division as sharing and grouping. Write division sentences using “÷” and “=” for situations that involve division. Make up number stories that involve division. Interpret division sentences with objects or pictures.

• Multiplication and Division: Word Problems – Solve word problems involving multiplication and division within 40.

• Halves and Quarters – Understand division as sharing and grouping.

• Time – Tell time on the hour. Understand how time on the hour is connected to events of the day. Tell time at half past the hour. Sequence events according to time.

• Numbers to 100: Tens and Ones – Count by tens. Count within 100 by making tens. Read and write numbers within 100. Write the numbers as number-words.

• Numbers to 100: Order of Numbers – Find the number that is 1 more or less or 10 more or less than a given number within 100. Compare and order numbers within 100. Arrange a group of 2-digit numbers in order. Count on or back by one or tens from a given number within 100.

• Addition within 100 – Without regrouping, add a 1-digit number to a 2-digit number within 100. With regrouping, add a 1-digit number to a 2-digit number within 100, using make-ten strategy. Add a 2-digit number and tens. Add two 2-digit numbers by first adding tens and then ones.

• Subtraction within 100 – Without regrouping, subtract a 1-digit number from a 2-digit number within 100. With regrouping, subtract a 1-digit number to a 2-digit number within 100, using subtract-from-ten strategy. Subtract tens from a 2-digit number. Subtract a two 2-digit from a 2-digit number by first subtracting tens and then ones.

• Word Problems within 100 – Solve 1- and 2-step word problems involving addition and subtraction within 100.

• Money – Recognize and name coins. Count and tell the amount of money in a set of coins up to $1.00. Understand the symbol ¢. Exchange a coin for a set of coins of a smaller denomination. Recognize and name bills. Count and tell the amount of money in a set of bills. Understand the symbol $. Change a bill for an equivalent set of bills of a smaller denomination. Compare the amount of money in two or three sets of coins or bills. Compare the price of two items in cents or dollars. Read the price of an item and make up and make up a set of money in coins or bills. Add or subtract cents within $1. Add or subtract dollars within $20. Solve word problems that involve addition or subtraction of cents or dollars within $20.

• Money Word Problems – Solve word problems that involve addition or subtraction of cents within $1 or dollars within $100.

• End-of-Year Review – Cumulative review of topics covered in 1A and 1B.

2A and 2A+ Classes

Overview: This is the first semester of our second grade course. 2A and 2A+ cover the same material. 2A is a normal paced class. It covers the material in 18 lessons. 2A+ is an accelerated class. It covers the material in 12 lessons.

Meets: 2A meets once a week for 2 hours. 2A+ meets once a week for 2.25 hours.
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the Placement Page.

Topics:

• Numbers to 1,000 – Relate 3-digit numbers to hundreds, tens, and ones. Read and write 3-digit numbers. Relate hundreds, tens and ones to currency bills. Rename currency bills. Relate 3-digit numbers to number discs. Rename number discs. Read and write 3-digit numbers and corresponding number words. Count up by 1′s, 10′s, or 100′s. Count back by 1′s, 10′s, or 100′s. Compare and order numbers less than 1,000. Evaluate number patterns.

• Meanings of Addition and Subtraction – Review part-whole concept of addition and subtraction. Use addition to find a whole. Use subtraction to find a part. Write fact families with numbers to 100. Compare sets by subtraction. Relate “more than” and “less than” to addition and subtraction. Review addition and subtraction of 2-digit numbers without renaming (i.e., carrying or borrowing). Solve word problems involving mental addition and subtraction within 100.

• Addition to 1000 without Renaming (a.k.a carrying) – Add ones, tens or hundreds. Add within 100, without renaming, using the formal algorithm for addition. Add a 2-digit number to a 3-digit number without renaming. Add a 3-digit number to a 3-digit number without renaming. Add within 1000 without renaming. Solve word problems involving addition within 1000 without renaming.

• Subtraction within 1000 without Renaming (a.k.a carrying or regrouping) – Subtract ones, tens or hundreds. Subtract within 100, without renaming, using the formal algorithm for subtraction. Subtract a 2-digit number to a 3-digit number without renaming. Subtract a 3-digit number to a 3-digit number without renaming. Subtract within 1000 without renaming. Solve word problems involving subtraction within 1000 without renaming.

• Subtraction with Renaming Within 1,000 – Subtract one or tens where there is renaming once. Subtract numbers within 100 where the tens are renamed using the formal algorithm for subtraction. Subtract a 1-digit or a 2-digit number from a 3-digit number where tens are renamed. Subtract a 3-digit number from a 3-digit number where tens are renamed. Subtract a 2-digit number from a 3-digit number where hundreds are renamed. Subtract a 3-digit number from a 3-digit number where hundreds are renamed. Subtract a 2-digit number from a 3-digit number with renaming twice. Subtract a 3-digit number from a 3-digit number with renaming twice. Subtract from a 3-digit number where renaming occurs twice before ones can be subtracted.

• Addition and Subtraction Word Problems – Use knowledge of addition and subtraction within 1,000 to solve word problems.

• Measuring Length – Understand meters, centimeters, yards, feet and inches as units of measurement. Measure a length to the nearest meter, centimeter, yard or foot. Estimate the length of an object as equal to, longer than, or shorter than one meter, one yard, one foot, or one inch. Find total length in meters by addition. Find difference in lengths by subtraction. Measure a curved length. Draw a straight line of a given length in centimeters or inch. Compare a yard with a foot. Compare a yard with a meter. Compare an inch with a centimeter.

• Length Word Problems – Use knowledge of metric and English measurements of length to solve word problems.

• Weight – Understand kilograms, grams, pounds, and ounces as units of measurement. Weigh objects to the nearest kilogram, pound, ounce or 50 grams. Add and subtract weights. Compare pounds and kilograms. Compare ounces and grams.

• Weight Word Problems – Use knowledge of metric and English measurements of weight to solve word problems.

• Multiplication Theory – Recognize equal groups. Find the total number in a collection of equal groups using repeated addition. Use mathematical language such as “3 fours”, “3 groups of 4″, or “4 three times” to describe equal groups. Write multiplication sentences using “x” and “=”. Make up number stories that involve multiplication. Write multiplication sentences for situations that involve multiplication. Interpret multiplication sentences with objects of pictures. Solve multiplication facts within 40 using repeated addition. Use rectangular arrays to illustrate multiplication facts.

• Multiplication Table of 2 – Count by twos. Write two multiplication sentences for a rectangular array. Relate counting by 2s to multiplication by 2. Build the multiplication table for 2. Relate facts of 2 more and 2 less. Memorize multiplication facts for 2. Solve word problems involving multiplication by 2.

• Division by 2 – Relate division facts to multiplication facts for 2. Memorize division facts for 2. Solve word problems involving division by 2.

• Multiplication and Division Word Problems – Use knowledge of multiplication tables of 2 and 3 to solve 1- and 2-step multiplication and division word problems.

• End-of-Semester Review – Cumulative review of topics covered in 2A.

2B and 2B+ Classes

Overview: This is the second semester of our second grade course. 2B and 2B+ cover the same material. 2B is a normal paced class. It covers the material in 18 lessons. 2B+ is an accelerated class. It covers the material in 12 lessons.

Meets: 2B meets once a week for 2 hours. 2B+ meet once a week for 2.25 hours.
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the Placement Page.

Topics:

• Methods of Mental Addition – Add one or tens to a 3-digit number. Add ones, tens or hundred to a 3-digit number. Add two-digit numbers. Add 99 or 98 to a 1-digit or 2-digit number. Add 99 or 98 to a 3-digit number.

• Methods of Mental Subtraction – Subtract one or tens from a 2-digit number. Subtract ones, tens or hundred from a 3-digit number. Subtract two-digit numbers. Subtract 99 or 98 from hundreds. Subtract 99 or 98 from 3-digit numbers. Practice mental addition and subtraction

• Mental Math Word Problems – Solve word problems using mental addition and subtraction

• Multiplying and Dividing by 4 – Write multiplication equations for fours. Write two multiplication equations for a rectangular array. Build multiplication table for 4. Memorize multiplication facts for 4. Relate division facts to multiplication facts for 4. Memorize multiplication facts for 4. Review multiplication and division facts for 2 and 3. Solve word problems.

• Multiplying and Dividing by 5 and 10 – Write multiplication equations for fives and tens. Write two multiplication equations for a rectangular array. Build multiplication tables for 5 and 10. Memorize multiplication facts for 5 and 10. Relate division facts to multiplication facts for 5 and 10. Memorize multiplication facts for 5 and 10.. Solve word problems involving multiplication and division by 5 and 10.

• Money: Dollars and Cents – Count money in a set of bills and coins. Recognize, read and write the decimal notation for money. Write amount of money in words and figures. Convert money from one denomination to another or between dollars and cents to cents. Make change for $1. Make change for $10. Solve word problems.

• Money: Addition – Add money by adding dollars and cents separately. Add money within $10 by first adding dollars, then cents. Add money within $10 using the formal algorithm for addition. Add money using mental strategies. Solve word problems

• Money: Subtraction – Subtract money by subtracting dollars and cents separately. Subtract money within $10 by first subtracting dollars, then cents. Subtract money within $10 using the formal algorithm for subtraction. Subtract money using mental strategies. Solve word problems

• Fractions – Recognize and name half and quarter. Read and write half (½) and quarter (¼) in fractional notation. Understand fractional notation. Identify and write different fractions of a whole. Name unit fractions up to ¹/₁₂. Compare and order fractions. Find fractions whose sum makes a whole.

• Telling Time – Tell time to the 5-minute interval. Read time notation. Tell time as minutes after the hour. Tell time to as minutes before the hour. Tell time to the quarter hour. Relate time to events of the day. Use a.m. and p.m. Find the duration of a time interval in minutes using a clock face. Find the duration of a time interval in hours using a clock face. Find the start or end time for a time interval.

• Capacity – Compare the capacity of containers. Understand the liter as a unit of measurement. Compare volume in liters. Understand cups, pints, quarts, and gallons as units of measurement. Compare units to each other. Solve world problems involving capacity.

• Graphs – Understand and create picture graphs with scales. Read and interpret picture graphs with scales.

• Geometry and Patterns – Identify basic shapes on 3-dimensional objects. Combine shapes into a common shape. Identify flat and curved faces on 3-dimensional objects. Make composite figures from basic shapes. Identify straight and curved lines. Make shapes with straight and curved lines. Identify half circles and quarter circles. Fit basic shapes together to make new shapes. Divide a shape into common shapes. Describe and continue a pattern according to 1 or 2 attributes of color, shape, size or orientation.

• Area and Perimeter – Understand the concepts area and perimeter. Find the area of a figure in square units. Compare the area of figures in square units. Measure the perimeter of a figure. Compare the area of figures to their perimeter.

• End-of-Year Review – Cumulative review of topics covered in 2A and 2B.

3A and 3A+ Classes

Overview: This is the first semester of our third grade course. 3A and 3A+ cover the same material. 3A is a normal paced class. It covers the material in 18 lessons. 3A+ is an accelerated class. It covers the material in 12 lessons.

Meets: 3A meets once a week for 2 hours. 3A+ meet once a week for 2.25 hours
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the Placement Page.

Topics:

• Numbers to 10,000 - Relate 4-digit numbers to thousands, hundreds, tens and ones. Read and write 4-digit numbers and corresponding number words. Relate each digit in a 4-digit number to its place value. Compare and order 4-digit numbers. Count on or back by 1, 10, 100 or 1,000. Recognize number patterns involving counting on or back by ones, tens, hundreds and/or thousands.

• Sum and Difference - Understand the terms sum and difference. Draw comparison models to represent mathematical statements. Draw part-whole models to represent mathematical statements. Review addition and subtraction of 3-digit numbers. Solve 1-step and 2-step word problems.

• Adding Ones, Tens, Hundreds and Thousands - Add ones, tens or hundreds to a 4-digit number. Add a number within 10,000 to a 4-digit number with renaming once, twice or three times.

• Subtracting Ones, Tens, Hundreds and Thousands - Subtract ones, tens or hundreds from a 4-digit number. Subtract a number within 10,000 from a 4-digit number with regrouping once, twice or three times. Subtract a number within 10,000 from a 4-digit number where regrouping occurs over several place values for one step.

• Word Problems within 10,000 - Solve one- and two-step word problems involving addition and/or subtraction using models and/or algebraic symbols.

• Multiplication and Division: Review of Concepts – Review multiplication concepts. Review multiplication facts for 2, 3, 4, 5 and 10. Review division concepts. Review division facts for 2, 3, 4, 5, and 10. Multiply a number by 0. Divide 0 by a number. Solve simple word problems involving multiplication and division.

• Multiplication and Division: Modeling Word Problems – Represent word problems involving division or multiplication with a part-whole model. Understand and use the concept of a “unit”. Review multiplication and division by 2, 3, 4, 5, and 10. In word problems, associate multiplication with “how many times as much” or “how many times more”. Represent word problems involving multiplication or division with a comparison model. Solve 2-step word problems using all four operations.

• Multiplying Ones, Tens and Hundreds - Multiply tens or hundreds by a 1-digit number. Write multiplication problems vertically. Relate the term product to multiplication. Multiply a 2-digit number by 2, 3, 4, or 5.Multiply a 2-digit number by 2, 3, 4 or 5 with renaming in the tens. Multiply a 3-digit number by 2, 3, 4 or 5.

• Quotients and Remainders – Understand the concept of a remainder in division. Relate the terms quotient and remainder to division. Understand the vertical representation for division. Divide a 2-digit number by 2. Identify odd and even numbers.

• Dividing Hundreds, Tens, and Ones – Divide a 3-digit number by 2. Divide a 2-digit number by 2, 3, 4, or 5. Divide a 3-digit number by 2, 3, 4, or 5.

• Multiplying and Dividing by 6 – Review facts for multiplication and division by 2, 3, 4, 5, and 10. Double numbers within 100 mentally. Determine new facts for multiplication by 6 from known facts. Learn facts for multiplication by 6 (four new facts). Multiply numbers within 1,000 by 6. Divide numbers within 1,000 by 6.

• Multiplying and Dividing by 7 – Determine new facts for multiplication by 7 from known facts. Learn facts for multiplication by 7 (three new facts). Multiply numbers within 1,000 by 7. Divide numbers within 1,000 by 7.

• Multiplying and Dividing by 8 – Determine new facts for multiplication by 8 from known facts. Learn facts for multiplication by 8 (two new facts). Multiply numbers within 1,000 by 8. Divide numbers within 1,000 by 8.

• Multiplying and Dividing by 9 – Determine new facts for multiplication by 9 from known facts. Learn facts for multiplication by 9 (one new fact). Multiply numbers within 1,000 by 9. Divide numbers within 1,000 by 9.

• Multiplication and Division Word Problems - Solve word problems involving multiplication and division by 2, 3, 4, 5, 6, 7, 8, 9 and 10.

• Money: Dollars and Cents - Recognize, read and write the decimal notation for money. Count money in a set of bills and coins. Convert dollars and cents to cents and cents to dollars and cents. Write amount of money in words and figures. Make change for $1, $10, $20, $50 or $100.

• Money: Addition and Subtraction - Add cents to dollars and cents. Add money by first making a whole number of dollars. Add money within $100 by first adding dollars, then cents. Add money within $100 using the formal algorithm of addition. Subtract cents from dollars and cents. Subtract cents from a whole number of dollars. Subtract cents by subtracting from $1. Subtract money within $100 by first subtracting dollars, then cents. Subtract money within $10 using the formal algorithm of subtraction. Subtract money from a multiple of $10 by mentally subtracting from 1000.

• Money: Word Problems - Solve word problems involving money.

• Order of Operations - Do mixed operations involving addition and subtraction without parentheses. Do mixed operations involving multiplication and division without parentheses. Do mixed operations involving all four operations without parentheses. Do mixed operations involving all four operations with parentheses.

• End-of-Semester Review – Cumulative review of topics covered in 3A.

3B and 3B+ Classes

Overview: This is the second semester of our third grade course. 3B and 3B+ cover the same material. 3B is a normal paced class. It covers the material in 18 lessons. 3B+ is an accelerated class. It covers the material in 12 lessons.

Meets: 3B meets once a week for 2 hours. 3B+ meet once a week for 2.25 hours.
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the Placement Page.

Topics:

• Methods of Mental Addition - Review mental addition of ones or tens. Add numbers within 100 by adding first the tens and then the ones. Add numbers within 100 by making tens. Add ones or tens to 3-digit numbers.

• Methods of Mental Subtraction - Review mental subtraction of ones and tens. Subtract numbers within 100 by subtracting first the tens and then the ones. Subtract numbers within 100 by subtracting from a ten. Subtract numbers within 1000 by subtracting from a hundred.

• Methods of Mental Multiplication - Review multiplication of tens or hundreds by a 1-digit number.

• Methods of Mental Division – Divide tens, hundreds, or thousands by a 1-digit number by removing and appending the correct number of 0′s.

• Length: Meters and Centimeters - Review meters and centimeters as units of length. Find the number of centimeters in a meter. Convert a measurement in meters and centimeters to centimeters and vice versa. Add meters and centimeters in compound units. Subtract centimeters in compound units.

• Length: Kilometers - Understand the kilometer as a unit of measurement. Convert a measurement in kilometers and meters to meters and vice versa. Add kilometers and meters in compound units. Subtract kilometers and meters in compound units.

• Length: Yards, Feet, Inches and Miles - Review yards, feet and inches as units of length. Measure in yards, feet and inches. Convert between yards and feet. Convert between feet and inches. Add or subtract yards and feet in compound units. Add or subtract feet and inches in compound units. Recognize the mile as a unit of length. Add or subtract miles.

• Length Word Problems - Apply knowledge of metric and English units of length to solve word problems.

• Weight: Kilograms and grams - Review kilograms and grams. Read scales. Estimate weights. Convert between kilograms and grams. Subtract grams from 1 kilogram. Add or subtract kilograms and grams in compound units.

• Weight: Pounds and Ounces - Review pounds and ounces. Read scales in pounds and ounces. Estimate weights. Convert between pounds and ounces. Subtract ounces from pounds. Add or subtract pounds and ounces in compound units.

• Weight: Word Problems - Apply knowledge of metric and English units of weight to solve word problems.

• Capacity: Liters and Milliliters - Understand the term capacity. Understand the milliliter and liter as units of measurement. Convert between liters and milliliters. Add or subtract milliliters and liters in compound units. Solve word problems involving capacity.

• Capacity: Gallons, Quarts, Pints and Cups - Understand gallons, quarts, pints and cups as units of measurement. Convert between gallons, quarts, pints and cups. Add or subtract gallons, quarts, pints or cups in compound units.

• Graphs - Relate bar graphs to picture graphs with scales. Read scales on bar graphs. Read and interpret bar graphs.

• Fractions of a Whole - Recognize and name fractions of a whole. Make a whole with a fraction. Visualize relative sizes of fractions of a whole. Compare and order unit fractions. Understand the terms numerator and denominator. Compare and order fractions with a common numerator. Compare and order fractions with a common denominator.

• Equivalent Fractions - Recognize and name equivalent fractions. Find equivalent fractions using fraction bars. Find equivalent fractions using multiplication. Find equivalent fractions using division. Find the simplest form of a fraction. Compare and order simple fractions.

• Adding and Subtracting Related Fractions - Add related fractions. Subtract related fractions. Give answers in simplest form.

• Time - Review a.m. and p.m. Understand the relative magnitudes of hours and minutes. Tell time to 1-minute intervals. Find the duration of a time interval using a clock face. Convert hours and minutes to minutes and vice versa. Find the duration of a time interval without using a clock face. Find the end time when given the start time and the time interval. Find the start time when given the end time and the time interval. Understand the second as a unit of measurement. Measure time in seconds. Convert from minutes and seconds to seconds and vice versa. Understand the calendar. Know the months of the year. Convert between years and months in compound units. Know the days of the week. Convert between weeks and days in compound units. Solve problems involving time.

• Angles - Identify angles in the environment. Relate size of angles to the degree of turning. Relate the number of angles to the number of sides of a polygon. Identify right angles. Classify angles as less than, equal to, or greater than a right angle.

• Perpendicular and Parallel Lines - Define perpendicular and parallel lines. Identify perpendicular and parallel lines. Draw perpendicular and parallel lines.

• Area and Perimeter - Find the area of a figure in square units. Compare the area of figures in square units. Measure and compare area in square centimeters or inches. Measure area in square meters, feet, or yards. Visualize and compare relative sizes in square centimeters, meters, inches, feet and yards. Measure the perimeter of a figure. Compare the area of figures to their perimeter. Find the perimeter of a rectilinear figure given the length of each side. Find the area of a rectangle given the length of each side. Solve problems involving area and perimeter.

• End-of-Year Review - Cumulative review of topics covered in 3A and 3B.

4A and 4A+ Classes

Overview: This is the first semester of our fourth grade course. 4A and 4A+ cover the same material. 4A is a normal paced class. It covers the material in 18 lessons. 4A+ is an accelerated class. It covers the material in 12 lessons.

Meets: 4A meets once a week for 2 hours. 4A+ meet once a week for 2.25 hours
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the Placement Page.

Topics:

• Numbers to 100,000 - Interpret 5-digit numbers in terms of ten thousands, thousands, hundreds, tens and ones. Read and write 5-digit numbers and corresponding number words. Relate each digit in a 5-digit number to its place value. Count on or back by 1, 10, 100, 1000 or 10,000. Recognize number patterns involving counting on or back by ones, tens, hundreds and/or thousands. Determine the scale of a number line and locate 4-digit and 5-digit numbers on a number line. Compare and order numbers within 10,000. Review mental math strategies for addition and subtraction of numbers of up to 2-digits. Add and subtract thousands and ten thousands. Multiply and divide thousands and ten thousands by 1-digit numbers.

• Rounding and Estimating - Round whole numbers to the nearest ten. Estimate the location of numbers on a number line marked in tens. Round whole numbers to the nearest hundred. Estimate the location of numbers on a number line marked in hundreds. Estimate the answer in addition and subtraction problems.

• Factors - Understand factors using rectangular arrays. Determine if a 1-digit number is a factor of a given whole number by using division. Learn rules of divisibility for 2, 3, 4, 5, 6, 9 and 10. List the factors of a given whole number up to 100. Find common factors of 2-digit numbers. Find the greatest common factor of 2-digit numbers.

• Multiples - Understand the concept of multiples. Relate factor to multiples. Determine if a whole number is a multiple of a 1-digit number. List the multiples of a 1-digit number. Relate the divisibility rules to multiples. Find common multiples. Find the lowest common multiple.

• Multiplication and Division of Whole Numbers - Multiply a 4-digit number by a 1-digit number and estimate the product.  Divide a 4-digit number by a 1-digit number and estimate the product.  Divide by 10. Use pictorial models (part-whole and comparison models). Multiply by tens, hundreds, and thousands. Multiply by a 2-digit number and estimate the product. Multiply by a 3-digit number and estimate the product. Solve word problems of up to 3 steps.

• Equivalent Fractions - Recognize and name equivalent fractions. Find equivalent fractions using fraction bars. Find equivalent fractions using multiplication. Find equivalent fractions using division. Find the simplest form of a fraction. Compare and order simple fractions.

• Adding and Subtracting Related Fractions - Add related fractions. Subtract related fractions. Give answers in simplest form.

• Mixed Numbers - Understand and write mixed numbers. Read and interpret number lines with mixed numbers. Order mixed numbers. Add a fraction less than one to a whole number. Subtract a fraction less than one from a whole number.

• Improper Fractions - Interpret improper fractions as multiples of unit fractions. Define improper fractions as a fraction whose numerator is equal to or greater than the denominator. Convert an improper fraction to a mixed number. Convert a mixed number to an improper fraction. Add and subtract fractions involving mixed numbers.

• Fraction of a Set - Understand fractions of a set of objects. Find the number of objects in a fraction of a set. Multiply a fraction by a whole number where the product is a whole number. Multiply a fraction by a whole number where the product is not a whole number. Relate fractions to units in a part-whole diagram. Express a part as a fraction of a whole. Determine the whole or the remaining part from the value of a fractional part of the whole. Solve word problems involving fractions of a set.

• Fraction Word Problems - Apply knowledge of fractions to solve word problems involving equivalent fractions, addition and subtraction of fractions, simplest form and fractions of a set.

• Tables and Graphs - Read and interpret data presented in a table or bar graph. Construct a bar graph from data given in a table. Construct a table from data given in a bar graph. Solve problems using data in a bar graph or a table.

• Measuring Angles - Understand the use of degrees for measuring angles. Recognize right angles as 90^o. Measure angles less than 180^o. Construct angles less than 180^o. Recognize angles of 180^o, 270^o, and 360^o. Estimate the measure of angles greater than 180^o. Construct angles greater than 180^o. Find unknown (complementary of supplementary) angles.

• Perpendicular and Parallel Lines - Recognize perpendicular lines. Construct perpendicular lines. Recognize parallel lines. Construct parallel lines.

• Area and Perimeter - Review area and perimeter of rectilinear figures. Find one dimension of a rectangle given its perimeter and the other dimension. Find one dimension of a rectangle given its area and the other dimension. Find the perimeter of a figure made up of rectangles and squares. Find the area of a figure made up of rectangles and squares. Find the area of a path around a rectangle.

• Area and Perimeter Word Problems - Apply knowledge of Area and Perimeter to solve word problems.

• End-of-Semester Review – Cumulative review of topics covered in 4A.

4B and 4B+ Classes

Overview: This is the second semester of our fourth grade course. 4B and 4B+ cover the same material. 4B is a normal paced class. It covers the material in 18 lessons. 4B+ is an accelerated class. It covers the material in 12 lessons.

Meets: 4B meets once a week for 2 hours. 4B+ meet once a week for 2.25 hours.
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the Placement Page.

Topics:

• Decimals: Tenths - Read and write 1-place decimal numbers which are less than 1. Express a fraction with a denominator of 10 as a decimal number. Make a whole with a tenth. Read and write 1-place decimal numbers greater than 1. Locate 1-place decimal numbers on a number line. Write a decimal number as a mixed number. Compare and order 1-place decimal numbers. Write improper fractions with denominator of 10 as decimal numbers. Rename tenths as ones.

• Decimals: Hundredths - Read and write 2-place decimal numbers. Express a fraction with a denominator of 100 as a decimal number. Relate each digit in a 2-digit decimal to its place value. Express a mixed number with a denominator of 100 as a decimal. Relate dollars and cents to decimals. Interpret 2-place decimals as the sum of whole numbers, tenths, and hundredths. Locate 2-place decimal numbers on a number line. Evaluate number patterns involving decimal numbers. Express a 2-place decimal number as a fraction in simplest form. Express a fraction with a denominator that is a factor of 100 as a decimal. Compare and order numbers to two decimal places. Add or subtract 0.1 or 0.01 to numbers having up to 2 decimal places. Add and subtract tenths and hundredths to numbers having up to 2 decimal places using mental math strategies.

• Decimals: Thousandths - Relate each digit in a 3-digit decimal to its place value. Read and write 3-place decimal numbers. Locate 3-place decimal numbers on a number line. Compare and order numbers to three decimal places. Mentally add or subtract digits from a decimal number. Express a number having up to 3 decimal places as a fraction in simplest form. Compare and order a mixture of decimal numbers and fractions.

• Decimals: Rounding Off - Round decimals numbers to the nearest whole number. Round decimal numbers to one decimal place.

• Decimals: Addition and Subtraction - Add tenths or hundredths. Add 1-, 2-, and 3-place decimal numbers. Estimate the sum of decimal numbers. Subtract 1- and 2-place decimal numbers. Use mental strategies to add and subtract 2-place decimal numbers close to 1. Solve word problems involving the addition and subtraction of decimal numbers.

• Decimals: Multiplication - Multiply tenths or hundredths by a 1-digit whole number. Multiply 1-place decimal numbers by a 1-digit whole number. Multiply 2-place decimal numbers by a 1-digit whole number. Solve word problems involving multiplication of decimal numbers. Use estimation to check the reasonableness of answers.

• Decimals: Division - Divide a number of up to 2 decimal places by a 1-digit number where the quotient is a tenth or hundredth. Divide a number of up to 2 decimal places by a 1-digit whole number. Divide a number of up to 2 decimal places by a 1-digit whole number where the quotient has the same number of decimal places as the dividend. Divide a number of up to 2 decimal places by a 1-digit whole number where decimal places have to be added to the dividend. Estimate to check the reasonableness of an answer. Round a quotient to one decimal place. Solve word problems involving division of decimal numbers.

• Decimals: The Four Operations - Add, subtract, multiply and divide numbers with up to 3 decimal places. Round decimals to nearest whole number or to one decimal place. Estimate answers.  Solve word problems involving the four operations of decimals.

• Decimals: Word Problems - Use addition, subtraction, multiplication and division to solve multi-step word problems involving decimals. Use models to illustrate word problems involving decimals.

• Measures - Review conversion factors for measurements. Multiply length, weight, volume and time in compound units. Divide length, volume and time in compound units.

• Symmetry - Identify symmetric figures. Identify and draw lines of symmetry. Complete a symmetric figure with respect to a line of symmetry.

• Solid Figures - Visualize solids drawn on isometric dot paper. Use cubes to build solids drawn on isometric dot paper. Determine the number of cubes used to make a solid drawn on isometric dot paper. Visualize and build new solids formed by adding and taking away unit cubes from a solid drawn on isometric dot paper.

• Volume - Find the volume of a solid in cubic units. Visualize the size of a cubic centimeter, cubic meter, cubic inch, cubic foot, and cubic yard. Find the volume of a cuboid given its length, width and height in cubic centimeters, inches, feet, meters or yards. Find the number of cubic inches in a cubic foot. Find the number of cubic feet in a cubic yard. Recognize the equivalency of 1 cm³ with 1 ml, and 1,000 cm³ with 1 liter. Covert cubic centimeters to liters and milliliters. Convert liters and milliliters to cubic centimeters.

• Volume Word Problems - Apply knowledge of volume to solve word problems.

• End-of-Year Review - Cumulative review of topics covered in 4A and 4B.

5A and 5A+ Classes

Overview: This is the first semester of our fifth grade course. 5A and 5A+ cover the same material. 5A is a normal paced class. It covers the material in 18 lessons. 5A+ is an accelerated class. It covers the material in 12 lessons.

Meets: 5A meets once a week for 2.25 hours; 5A+ meets once a week for 2.5 hours.
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the Placement Page.

Topics:

• Place Value to Millions – Interpret numbers within 1,000,000 in terms of place value. Read and write 7-digit numbers and corresponding number words. Evaluate number patterns involving counting on or back by place value. Compare and order numbers within 10,000,000.

• Approximation and Estimation - Round whole numbers to the nearest ten, hundred, or thousand. Estimate the answer in addition and subtraction. Estimate the answer in multiplication and division of a whole number by a 1-digit number.

• Multiplying by 10s, 100s, and 1000s - Mentally multiply 2-digit numbers by 1-digit numbers. Multiply whole numbers by tens, hundreds or thousands. Estimate the product of a whole number and a 2-digit number.

• Dividing by 10s, 100s, and 1000s - Divide whole numbers by tens, hundreds or thousands. Estimate the quotient when a whole number is divided by a 2-digit number.

• Order of Operations - Perform mental math. Do mixed operations involving addition and subtraction without parentheses. Do mixed operations involving multiplication and division without parentheses. Do mixed operations involving all four operations without parentheses. Do mixed operations involving all four operations with parentheses.

• Multiplication - Multiply a 2-digit, 3-digit, or 4-digit number by a 2-digit number.

• Division - Divide a 2-digit or 3-digit number by a 2-digit number where the quotient is 1 digit. Divide a 2-digit or 3-digit number by a 2-digit number where the quotient is 2 digits. Divide a 4-digit number by a 2-digit number.

• Word Problems - Review part-whole and comparison models for addition, subtraction, multiplication and division. Solve 2-step word problems involving multiplication and division by 2-digit numbers. Solve multi-step word problems involving multiplication and division by 2-digit numbers.

• Fractions and Division - Review equivalent fractions, simplest form, improper fractions, and mixed numbers. Associate division with fractions. Change an improper number to a mixed number or a whole number by division. Express the quotient as a whole number or a mixed number.

• Addition and Subtraction of Unlike Fractions - Add unlike fractions. Subtract unlike fractions. Solve simple word problems involving the addition and subtraction of unlike fractions.

• Addition and Subtraction of Mixed Numbers - Add mixed numbers. Subtract mixed numbers. Solve simple word problems involving the addition and subtraction of mixed numbers.

• Product of a Fraction and a Whole Number - Multiply a proper fraction by a whole number. Convert a fraction of a measurement to a smaller unit of measurement by multiplying by a conversion factor. Covert a measurement expressed as a mixed number to a smaller unit of measurement. Express a part of a quantity as a fraction. Solve simple word problems.

• Product of Fractions - Illustrate a fraction of a fraction with rectangular girds. Multiply fractions by fractions.

• Dividing a Fraction by a Whole Number – Illustrate a fraction divided by a whole number with rectangular grids. Divide fractions by whole numbers.

• Fractions: Word Problems - Solve multi-step word problems involving the addition, subtraction, multiplication and division of fractions.

• Area of Triangles - Derive the formula for the area of a triangle. Find corresponding heights for different bases of a triangle. Find the area of a triangle using a formula. Solve problems involving area of a triangle and area of a rectangle.

• Ratios and Equivalent Ratios - Compare two quantities using ratios. Interpret a given ratio in terms of units. Find equivalent rations. Express a ratio of two quantities in simplest form. Review common factors. Use the comparison model to represent a ratio of two quantities. Solve word problems involving ratios of two quantities.

• Comparing three quantities - Compare three quantities using ratios. Write a given ratio of three quantities in simplest form. Solve word problems involving ratios of three quantities.

• Angles - Estimate and measure angles. Construct angles of a given size. Tell direction in relation to an 8-point compass. Tell the angle between various points of the compass. Understand clockwise and counterclockwise turning in relation to an 8-point compass. Recognize that vertically opposite angles of intersecting lines are equal. Recognize that adjacent angles on a straight line add up to 180^o. Recognize that all the angles around a point (or pair of intersecting lines) add up to 360^o. Find unknown angles involving complementary angles, supplementary angles, angles at a point, and vertically opposite angles.

• End-of-Semester Review – Cumulative review of topics covered in 5A.

5B and 5B+ Classes

Overview: This is the second semester of our fifth grade course. 5B and 5B+ cover the same material. 5B is a normal paced class. It covers the material in 18 lessons. 5B+ is an accelerated class. It covers the material in 12 lessons.

Meets: 5B meets once a week for 2.25 hours; 5B+ meets once a week for 2.5 hours.
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the Placement Page.

Topics:

• Decimals: Approximation and Estimation - Review decimal numbers and fractions. Round decimal numbers to two decimal places. Review dividing a decimal number by a whole number. Divide a decimal number by a 1-digit whole number and round the quotient to two decimal places. Express a fraction as a decimal number correct to two decimal places.

• Decimals: Multiplication and Division by Tens, Hundreds, or Thousands - Multiply or divide a decimal number by tens, hundreds or thousands.

• Decimals: Multiplying by a 2-Digit Whole Number - Estimate the product in multiplication of decimal numbers. Multiply a decimal number of up to 2 decimal places by a 2-digit whole number.

• Decimals: Conversion of Measurements - Convert a measurement in a decimal number to a smaller unit. Convert a measurement in a decimal number to a compound unit. Convert a measurement smaller than the conversion factor to a larger unit. Convert a measurement greater than the conversion factor to a larger unit.

• Decimals: Word Problems - Solve word problem involving decimals.

• Percentage - Understand percentage. Express a fraction with a denominator of 10 or 100 as a percentage. Express a decimal number as a percentage. Express a percentage as a decimal number. Express a percentage as a fraction in simplest form.

• Writing Fractions as a Percentage - Express a fraction as a percentage. Express a fraction with a denominator that is a multiple of 100 as a percentage. Solve word problems which involve finding the percentage for a part of a whole.

• Percentage of a Quantity - Find the value of a percentage part when given the whole. Solve word problems which involve finding the value for a percentage part of a whole. Solve word problems which involve interest rates or percent discounts. Solve word problems which involve percent increase or decrease.

• Average - Understand average. Find the average of a set of data. Find the average when given the total amount and the number of items. Find the total when given the average and the number of items. Multiply in compound units. Solve problems that involve averages of compound units of measurement. Find the average of a set of data that involve measurement in compound units. Solve word problems that involve averages.

• Rate - Understand rate as one quantity per unit of another quantity. Find a total quantity when given the relationship of the different units. Draw line diagrams for rate problems. Use an arrow to show the relationship between two quantities in a rate problem. Solve word problems involving a given rate. Solve word problems of up to 3-steps that involve rate. Solve problems using rate tables.

• Graphs - Understand the relationship between data in a table and the data in a line graph. Read and interpret data in a line graph. Solve problems using data in a line graph. Construct a line graph. Understand and use conversion graphs.

• Triangles - Recognize that the sum of the angles of a triangle is 180^o. Find the unknown angle of a triangle when given the other two angle3s. Recognize that the sum of the angles opposite a right angle of a triangle is 90^o. Find the unknown angle of a right triangle when the other angle is given. Recognize that the exterior angle of a triangle is equal to the sum of the opposite interior angles. Find an unknown angle in problems involving exterior angles of a triangle. Explore angle and side properties of isosceles and equilateral triangles.  Find unknown angles in isosceles and equilateral triangles. Find an unknown angle from the angle properties of triangles.

• Four-Sided Figures (Parallelograms, Rhombuses, and Trapezoids) – Investigate properties of parallelograms, rhombuses, and trapezoids. Recognize that opposite angles of a parallelogram are equal and that the sum of the angles between parallel sides is 180^o. Recognize that a diagonal bisects a rhombus (or square) into equilateral triangles. Find Unknown  angles in problems involving trapezoids and triangles.

• Geometric Constructions (Triangles, parallelograms, rhombuses, and trapezoids) – Construct a triangle when given the measurement of two angles and the included side. Construct a triangle when given two sides and their included angle. Construct a rectangle when given its length and width. Construct a parallelogram when given the measurements of two adjacent sides and an angle. Construct a rhombus when given the measurements of one side and one angle.

• Volume - Find the volume of solids made from unit cubes. Find the side of a cube when given its volume. Find one dimension of a cuboid if given its volume and other two dimensions or the area of a face. Review the equivalency of one liter with 1,000 cm³. Find a height of water in rectangular-based containers when given the volume of water in liters and the length and width of the base. Solve word problems of up to 2-step involving volume. Recognize that the volume of the liquid displaced by a solid is equal to the volume of the solid. Solve word problems of up to two-steps involving the displacement of a liquid by a solid

• Tessellations - Understand tessellation. Identify the shape used in a tessellation. Draw a tessellation on dot paper. Determine whether a shape can tessellate. Explore properties of shapes that can tessellate. Make different tessellations with a given shape. Make shapes that can tessellate.

• End-of-Year Review - Cumulative review of topics covered in 5A and 5B.

6A Classes

Overview: This is the first semester of our sixth grade course.

Meets: Once a week for 2.5 hours.
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the Placement Page.

Topics:

• Algebraic Expressions – Use letters to represent unknown numbers. Write an algebraic expression in one variable using addition or subtraction. Find the value of an algebraic expression by substitution. Write an algebraic expression using multiplication or division. Find the value of an algebraic expression by substitution. Write an algebraic expression using more than one operation. Use exponents in algebraic equations. Simplify simple algebraic expressions by using addition or subtraction to combine like terms.

• Algebraic Expressions: Word Problems - Use algebraic expressions to solve word problems.

• Solid Figures – Associate two-dimensional drawings with three-dimensional shapes. Visualize pyramids, prisms, and cylinders from two-dimensional drawings. Identify nets of cubes, cuboids, prisms, and pyramids. Identify a solid represented by a net. Determine whether a figure can be the net of a given solid. Determine whether a solid can be formed from a given net.

• Ratio and Fractions – Compare quantities using ratios. Express a ration in its simplest form. Relate ratios to units. Review the use of pictorial models in solving word problems. Express a ratio as a fraction of a quantity and vice versa. Solve word problems involving ratios and fractions.

• Ratio and Proportion – Understand ratio as proportion. Solve word problems that involve direct proportions.

• Changing Ratios – Solve word problems that involve finding a new ratio after a change. Solve word problems where there is a transfer from one quantity to another. Solve ratio problems that involve only one quantity changing. Solve ration problems that involve more than one quantity changing.

• General Review - Review material covered in first third of the 6A (Algebra, Solid Figures and Ratios).

• Percentage: Part of a Whole as a Percentage - Express part of a whole as a fraction or as a percentage. Express a fraction as a percentage. Express a percentage as a fraction in simplest form. Express a decimal of up to 3 decimal places as a percentage. Express a percentage as a decimal. Solve word problems which involve percentage. Find the percentage of a percent. Review the meaning of tax, percent increase, percent decrease, and discount

• Percentage: One Quantity as a Percentage of Another - Express one quantity as a percentage of another, using the fraction method. Express one quantity as a percentage of another, using the unitary method. Find percent increase, percent decrease, and discounts. Relate selling price to cost price as a percentage. Find amounts when given their increase or decrease in percentage.

• Percentage: Solving Percentage Problem by Unitary Method - Find the whole when given the value of a percentage part, using the unitary method. Find an original value when given a new value after its percent increase or decrease. Solve word problems which involve percentage by using the unitary method.

• Percentage Review - Review material covered in second third of the 6A (Percentages).

• Algebra and Solid Figure Word Problems - Review algebra and solid figures by solving word problems

• Ratio, Proportion, and Percentages Word Problems - Review ratio, proportion, and percentages by solving word problems

• Speed – Interpret speed as a rate of distance traveled per unit time. Read and write units of speed. Find distance when speed and time are given. Find speed when distance traveled and time are given. Find time when average speed and distance are given. Solve 2-step word problems that involve speed. Draw diagrams to help solve word problems involving speed. Find average speed for different speeds traveled on different parts of a trip. Solve multi-step word problems that involve speed.

• End-of-Semester Review – Cumulative review of topics covered in 6A.

6B Classes

Overview: This is the second semester of our sixth grade course.

Meets: Once a week for 2.5 hours.
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the Placement Page.

Topics:

• Fractions: Division - Divide a whole number by a unit fraction. Divide a fraction by a whole number. Divide a fraction by a unit fraction. Divide a whole number by a fraction. Divide a fraction by a fraction.

• Fractions: Order of Operations - Do mixed operations which involve addition and subtraction of fractions, without parentheses. Do mixed operations which involve multiplication and division of fractions, without parentheses. Do mixed operations which involve all four operations with fractions, without parentheses. Do mixed operations which involve all four operations with fractions, with parentheses.

• Fractions: Word Problems - Solve word problems involving fractions using pictorial models.

• Circles: Radius, Diameter, and Circumference - Relate the circumference of a circle to its diameter. Find the circumference of a circle when given its radius. Find the perimeter of a semicircle or quarter circle and related figures. Find the perimeter of a compound shapes.

• Circles: Area - Relate the area of a circle to its radius. Find the area of a circle when given its diameter or radius. Find the area of a semicircle or quarter circle and related figures. Find the area of a compound shape made up of squares, rectangles, triangles, semicircles and/or quarter circles.

• Circles: Word Problems - Solve word problems involving finding the area and/or perimeter of compound shapes.

• Graphs: Pie Charts - Understand pie charts. Read and interpret pie charts with data given as whole numbers. Read and interpret pie charts with data given as fractions. Read and interpret pie charts with data given as percentages.

• Volume - Find the volume of a cuboid (a rectangular solid). Find the number of cubes of a given side that are needed to fill a cuboid. Find the number of cubes of a given size that can be cut from a cuboid. Find the edge of a cube when given its volume and two dimensions or its volume and the area of a face. Convert volume of a liquid from cm³ to liters and milliliters and vice versa. Solve multi-step word problems involving the volume of a liquid in a rectangular tank.

• Volume: Word Problems - Solve multi-step word problems involving the displacement of a liquid by a solid. Solve multi-step word problems involving the rate of flow a liquid.

• General Review: Circles, Pie Graphs, Volume - Solve word problems to review circles, pie graphs and volume.

• Review of Triangles and 4-Sided Figures - Review the angle properties of triangles, right triangles, isosceles triangles, equilateral triangles, parallelograms, rhombuses, and trapezoids. Use the angle properties of triangles, right triangles, isosceles triangles, equilateral triangles, parallelograms, rhombuses, and trapezoids to calculate unknown angles.

• Triangles and 4-Sided Figures - Use the angle properties of triangles, right triangles, isosceles triangles, equilateral triangles, parallelograms, rhombuses, and trapezoids to calculate unknown angles.

• Whole Numbers: Word Problems - Review whole numbers. Apply knowledge of whole numbers to solve multi-step word problems.

• Decimal: Word Problems - Review decimals. Apply knowledge of decimals to solve multi-step word problems.

• Area and Perimeter: Word Problems - Review area and perimeter of rectangles, squares, circles, semi-circles, and quadrants. Apply knowledge of area and perimeter to solve multi-step word problems.

• Bar and Line Graphs, Fractions, Ratios: Word Problems - Review bar and line graphs, fractions and ratios. Apply knowledge to solve multi-step word problems.

• Average, Rate, Percentage and Speed: Word Problems - Review average, rate, percentage and speed. Apply knowledge to solve multi-step word problems.

• End-of-Year Review - Cumulative review of topics covered in 6A and 6B.

7A Classes

Overview: This is the first semester of our seventh grade course.

Meets: Once either once a week for 3 hours or twice a week for 1.5 hours each time.
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the page.

Topics:

• Review of Whole Numbers
  • System of numeration
  • The four operations
  • Approximation
  • Estimation
  • Laws of addition and multiplication
  • Mental calculation
  • Factor and multiples
  • Prime numbers and prime factorization
  • Greatest common factor
  • Least common multiple
  • Number patterns
• Fractions and Decimals
  • Four operations on fractions
  • Four operations on decimals
  • Units of measurement (length, mass, time, capacity)
  • Profit and loss word problems
  • Approximation and estiamtion
  • Significant figures
  • Conversion between decimals and fractions
• Problem-Solving Heuristics
• Real Mumbers
  • Negative numbers
  • Integers
  • Squares and square roots
  • Cubes and cube roots
  • Rational and irrational numbers
  • Order of calculation
  • Mental calculation and estimation
• Algebraic Expressions
  • Writing algebraic expressions
  • Algebraic notation
  • Evaluation of algebraic expressions
  • Algebraic terms
  • Use of brackets
  • Collecting like terms
• Equations and Formulae
  • Eqivalent equations
  • Solving equations
  • Equations with decimal and fractional coefficients
  • Evaluation of formulae
  • Algebraic word problems
• Rate, Ratio and Percentage
  • Rate
  • Speed
  • Ratio
  • Scale
  • Direct and inverse proportions
  • Percentage

7B Classes

Overview: This is the second semester of our seventh grade course.

Meets: Once either once a week for 3 hours or twice a week for 1.5 hours each time.
Note: Classes may be longer and/or meet more frequently during the summer.

Topics:

• Financial Transactions
  • Earning, profit and loss, commissions, and discounts
  • Simple and compound interest
  • Hire purchase
  • Taxation and money exchange
• Collection and Presentation of Statistics
  • Tabulation
  • Fequentcy tables
  • Pie charts
  • Bar charts
  • Pictograms
  • Line graphs
  • Dot diagrams
  • Histograms
  • Stem and leaf diagrams
• Introduction to Geometry
  • Lines, line segments, rays and angles
  • Angle properties related to straight lines
  • Perpendicular and parallel lines
  • Angle properties related to parallel lines
  • Constructions
• Polygons
  • Angle properties of triangles
  • Isosceles and equilateral triangles
  • Construction of quadrilaterals
  • Properties of quadrilaterals
• Spatial Visualization
  • Patterns and designs
  • Constructing geometric patterns from number patterns
  • Tesselations
  • Three-dimensional figures
  • Vertical and horizontal lines and planes
  • Nets of solids
• Area and Perimeter
  • Perimeter and area of polygons
  • Circumference and area of circles
• Volume, Surface and Density
  • Volume and surface area of prisms and cylinders
  • Density

8A Classes

Overview: This is the first semester of our eighth grade course.

Meets: Once either once a week for 3 hours or twice a week for 1.5 hours each time.
Note: Classes may be longer and/or meet more frequently during the summer.

Placement: To access the placement test for this class, please visit the page.

Topics:

• Scientific Notation
  • Scientific notation
  • Calculators and scientific notation
  • Number sequences
• Algebraic Manipulation and Formulae
  • Polynomials
  • Expansion and algebraic equations
  • Factorisation of algebraic equations
  • Algebraic fractions
  • Formulae
• Solutions of Equations
  • Linear equations
  • Word problems involving simple linear equations
  • Simple fractional equations
  • Word problems involving simple fractional equations
  • Simultaneous equations
  • Word problems involving simultaneous equations
• Cartesian Coordianates and Graphs
  • Rectangular coordinates
  • Scales and graphs
  • Practical applications – straight line, conversion and travel graphs
• Graphs of equations
  • Graphs of linear equations
  • Lines parallel to x- or y-axis
  • Graphs of quadratic equations
  • Graphical solutions of linear equations

8B Classes

Overview: This is the second semester of our eighth grade course.

Meets: Once either once a week for 3 hours or twice a week for 1.5 hours each time.
Note: Classes are longer and/or meet more frequently during the summer.

Topics:

• Applying Mathematics
  • Earnings
  • Spending
  • Simple and compound interest
  • Profit and loss
  • Discounts
  • Commissions
  • Foreign exchange
  • Hire purchase
  • Taxation
  • Average speed
  • Rate, ratio and proportion
  • Percentage
  • Financial transactions
• Mensuration
  • Arc length and sector area
  • Spheres
  • Pyramids
  • Cones
• Geometry
  • Congruent figures
  • Similar figures
  • Angle properties of polygons
  • Tesselation patterns of polygons
  • Scale drawing.
• Symmetry
  • Line symmetry
  • Rotational symmetry
  • Symmetrical properties of regular polygons
  • Plane symmetry
  • Symmetrical properties of prisms, cylinders, pyramids and cones
• Statistics
  • Arithmetic mean
  • Mode
  • Median