#### MATH PROGRAM

#### WHY MATH TUTORING IS IMPORTANT?

Math tutoring is important because each student learns in a different way. No matter how well his or her teacher explains the material, some students simply need more time to practice the skill. Math tutoring provides a supportive environment for students who need this time to be guided in the right direction. Also, math tutoring is proven to improve academic achievement for students. It has been proven that students who attended their after school tutoring sessions showed more of a learning gain in math than those who did not. Results as these prove that spending time to develop your skills will lead to improvement. However, this doesn’t mean that tutors can get you straight A’s, but they can help you to gain a comfortable understanding of your subject and improve your academic performance. The importance of performing at your academic best in immeasurable; education is one of the most important factors in any person’s life and tutors are there to make your education experience smoother

#### WHY CHOOSE ETON LEARNERS MATHEMATICS?

Our proprietary method consists of three key components which are closely monitored and adjusted to address each child’s learning goals:

**Assessments:** Students start by taking a customized assessment which pinpoints their needs, allowing us to meet them where they are and take them where they need to go. These assessments continue throughout their instruction to ensure progress and skill retention.

**Customized Learning Plans:** We then design a customized learning plan for teaching the concepts the student needs to master, and use a combination of proprietary materials and instruction techniques to ensure your child masters these concepts.

**Specially Trained, Caring Instructors Who Teach:** Our specially trained instructors implement the learning plan and work with each student to ensure they master the material. Our mathematics program provides the foundation and support to succeed at each stage:

**Elementary School:** Building math foundation, mastering computation and problem solving with whole and rational numbers, and understanding number sense

**Middle School:** Continuing to build strong math foundation, mastering “the how and why” (algebra readiness), helping with homework, and filling in gaps needed for advanced classes

**High School:** Filling in foundational gaps, addressing different levels of knowledge, helping with test preparation, and assisting with homework

Our Math Tutoring is a leading provider of tutoring and supplemental Education Services to students of all ages and skill levels

We focus on every child individually and their needs by providing with homework support, preparing them for exams and helping them understand math concepts and achieve better grade

All of our Math Programs are in accordance with the Qatar Ministry of Education Programs, so what we teach students at our center is exactly what's being covered at school. By our professionalism and research, we have put together a unique approach to tutoring, one that would lead your child to a strong basis in math, build self-confidence, aim high and achieve success.

### OUR UNIQUE METHOD

Our programs are designed to give kids more than they get at school. Our specially trained instructors are exceptional at math and love working with kids—they make all the difference.

Our educational materials and teaching techniques are designed to challenge students in year 1–12 beyond what they’re learning in school and broaden their skills in mathematics. In our center, we nurture and grow your child’s natural enthusiasm for math by broadening skills and challenging students to think the way that natural mathematical thinkers do.

Working in a small group environment or one-on- one, under the personal direction of highly qualified instructors, Eton Learners students develop cognitive learning techniques and study skills that help them perform better in daily schoolwork, classroom tests and public examinations.

**We teach students how to:**

- Study Efficiently
- Increase Thinking Skills
- Be More Organized
- Focus
- Create Independency
- Develop New Learning Strategies

**Results:**

- Increased Confidence
- Motivation
- Homework Success
- BETTER GRADES in school
- High scores in public exams such as SAT, ACT, IB and IGSCE

### ELEMENTARY SCHOOL MATH PROGRAM

At our center, we know how vital learning math is in elementary school—it forms the foundation for all your child’s future math studies. To make it understandable, we take an orderly, logical approach to teaching it to your child. We begin with computation and problem solving using whole numbers, and then move on to computation and problem solving with rational numbers—fractions, decimals, percentages, and negative numbers. (Interesting fact: In math, the word “rational” comes from the mathematical term “ratio.” It has nothing to do with being reasonable.) This foundation we give them is essential for pre-algebra and algebra, which they will encounter in middle school.

### OUR METHOD

Elementary school students work one to one with our instructors in a unique combination of mental, verbal, visual, tactile, and written exercises. Standards. Beyond teaching student’s all-important math concepts and skills, our special program helps them build number sense by showing them just how numbers work. As it progresses, students get more and more comfortable with numbers. We call this numerical fluency—the ability for elementary school kids to effortlessly recall addition and subtraction facts—a valuable asset when they face upcoming challenges in math.

Each child is evaluated with a written and verbal assessment unique to our program. Based on the assessment results, we create a custom program designed to help close educational gaps they may have and make it easier for them to jump ahead when they’re ready for advanced math challenges. Additionally, we help children understand their school homework as part of each session, as well as help them prepare for school tests, standardized tests, and various school entrance exams.

- Number and Algebra
- Number and place value
- Develop confidence with number sequences to and from 100 by ones from any starting point.
- Skip count by twos, fives and tens starting from zero
- Recognize, model, read, write and order numbers to at least 100. Locate these numbers on a number line
- Count collections to 100 by partitioning numbers using place value
- Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts

- Fractions and decimals
- Recognize and describe one-half as one of two equal parts of a whole.

- Money and financial mathematics
- recognize, describe and order Qatari coins according to their value Patterns and algebra
- Investigate and describe number patterns formed by skip-counting and patterns with objects

- Measurement and Geometry
- Using units of measurement
- Measure and compare the lengths and capacities of pairs of objects using uniform informal units
- Tell time to the half-hour
- Describe duration using months, weeks, days and hours

- Shape
- recognize and classify familiar two-dimensional shapes and three-dimensional objects using obvious features

- Location and transformation
- Give and follow directions to familiar locations

- Statistics and Probability
- Chance
- Identify outcomes of familiar events involving chance and describe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’

- Data representation and interpretation
- Choose simple questions and gather responses and make simple inferences
- Represent data with objects and drawings where one object or drawing represents one data value. Describe the displays

### YEAR 1 ACHIEVEMENT STANDARD

By the end of our Year 1 program, students will be able to:

- Describe number sequences resulting from skip counting by 2s, 5s and 10s.
- They identify representations of one half.
- They recognize Qatari coins according to their value. Students explain time durations.
- They describe two-dimensional shapes and three-dimensional objects. Students describe data displays.
- Students count to and from 100 and locate numbers on a number line.
- They carry out simple additions and subtractions using counting strategies.
- They partition numbers using place value.
- They continue simple patterns involving numbers and objects. Students order objects based on lengths and capacities using informal units.
- They tell time to the half-hour.
- They use the language of direction to move from place to place.
- Students classify outcomes of simple familiar events.
- They collect data by asking questions, draw simple data displays and make simple inferences.

- Whole Numbers
- Numbers up to 1000
- counting in tens/ hundreds,
- number notation and place values (hundreds, tens, ones),
- reading and writing numbers in numerals and in words,
- comparing and ordering numbers,
- number patterns.

- Addition and subtraction
- addition and subtraction of numbers up to 3 digits,
- solving up to 2-step word problems involving addition and subtraction.

- Multiplication and division
- building up the multiplication tables of 2, 3, 4, 5 and 10 and committing to memory,
- use of the division symbol (÷) to write a mathematical statement for a given situation,
- recognizing the relationship between multiplication and division,
- multiplication and division within the multiplication tables,
- solving 1-step word problems involving multiplication and division within the multiplication tables.

- Mental calculation
- a 3-digit number and ones,
- a 3-digit number and tens,
- a 3-digit number and hundreds.
- multiplication and division within the multiplication tables of 2, 3, 4, 5 and 10.

- FRACTIONS Fraction of a whole
- interpretation of fraction as part of a whole,
- reading and writing fractions,
- comparing and ordering
- * unit fractions,
- * like fractions.
- Include addition and subtraction of like fractions within one whole.

- MEASUREMENT Length, mass and volume
- estimation and measurement of
- length in meters/ centimeters,
- mass in kilograms/ grams,
- volume of liquid in liters,
- drawing a straight line of given length,
- use of the appropriate measures and their abbreviations cm, m, g, kg
- comparing
- lengths,
- masses,
- volumes,
- solving word problems involving length/ mass/ volume.

- Time
- telling and writing time to 5 minutes,
- use of ‘a.m.’ and ‘p.m.
- use of abbreviations h and min,
- drawing hands on the clock face to show time,
- duration of one hour/ half hour from an o’clock time.

- Money
- counting the amount of money in a given set of notes and coins,
- reading and writing money in decimal notation,
- comparing two or three amounts of money,
- converting an amount of money in decimal notation to cents only, and vice versa,
- solving word problems involving money in Qatar riyals only (or in dirhams only).

- GEOMETRY 2-D and 3-D figures
- identifying, naming and describing
- semicircle
- quarter circle,
- identifying the basic shapes that make up a given figure,
- forming different 2-D figures with cut-outs of
- rectangle
- square
- triangle
- semicircle
- quarter circle,
- forming different 3-D figures with concrete models of
- cube
- cuboid
- cone
- cylinder,
- copying figures on dot grid or square grid
- Patterns
- making/ completing patterns with 2-D cut-outs according to one or two of the following attributes
- shape
- size
- orientation
- color

- Line, curve and surface
- identifying lines (straight lines) and curves,
- identifying flat faces of a 3-D object

- DATA ANALYSIS Picture graphs
- making picture graphs with scales,
- reading and interpreting picture graphs with scales,
- solving problems using information presented in picture graphs

### YEAR 2 ACHIEVEMENT STANDARD

- By the end of our Year 2 program, students will be able to:
- recognize increasing and decreasing number sequences involving 2s, 3s and 5s.
- They represent multiplication and division by grouping into sets.
- They associate collections of Qatari coins with their value.
- Students identify the missing element in a number sequence.
- Students recognize the features of three-dimensional objects.
- They interpret simple maps of familiar locations. They explain the effects of one-step transformations.
- Students make sense of collected information.
- Students count to and from 1000.
- They perform simple addition and subtraction calculations using a range of strategies.
- They divide collections and shapes into halves, quarters and eighths. Students order shapes and objects using informal units.
- They tell time to the quarter-hour and use a calendar to identify the date and the months included in seasons.
- They draw two-dimensional shapes.
- They describe outcomes for everyday events.
- Students collect, organize and represent data to make simple inferences

Number & Place Value

- count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number.
- recognize the place value of each digit in a 3-digit number (100s, 10s, 1s).
- compare and order numbers up to 1,000.
- identify, represent and estimate numbers using different representations.
- read and write numbers up to 1,000 in numerals and in words.
- solve number problems and practical problems involving these ideas.
- Addition & Subtraction add and subtract numbers mentally, including:
- a three-digit number and 1s
- a three-digit number and 10s
- a three-digit number and 100s

- add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction
- estimate the answer to a calculation and use inverse operations to check answers
- solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

Multiplication & Division- recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
- write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods
- solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.

- Fractions
- count up and down in tenths; recognize that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10
- recognize, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
- recognize and use fractions as numbers: unit fractions and non-unit fractions with small denominators
- recognize and show, using diagrams, equivalent fractions with small denominators
- add and subtract fractions with the same denominator within one whole
- compare and order unit fractions, and fractions with the same denominators
- solve problems that involve all of the above.

- Measurement
- measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
- measure the perimeter of simple 2-D shapes.
- add and subtract amounts of money to give change, using both £ and p in practical contexts
- tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks
- estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o'clock, am/pm, morning, afternoon, noon and midnight
- know the number of seconds in a minute and the number of days in each month, year and leap year
- compare durations of events

- Properties of Shapes
- draw 2-D shapes and make 3-D shapes using modelling materials; recognize 3-D shapes in different orientations and describe them
- recognize angles as a property of shape or a description of a turn
- identify right angles, recognize that 2 right angles make a half-turn, 3 make three quarters of a turn and 4 a complete turn; identify whether angles are greater than or less than a right angle
- identify horizontal and vertical lines and pairs of perpendicular and parallel lines.

- Statistics
- interpret and present data using bar charts, pictograms and tables
- solve one-step and two-step questions using information presented in scaled bar charts and pictograms and tables.

### YEAR 3 ACHIEVEMENT STANDARD

- By the end of our Year 3 program, students will be able to:
- recognize the connection between addition and subtraction and solve problems using efficient strategies for multiplication.
- They model and represent unit fractions.
- They represent money values in various ways.
- Students identify symmetry in the environment.
- They match positions on maps with given information.
- Students recognize angles in real situations.
- They interpret and compare data displays.
- Students count to and from 10 000.
- They classify numbers as either odd or even.
- They recall addition and multiplication facts for single-digit numbers.
- Students correctly count out change from financial transactions.
- They continue number patterns involving addition and subtraction.
- Students use metric units for length, mass and capacity.
- They tell time to the nearest minute. Students make models of three-dimensional objects.
- They conduct simple data investigations for categorical variables

- Whole Numbers

Numbers up to 100 000- number notation and place values (ten thousands, thousands, hundreds, tens, ones),
- reading and writing numbers in numerals and in words,
- comparing and ordering numbers,
- number patterns,
- rounding off numbers to the nearest 10 or 100,
- use of the approximation symbol

- Multiplication and division
- multiplication of a 4-digit number by a 1-digit number,
- multiplication of a 3-digit number by a 2-digit number,
- division of a 4-digit number by a 1-digit number,
- solving up to 3-step word problems involving the 4 operations,
- estimation of answers in calculations involving the 4 operations,
- checking reasonableness of answers

- Factors and multiples
- determining if a 1-digit number is a factor of a given number,
- listing all factors of a given number up to 100,
- finding the common factors of two given numbers,
- recognizing the relationship between factor and multiple,
- determining if a number is a multiple of a given 1-digit number,
- listing the first 12 multiples of a given 1-digit number,
- finding the common multiples of two given 1-digit numbers.
- Exclude 'highest common factor' (H.C.F.) and 'lowest common multiple’ (L.C.M.).

- FRACTIONS

Mixed numbers and improper fractions- concepts of mixed numbers and improper fractions,
- expressing an improper fraction as a mixed number, and vice versa,
- expressing an improper fraction/mixed number in its simplest form.
- (Denominators of given fractions should not exceed 12.)

- Addition and subtraction
- like fractions,
- related fractions.
- (Denominators of given fractions should not exceed 12.)
- Exclude calculations involving more than 2 different denominators

- Fraction of a set of objects
- Include interpretation of fraction as part of a set of objects

- Multiplication
- multiplication of a proper/improper fraction and a whole number,
- solving up to 2-step word problems involving addition, subtraction and multiplication,
- using unitary method to find the whole given a fractional part

- DECIMALS

Decimals up to 3 decimal places- notation and place values (tenths, hundredths, thousandths),
- identifying the values of the digits in a decimal,
- use of the number line to display decimals,
- comparing and ordering decimals,
- conversion of a decimal to a fraction,
- conversion of a fraction whose denominator is a factor of 10 or 100 to a decimal,
- rounding off decimals to
- the nearest whole number,
- 1 decimal place,
- 2 decimal places.

- Addition and subtraction
- addition and subtraction of decimals (up to 2 decimal places),
- estimation of answers in calculations,
- checking reasonableness of answers

- Multiplication and division
- division of a whole number by a whole number with answer in decimal form,
- multiplication and division of decimals (up to 2 decimal places) by a 1-digit whole number,
- solving up to 2-step word problems involving the 4 operations,
- rounding off answers to a specified degree of accuracy,
- estimation of answers in calculations,
- checking reasonableness of answers

- MEASUREMENT

Time- measurement of time in seconds (s),
- 24-hour clock,
- solving word problems involving time in 24-hour clock.

- multiplication and division of money in decimal notation,
- solving word problems involving the 4 operations of money in decimal notation

- finding the area of a composite figure made up of rectangles and squares,
- finding one dimension of a rectangle given the other dimension and its area/ perimeter,
- finding the length of one side of a square given its area/ perimeter,
- solving word problems involving the area/ perimeter of squares and rectangles.

- Perpendicular and parallel lines
- drawing of perpendicular and parallel lines using ruler and set squares,
- use of the terms ‘vertical’ and ‘horizontal

- using notation such as ∠ABC and ∠x to name angles,
- estimation and measurement of angles in degrees,
- drawing an angle using a protractor,
- associating
- turn/ right angle with 90o
- turn with 180o
- turn with 270o
- a complete turn with 360 o
- 8-point compass.

- properties of rectangle and square,
- finding unknown angles

- identifying symmetric figures,
- determining whether a straight line is a line of symmetry of a symmetric figure,
- completing a symmetric figure with respect to a given horizontal/vertical line of symmetry,
- designing and making patterns

Tables

- completing a table from given data,
- reading and interpreting tables,
- solving problems using information presented in tables.

- reading and interpreting line graphs,
- solving problems using information presented in line graphs.

### YEAR 4 ACHIEVEMENT STANDARD

- By the end of our Year 4 program, students will be able to:
- choose appropriate strategies for calculations involving multiplication and division.
- They recognize common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two decimal places.
- Students solve simple purchasing problems.
- They identify and explain strategies for finding unknown quantities in number sentences.
- They describe number patterns resulting from multiplication.
- Students compare areas of regular and irregular shapes using informal units.
- They solve problems involving time duration.
- They interpret information contained in maps.
- Students identify dependent and independent events.
- They describe different methods for data collection and representation, and evaluate their effectiveness.
- Students use the properties of odd and even numbers.
- They recall multiplication facts to 10 x 10 and related division facts.
- Students locate familiar fractions on a number line.
- They continue number sequences involving multiples of single digit numbers.
- Students use scaled instruments to measure temperatures, lengths, shapes and objects.
- They convert between units of time. Students create symmetrical shapes and patterns.
- They classify angles in relation to a right angle.
- Students list the probabilities of everyday events.
- They construct data displays from given or collected data.

- Number & Place Value
- read, write, order and compare numbers up to 10 000 000 and determine the value of each digit
- Round any whole number to a required degree of accuracy
- use negative numbers in context, and calculate intervals across 0
- solve number and practical problems that involve all of the above.

- Addition, Subtraction, Multiplication & Division
- multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
- divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
- divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
- perform mental calculations, including with mixed operations and large numbers.
- identify common factors, common multiples and prime numbers
- use their knowledge of the order of operations to carry out calculations involving the 4 operations
- solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
- solve problems involving addition, subtraction, multiplication and division
- use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

- Fractions (decimals & percentages)
- use common factors to simplify fractions; use common multiples to express fractions in the same denomination
- compare and order fractions, including fractions >1
- add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
- multiply simple pairs of proper fractions, writing the answer in its simplest form
- divide proper fractions by whole numbers
- associate a fraction with division and calculate decimal fraction equivalents for a simple fraction.
- identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers are up to three decimal places
- multiply one-digit numbers with up to 2 decimal places by whole numbers
- use written division methods in cases where the answer has up to 2 decimal places
- solve problems which require answers to be rounded to specified degrees of accuracy
- recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

- Ratio & Proportion
- solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
- solve problems involving the calculation of percentages and the use of percentages for comparison
- solve problems involving similar shapes where the scale factor is known or can be found
- solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

- Algebra
- use simple formulae
- generate and describe linear number sequences
- express missing number problems algebraically
- find pairs of numbers that satisfy an equation with two unknowns
- enumerate possibilities of combinations of 2 variables.

- Measurement
- solve problems involving the calculation and conversion of units of measure, using decimal notation up to 2 decimal places where appropriate
- use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to 3 decimal places
- convert between miles and kilometers
- recognize that shapes with the same areas can have different perimeters and vice versa
- recognize when it is possible to use formulae for area and volume of shapes
- calculate the area of parallelograms and triangles
- calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimeters (cm3) and cubic meters (m3), and extending to other units

- Properties of Shape
- draw 2-D shapes using given dimensions and angles
- recognize, describe and build simple 3-D shapes, including making nets
- compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
- illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
- recognize angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.

- Position & Direction
- describe positions on the full coordinate grid (all 4 quadrants)
- draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

- Statistics
- interpret and construct pie charts and line graphs and use these to solve problems
- calculate and interpret the mean as an average.

### YEAR 5 ACHIEVEMENT STANDARD

- By the end of our Year 5 program, students will be able to:
- solve simple problems involving the four operations using a range of strategies.
- They check the reasonableness of answers using estimation and rounding.
- Students identify and describe factors and multiples.
- They identify and explain strategies for finding unknown quantities in number sentences involving the four operations.
- They explain plans for simple budgets.
- Students connect three-dimensional objects with their two-dimensional representations.
- They describe transformations of two-dimensional shapes and identify line and rotational symmetry.
- Students interpret different data sets.
- Students order decimals and unit fractions and locate them on number lines.
- They add and subtract fractions with the same denominator.
- Students continue patterns by adding and subtracting fractions and decimals.
- They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles.
- They convert between 12- and 24-hour time.
- They measure and construct different angles.
- Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1.
- Students pose questions to gather data, and construct data displays appropriate for the data.

** FRACTIONS **

- Concepts of fractions
- fraction of a whole,
- fraction of a set of objects

- Equivalent fractions
- recognizing and naming equivalent fractions,
- listing the first 8 equivalent fractions of a given fraction,
- writing the equivalent fraction of a fraction given the denominator or the numerator,
- expressing a fraction in its simplest form,
- comparing fractions with respect to half,
- comparing and ordering unlike fractions.
- (Denominators of given fractions should not exceed 12.)

- Mixed numbers and improper fractions
- expressing an improper fraction as a mixed number, and vice versa,
- expressing an improper fraction/mixed number in its simplest form.

- Four operations
- Include division of a whole number/proper fraction by a proper fraction without using calculators.
- division of an improper fraction/mixed number by a proper fraction,
- division by an improper fraction/mixed number.

- PERCENTAGE
- finding the whole given a part and the percentage,
- finding percentage increase/decrease,
- solving word problems involving percentage

- RATIO
- expressing one quantity as a fraction of another, given their ratio, and vice versa,
- finding how many times one quantity is as large as another, given their ratio, and vice versa,
- expressing one quantity as a fraction of another given the two quantities,
- finding the whole/ one part when a whole is divided into parts in a given ratio,
- solving word problems involving 2 pairs of ratios

- SPEED
Distance, time and speed

- concepts of speed and average speed,
- relationship between distance, time and speed
- Distance = Speed × Time,
- Speed = Distance ÷ time,
- Time = Distance ÷ speed,
- calculation of speed, distance or time given the other two quantities,
- writing speed in different units such as km/h, m/min, m/s and cm/s,
- solving up to 3-step word problems involving speed and average speed.

- MEASUREMENT
Area and circumference of circle

- use of formulae to calculate the area and circumference of a circle,
- finding the area and perimeter of
- semicircle (half circle)
- quarter circle
- solving word problems involving area and perimeter.

- Area and perimeter of composite figure
- Include finding the area and perimeter of a figure made up of some of the following shapes: square,
- rectangle,
- triangle,
- semicircle and quarter circle.

- Volume of cube and cuboid
- finding one dimension of a cuboid given its volume and the other dimensions,
- finding the length of one edge of a cube given its volume,
- finding the height of a cuboid given its volume and base area,
- finding the area of a face of a cuboid given its volume and one dimension,
- use of the symbols
- solving word problems involving volume of a cube/ cuboid

- GEOMETRY
Geometrical figures

- Include finding unknown angles in geometrical figures involving square,
- rectangle,
- parallelogram,
- rhombus,
- trapezium and triangle
Triangle

- identifying and naming the following types of triangles
- isosceles triangle,
- equilateral triangle,
- right-angled triangle,
- use of the property that the angle sum of a triangle is 180o,
- drawing a triangle from given dimensions using ruler, protractor and set squares.

- Angles in geometric figures
- Include finding unknown angles in geometrical figures using the properties of:
- angles on a straight line,
- angles at a point,
- vertically opposite angles,
- a square, a rectangle and a triangle

- Nets
- 2-D representation of cube, cuboid, cone, cylinder, prism and pyramid,
- identifying nets of the following solids
- cube,
- cuboid,
- prism,
- pyramid,
- identifying the solid which can be formed by a given net,
- making 3-D solids from given nets.

- DATA ANALYSIS
Pie charts

- reading and interpreting pie charts,
- solving 1-step problems using information presented in pie charts.

- ALGEBRA
Algebraic expressions in one variable

- representation of an unknown number using a letter,
- simple algebraic expressions such as
- y ± 2, 6 ± y
- y + y
- 3y
- y2
- 35±y

- interpreting * 3y as y + y + y or 3 × y * y2 as y ÷ 2 or 21 × y * 35±y as (3 ± y) ÷ 5 or 51 × (3 ± y)
- simplification of algebraic expressions,
- evaluation of simple algebraic expressions by substitution,
- solving word problems involving algebraic expressions.
- simplification of expressions involving
- fractional coefficients brackets

### YEAR 6 ACHIEVEMENT STANDARD

- By the end of our Year 6 program, students will be able to:
- recognize the properties of prime, composite, square and triangular numbers.
- They describe the use of integers in everyday contexts.
- They solve problems involving all four operations with whole numbers.
- Students connect fractions, decimals and percentages as different representations of the same number.
- They solve problems involving the addition and subtraction of related fractions.
- Students make connections between the powers of 10 and the multiplication and division of decimals.
- They describe rules used in sequences involving whole numbers, fractions and decimals.
- Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation.
- They make connections between capacity and volume.
- They solve problems involving length and area.
- They interpret timetables.
- Students describe combinations of transformations.
- They solve problems using the properties of angles.
- Students compare observed and expected frequencies.
- They interpret and compare a variety of data displays including those displays for two categorical variables.
- They interpret secondary data displayed in the media.
- Students locate fractions and integers on a number line.
- They calculate a simple fraction of a quantity.
- They add, subtract and multiply decimals and divide decimals where the result is rational.
- Students calculate common percentage discounts on sale items.
- They write correct number sentences using brackets and order of operations.
- Students locate an ordered pair in any one of the four quadrants on the Cartesian plane.
- They construct simple prisms and pyramids.
- Students describe probabilities using simple fractions, decimals and percentages.

### MIDDLE SCHOOL MATH PROGRAM

In our middle school program, students master computation and problem solving with rational numbers, i.e., fractions, decimals, and percentage, as part of the process of algebra readiness—preparing for first-year algebra (algebra I). This creates a solid mathematical foundation for future subjects such as algebra II, geometry, trigonometry, and pre-calculus.

### OUR APPROACH

Middle school students engage one to one with our instructors in a unique combination of mental, verbal, visual, tactile, and written exercises. Basic math concepts and skills are blended with a program specifically designed to help students build number sense. This special program shows them how and why the useful number rules they’re learning work so they are able to understand how they can be applied to interesting areas such as computer science, biology, and psychology.

Middle school math builds upon elementary math’s foundation and focuses on explaining why mathematical rules work so that children learn and understand the rules, not just memorize them.

We also help students understand their homework as part of each session and prepare them for school tests, as well as standardized tests such as high school entrance exams.

- Number
- Students will learn how to:
- use place value for decimals, measures and integers of any size
- order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, ≤, ≥
- use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorization, including using product notation and the unique factorization property
- use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
- use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
- recognize and use relationships between operations including inverse operations
- use integer powers and associated real roots (square, cube and higher), recognize powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations
- interpret and compare numbers in standard form A x 10n 1≤Awhere n is a positive or negative integer or zero
- work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 2 7 or 0.375 and 8 3)
- define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%
- interpret fractions and percentages as operators
- use standard units of mass, length, time, money and other measures, including with decimal quantities
- round numbers and measures to an appropriate degree of accuracy (for example, to a number of decimal places or significant figures)

- Algebra
- Students will learn how to:
- use and interpret algebraic notation, including: ab in place of a × b , 3y in place of y + y + y and 3 × y , a2 in place of a × a, a3 in place of a × a × a; a2 b in place of a × a × b , b a in place of a ÷ b , coefficients written as fractions rather than as decimals , brackets , substitute numerical values into formulae and expressions, including scientific formulae
- understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
- simplify and manipulate algebraic expressions to maintain equivalence by: collecting like terms and multiplying a single term over a bracket
- taking out common factors
- expanding products of two or more binomials
- understand and use standard mathematical formulae; rearrange formulae to change the subject
- model situations or procedures by translating them into algebraic expressions or formulae and by using graphs
- use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
- work with coordinates in all four quadrants
- recognize, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
- interpret mathematical relationships both algebraically and graphically
- reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations
- find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs
- generate terms of a sequence from either a term-to-term or a position-to-term rule
- recognize arithmetic sequences and find the nth term
- recognize geometric sequences and appreciate other sequences that arise

- Ratio, proportion and rates of change
- Students will learn how to:
- change freely between related standard units (for example time, length, area, volume/capacity, mass)
- use scale factors, scale diagrams and maps
- express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
- use ratio notation, including reduction to simplest form
- divide a given quantity into two parts in a given part: part or part: whole ratio; express the division of a quantity into two parts as a ratio
- understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
- relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
- solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
- solve problems involving direct and inverse proportion, including graphical and algebraic representations
- use compound units such as speed, unit pricing and density to solve problems

- Geometry and measures
- Students will learn how to:
- derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)
- calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
- draw and measure line segments and angles in geometric figures, including interpreting scale drawings
- derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognize and use the perpendicular distance from a point to a line as the shortest distance to the line
- describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
- use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
- derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures (for example, equal lengths and angles) using appropriate language and technologies
- identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
- identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids
- apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
- understand and use the relationship between parallel lines and alternate and corresponding angles
- derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons
- apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs
- use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
- use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
- interpret mathematical relationships both algebraically and geometrically.

- Probability
- Students will learn how to:
- record, describe and analyze the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale
- understand that the probabilities of all possible outcomes sum to 1
- enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
- generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities. Statistics
- Students will learn how to:
- describe interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)
- construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
- describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.

### YEAR 7 ACHIEVEMENT STANDARD

- By the end of our Year 7 program, students will be able to:
- solve problems involving the comparison, addition and subtraction of integers.
- They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots.
- They solve problems involving percentages and all four operations with fractions and decimals.
- They compare the cost of items to make financial decisions. Students represent numbers using variables.
- They connect the laws and properties for numbers to algebra.
- They interpret simple linear representations and model authentic information.
- Students describe different views of three-dimensional objects.
- They represent transformations in the Cartesian plane.
- They solve simple numerical problems involving angles formed by a transversal crossing two lines.
- Students identify issues involving the collection of continuous data.
- They describe the relationship between the median and mean in data displays.
- Students use fractions, decimals and percentages, and their equivalences.
- They express one quantity as a fraction or percentage of another.
- Students solve simple linear equations and evaluate algebraic expressions after numerical substitution.
- They assign ordered pairs to given points on the Cartesian plane.
- Students use formulas for the area and perimeter of rectangles and calculate volumes of rectangular prisms.
- Students classify triangles and quadrilaterals.
- They name the types of angles formed by a transversal crossing parallel line.
- Students determine the sample space for simple experiments with equally likely outcomes and assign probabilities to those outcomes.
- They calculate mean, mode, median and range for data sets
- They construct stem-and-leaf plots and dot-plots.

- Number
- Students will be thought how to :
- apply systematic listing strategies, {including use of the product rule for counting}
- {estimate powers and roots of any given positive number}
- calculate with roots, and with integer {and fractional} indices
- calculate exactly with fractions, {surds} and multiples of π; {simplify surd expressions involving squares (for example 12 4 3 4 3 2 3 = ×= × = ×) and rationalize denominators}
- calculate with numbers in standard form A 10n, where 1 ≤ A < 10 and n is an integer
- {change recurring decimals into their corresponding fractions and vice versa}
- identify and work with fractions in ratio problems
- apply and interpret limits of accuracy when rounding or truncating, {including upper and lower bounds}.

- Algebra I
- Students will be thought how to:
- simplify and manipulate algebraic expressions (including those involving surds {and algebraic fractions}) by:
- factorizing quadratic expressions of the form 2 x bx c + + 2 ax bx c + +, including the difference of two squares; {factorizing quadratic expressions of the form}
- simplifying expressions involving sums, products and powers, including the laws of indices
- know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments {and proofs}
- where appropriate, interpret simple expressions as functions with inputs and outputs; {interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’}
- use the form y mx c = + to identify parallel {and perpendicular} lines; find the equation of the line through two given points, or through one point with a given gradient
- identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square}
- recognize, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function 1 y = x y x = cos with x ≠ 0, {the exponential function x y k = y x = sin for positive values of k, and the trigonometric functions (with arguments in degrees), and y x = tan for angles of any size}
- {sketch translations and reflections of the graph of a given function}
- plot and interpret graphs (including reciprocal graphs {and exponential graphs}) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration
- {calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts}
- {recognize and use the equation of a circle with center at the origin; find the equation of a tangent to a circle at a given point}
- solve quadratic equations {including those that require rearrangement} algebraically by factorizing, {by completing the square and by using the quadratic formula}; find approximate solutions using a graph
- solve two simultaneous equations in two variables (linear/linear {or linear/quadratic}) algebraically; find approximate solutions using a graph
- {find approximate solutions to equations numerically using iteration}
- translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution
- solve linear inequalities in one {or two} variable{s}, {and quadratic inequalities in one variable}; represent the solution set on a number line, {using set notation and on a graph}
- recognize and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (r n where n is an integer, and r is a positive rational number {or a surd}) {and other sequences}
- deduce expressions to calculate the nth term of linear {and quadratic} sequences

- Ratio, proportion and rates of change
- Students will be thought how to:
- compare lengths, areas and volumes using ratio notation and/or scale factors; make links to similarity (including trigonometric ratios)
- convert between related compound units (speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts
- understand that X is inversely proportional to Y is equivalent to X is proportional to 1 Y; {construct and} interpret equations that describe direct and inverse proportion
- interpret the gradient of a straight line graph as a rate of change; recognize and interpret graphs that illustrate direct and inverse proportion
- {interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of instantaneous and average rate of change (gradients of tangents and chords) in numerical, algebraic and graphical contexts}
- set up, solve and interpret the answers in growth and decay problems, including compound interest {and work with general iterative processes}.

- Geometry and measures
- Students will be thought how to:
- interpret and use fractional {and negative} scale factors for enlargements
- {describe the changes and invariance achieved by combinations of rotations, reflections and translations}
- identify and apply circle definitions and properties, including: Centre, radius, chord, diameter, circumference, tangent, arc, sector and segment
- apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results
- construct and interpret plans and elevations of 3D shapes
- interpret and use bearings
- calculate arc lengths, angles and areas of sectors of circles
- calculate surface areas and volumes of spheres, pyramids, cones and composite solids
- apply the concepts of congruence and similarity, including the relationships between lengths, {areas and volumes} in similar figures, apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in two {and three} dimensional figures
- know and apply the sine rule, and cosine rule, to find unknown lengths and angles
- know and apply to calculate the area, sides or angles of any triangle
- describe translations as 2D vectors
- apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; {use vectors to construct geometric arguments and proofs}.

- Probability
- Students will be thought how to:
- apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one
- use a probability model to predict the outcomes of future experiments; understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
- calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions
- calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams.

- Statistics
- Students will be thought how to:
- infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling
- interpret and construct tables and line graphs for time series data
- construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use
- interpret, analyze and compare the distributions of data sets from univariate empirical distributions through:
- appropriate graphical representation involving discrete, continuous and grouped data, {including box plots}
- appropriate measures of central tendency (including modal class) and spread {including quartiles and inter-quartile range}
- apply statistics to describe a population
- use and interpret scatter graphs of bivariate data; recognize correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends

### YEAR 8 ACHIEVEMENT STANDARD

- By the end of our Year 8 program, students will be able to:
- solve everyday problems involving rates, ratios and percentages.
- They describe index laws and apply them to whole numbers.
- They describe rational and irrational numbers.
- Students solve problems involving profit and loss.
- They make connections between expanding and factorizing algebraic expressions.
- Students solve problems relating to the volume of prisms.
- They make sense of time duration in real applications.
- They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals.
- Students model authentic situations with two-way tables and Venn diagrams.
- They choose appropriate language to describe events and experiments.
- They explain issues related to the collection of data and the effect of outliers on means and medians in that data.
- Students use efficient mental and written strategies to carry out the four operations with integers.
- They simplify a variety of algebraic expressions.
- They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume.
- They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites.
- They name the features of circles and calculate the areas and circumferences of circles.
- Students determine the probabilities of complementary events and calculate the sum of probabilities

- Number and Algebra

Real numbers- Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding too simple rate problems
- Apply index laws to numerical expressions with integer indices
- Express numbers in scientific notation

- Money and financial mathematics
- Solve problems involving simple interest

- Patterns and algebra
- Extend and apply the index laws to variables, using positive integer indices and the zero index
- Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate
- Linear and non-linear relationships
- Find the distance between two points located on the Cartesian plane using a range of strategies, including graphing software
- Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software
- Sketch linear graphs using the coordinates of two points and solve linear equations
- Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations

- Measurement and Geometry

Using units of measurement- Calculate areas of composite shapes
- Calculate the surface area and volume of cylinders and solve related problems
- Solve problems involving the surface area and volume of right prisms
- Investigate very small and very large time scales and intervals

- Geometric reasoning
- Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar
- Solve problems using ratio and scale factors in similar figures

- Pythagoras and trigonometry
- Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles
- Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles
- Apply trigonometry to solve right-angled triangle problems

- Statistics and Probability

Chance- List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events
- Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or'
- Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians

- Data representation and interpretation
- Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly and from secondary sources
- Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’
- Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (center) and spread

### YEAR 9 ACHIEVEMENT STANDARD

By the end of our Year 9 program, students will be able to:

- solve problems involving simple interest.
- They interpret ratio and scale factors in similar figures.
- Students explain similarity of triangles.
- They recognize the connections between similarity and the trigonometric ratios. Students compare techniques for collecting data from primary and secondary sources.
- They make sense of the position of the mean and median in skewed, symmetric and bi-modal displays to describe and interpret data.
- Students apply the index laws to numbers and express numbers in scientific notation.
- They expand binomial expressions.
- They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment.
- They sketch linear and non-linear relations. Students calculate areas of shapes and the volume and surface area of right prisms and cylinders.
- They use Pythagoras’ Theorem and trigonometry to find unknown sides of right-angled triangles.
- Students calculate relative frequencies to estimate probabilities, list outcomes for two-step experiments and assign probabilities for those outcomes.
- They construct histograms and back-to-back stem-and-leaf plots.

### HIGH SCHOOL MATH PROGRAM

In high school, students focus on higher math—including algebra I, geometry, algebra II, trigonometry, and pre-calculus—in preparation for high school exit exams, college placement exams, and standardized college entrance exams such as the SAT and the ACT.

#### OUR APPROACH

By the time they reach high school, all students perform at different skill levels. To determine each student’s abilities, we give each one a written and verbal assessment. Based on the assessment results, our team builds a customized learning plan designed to fit the student’s specific needs in two important ways—to avoid spending time on things they already know and to strengthen the things they need help on.

We understand the pressures and busy schedules our high school students face, so our focus is to help with immediate problems, such as homework help and test prep, while filling in any foundational gaps in their mathematical knowledge. The goal is to enhance their performance in the crucial exams they’ll be taking that can have a great effect on their future—high school exit exams, college placement exams, and standardized college entrance exams such as the SAT and the ACT.

- Number and Algebra Money and financial mathematics
- Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies

- Patterns and algebra
- factorize algebraic expressions by taking out a common algebraic factor
- Simplify algebraic products and quotients using index laws
- Apply the four operations to simple algebraic fractions with numerical denominators
- Expand binomial products and factorize monic quadratic expressions using a variety of strategies
- Substitute values into formulas to determine an unknown

- Linear and non-linear relationships
- Solve problems involving linear equations, including those derived from formulas
- Solve linear inequalities and graph their solutions on a number line
- Solve linear simultaneous equations, using algebraic and graphical techniques, including using digital technology
- Solve problems involving parallel and perpendicular lines
- Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate
- Solve linear equations involving simple algebraic fractions
- Solve simple quadratic equations using a range of strategies

- Measurement and Geometry

Using units of measurement- Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids

- Geometric reasoning
- Formulate proofs involving congruent triangles and angle properties
- Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes Pythagoras and trigonometry
- Solve right-angled triangle problems including those involving direction and angles of elevation and depression

- Statistics and Probability

Chance- Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events.
- Investigate the concept of independence
- Use the language of ‘if ...then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language

- Data representation and interpretation
- Determine quartiles and interquartile range
- Construct and interpret box plots and use them to compare data sets
- Compare shapes of box plots to corresponding histograms and dot plots
- Use scatter plots to investigate and comment on relationships between two numerical variables
- Investigate and describe bivariate numerical data where the independent variable is time
- Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data

### YEAR 10 ACHIEVEMENT STANDARD

- By the end of our Year 10 program, students will be able to:
- Recognize the connection between simple and compound interest.
- They solve problems involving linear equations and inequalities.
- They make the connections between algebraic and graphical representations of relations.
- Students solve surface area and volume problems relating to composite solids.
- They recognize the relationships between parallel and perpendicular lines.
- Students apply deductive reasoning to proofs and numerical exercises involving plane shapes.
- They compare data sets by referring to the shapes of the various data displays.
- They describe bivariate data where the independent variable is time.
- Students describe statistical relationships between two continuous variables.
- They evaluate statistical reports.
- Students expand binomial expressions and factorize monic quadratic expressions.
- They find unknown values after substitution into formulas.
- They perform the four operations with simple algebraic fractions.
- Students solve simple quadratic equations and pairs of simultaneous equations.
- They use triangle and angle properties to prove congruence and similarity.
- Students use trigonometry to calculate unknown angles in right-angled triangles.
- Students list outcomes for multi-step chance experiments and assign probabilities for these experiments.
- They calculate quartiles and inter-quartile ranges.

### HIGH SCHOOL HOMEWORK HELP

Our experienced math instructors provide homework and study help that addresses gaps in knowledge. As these gaps close, students understand the material better, boost homework confidence, and raise their assignment grades. With this help, instead of seeing homework as a burden, students begin to see it as a welcome challenge and an opportunity for further learning

### TEST PREPARATION

Students who prepare for standardized tests such as the SAT, ACT, IB, IGSCE, High school exit exams, and college placement exams at our Center enjoy a substantial advantage over those who don’t.

#### OUR UNIQUE STRATEGY

We provide each student with a test prep curriculum customized to their specific needs. To assess their math skills, each student is given a math skills assessment. Based on the strengths and weaknesses identified in this assessment, we develop a personal instruction plan for the student. Working with that—and giving them practical practice in test taking—we optimize their performance.

The result: enhanced results on the actual exams and a more positive step into their future

#### A Sample of the Work Your Child Will Be Doing to Become Ready for College and Career

- Number and Quantity
- Working with rational and irrational numbers, including working with rational exponents (e.g., rewriting (53) 1/2 as 5√5)
- Solving problems with a wide range of units and solving problems by thinking about units (e.g., “The Trans Alaska Pipeline System is 800 miles long and cost $8 billion to build. Divide one of these numbers by the other. What is the meaning of the answer?”; “Greenland has a population of 56,700 and a land area of 2,175,600 square kilometers. By what factor is the population density of the United States, 80 persons per square mile, larger than the population density of Greenland?”)

- Algebra
- Solving real-world and mathematical problems by writing and solving nonlinear equations, such as quadratic equations (ax2 + bx + c = 0)
- Interpreting algebraic expressions and transforming them purposefully to solve problems (e.g., in solving a problem about a loan with interest rate r and principal P, seeing the expression P(1+r) n as a product of P with a factor not depending on P)

- Functions
- Analyzing functions algebraically and graphically, and working with functions presented in different forms (e.g., given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum)
- Working with function families and understanding their behavior (such as linear, quadratic, and exponential functions)

- Modeling
- Analyzing real-world situations using mathematics to understand the situation better and optimize, troubleshoot, or make an informed decision (e.g., estimating water and followingd negativeativeeds in a disaster area, or using volume formulas and graphs to find an optimal size for an industrial package)

- Geometry
- Proving theorems about triangles and other figures (e.g., that the angles in a triangle add to 180º)
- Solving applied problems involving trigonometry of right triangles
- Using coordinates and equations to describe geometric properties algebraically (e.g., writing the equation for a circle in the plane with specified center and radius) Statistics and Probability
- Making inferences and justifying conclusions from sample surveys, experiments, and observational studies
- Working with probability and using ideas from probability in everyday situations (e.g., comparing the chance that a person who smokes will develop lung cancer to the chance that a person who develops lung cancer smokes