## CONTENTS Almost on the threshold of high school, Grade 8 is always considered to be the fun grade. This is also the year where academic competition starts to rise and directions towards future careers begin to be mapped. Strengthening of mathematics concept in this grade also becomes imperative. Moving from the world of basic decimals and fractions, Grade 8 further explores equations and proportional relationships and introduces the concepts of quadrants and axes. ## Number theory The study of whole numbers and their properties is called Number theory. Number theory is a large and interesting area in mathematics, including studying Prime numbers, rational numbers and so on. Number theory is important because it helps you to understand and master how the numbers function which helps with logical reasoning skills.

Factors

Divisibility rules

Prime or composite

Prime factorization

Greatest common factor

Least common multiple

GCF and LCM: word problems

Classify numbers

## Integers Integers are like whole numbers which means they do not have fraction or decimal part but unlike whole numbers they can be negative. Understanding integers will help you to understand that negative and positive numbers are used together to describe quantities having opposite direction or values.

Integers on number lines

Graph integers on horizontal and vertical number lines

Absolute value and opposite integers

Compare and order integers

Integer inequalities with absolute values

## Operations with integers Four basic operations with integer numbers. In the primary grades, students develop an understanding of part-whole concepts – they learn that two or more parts can be combined to create a whole (addition) or they can be separated from a whole (Subtraction). The multiplication of numbers is repeated addition. Separation of partitioning of objects from a set for an equal share without any disparity in the fixed number of groups.

Add and subtract integers using counters

Add and subtract three or more integers

Add and subtract integers: word problems

Integer multiplication and division rules

Multiply and divide integers

Evaluate numerical expressions involving integers

## Operations with fractions Four basic operations with fraction numbers. We can add or subtract fractions like the normal numbers if their denominators are equal. If the denominators are not equal, we must change it by multiplying or dividing but we have to apply the same to the top (numerators). Multiplying the fractions is quite easy, you have to just multiply the numerators and denominators to each other and at the end just simplify the fraction if needed. To divide the fractions, you need to upside down the second fraction and then multiply them together.

Write fractions in lowest terms

Least common denominator

Add and subtract fractions with like denominators

Subtract fractions with unlike denominators

Inequalities with addition and subtraction of fractions and mixed numbers

Reciprocals and multiplicative inverses

Multiply fractions and whole numbers

Multiply two fractions using models

Multiply fractions

Divide whole numbers by unit fractions using models

Divide whole numbers and unit fractions

Divide fractions

## Rational numbers A Rational number is made by dividing two integers (integer is a number with no fraction or decimal part). Most of the numbers we use in everyday life are rational numbers. If you can write a number as a simple fraction, then it is a rational number.

Identify rational and irrational numbers

Round decimals and mixed numbers

Absolute value of rational numbers

Convert between decimals and fractions or mixed numbers

Compare rational numbers

Put rational numbers in order

## Operations with rational numbers Four basic operations with rational numbers. If you can write a number as a simple fraction, then it is a rational number, so can simply follow the rules of operation for fraction numbers.

Add and subtract rational numbers: word problems

Multiply and divide rational numbers

Multiply and divide rational numbers: word problems

Evaluate numerical expressions involving rational numbers

Apply multiplication and division rules

Apply addition, subtraction, multiplication and division rules

## Exponents and roots The exponent of a number tells us how many times to multiply that number with itself. It is written as a small number to the right and above the base number.

Understanding exponents

Evaluate exponents

Solve equations with variable exponents

Exponents with negative bases

Exponents with decimal and fractional bases

Square roots of perfect squares

Estimate square roots

Relationship between squares and square roots

Solve equations involving squares and square roots

## Scientific notation Scientific notation is a way of representing a number where that number is written in two parts: just the digits with the decimal point placed after the first digit, followed by power of 10.

Convert between standard and scientific notation

Compare numbers written in scientific notation

## Ratios, rates and proportions A ratio shows the relative sizes of two or more values, in other words a Ratio compares values. A ratio says how much of one thing there is compared to another thing. For example, if there is 1 boy and 3 girls, we can write the ratio like 1:3 (for every 1 boy there are 3 girls.) Ratio, rates and proportion skills are useful to understand the association between two quantities.

Understanding ratios

Identify equivalent ratios

Write an equivalent ratio

Equivalent ratios: word problems

Unit rates
Compare ratios: word problems

Solve proportions: word problems

Do the ratios form a proportion?

Do the ratios form a proportion: word problems

Solve proportions

Estimate population size using proportions

Scale drawings: word problems

## Proportional relationships Proportion says that two ratios or fractions are equal. When quantities have the same relative size when say they have proportional relationship; or in other word they have the same ratio. Understanding of ratios and proportional relationships is very important to enhance math skills of fractions, decimals, rates, and etc.

Find the constant of proportionality from a table

Write equations for proportional relationships from tables

Identify proportional relationships by graphing

Find the constant of proportionality from a graph

Write equations for proportional relationships from graphs

Identify proportional relationships

Graph proportional relationships

Interpret graphs of proportional relationships

Write and solve equations for proportional relationships

## Percents “Percent” comes from the Latin Per Centum. The Latin word Centum means 100. When we say Percent, we mean per 100, so 1 percent means 1 per 100. We use the symbol % to show the percent. For example, 50% means 50 per 100. Understanding percentages is important for math skills and real life, for example stores advertise discounts on their products by using percents, like 30% off on math books.

Convert between percents, fractions and decimals

Compare percents to fractions and decimals

Find what percent one number is of another

Find what percent one number is of another: word problems

Estimate percents of numbers

Percents of numbers and money amounts

Percents of numbers: word problems

Compare percents of numbers

Solve percent equations

Percent of change

Percent of change: word problems

## Consumer math Consumer math is about learning spending money skills by using basic math skills such as basic operations, percent and other skills. Consumer math is an important skill for everyday life, you will learn how to calculate sale prices, tax and interests.

Price lists

Unit prices

Unit prices: find the total price

Percent of a number: tax, discount and more

Find the percent: tax, discount and more

Sale prices: find the original price

Multi-step problems with percents

Estimate tips

Simple interest

Compound interest

## Units of measurement A quantity used as a standard of measurement; it is how much makes up “1” of the measurement. So, 1 second is a unit of time or the basic unit of length in metric is meter so 1 meter is a unit of length. Measurement provides a meaningful context for the use of number skills and spatial concepts.

Convert rates and measurements: metric units

Metric mixed units

Convert square and cubic units of length

Convert between cubic metres and litres

Precision

## Problem solving A question that needs a solution. In mathematics some problems use words, so you need to learn how to interpret them into mathematical expressions and find the appropriate answer to the question. Problem solving is important skill in life which helps you to tackles the problem in life and find the best solution for them.

Multi-step word problems

Guess-and-check word problems

Use Venn diagrams to solve problems

Elapsed time word problems

## Coordinate plane The plane containing X axis and Y axis is called coordinate plane. Cartesian coordinated can be used to pinpoint where we are on a map or graph. We can mark a point on a graph by how far along and how far up it is, the point (10,6) is 10 units along and 6 units up. Coordinate plane is exciting and important for learning math and it has important use in real life like mapping an area or arranging furniture in your room.

Coordinate plane review

Follow directions on a coordinate plane

Find the distance between two points

## Two-dimensional figures Two-dimensional geometry or plane geometry is about flat shapes like triangles and circles. Two-dimensional figures have only two dimensions such as width and height but no thickness. It also known as “2D”.

Identify and classify polygons

Classify triangles

Identify trapezoids

Find missing angles in triangles and quadrilaterals

Interior angles of polygons

Identify complementary, supplementary, vertical, adjacent and congruent angles

Find measures of complementary, supplementary, vertical and adjacent angles

Transversal of parallel lines

Find lengths and measures of bisected line segments and angles

Parts of a circle

## Transformations and congruence When we change a shape by using Turn, flip, slide or resize it is called transformation. If one shape can become another using Turn, Flip or Slide then shapes are congruent. Congruence keeps the size, area, angles and line lengths of the shape.

Symmetry

Identify reflections, rotations and translations

Translations: graph the image

Translations: find the coordinates

Reflections: graph the image

Reflections: find the coordinates

Rotations: graph the image

Rotations: find the coordinates

Side lengths and angle measures of congruent figures

Congruence statements and corresponding parts

## Transformations and similarity When we change a shape by using Turn, flip, slide or resize it is called transformation. Two shapes are similar when one can become the other after a resize, flip, slide or turn. When two shapes are similar then the corresponding angles are equal, and the lines are in proportion. This can make life a lot easier when solving geometry problems.

Similar and congruent figures

Dilations: graph the image

Dilations: find the coordinates

Dilations: scale factor and classification

Side lengths and angle measures of similar figures

## Pythagorean theorem In a right-angled triangle, the square of the long side is equal to the sum of the squares of the other two sides.

Pythagorean theorem: find the length of the hypotenuse

Pythagorean theorem: find the missing leg length

Pythagorean theorem: find the perimeter

Pythagorean theorem: word problems

Converse of the Pythagorean theorem: is it a right triangle?

## Three-dimensional figures Having three dimensions such as Height, Width and Depth, like any real-world object is a three-dimensional figure. Three-dimensional geometry is about solid shapes like spheres or cubes. It is also known as “3D”.

Parts of three-dimensional figures

Nets of three-dimensional figures

Front, side and top view

Base plans

Similar solids

## Geometric measurement Geometric measurement is studying the properties of shapes by measuring them, like finding the Area or Perimeter of a shape.

Perimeter

Area

Area between two shapes

Area and perimeter: word problems

Circles, semicircles and quarter circles

Circles: word problems

Volume

Surface area of prisms and cylinders

Surface area of pyramids

Volume and surface area of similar solids

Perimeter, area and volume: changes in scale

## Number sequences A pattern is a series or sequence that repeats. Mathematics patterns are sequences that repeat according to a rule or rules. Numbers can have interesting patterns, like Arithmetic sequences Geometric sequences and so on. Number sequence is a list of numbers in a special order.

Identify arithmetic and geometric sequences

Arithmetic sequences

Geometric sequences

Number sequences: mixed review

Number sequences: word problems

Evaluate variable expressions for number sequences

Write variable expressions for arithmetic sequences

## Expressions and properties Numbers, symbols and operators grouped together that show the value of something is called an expression. A variable is a symbol for a number we do not know yet. Understanding algebraic expressions help you to understand real life relationships and increase logical thinking skills.

Write variable expressions

Write variable expressions from diagrams

Write variable expressions: word problems

Evaluate one-variable expressions

Evaluate multi-variable expressions

Evaluate absolute value expressions

Evaluate rational expressions

Identify terms and coefficients

Sort factors of expressions

Multiply using the distributive property

Simplify variable expressions using properties

Add, subtract and multiply linear expressions

Factors of linear expressions

Identify equivalent linear expressions

## One-variable equations An equation says that two things are equal, it will have an equal sign “=”. A variable is a symbol for a number we do not know yet. A single variable equation (one-variable equation) is an equation in which there is only one variable used. Note that the variable can be used multiple times or used on either side of the equation; all that matters is that the variable remains the same.

Which x satisfies an equation?

Write an equation from words

Model and solve equations using algebra tiles

Write and solve equations that represent diagrams

Properties of equality

Solve one-step equations

Solve two-step equations

Solve equations involving like terms

Solve equations: complete the solution

Solve equations: word problems

## Linear functions A function related an input to an output. It works like a machine that takes something in (input) and at the end gives us something back (output). F(x) is the traditional way of expressing functions. Each function has three parts the Input, the Relationship and the Output. Linear equations are equations that make a straight line when graphed.

Does (x, y) satisfy the linear function?

Rate of change

Constant rate of change

Complete a table for a linear function

Complete a table and graph a linear function

Graph a line from an equation

Interpret the graph of a linear function: word problems

Write a linear function from a table

Write linear functions: word problems

## Data and graphs A collection of facts, such as numbers, measurements or observations is called data. We can create a table with the data. A diagram of values, usually shown as lines is called graph. Understanding data and the appropriate graph related to it can help interpreting data.

Interpret tables

Interpret bar graphs

Create bar graphs

Interpret line graphs

Create line graphs

Interpret line plots

Create line plots

Interpret stem-and-leaf plots

Create stem-and-leaf plots

Interpret histograms

Create histograms

Create frequency charts
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Interpret box-and-whisker plots

Scatter plots

Interpret circle graphs

Circle graphs and central angles

Choose the best type of graph

## Statistics Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of data. Statistics is a strong tool in everyday life to get answers about data and make concrete decisions.

Calculate mean, median, mode and range

Interpret charts to find mean, median, mode and range

Mean, median, mode and range: find the missing number

Changes in mean, median, mode and range

Quartiles

Identify representative, random and biased samples