Grade 9 Math

CONTENTS

The first year of high school and the year of changes. Grade 9 is always a complex year for children, dealing with the changes in the high school curriculum and more complex study patterns. This is also the year students make up their minds whether mathematics is going to be their preferred subject or not.

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Numbers

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.

Classify numbers

Compare rational numbers

Put rational numbers in order

Number lines

Convert between decimals and fractions

Square roots of perfect squares

Square roots of fractions and decimals

Estimate square roots

Operations

Four basic operations of mathematics including Addition, Subtraction, multiplication, and division. Evaluating the expressions including these operations.

Add, subtract, multiply and divide integers

Evaluate numerical expressions involving integers

Evaluate variable expressions involving integers

Add and subtract rational 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

Evaluate variable expressions involving rational numbers

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.

Identify equivalent ratios

Write an equivalent ratio

Unit rates

Unit prices

Solve proportions

Solve proportions: word problems

Scale drawings: word problems

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

Solve percent equations

Percent word problems

Percent of change

Percent of change: word problems

Geometry

Geometry is branch of mathematics which deals with shapes, lines and space. Two-dimensional geometry or plane geometry is about flat shapes like triangles and circles. Three-dimensional geometry is about solid shapes like spheres or cubes. Understanding geometry helps us to discover patterns, find areas, volumes and angles and to better understand the world around us.

Perimeter

Area

Area of compound figures

Area between two shapes

Symmetry

Count lines of symmetry

Draw lines of symmetry

Interior angles of polygons

Transversal of parallel lines

Volume of prisms and pyramids

Volume of cones and cylinders

Volume of spheres

Nets of three-dimensional figures

Surface area of prisms and pyramids

Surface area of cones and cylinders

Surface area of spheres

Similar figures: side lengths and angle measures

Similar triangles and indirect measurement

Area and perimeter of similar figures

Similar solids

Volume and surface area of similar solids

Perimeter, area and volume: changes in scale

Identify reflections, rotations and translations

Reflections, rotations and translations: find the coordinates

Reflections, rotations and translations: graph the image

Dilations and scale factors

Pythagorean theorem

Pythagorean theorem: word problems

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

Circles

A circle is a two-dimensional shape made by drawing a curve that is always the same distance from a center.

Parts of a circle

Circles: calculate area, circumference, radius and diameter

Circles: word problems

Central angles

Arc measure and arc length

Area of sectors

Circle measurements: mixed review

Arcs and chords

Tangent lines

Perimeter of polygons with an inscribed circle

Inscribed angles

Angles in inscribed right triangles

Angles in inscribed quadrilaterals I

Angles in inscribed quadrilaterals II

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

Quadrants and axes

Distance between two points

Properties

A character or quality that something has is called property. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Properties of addition and multiplication

Distributive property

Simplify variable expressions using properties

Properties of equality

Exponents

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

Exponents with integer bases

Exponents with decimal and fractional bases

Negative exponents

Multiplication with exponents – integral bases

Division with exponents – integral bases

Multiplication and division with exponents – integral bases

Power rule – integral bases

Multiplication with exponents – variable bases

Division with exponents – variable bases

Multiplication and division with exponents – variable bases

Power rule – variable bases

Evaluate expressions using properties of exponents

Identify equivalent expressions involving exponents

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

Multiply numbers written in scientific notation

Divide numbers written in scientific notation

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.

Word problems: mixed review

Word problems with money

Consecutive integer problems

Rate of travel: word problems

Weighted averages: word problems

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

Evaluate variable expressions for number sequences

Write variable expressions for arithmetic sequences

Write variable expressions for geometric sequences

Number sequences: mixed review

Variable expressions and equations

Numbers, symbols and operators grouped together that show the value of something is called an expression. 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.

Write variable expressions

Simplify variable expressions involving like terms and the distributive property

Identify equivalent linear expressions

Write variable equations

Does x satisfy the equation?

Solve equations using order of operations

Rearrange multi-variable equations

Solve equations

Solving an equation is the process of finding a value (or values) that we can put in place of a variable which makes the equation true. Solving an equation is like solving a puzzle which means there are things we can (an cannot) do.

Model and solve equations using algebra tiles

Write and solve equations that represent diagrams

Solve one-step linear equations

Solve two-step linear equations

Solve advanced linear equations

Solve equations with variables on both sides

Solve equations: complete the solution

Find the number of solutions

Create equations with no solutions or infinitely many solutions

Solve linear equations: word problems

Solve linear equations: mixed review

Single-variable inequalities

In mathematics sometimes we only know that something is greater or smaller than. Inequality tells us about the relative size of two values. A single-variable inequality is a mathematical statement that relates a linear expression as either less than or greater than another. Learning equations and inequalities helping to get ready for more advanced math problems.

Graph inequalities

Write inequalities from graphs

Identify solutions to inequalities

Solve one-step linear inequalities: addition and subtraction

Solve one-step linear inequalities: multiplication and division

Solve one-step linear inequalities

Graph solutions to one-step linear inequalities

Solve two-step linear inequalities

Graph solutions to two-step linear inequalities

Solve advanced linear inequalities

Graph solutions to advanced linear inequalities

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 bar graphs, line graphs and histograms

Create bar graphs, line graphs and histograms

Interpret circle graphs

Interpret stem-and-leaf plots

Interpret box-and-whisker plots

Interpret a scatter plot

Scatter plots: line of best fit

Relations and functions

A relation is a set of inputs and outputs, while a function is a relation with one output for each input. 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.

Relations: convert between tables, graphs, mappings and lists of points

Identify independent and dependent variables

Identify functions

Identify functions: vertical line test

Find values using function graphs

Evaluate a function

Evaluate a function: plug in an expression

Complete a function table from a graph

Complete a function table from an equation

Interpret the graph of a function: word problems

Direct variation

A relationship between two variables in which one is a constant multiple of the other is called direct variation. The statement “Y varies directly as X” means that when X increases, Y increases by the same factor.

Identify proportional relationships

Find the constant of variation

Graph a proportional relationship

Write direct variation equations

Write and solve direct variation equations

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.

Identify linear functions

Find the slope of a graph

Find the slope from two points

Find a missing coordinate using slope

Slope-intercept form: find the slope and y-intercept

Slope-intercept form: graph an equation

Slope-intercept form: write an equation from a graph

Slope-intercept form: write an equation

Slope-intercept form: write an equation from a table

Slope-intercept form: write an equation from a word problem

Linear equations: solve for y

Write linear functions to solve word problems

Complete a table and graph a linear function

Compare linear functions: graphs, tables and equations

Write equations in standard form

Standard form: find x- and y-intercepts

Standard form: graph an equation

Equations of horizontal and vertical lines

Graph a horizontal or vertical line

Point-slope form: graph an equation

Point-slope form: write an equation

Point-slope form: write an equation from a graph

Slopes of parallel and perpendicular lines

Write an equation for a parallel or perpendicular line

Transformations of linear functions

Systems of linear equations

Two or more equations containing common variables is called the system of equations. A system of equations in which every equation is linear is called system of linear equations. For any linear system, there are three possible outcomes: there is only one solution, there are infinitely solutions or there are no solutions at all. If the number of equations is more than the variables the system is called overdetermined, while if the variables are more than the equations the system is called underdetermined.

Is (x, y) a solution to the system of equations?

Solve a system of equations by graphing

Solve a system of equations by graphing: word problems

Find the number of solutions to a system of equations by graphing

Monomials

A polynomial with just one term is called a Monomial.

Identify monomials

Multiply monomials

Multiply monomials to find area

Divide monomials

Multiply and divide monomials

Powers of monomials

Polynomials

The sum or difference of terms which have variables raised to positive integer powers and which have coefficients. A polynomial can have constants, variables and exponents, but never division by variable. Even though the poly- means many the polynomials terms should be finite.

Polynomial vocabulary

Model polynomials with algebra tiles

Add and subtract polynomials using algebra tiles

Add and subtract polynomials

Add polynomials to find perimeter

Multiply a polynomial by a monomial

Multiply polynomials to find area

Divide a polynomial by a monomial

Logic

One area of mathematics that has its roots deep in philosophy is the study of logic. Mathematical log helps to detect whether a statement is valid or invalid.

Identify hypotheses and conclusions

Counterexamples

Probability

Probability is the chance of something happening or how likely it is that some event will happen. Probability is a number between 0 (not happening) to 1 (certainly happening).

Theoretical probability

Experimental probability

Compound events: find the number of outcomes

Identify independent and dependent events

Probability of independent and dependent events

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

Quartiles

Identify biased samples

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