IntoMath Grade 9 Lessons

In this lesson you will learn about linear relations and what they mean. One of the most common examples of a linear relation is the relationship between distance and time when a distance changes over time at a constant rate. A linear relation is represented by a straight-line – a relationship between a variable and a constant. Linear relations can be expressed in 4 different ways: a graph, a table of values, a word description and an equation. In this lesson we will compare two objects moving and discuss the relationship between distance, time and speed while comparing the graphs representing the motion patterns of the two objects. You will learn why the equation D = vt (or D = st) is a direct proportion and how knowing the time and speed one can determine the distance traveled. Watch the video lesson, complete the note and additional practice in order to improve your understanding of the concept. More free math games and activities: intomath.org

In this lesson we are discovering the distributive property of multiplication, as well as common factoring. According to the distributive property, a(b + c) = ab + bc. When multiplying the sum or difference of two terms by another term, it is possible to find the product of each pair of terms first and then add/subtract them. This is how we expand brackets and simplify algebraic expressions. ​Distributive property is used to simplify expressions, solve equations and word problems. It is a part of virtually every math course in high school and the skill is transferable to other concepts. ​The opposite (inverse) operation to distribution is common factoring. This is when we are given the expanded form of an algebraic expression and need to determine the Greatest Common Factor, that all the other terms of the expression are divisible by – the term that goes outside of the brackets. ​For a more detailed explanation of these processes with examples watch the video lesson above, then check out the accompanying note and complete additional math practice on this topic. More free math help and activities: intomath.org

Exponents are very important and powerful. Read this blog post based on an ancient Indian legend about the creator of chess. This lesson teaches about exponents. An exponent shows how many times the number needs to be multiplied by itself. For example, 5³ = 5 × 5 × 5 = 125. In the order of operations, BEDMAS, exponents come right after operations in brackets. Sometimes exponents are used with variables. Then, exponent laws are used in order to simplify expressions with variables. This lesson explains how to use general exponent laws and provides insight into operations with exponents. Negative exponents make the base turn into its reciprocal. Any number (except 0) or an algebraic term raised to the exponent of 0 is equal to 1. When raising a fraction to an exponent it is necessary to raise both the numerator and the denominator to that exponent separately. More free math help and activities: intomath.org

In this lesson you will learn about different types of algebraic expressions: monomials, binomials, trinomials and polynomials. You will see how two monomials could be multiplied or added/subtracted. For example 2m × 3m = 6m² or 4m + 12m = 16m. In math, a polynomial is an expression consisting of coefficients and variables. These coefficients and variables are called “terms”. Terms in a polynomial are separated by operations of addition, subtraction, multiplication. Variables have only positive integer exponents. This lesson also explains how algebraic expressions with brackets can be simplified by distributing a monomial in front of the bracket by every term inside the bracket. For example, an expression 3(2s -3) could be expanded to 6s – 9. This may be followed by collecting like terms (monomials within polynomials that only differ from each other by their coefficient) if there are more than one bracket. More free math help and activities: intomath.org

In this lesson you will learn what a linear equation is and what it means to “solve an equation”. In order to solve an equation, we need to complete inverse operations in the reverse BEDMAS order. The solution or root is the value that we get when we solve an equation. This lesson explains the steps of solving linear equations with brackets. From simplifying the expressions with brackets on both sides of the equal sign; identifying, rearranging and collecting like terms to isolating for the unknown variable by dividing by its coefficient. In this lesson you will see a concrete example of how to solve an equation that contains brackets, does not initially look like a linear equation, but simplifies to it. Practice exercises will help you master the skills required for solving linear equations with brackets and multi-step equations. More free math help and activities: intomath.org

This lesson builds up on the previous one and takes it further. You will discover a linear function and its meaning. You will also find out how to represent a linear function in 4 different ways: equation, table of values, graph and words. You will learn about two types of linear functions: one that passes through the origin when graphed and the other one that doesn’t. This lesson will explain what each letter stands for in the equation y = mx + b. When the relationship is linear, the rate of change is constant. We have already observed it in the previous lesson. The relationship between distance and time is a great example of a linear function. When graphed it produces a straight line. The slope of a line represents the rate of change of one quantity in relation to the other. It can be calculated using any two points that sit on the line. Since each point has the coordinates (ordered pair), the slope of a line is calculated by finding the difference between x and y coordinates of the points respectively. We use letter “m” to represent the slope of a line: m = (y2 – y1)/(x2 – x1) Practice exercises will help you master the skills.​ More free math help and activities: intomath.org

In this lesson you will learn how to calculate surface area and volume of the given 3D shapes. Volume is how much space the shape has inside (its capacity). Surface Area is the total outside surface of the shape. In order to calculate the volume of a square-based pyramid, we multiply the area of the base by the height of the pyramid. Sometimes, the height is unknown and needs to be determined using the height of the lateral surface and Pythagorean Theorem. The process for finding the volume of a cone is similar. In order to calculate the surface area of any 3D shape, we need to determine the area of all 2D shapes that make up the 3D figure and add them together. Thus, the surface area of a square-based pyramid would be the sum of the areas of 4 triangular faces and the area of a square base. Depending on the situation, we may need to exclude some of the faces from our calculations when determining surface area and volume (for example, the floor inside the house when determining the area of the walls to be painted, etc.) More free math help and activities: intomath.org