Linear Equations
Objectives
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
NA 3-6 Record and interpret additive and simple multiplicative strategies, using words, diagrams and symbols, with an understanding of equality.
NA 3-7 Generalise the properties of addition and subtraction with whole numbers.
NA 4-1 Use a range of multiplicative strategies when operating on whole numbers.
NA 4-4 Understand addition and subtraction of fractions, decimals and integers.
NA 4-8 Generalise properties of multiplication and division with whole numbers.
NA 5-8 Generalise properties of operations with fractional numbers and integers.
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
NA 3-6 Record and interpret additive and simple multiplicative strategies, using words, diagrams and symbols, with an understanding of equality.
NA 3-7 Generalise the properties of addition and subtraction with whole numbers.
NA 4-1 Use a range of multiplicative strategies when operating on whole numbers.
NA 4-4 Understand addition and subtraction of fractions, decimals and integers.
NA 4-8 Generalise properties of multiplication and division with whole numbers.
NA 5-8 Generalise properties of operations with fractional numbers and integers.
In this unit you will learn:
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Homework Book Pages for this unit:
Dragon Maths 6: Pages 53 - 64 Level 3/4: Pages 46 - 54 Level 4: 45 - 53 Level 5: 57 - 61 |
1) Solving equations using tables
Check out this website: http://www.mathwarehouse.com/algebra/linear_equation/linear-equation-table-examples-graphs.php |
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2) Solving equations using graphs
To solve an equation using a graph, construct a table of values from the equation and plot the points on the cartesian plane.
- If a set of coordinates or ordered pairs lies on a straight line when plotted, there is a linear relationship or linear relation between the points. The line can be extended to higher and lower values, and other ordered pairs which satisfy the linear relation can be 'read off'. The graph formed is called a linear graph.
- The value x can be solved for a particular value of y by reading off its value at the intersection of the line graph with that value of y.
- To plot a linear relation from a rule, construct a table of values by substituting each x-value into a rule.
- Draw a straight line through the points only if it makes sense to do so, i.e. if the data obtained from the rule is continuous.
3) Solving Equations Using Algebra
- Equivalent expressions can be written as an equation by using an equals sign between them: e.g. x + 4 = 14, 5x = 3 0, 3x + 6 = 19
- An equation remains equivalent or balanced if you:
- add the same number to both sides
- subtract the same number from both sides
- multiply both sides by the same number
- divide both sides by the same number
- Addition and subtraction are opposite operations
- Multiplication and division are opposite operations
Solving Algebraic Equations that involve ONE STEP...
Have a go at these worksheets on One-Step Equations Addition, Subtraction, Multiplication and Division.
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Have some fun with these algebraic games...
Match Like Terms Game
Click on all the terms that match the one at the top. http://www.mathwarehouse.com/games/our-games/like-terms-games/matching-action/play-matching-action/ |
Solving Equations
Try your luck against the clock. Or click on practice to take you time. Record you best time at the bottom of the page http://www.xpmath.com/forums/arcade.php?do=play&gameid=69 |
Hoop Shoot
Solve the equation and then make the shot. There are two games, one with addition and subtraction, the one underneath is multiplication and division. http://www.math-play.com/One-Step-Equation-Game.html |
Expressions Millionaire
Really good game to practice Algebraic Expressions. If you are playing Two Player then click No when asked about wireless. http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-game.html |
Algebra Meltdown
Select the correct number to make up the scientist's totals. https://www.mangahigh.com/en-au/games/algebrameltdown |
Solving Algebraic Equations that involve One Step...
Solving Algebraic Equations that involve Two STEPS...
Trying to solve an equation with variables and fractions? Just perform the order of operations in reverse! To see what it takes, watch this tutorial.
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4) Solving Equations with unknowns on BOTH SIDES...
Trying to solve an equation with variables and fractions on both sides of the equation?
You can bet it involves finding a common denominator! To see what it takes, watch this tutorial.
You can bet it involves finding a common denominator! To see what it takes, watch this tutorial.
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5) Solving Equations involving BRACKETS
Trying to solve an equation with brackets.
To see what it takes, watch this tutorial and consolidate your learning by doing this worksheet.
To see what it takes, watch this tutorial and consolidate your learning by doing this worksheet.
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