Level 5 NZ Curriculum Achievement Objectives for Linear Algebra
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 5-7: Form and solve linear equations.
NA 5-8: Generalise the properties of operations with fractional numbers and integers.
NA 5-9: Relate tables, graphs, and equations to linear relationships found in number and spatial patterns.
NA 5-7: Form and solve linear equations.
NA 5-8: Generalise the properties of operations with fractional numbers and integers.
NA 5-9: Relate tables, graphs, and equations to linear relationships found in number and spatial patterns.
In this unit you will revise:
1) Multiplying Terms 2) Dividing Terms 3) Adding and Subtracting Terms 4) Expanding Brackets 6) Solving One Step Equations 7) Solving Two Step Equations |
In this unit you will learn:
1) Multiplying more complex terms 2) Dividing more complex terms 3) Adding and Subtracting more complex terms 4) Expanding Brackets (with variables) 5) Factorizing 8) Solving equations with unknowns on both sides 9) Solving equations with brackets 10) Gradient of a line 11) Y - Intercept of a line 12) Writing the equation of a line |
- An algebraic expression is a group of variables and numbers joined together with +, -, x or divide signs; m + 2, 3x + 5y, 7xy - 3 are all algebraic expressions.
- Each part of an expression is called a term. The expression 3x + 5y has two terms: 3x and 5y.
- The number in front of a term is called a coefficient. In the expression 3x + 5y, 3 is the coefficient of x, and 5 is the coefficient of y.
- A number without a variable is called a constant term. In the expression 4x + 7, the number 7 is a constant term.
Visit this website to have a go at Algebraic Expressions http://www.mathgoodies.com/lessons/vol7/expressions.html
1) Multiplying Terms
We can multiply any terms together. To do this we multiply the numbers and add the exponents on each variable.
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Check out these websites:
http://www.bbc.co.uk/bitesize/ks3/maths/algebra/formulae2/revision/3/ https://www.mathsisfun.com/algebra/polynomials-multiplying.html Homework
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2) Dividing Terms
We can divide any terms. To do this we divide the numbers and subtract the exponents on each variable.
Homework
algebra-dividing-terms_homework_answers.pdf | |
File Size: | 123 kb |
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3) Adding and Subtracting Terms
We can only add and subtract LIKE TERMS. Like terms are terms that have the same variables with the same exponents.
Look at the examples below for adding and subtracting terms.
Homework
algebra-collecting-like-terms_homework_answers.pdf | |
File Size: | 198 kb |
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4) Expanding Brackets
The term outside the bracket must be multiplied by everything inside the brackets. Then simplilfy if possible.
Eg) 4(2a + b) = 4 X 2a + 4 X b = 8a + 4b
Eg) 4(2a + b) = 4 X 2a + 4 X b = 8a + 4b
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Check out these websites:
https://www.mathsisfun.com/algebra/expanding.html
http://studymaths.co.uk/topics/expandingAndSimplifyingExpressions.php
https://www.mathsisfun.com/algebra/expanding.html
http://studymaths.co.uk/topics/expandingAndSimplifyingExpressions.php
Homework
algebra-expanding-brackets_homework_answers.pdf | |
File Size: | 246 kb |
File Type: |
5) Factorizing
Factorizing means to split up the expression into terms that are being multiplied together to give the original expression. To do this we look for common factors that can be divided out of EACH term.
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Homework
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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
6) 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 |
7) 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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8) 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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9) 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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10) Substitution
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