Algebraic Expressions
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:
NA3-6: Record and interpret additive and simple multiplicative strategies, using words, diagrams and symbols, with an understanding and equality.
NA3-7: Generalise the properties of addition and subtraction with whole numbers.
NZ4-1: Use a range of mulitplicative strategies when operating on whole numbers.
NA4-2: Understand addition and subtraction of fractions, decimals and integers.
NA5-8: Generalise properties of operations with fractional numbers and integers.
NA3-6: Record and interpret additive and simple multiplicative strategies, using words, diagrams and symbols, with an understanding and equality.
NA3-7: Generalise the properties of addition and subtraction with whole numbers.
NZ4-1: Use a range of mulitplicative strategies when operating on whole numbers.
NA4-2: Understand addition and subtraction of fractions, decimals and integers.
NA5-8: Generalise properties of operations with fractional numbers and integers.
What you will learn:
1. How to write an algebraic expression.
2. Adding, Subtracting, Multiplying and Dividing Algebraic Expressions
3. Simplifying Algebraic Expressions
4. Substitution
5. Recap on Integers
6. Multiplying and Dividing with Indices
7. Expanding Single Brackets
1. How to write an algebraic expression.
2. Adding, Subtracting, Multiplying and Dividing Algebraic Expressions
3. Simplifying Algebraic Expressions
4. Substitution
5. Recap on Integers
6. Multiplying and Dividing with Indices
7. Expanding Single Brackets
- 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
What is a variable?
Combining like terms in Algebra
Algebraic Vocabulary and the difference between an Expression and an Equation.
Have a go at these worksheets. The first one is EASY, then MEDIAN level, and the last one is a good CHALLENGE!
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2) Adding, Subtracting, Multiplying and Dividing Algebraic Expressions
- The same rules apply for algebra as for integers:
- a x b = -a x -b = ab
- a x -b = -a x b = -ab
- Squaring a variable: a x a = a2
- Multiplicative identity is 1: a x 1 = a
- The same rules apply for algebra as for integers: a + a = 2a a - a = 0
- Addition can be done in any order: a + b = b + a
- For subtraction the order is important: a - b = b - a
3) Simplifying Algebraic Expressions
Visit this website to have a go... https://www.mathsisfun.com/algebra/simplify.html
4) Substitution
Check out these website on the Substitution method for solving algebraic expressions.
5) Recap on Integers
- Rule: The sum of any integer and its opposite is equal to zero. Summary: Adding two positive integers always yields a positive sum; adding two negative integers always yields a negative sum. To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values.
Check out these websites to practice your INTEGERS...
6) Multiplying and Dividing with Indices
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7) Expanding Single Brackets
Use the 'x' in the word to remind yourself that you are multiplying to expand, make bigger and then tidy up.
8) Factorising - Put the brackets back in!
- To get the terms inside the bracket, find and then . Remember to multiply out the brackets now to check that the answer is correct.factorise To put an expression into brackets. For example, 18x + 12y = 6(3x + 2y) .
Check out these websites...