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Linear Algebra
Match stick patterns and number sequences are a type of linear algebra using "n" as the sequence number which is being found.
Example Arithmetic sequence 3n + 2 = Example Geometric Sequence un=u1r(n-1)
An equation says two quantities are equal something = something else
x + 5 = 9 is a linear equation
To solve an equation means finding the value of an unknown variable (often called x but can be any letter)
You can solve equations by rearranging the equation so the variable is by itself.
x + 5 = 9 becomes x = 9 - 5
To move numbers use the opposite operation on the other side
+ becomes - - becomes +
x becomes ÷ ÷ becomes x
Being able to rearrange an equation is an important skill that is used in many maths and science topics.
Start at the lowest level and practice the basic operations first.
The aim is to get the unknown subject on one side of the equal sign and everything else on the other side.
To move something you do the opposite operation on both sides.
That cancels it out (makes it disappear from the side you are moving it from)
Level 1 - Formulas which can be rearranged by adding or subtracting terms from both sides
Example: Make e the subject of the formula d = e - f
Level 2 - Formulas which can be rearranged by multiplying or dividing both sides by a value
Example: Rearrange the formula n = mp
Level 3 - Formulas which can be rearranged by adding, subtracting, multiplying or dividing both sides by a value
Example: Rearrange the formula b = a + cd
Level 4 - Formulas including brackets or expressions in the numerator or denominator of a fraction
Example: Rearrange the formula p = s(t + 2)
Level 5 - Formulas including squares or square roots
Example: Rearrange the formula d² = 2a + 1
Level 6 - Finding the unknown which is not the subject of a formula
Example: If m = n² + 2p, find p when m=8 and n=10
Level 7 - Rearrange the formulae where the new subject appears twice; fill in the blanks
Example: Rearrange the formula ax + b = cx + g to make x the subject
Level 8 - Rearrange the formulae where the new subject appears twice; show your working
Example: Rearrange the formula a(3-x)=5x to make x the subject
Patterns & Sequences
Patterns & Sequences
Jump x n + (or -) the difference between the jump and the first number in the sequence
Example 2n + 3
These sequences are addition or subtraction patterns.
Find the jump between the numbers. Then find the difference between the jump and the first number in the sequence (This will either be plus or minus) 3n - 2
Equations & Graphs
Equations & Graphs
y = mx + b.
m is the gradient (slope)
b is the y intercept
Figure it out activities
Below are GeoGebra tools
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