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Introduction to Positive and Negative Numbers

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Percentages - Practice Questions & Answers

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Whole Numbers and Place Value - Entry Level

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L1 & L2 - Charts and Graphs - Practice Questions

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Shape and Scale Drawings - Practice Questions

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Shape and Scale Drawings - Practice Questions

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Perimeter, Area and Volume - Presentation

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Perimeter, Area and Volume - Presentation

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Angles are used in daily life. Engineers and architects use angles for designs, roads, buildings and sporting facilities. Athletes use angles to enhance their performance. Carpenters use angles to make chairs, tables and sofas. Artists use their knowledge of angles to sketch portraits and paintings.

If two lines meet (or intersect) at a point, then an angle is formed. The point of intersection of the lines is called the vertex.

An angle is shown below.

Lines AB and AC meet at the point A to form an angle. The point A is the vertex of the angle, and the lines that meet to make the angle are called the arms of the angle.

Naming Angles

Size of an Angle

The amount of turn from one arm of the angle to the other is said to be the size of an angle.

The size of an angle is measured in degrees; and the symbol used to represent degree is º. There are 360º in a full turn (or circle).

Note:

A degree is defined such that the angle of one full turn (or circle) is 360 degrees.

Measuring Angles

A protractor is used to measure angles. In this section, we will consider the use of a protractor that has the shape of a semi-circle and two scales marked from 0º to 180º.

The two scales makeit easy for us to measure angles facing different ways.

To measure the size of angle ABC, place the protractor over the angle so that the centre of the protractor is directly over the angle's vertex, B; and the base line of the protractor is along the arm, BA, of the angle.

We use the inner scale to measure the angle ABC, as the arm AB passes through the zero of the inner scale. Following the inner scale around the protractor, we find that the other arm, BC, passes through the inner scale at 60º. So, the size of angle ABC is 60 degrees. We write this as follows:

To measure the size of angle PQR, place the protractor over the angle so that the centre of the protractor is directly over the angle's vertex, Q; and the base line of the protractor is along the arm, PQ, of the angle.

We use the outer scale to measure the angle PQR, as the arm PQ passes through the zero of the outer scale. Following the outer scale around the protractor, we find that the other arm, QR, passes through the outer scale at 120º. So, the size of angle PQR is 120 degrees. We write this as follows:

Types of Angles

Angles are classified according to their size.

An acute angle is greater than 0º and less than 90º.

A right angle equals exactly 90º.

Note that a right angle is marked on the diagram as a small square.

An obtuse angle is greater than 90º and less than 180º.

A straight angle equals exactly 180º.

A reflex angle is greater than 180º and less than 360º.

A perigon (or a revolution) is an angle that equals exactly 360º.

Measuring Reflex Angles

Recall that:

A protractor can be used to measure the size of an acute angle (between 0º and 90º) and an obtuse angle (between 90º and 180º).

Now, we will use a protractor to measure the reflex angle PQR.

To measure the reflex angle PQR, extend the arm PQ to A to form angle PQA which is a straight angle. Then measure the size of the angle AQR and add 180º.

Key Terms

point, angle, vertex, arms of the angle, size of an angle, degrees, protractor, inner scale, outer scale, acute angle, right angle, obtuse angle, straight angle, reflex angle, perigon, revolution

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Angles are used in daily life. Engineers and architects use angles for designs, roads, buildings and sporting facilities. Athletes use angles to enhance their performance. Carpenters use angles to make chairs, tables and sofas. Artists use their knowledge of angles to sketch portraits and paintings.

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Level 1 - Converting Measures - Assignment

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Level 1 - Converting Measures - Assignment

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Level 1 - Converting Measures - Assignment

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Operations

"Operations" mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.

But, when you see something like...

... what part should you calculate first?

Start at the left and go to the right?
Or go from right to left?
Warning: Calculate them in the wrong order, and you can get a wrong answer !
So, long ago people agreed to follow rules when doing calculations, and they are:

Order of Operations

Do things in Brackets First

Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract

Multiply or Divide before you Add or Subtract

Otherwise just go left to right

How Do I Remember It All ... ? BODMAS !

Divide and Multiply rank equally (and go left to right).

Add and Subtract rank equally (and go left to right)

So do it this way:

After you have done "B" and "O", just go from left to right doing any "D" or "M" as you find them.

Then go from left to right doing any "A" or "S" as you find them.

Note: the only strange name is "Orders". You may prefer GEMS ( Grouping, Exponents, Multiply or Divide, Add or Subtract). Or in the US where they say "Parentheses" instead of Brackets, so it is " PEMDAS".

Examples

Example: How do you work out 3 + 6 × 2 ?

Multiplication before A ddition:

Example: How do you work out (3 + 6) × 2 ?

B rackets first:

Example: How do you work out 12 / 6 × 3 / 2 ?

Multiplication and D ivision rank equally, so just go left to right:

A practical example:

Example: Sam threw a ball straight up at 20 meters per second, how far did it go in 2 seconds?

Sam uses this special formula that includes gravity:

height = velocity × time − (1/2) × 9.8 × time ²

Sam puts in the velocity of 20 meters per second and time of 2 seconds:

height = 20 × 2 − (1/2) × 9.8 × 2 ²

Now for the calculations!
The ball reaches 20.4 meters after 2 seconds
Exponents of Exponents ...

What about this example?

Exponents are special: they go top-down (do the exponent at the top first). So we calculate this way:
And finally, what about the example from the beginning?
295, 1565, 1571, 296, 1567, 380, 1569, 3852, 3853, 382

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Learn how to calculate things in the correct order. Calculate them in the wrong order, and you can get a wrong answer!

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Converting between Fractions, Decimals and Percentages - Assignment

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Converting between Fractions, Decimals and Percentages - Assignment

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Converting Fractions Decimals and Percentages - Assignment

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Converting between Fractions, Decimals and Percentages - How to ...

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Converting between Fractions, Decimals and Percentages - How to ...

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How to Convert Fractions Percentages and Decimals

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One Number as a Fraction of another - Video

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One Number as a Fraction of another - Video

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Expressing one quantity as a fraction of another

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Maths Tutorials - Finding Fractions of Amounts

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This tutorial looks at finding fractions of amounts where the numerator is not 1. This is the second in a series of two videos on finding fractions of amounts. It is recommended that you watch the first video before watching this one; you can find it here: http://www.youtube.com/watch?v=E2QvVicQcMo&feature=youtu.be If you've enjoyed this video, please consider visiting my website http://www.norledgemaths.weebly.com for additional homework help.

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Lattice Method of Multiplication - Explanation

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Lattice Method of Multiplication - Explanation

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Grid Method of Multiplication - Explanation

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Grid Method of Multiplication - Explanation

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Column or Traditional Method of Multiplication

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How do we divide when there are decimal points involved?

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Lattice Method of Multiplication - Video

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Lattice Method of Multiplication - Video

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Grid/Box Method of Multiplication - Video

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Grid/Box Method of Multiplication - Video

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Long Multiplication using the Grid (or Box) Method

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Traditional Method of Multiplication by 2 digits - Video

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Traditional Method of Multiplication by 2 digits - Video

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Math Antics - Multi-Digit Multiplication Pt 2

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Traditional Method of Multiplication by 1 digit - Video

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Traditional Method of Multiplication by 1 digit - Video

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Math Antics - Multi-Digit Multiplication Pt 1