Forms 4 2016: Maths

Time Measurement

Ever since human being first noticed the regular movement of the sun and stars, we figured out how to measure time. We can identify how time goes by thanks to daylight, night, seasons like winter or summer, or the migration of animals and birds, to name a few...

So, what is Time? Time is the ongoing sequence of events taking place: The past, the present and the future. We measure time using seconds, minutes, hours, days, weeks, years, etc.

How do we measure Time nowadays?

Seconds

1 Minute = 60 seconds

1 Hour = 60 minutes

1 Day = 24 hours

1 Week = 7 days

1 Month = 4 weeks

1 Year = 12 Months

1 Lustrum = 5 years

1 Decade = 10 years

1 Century = 100 years

1 Millennium = 1000 years

We can also measure time in seasons (autumn, for example), trimester (3 months) or semester (6 months)

Fractions

You may be wondering "what are fractions?". Well, a fraction represents part of a whole. When something is broken up into a number of parts, the fraction shows how many of those parts you have.

Please watch these videos about Introduction to Fractions!

Watch this video from 0:56 onwards

Look at the picture below and see how a whole can be broken up into different equal parts and fractions.

Are you ready to show what you've learned so far? Play these games!

Fractions Splat (choose the level you want)
Pizza Game (match the pizza slices with fractions)
Fraction Fling (show your math abilities!)

Types of Fractions

Proper Fraction

Improper Fraction

Mixed Fraction

Proper Fraction

A Proper Fraction is one when the numerator is less than the numerator.

Improper Fraction

An Improper Fraction is one where the numerator is greater than the denominator.

Mixed Fraction

A Mixed Fraction has both a whole number part and a fractional part.

Equivalent Fraction

If the numerator and the denominator are the same, then the fraction has the same equivalent value as 1.

Show your knowledge playing these games:

Mixed Fractions

Mixed numbers and Improper Fractions

Improper Fractions and Mixed numbers Game

Fraction Splat

Area and Perimeter

Area and Perimeter are different ways of measuring a shape. Area is the amount of space inside the shape, whereas Perimeter is the distance around the edges.

You can watch a video and learn more about Area and Perimeter HERE

Area

Area is the size of a surface. It is the amount of space inside the boundary of a flat (2D) object, such as a triangle or a circle.

So, how do we calculate Area?

Let's calculate the Area of one of the previous figures:

Have fun playing these games about Area!

Area Game 1

Area Game 2

Perimeter

Perimeter is the distance around the outside of a shape, calculated by adding the length of all sides together.

How to find the Perimeter in polygons? Click here!

Perimeter Game

Activities and Exercises on Area and Perimeter

Do not forget to write your answers in your notebook!

Exercise 1: Perimeter & Area 1
Exercise 2: Perimeter & Area 2

Exercise 3: Area of a Rectangle

Exercise 4: Area and Perimeter

What is Volume?

Basically, Volume is the measurement of how much space a 3D object takes up, which is measured by cubic units (for example, m³)

Please watch this VIDEO about Volume! Pay attention to it and do not forget to take notes.

Let's calculate the volume of a box:

If you know how to multiply you can find the volume of a cube or box. We learned earlier that the surface area of a flat rectangle was the length times the width, but that was just a flat two-dimensional object.

Read more at: http://www.ducksters.com/kidsmath/finding_the_volume_of_a_cube_or_box.php
This text is Copyright © Ducksters. Do not use without permission.

If you know how to multiply you will be able to fin the volume of a cube or a box. We learned earlier that the surface area of a flat reclangle was the lenght by the width, but that was only a 2D shape. Look at this box below:

You see than when dealing with a box, or 3D objects, we have to consider three measurements: Length (L), Width (W), and Height (H). The formula is:

L x W x H

Here we see that Length = 12 Width = 4 Height = 3 Volume = length x width x height Volume = 12 x 4 x 3 = 144

Read more at: http://www.ducksters.com/kidsmath/finding_the_volume_of_a_cube_or_box.php
This text is Copyright © Ducksters. Do not use without permission.

Now, look at the box again, but with its measures

Here we see that...
Length = 12
Width = 4
Height = 3

Volume = Length x Width x Heigth
Volume = 12 x 4 x 3
Volume = 144

If the measurements were in meters, there would be 12 m, 4 m, and 3 m. So, the result would be 144 m³

Put in practice your knowledge about Volume in the following links

Volume Game 1

Volume Game 2

Geometry

Two-dimensional / 2D Shapes:

These are some examples for 2D (flat) shapes. Instead of trapezoid, you can also say trapezium. This is because in the United States the English speakers use the word trapezoid, meanwhile in the United Kingdom they use trapezium.

Three-dimensional / 3D Shapes:

3D – shapes are called like this because they have three dimensions: length, width and height.

This is what we call the different parts of a 3D shape:

Don’t forget: Face = Cara

Edge = Arista

Vertice = Vértice

Look at the two pyramids in the lower left corner: They are almost the same, but have different bases. On the left side, we have the square-based pyramid. The base is shaped like a square. On the right side, we have the triangular-based pyramid. The base is shaped like a triangle.

This way you can describe basically any 3D shape. For example, what would a pentagonal prism look like? Check your answer here.

Play these games to practice your knowledge!

2D and 3D Shapes
Identify the shapes
Shapes Splat
3D Shapes
Magical Shape Hunt
Creating Shapes
Nets

Angles:

An angle measures the amount of a turn, measured in degrees. The symbol for degrees is º. Depending on the degrees, the names of the angles change:

One trick for remembering the acute angle is that the letter A also has an acute angle:

How can we measure the degrees of an angle?

A right angle always has 90º (read: ninety degrees).

A straight angle always has 180º.

A full rotation is 360º.

Look at the image above:

An acute angle must have less than 90º.

An obtuse angle has more than 90º, but less than 180º.

A reflex angle has more than 180º.

If we want to know the exact number of degrees, we use the protractor.

Watch this video on how to measure and draw angles.

This video summarizes the most important things about angles.

Game - Alien Angles

Game 2 - Measuring angles

Game 3 - Estimating angles

Transformations:

Transformations allow us to change the place of a 2D shape in a grid. The shape can either rotate, reflect or translate.

Rotation

Turn!

Rotation means turning around a point, for example the centre, in form of a circle.

Here is an example for a rotation:

90° clockwise

180° (anti)clockwise

Reflection

Flip!

Reflection is when we flip an image along a mirror line. Make sure that the distance from the figure to the line is the same. The figure stays the same, it just faces a different direction.

Translation

Slide!

Translation is moving the figure to another place. Every point has to move into the same direction and in the same distance.

Remember: After any of those transformations (turn, flip or slide), the shape still has the same size, area, angles and line lengths.

Try it yourself!

Game 1 - Transformations

Game 2 - Transformations 2

Graphs Game 1 - Graphs and Data
Game 2 - Bar Graph
Game 3 - Interpreting Data
Game 4 - Data Research

Coordinates

Coordinates show us the exact position of a point in a grid.

First we have to get to know the two axes. The x-axis moves from the left to the right, the y-axis from the bottom to the top.

We always talk about the x-axis first and then about the y-axis. For example, we say: The shape gets moved 30 Units (for example cm or m) in the x-direction and 20 Units in the y-direction. The x-direction is always the movement to the right and the y-direction the movement upwards.

We write: (x, y)

Example: (30, 20)

Here’s an example for the coordinates (3,4) and (4,3):