MATHS

Math Games

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.

Transformations

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!

Coordinates

But imagine you have to move a figure (translation). How do you know how much and in which direction you have to move the shape? That’s what we use coordinates for. They show us the exact position of a point.

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):

Information taken from: http://www.mathsisfun.com/geometry/transformations.html

http://www.bbc.co.uk/bitesize/ks2/maths/shape_space/transformation/read/2/

Computing Lab

GEOMETRY

Perspectives

The perspectives of a three-dimensional figure can be represented on a plane with two- dimensional figures in the following way:

Angles

An angle measures the amount of turn.

Check this! Angles

There are different types of angles, as the angle increases, the name changes:

Type of Angle	Description
Acute Angle	An angle that is less than 90°
Right Angle	An angle that is 90° exactly
Obtuse Angle	an angle that is greater than 90° but less than 180°
Straight Angle	an angle that is 180° exactly
Reflex Angle	an angle that is greater than 180

Lets sing the songs! Angles

Types of angles

To measure angles you can use a protractor, which is a semicircle divided into 180 equal parts, which are called degrees (°).

The angle is measured by the number of degrees it has.

To use it you should:

1. Match the center of the protractor with the vertex of the angle.

2. Align one side of the angle with 0 on the protractor. The angle is measured counter-clockwise.

3. The number the other side marks on the protractor is its measurement.

Song about isometric transformations

Check these videos and learn!
Perimeter and Area
Decimal Numbers
More decimals!
How to read decimals!
Equivalent Fractions
Perimeter and area song

Fractions

Hello kids , here there are some links for you to have fun playing with fractions.

Fractions

A fraction is a part of a whole, for example ¹/₂. Equivalent fractions are fractions that look different but show the same amount. Improper fractions have numerators that are higher than the denominator, while mixed fractions contain whole numbers and fractions.

In order to compare fractions, you need to change them so they have the same denominator. Fractions can be converted into decimals.

A fraction is a part of a whole. There are two numbers to every fraction:

The top number of the fraction is called the numerator. The bottom number is called the denominator.

To find a fraction of a quantity:

Divide the quantity by the denominator: (in the example above) 9 ÷ 4 = 2 r 1 = 2 ¹/ ₄

Now, to find ²/ ₅ of £15, for example:

· Divide 15 by 5 (the denominator): 15 ÷ 5 = 3

· Multiply the answer 3 by 2 (the numerator): 3 x 2 = 6

· So ²/ ₅ of £15 is £6

Activity (When you are ready, we check the answers in class)

· The top number in a fraction is called the...

· Denominator

· Numerator

· Fraction

· The bottom number in a fraction is called the...

· Denominator

· Numerator

· Fraction

· Eight thirds is an improper fraction. Which mixed number is equal to it?

· Two and three thirds

· Two and a half

· Two and two thirds

· 19 fifths is an improper fraction. Which mixed number is equal to it?

· Five and three fifths

· Three and four fifths

· Four and five fifths

· Which fraction is the smallest?

· One half

· One quarter

· Six eighths

· Which fraction is the biggest?

· One quarter

· Three quarters

· Seven eighths

· Jack has 12 chocolates. He gives one quarter of them to his friend. How many chocolates is this?

· 7

· 3

· 5

· Emma has a box of 15 chocolates. 10 are milk chocolate. What fraction is this?

· One third

· One fifth

· Two thirds

· Lucy has a bag of 6 counters. 5 of them are red. The rest are blue. What fraction are blue?

· One sixth

· Two sixths

· Five sixths

10.

· A pizza is divided into 8 pieces. 2 pieces are eaten. What fraction is left?

· One half

· Six eighths

· One eighth

How to read a fraction?

In a fraction, the denominator tells us how many parts the whole is divided into, and the numerator tells us how many of those parts we're dealing with.

We can read this fraction as four-fifths, four over five, or four divided by five.

The number above the bar is called the numerator, and the number below the bar is called the denominator.

Proper fraction: numerator is less than the denominator. (Ex. 1/2, 2/5)

Improper fraction: numerator is greater than or equal to denominator. (Ex. 3/2, 8/5)

Mixed number: whole number and a fraction. (Ex. 2 3/5, 4 6/7)

Equivalent fractions: fractions that represent the same number. (Ex. 1/3 = 2/6 = 3/9)

Reciprocal: the multiplicative inverse of a number. For a fraction, it's obtained by "turning the fraction over". (Ex. 3/7 and 7/3)

Now read the following:

1/2 = a half

11/16 = eleven sixteenth

1/3 = a/one third

4 2/5 = four and two fifths

1/4 = a/one quarter

1/16 = a/one sixteenth

236/407 = two hundred and thirty six over four hundred and seven

0.3 = nought point three

0.527 = nought point five two seven

8.9 = eight point nine

1.5 = one and a half

2.5 = two and a half

With fractions below 1, we use “of” before nouns. Half is a little bit different.
For example, “three quarters of an hour”, “eight tenth of a mile”, “a fifth of students”.

For decimals below 1, you can use “of” or a “plural noun”.
For example, “nought point seven of a mile” = “nought point seven miles”.

Fractions and decimals over 1 are normally followed by plural nouns.
For example, “one and a half hours”, “2.7 millimeters”.

To express amounts and measurements, use singular verbs with fractions and decimals.
“3.6 kilometers IS about 2 miles”.

But to express numbers of people or things, use plural verbs.
“Half the students ARE tired”.

“A fifth of the tickets HAVE been sold”.

We can use “a” or “one”.
A hundred (less formal); one hundred (more formal).

"A" can only be used at the beginning of a number.
“A/one hundred” BUT “three thousands one hundred”.