**Mathematics**

The study of numbers, patterns, space, and change.

**Number.**

A number is a count or measurement.

They are really an idea in our minds. We write or talk about numbers using numerals such as “5” or “five”. We could also hold up 5 fingers, or tap the table 5 times. These are all different ways of referring to the same number.

There are also different types of numbers, such as whole numbers (1,2,3) decimals (1.48, 50.5), fractions (1/2, 3/8), and more.

**Number word**

The written word for a number (e.g. 6 is six).

**Number sentence**

A mathematical statement that shows how two quantities are related

e.g.3+8=11

**Zero**

The whole number between -1 and 1, with the symbol 0

Shows that there is no amount.

Example: 6 – 6 = 0 (the difference between six and six is zero)

Also useful as a “place-holder” so that you can write a numeral properly.

Example: 502 (five hundred and two) could be mistaken for 52 (fifty two) without the zero in the tens place.

**Whole Number**

The numbers {0, 1, 2, 3, …} etc.

There is no fractional or decimal part. And no negatives.

Example: 5, 49 and 980 are all whole numbers.

** Expanded form**

A way to write a number that shows the value of each digit. (e.g.In expanded form, 365 is 300+60+5)

**Even Number**

Multiple of 2. The even numbers are { . . . , 0, 2,4,6, . . . }.

**Odd Number**

Is not a multiple of 2. The odd numbers are { . 1, 3, 5, .}.

**Cardinal Numbers**

The numbers 1, 2, 3, . . . Cardinal numbers are used to describe the number of elements in either finite or infintite sets.

**Ordinal Numbers**

Numerical words that indicate order. The ordinal numbers are: first, second, third, fourth, etc.

**Tenth**

One part in ten equal parts.

A tenth of these 100 blocks is highlighted.

Example: one tenth of 50 is 5.

**Hundredth**

One part in a hundred equal parts.

1/100th

Example: 1 cent is a hundredth of 1 Euro

**Rouding to the nearest hundred**

Estimating a number to the closest number of hundreds. e.g. 83 rounds up to 100.

**Rounding to the nearest tens**

Estimating a number to the closest number of tens. e.g. 83 rounds up to 90, and round down to 80.

**Number Line**

A line with numbers placed in their correct position.

Useful for addition and subtraction, and for showing relations between numbers.

**Skip count**

To count without using every number acording to a pattern. e.g. 0 5 10 15 20.. skip counting by 5s.

**Digit**

Any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 used to write numbers. For example, the digits in the number 361 are 3, 6, and 1.

**Pattern**

Things that are arranged following a rule or rules.

Example: these tiles are arranged in a pattern

Another Example: there is a pattern in these numbers: 2, 7, 12, 17, 22, … The rule is “start at 2 and add 5 each time”

**Number Pattern**

A list of numbers that follow a certain sequence or pattern.

Example: 1, 4, 7, 10, 13, 16, 19, … starts at 1 and jumps 3 every time.

Another Example: 2, 4, 8, 16, 32, … doubles each time.

**Linear pattern**

A pattern in which the difference between each item and the next is always the same. e.g. 2.4.6.8….., 98.96.94…..

**No linear pattern**

A pattern in which the difference between each term and the next does not stay the same. e.g. 1.3.6.10…..

**Increase**

Make something bigger (in size or quantity).

**Decrease**

Make something smaller (in size or quantity).

**Attribute**

A property of an object or person etc.

Something you can say it has (such as size or color).

Example: The attributes of a dog include height, speed and color.

**Operation**

A mathematical process.

The most common are add, subtract, multiply and divide (+, -, ×, ÷ ).

But there are many more, such as squaring, square root, etc.

If it isn’t a number it is probably an operation.

Example: In 25 + 6 = 9, the operation is add.

**Fact**

An addition, subtraction, multiplication, or division sentence. (e.g.9+9=18)

**Fact family**

A set of numbers sentences, each fact uses the same numbers

2+3=5 5-3=2

3+2=5 5-2=3

**Sum**

The result of adding a set of numbers or algebraic expressions.

**Add**

To bring two or more numbers (or things) together to make a new total.

Here 1 ball is added to 1 ball to make 2 balls.

If you add 2 and 3 you get 5.

**Plus**

Another word for add.

Example: 30 cents plus 20 cents equals 50 cents.

The symbol is +

**Addition**

Addition is finding the total, or sum, by combining two or more numbers.

Example: 5 + 11 + 3 = 19 is an addition.

Any of the numbers that are** added** together.

Example: In 2 + 3 = 5, the 2 and the 3 are addends.

The simbol of addition is +

**Subtract – Subtraction.**

To take one number away from another.

If you have 5 apples and you subtract 2, you will be left with 3.

The symbol of subtraction is –

Example: 5 – 2 = 3

**minuend – subtrahend = difference**

Example: in 8 – 3 = 5, 8 is the minuend and 3 is the subtrahend.

**Equal**

Exactly the same amount or value

Examples:

3 + 4 is equal to 7

1 Dollar is equal to 100 Cents

60 seconds is equal to 1 minute

The symbol is =

**Brackets**

Brackets are symbols used in pairs to group things together.

Types of brackets include:

parentheses or “round brackets” ( )

“square brackets” or “box brackets” [ ]

braces or “curly brackets” { }

**Greater Than**

**Bigger.**

The symbol > means greater than (the symbol < means **less than**). Example: 5 > 3 shows that 5 is greater than 3.

**Closed curve.**

A curve that joins up so there are no end points.

Example: an ellipse is a closed curve.

If you can draw it without lifting your pencil and you end up where you started, then it will be a closed curve.

**Open Curve**

A curve with end points (in other words, the ends don’t join up).

**Line**

A long thin mark made by a pen, pencil, etc.

In geometry a line:

· is straight (no curves),

· has no thickness, and

· extends in both directions without end (infinitely).

**Curved Line**

A line that is not straight

But in geometry a line is always straight (not curved).

**Twice**

Two times as many.

8 is twice 4

**Pair**

Two together. Often with something in common.

Example: {12,7} is a pair of numbers

**Double**

Make twice as big. Multiply by 2.

Example: Double 4 is 8.

**Triple**

To make something three times as large (multiply by three)

Triple 6 is 18 (because 3 × 6 = 18)

Or, a set of three things together.

Triple “R” is “RRR”.

**Whole**

All of something. Complete.

**Half**

One of two equal parts of a whole.

Example: my friend and I shared a pie. We had half each.

**Smallest.**

Example: The 1 cent has the least value of these coins

Example: The least of {16,4,9} is 4.

**Dozen**

12 items

Example: a dozen eggs

**Multiplication**

The basic idea of multiplication is repeated addition.

For example: 5 × 3 = 5 + 5 + 5 = 15.

**Multiplier**

The number that you are multiplying by.

But because you can multiply the two numbers in any order, it is better to use the word “factor”.

**Factor**

Factors are the numbers you multiply together to get another number:

Example: 3 and 4 are factors of 12, because 3× 4=12.

Also 2 × 6=12 so 2 and 6 are also factors of 12, and 1 × 12=12 so 1 and 12 are factors of 12 as well.

So ALL the factors of 12 are 1,2,3,4,6 and 12.

**Times**

Another word for multiply

Example: 3 times 5 is 15

The symbol is ×

Example: 3 × 5 = 15

**Ruler**

A tool used to rule straight lines and measure distances.

Our ruler is marked in cm along the top and inches along the bottom.

**Table**

Numbers or quantities arranged in rows and columns.

This is a table of what sport people play at a school.

**Tables**

A short name for the multiplication tables.

“He learnt his tables up to 8 times 8”.

**Timetable**

A table of information showing when things will happen.

Examples: this is part of a bus timetable.

**Shape**

The form of an object – how it is laid out in space (not what it is made of, or where it is).It is an attribute.

**Common shapes are:**

**Two dimensional:** Circles, squares, triangles, … etc

**Three dimensional**: Spheres, cubes, pyramids, … etc

**Similar**

Identical in shape but not necessarily the same size.

**Side**

One of the lines that make a flat (2-dimensional) shape.

Or one of the surfaces that make a solid (3-dimensional) object.

**Face**

Any of the individual surfaces of a solid object.

Example: this tetrahedron has 4 faces (there is one face you can’t see)

**Vertex**

A point where two or more straight lines meet. A corner.

Example: a corner of a polygon (2D) or of a polyhedron (3D).

The plural of vertex is “vertices”.

**Polygon**

A plane shape (two-dimensional) with straight sides.

Examples: triangles, rectangles and pentagons.

(Note: a circle is not a polygon because it has a curved side)

**Triangle**

A 3-sided polygon (a flat shape with straight sides).

**Square**

A 4-sided polygon (a flat shape with straight sides) where all sides have equal length and every angle is a right angle (90°), and 4 squares corners.

**Rectangle**

A four-sided polygon (a flat shape with straight sides) where every angle is a right angle (90°).

Also opposite sides are parallel and of equal length.

**Circle**

A 2-dimensional shape made by drawing a curve that is always the same distance from a center

**Translate**

To move a shape, without rotating or flipping it. To “slide”.

The shape still looks exactly the same, just in a different place.

**Flip**

Turn something over. To make a mirror image of.

Example: this shape is flipped over the line.

**Dimension**

A measurement of length in one direction.

Examples: width, depth and height are dimensions.

In Physics it can also mean any physical measurement such as length, time, mass.

**Measure**

To find a number that shows the size or amount of something.

Usually the number is in reference to some standard measurement, such as a meter or kilogram.

Here some scales are used to measure weight.

Dimension.

A way to describe how an object can be measured (e.g. A line has only lenght, so it is 1-dimensinal, a rectangle has lenght and width, so it is 2-dimensional, a cube has lenght, width and height, so it is 3-dimensional

**Weight**

“Heaviness”. The downward force caused by gravity on an object.

The weight of an object can be different in different situations (such as in a moving elevator, or on the moon) while the mass stays the same.

Weight uses the units of mass. For example grams, kilograms and, tonnes (Metric) .

**Height**

The vertical distance from top to bottom.

**Length**

Distance. How far from end to end.

Example: the length of this guitar is about 1 meter

**Width**

The distance from side to side.

Example: the width of this door is 80 cm.

**Metric System**

A system of measuring based on:

· The meter for length

· The kilogram for mass

· The second for time

Examples:

A kilometer is 1,000 meters

A meter is 100 centimeters.

**Capacity**

The amount that something can hold.

Usually it means volume, such as milliliters (ml) or liters (l) in Metric.

Example: “The bucket has a capacity of 9 liters”

Capacity can also be general: “He has a great capacity for work”

Litre | Liter

A Metric unit of volume.

Mostly used to measure liquids

The abbreviation is L

1 liter = 1,000 milliliters (ml)

**Metre | Meter**

The basic unit of length (or distance) in the Metric System.

The abbreviation is m.

Centimeter

A centimeter (UK: centimetre) is a measure of length. There are 100 centimeters in a meter. 2.54 cm = 1 inch.

The abbreviation is cm.

**Kilo-**

A prefix meaning one thousand

Example: a kilogram is a thousand grams.

**Cent**

The smallest money value in many countries.

100 cents equals one dollar in the US, Canada and Australia.

100 cents equals one euro in Europe.

**Bar Graph**

A graph drawn using rectangular bars to show how large each value is.

The bars can be horizontal or vertical.

Horizontal

Going side-to-side, like the horizon.

Parallel to the horizon.

(Up-down is called vertical)

**Column**

An arrangement of figures, one above the other.

This is a column of numbers:

12

25

17

92

14

**Row**

Things lying side-by-side. Objects, People, Numbers, etc in a horizontal line.

Example: a row of numbers: 5, 7, 11, 20, 22

(Note: columns go up-down)

**Line Graph**

A graph that uses points connected by lines to show how something changes in value (as time goes by, or as something else happens).

**Data**

Information gathered in a survey, in an experiment, or by observing (e.g, Data can be in words like a list of students´names, in numbers like quiz marks, or in pictures like drawings of favourite pets. A collection of facts, such as values or measurements.

**Range**

The difference between the greatest and the least values in a set of data. e.g. For the numbers 1.2.5.7.9.11.12 the range is 12-1=11.

**Date**

The exact day, month and/or year.

Examples:

The date of my appointment is March the 25th.”

“His birth date was 23 November 2006.”

**Day**

The 24 hour period from midnight to the next midnight.

It is how long the Earth takes to spin once on its axis.

It can also mean just the time from sunrise to sunset (the rest of the 24 hours being “night”).

**Midday**

The middle of the day. 12 O’clock Noon. 12:00

**Midnight**

The middle of the night.12 o´clock :24:00

**AM**

Is the half of the day from midnight to midday. What we call morning.

**PM**

Is the half of the day from midday to midnight.What we call afternoon, evening and night till 24:00

**Time**

Time is the ongoing sequence of events taking place. The past, present and future.

We measure time using seconds, minutes, hours, days, weeks, months and years.

Clocks measure time.

**Hour**

A period of time equal to 1/24 (a twenty-fourth) of a day.

1 Day = 24 Hours

1 Hour = 60 minutes.

Example: The amount of time between 5:00 and 6:00 is one hour.

**Calendar**

A diagram that shows what day and month it is.

**Digital Clock or Watch**

A clock or watch that shows the time using numbers, not hands.

**Analog Clock or Watch**

A clock or watch is called “analog” when it has moving hands and hours marked from 1 to 12 to show you the time.

**Hour Hand**

The small hand on a clock that points to the hours.

It goes once around the clock every 12 hours (half a day).

Example: in the clock on the left, the hour hand is just past the “8” so you know the time is just past “8 O’clock”

(And the large hand is the minute hand and it shows that it is 18 past the hour, so it is 18 past 8).

**OneWeek**

Seven days

**One Term**

Three months

**One Year**

Twelve months.

Three terms.

365 days.

**Century**

A unit of measurement for time, 100 years.

**Millennium**

1000 years.

**Fortnight**

A time period of 14 days (2 weeks).

The word comes from “fourteen nights”

**Leap Year**

A leap year is a year containing an extra day. It has 366 days instead of the normal 365 days.

The extra day is added in February, which has 29 days instead of the normal 28 days.

Leap years occur every 4 years. 2008 is a leap year and so is 2012.

Except that every 100 years special rules apply. For example 1900 was not a leap year, but 2000 was.

**Compass**

An instrument that shows us direction (such as North, South, East and West) by means of a small magnetic needle that points North/South.

**Balance Scales**

A device for weighing. It has a balanced beam and two pans. When the pans contain exactly the same mass the beam will be in balance. You can place an object in one pan and standard weights in the other to find what the object weighs.

**Sign**

When used with a name, it means a symbol used instead of words, such as the “Stop” sign shown.

Example: “%” is the percent sign.

When used on its own, such as just saying “sign”, it means negative or positive.

Example: what sign is the number? Is it negative?