Forms of numbers
There are four ways of writing a number:
 Standard form shows the way we usually write them: 438
 Word form shows the number written as all words: four hundred and thirtyeight.
 Expanded form or expanded notation shows the value of each digit: 400 + 30 +8
 Place value shows the place value of each digit: 4 hundreds, 3 tens, 8 units.
Place Value
Numbers have digits:
Each digit is a different place value. But… what does “Place Value” mean?
Place Value is the value of a digit in a number.
Look at this chart:
The number 1,342,365 has 1 millions, 3 hundred thousands, 4 ten thousands, 2 thousands, 3 hundreds, 6 tens and 5 units (or ones in American English).
Now, try this exercises:
What number might I be?
 Are you in between 100 and 300? = No
 Are you an odd number? = Yes
 Are you less than 500? = Yes
 Are you greater than 350? = Yes
 Are you greater than 450? = No
 Are you less than 400? = Yes
 Are you in between 360 and 370? = No
 Are you in between 380 and 390? = Yes
 Are you more than 384? = No
What numbers could I be? __________
Comparing and ordering numbers
Symbol 
Meaning 
Example in symbols 
Example in words 
> 
Greater than More than Bigger than Larger than 
7 > 4 
7 is greater than 4 7 is more than 4 7 is bigger than 4 7 is larger than 4 
< 
Less than Fewer than Smaller than 
4 < 7 
4 is less than 7 4 has fewer than 7 4 is smaller than 7 
= 
Equal to Same as 
7 = 7 
7 is equal to 7 7 is the same as 7 
Addition and subtraction
In addition, the two (or more) numbers being added together are called addens. The total is called the sum.
123 + 140 = 263
addend addend sum
In a subtraction, the first term is called the minuend, the second term is the subtrahend and the result is the difference.
364 – 152 = 212
minuend subtrahend difference
Multiplication
There are three numbers in a multiplication problem. The two terms that are being multiplied together are the factors (multiplicand and multiplier). The product is the result or anwer of multiplying the multiplicand by the multiplier.
Try these games:
Now, this game will help you practise problem solving:
Division
There are four terms in a division: The dividend (the number that is being divided), the divisor (the number that the dividend will be divided by), the quotient (the number of times the divisor will go into the dividend) and the remainder (the number that is less than the divisor and is too small to be divided by the divisor to form a whole number).
In the division 7 : 3 = 2 R = 1
7 is the dividend; 3 is the divisor; 2 is the quotient and 1 is the remainder.
Game: Connect four
Problem solving
Can you solve this problem? Try it! Good luck!
There are three baskets. Each basket holds 2 pears and 3 apples.
a. How many fruits are there in each basket?
b. How many fruits are there altogether?
c. How many apples are there altogether?
Answers: a._____________ b. _______________ c.______________
Measurement
February 2011
Illustrated lessons:
Decimals
February 2011
As with whole numbers, a digit in a decimal number has a value which depends on the place of the digit. This table shows the decimal place value for various positions:
Note that adding extra zeros to the right of the last decimal digit does not change the value of the decimal number.
Place (underlined)  Name of Position 
1.234567  Units (ones) position 
1.234567  Tenths 
1.234567  Hundredths 
1.234567  Thousandths 
1.234567  Ten thousandths 
1.234567  Hundred Thousandths 
1.234567  Millionths 
Example:
In the number 3.762, the 3 is in the units place, the 7 is in the tenths place, the 6 is in the hundredths place, and the 2 is in the thousandths place.
How to read decimal numbers
February 2010
A decimal number may be larger than 1. The word and may be used to indicate the decimal point so it should not be used in other parts of the name of the decimal. The decimal 234.987 could be pronounced Two hundred thirtyfour AND nine hundred eightyseven thousandths. This number can also be pronounced Two hundred thirty four point nine hundred eightyseven.
Place value of decimals
February 2011
Decimal numbers, such as O.6495, have four digits after the decimal point. Each digit is a different place value.
The first digit after the decimal point is called the tenths place value. There are six tenths in the number O.6495.
The second digit tells you how many hundredths there are in the number. The number O.6495 has four hundredths.
The third digit is the thousandths place.
The fourth digit is the tenthousandths place which is five in this example.
Therefore, there are six tenths, four hundredths, nine thousandths, and five tenthousandths in the number 0.6495.
Ordering decimals
February 2011
Guess the decimal number
February 2011
Indentifying decimals on a number line
February 2011
Fraction of an amount
Janvier 2011
To find the fraction of an amount, you multiply the amount by the numerator and then you divide the result by the denominator.
4/5 of 20 = 16
Mixed Fractions
Janvier 2011
There are three types of fractions:
Proper Fractions:  The numerator is less than the denominator 

Examples: ^{1}/_{3}, ^{3}/_{4}, ^{2}/_{7}  
Improper Fractions:  The numerator is greater than (or equal to) the denominator 
Examples: ^{4}/_{3}, ^{11}/_{4}, ^{7}/_{7}  
Mixed Fractions:  A whole number and proper fraction together 
Examples: 1 ^{1}/_{3}, 2 ^{1}/_{4}, 16 ^{2}/_{5} 
A mixed fraction or a mixed number is a whole number and a proper fraction combined, such as 2 ^{3}/_{8} and 7 ^{1}/_{4}
1 ^{3}/_{4}  ^{7}/_{4}  
= 
Try this game
Equivalent Fractions
Janvier 2011
Equivalent fractions have the same value. If you multiply or divide both the numerator and the denominator of a fraction by the same number, the fraction keeps its value.
Example:
× 2  × 2  


1  =  2  =  4 
—–  —–  —–  
2  4  8  


× 2  × 2 
These fractions are really the same:
^{1}/_{2}  ^{2}/_{4}  ^{4}/_{8}  
=  = 
Find pairs of equivalent fractions as fast as you can.
Find the fraction which is not equivalent to the others.
Adding Fractions
Janvier 2011
To add fractions, firstly, we have to make sure the bottom numbers (the denominators) are the same. Then, we add the top numbers (the numerators) and put the answer over the same denominator.
Example:
1  +  1  =  1 + 1  =  2 
—  —  ——  —  
4  4  4  4 
Fractions
Janvier 2011
A fraction is part of an entire object. A fraction consists of two numbers separated by a line: The numerator (the top number) tells how many fractional pieces there are, the denominator tells how many pieces an object is divided into.
The fraction 3/8 tells us that we have three pieces and the whole object is divided into eight pieces.
Activities:
Activities
Polygons
June 2010
A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.
Examples:
Regular polygons
A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same.
Examples:
Types of polygons
Types of polygons based on the number of sides:
Name  Sides  Angles 
Triangle  3  3 
Quadrilateral  4  4 
Pentagon  5  5 
Hexagon  6  6 
Heptagon  7  7 
Octagon  8  8 
Nonagon  9  9 
Decagon  10  10 
Triangle
A threesided polygon. The sum of the angles of a triangle is 180 degrees.
Examples:
Equilateral Triangle or Equiangular Triangle
A triangle having all three sides of equal length. The angles of an equilateral triangle all measure 60 degrees.
Examples:
Isosceles Triangle
A triangle having two sides of equal length.
Examples:
Scalene Triangle
A triangle having three sides of different lengths.
Examples:
Acute Triangle
A triangle having three acute angles.
Examples:
Obtuse Triangle
A triangle having an obtuse angle. One of the angles of the triangle measures more than 90 degrees.
Examples:
Right Triangle
A triangle having a right angle. One of the angles of the triangle measures 90 degrees. The side opposite the right angle is called the hypotenuse. The two sides that form the right angle are called the legs.
Examples:
Quadrilateral
A foursided polygon. The sum of the angles of a quadrilateral is 360 degrees.
Examples:
Rectangle
A foursided polygon having all right angles. The sum of the angles of a rectangle is 360 degrees.
Examples:
Square
A foursided polygon having equallength sides meeting at right angles. The sum of the angles of a square is 360 degrees.
Examples:
Parallelogram
A foursided polygon with two pairs of parallel sides. The sum of the angles of a parallelogram is 360 degrees.
Examples:
Rhombus
A foursided polygon having all four sides of equal length. The sum of the angles of a rhombus is 360 degrees.
Examples:
Trapezoid
A foursided polygon having exactly one pair of parallel sides. The two sides that are parallel are called the bases of the trapezoid. The sum of the angles of a trapezoid is 360 degrees.
Examples:
Anagram quiz
Try this game. You have 30 seconds to work out each anagram. Can you do it before the time runs out?
Angles quiz
This game is a fun way to assess your knowledge about measuring and classifying angles.
Angle bisector
May 2010
The bisector of an angle, also called angle bisector is the line or line segment that divides the angle into two equal parts.
Perpendicular bisector of a line segment.
The perpendicular bisector of a line segment AB is the line through the midpoint (M) perpendicular to AB. We adopt the following steps to bisect the line segment AB perpendicularly using a ruler and a compass. 

Step 1  Draw an arc with centre A and with a radius of more than half of the length of AB. 
Step 2  Using the same radius, draw an arc with centre B to cut the arc drawn in Step 1 at P and Q. 
Step 3  Join PQ. 

Complementary and supplementary angles
Two angles are complementary if the sum of these angles equals 90º.
The angles don’t have to be together.
Two angles are called supplementary if the sum of these angles equals 180º.
Complementary and supplementary angles
Types of angles
Try with angles!
Make an angle and mesure it with the protractor:
Working with angles
may 2010
An angle is formed by two rays with the same vertex. We use the protractor to mesure angles.
Measurement
April 2010
Illustrated lessons:
Decimals
february 2010
As with whole numbers, a digit in a decimal number has a value which depends on the place of the digit. This table shows the decimal place value for various positions:
Note that adding extra zeros to the right of the last decimal digit does not change the value of the decimal number.
Place (underlined)  Name of Position 
1.234567  Units (ones) position 
1.234567  Tenths 
1.234567  Hundredths 
1.234567  Thousandths 
1.234567  Ten thousandths 
1.234567  Hundred Thousandths 
1.234567  Millionths 
Example:
In the number 3.762, the 3 is in the units place, the 7 is in the tenths place, the 6 is in the hundredths place, and the 2 is in the thousandths place.
How to read decimal numbers
february 2010
A decimal number may be larger than 1. The word and may be used to indicate the decimal point so it should not be used in other parts of the name of the decimal. The decimal 234.987 could be pronounced Two hundred thirtyfour AND nine hundred eightyseven thousandths. This number can also be pronounced Two hundred thirty four point nine hundred eightyseven.
Place value of decimals
february 2010
Decimal numbers, such as O.6495, have four digits after the decimal point. Each digit is a different place value.
The first digit after the decimal point is called the tenths place value. There are six tenths in the number O.6495.
The second digit tells you how many hundredths there are in the number. The number O.6495 has four hundredths.
The third digit is the thousandths place.
The fourth digit is the tenthousandths place which is five in this example.
Therefore, there are six tenths, four hundredths, nine thousandths, and five tenthousandths in the number 0.6495.
Ordering decimals
february 2010
Guess the decimal number
february 2010
Indentify decimals on a number line
february 2010
Statistics
january 2010
Statistics is a branch of mathematics. It’s a set of concepts, rulers and procedures that helps us to organize numerical information in form of tables, graphs and charts in order to draw conclusions and make predictions.
Statistical mean or average
january 2010
To find the mean of a group of numbers:
 Add the numbers together.
 Divide by how the numbers were added together.
For example: Find the mean of the following numbers: 2, 5, 8, 9
Answer: (2+5+8+9) : 4 = 12
Statistical mode
january 2010
The statistical mode is the number that occurs most frequently in a set of numbers.
For example: The mode of 2, 4, 5, 5, 5, 7, 8, 8, 9, 12 is 5.
Mode, median and mean and then quiz the following activity
Mean, median and mode calculator
Statistical median
january 2010
The statistical median is middle number of a group of numbers that have been arranged in order by size. If there is an even number of terms, the median is the mean of the two middle numbers:
To find the median of a group of numbers:
 Arrange the numbers in order by size.
 If there is an odd number of terms, the median is the center term.
 If there is an even number of terms, add the two middle terms and divide by 2.
Apply the concepts of median and mean
Statistical range
january 2010
The statistical range is the difference between the lowest and highest valued numbers in a set of numbers.
To find the range of a group of numbers:
 Arrange the numbers in order by size.
 Subtract the smallest number from the largest number.
Use range, mean, median and mode
Calculate mean, median, mode and range
Statistical graphs
january 2010
Read the graph and answer questions
Collect data, tally marks and select the appropriate graph
Survey a small group and create different graphs, and then take this quiz
Pictographs
A pictograph uses an icon to represent a quantity of data values.
Pie chart (circle graph)
A pie chart displays data as a percentage of the whole.
Enter data to create a circle graph
Histogram
A histogram displays continuous data in ordered columns.
Bar graph
A bar graph displays data in separate columns. A double bar graph can be used to compare two data sets.
Enter data to create a bar graph
Line graph
A line graph plots continuous data as points and then joins them with a line.
Fraction of an amount
december 2009
To find the fraction of an amount, you multiply the amount by the numerator and then you divide the result by the denominator.
4/5 of 20 = 16
Mixed Fractions
december 2009
There are three types of fractions:
Proper Fractions:  The numerator is less than the denominator 

Examples: ^{1}/_{3}, ^{3}/_{4}, ^{2}/_{7}  
Improper Fractions:  The numerator is greater than (or equal to) the denominator 
Examples: ^{4}/_{3}, ^{11}/_{4}, ^{7}/_{7}  
Mixed Fractions:  A whole number and proper fraction together 
Examples: 1 ^{1}/_{3}, 2 ^{1}/_{4}, 16 ^{2}/_{5} 
A mixed fraction or a mixed number is a whole number and a proper fraction combined, such as 2 ^{3}/_{8} and 7 ^{1}/_{4}
1 ^{3}/_{4}  ^{7}/_{4}  
= 
Try this game
Equivalent Fractions
december 2009
Equivalent fractions have the same value. If you multiply or divide both the numerator and the denominator of a fraction by the same number, the fraction keeps its value.
Example:
× 2  × 2  


1  =  2  =  4 
—–  —–  —–  
2  4  8  


× 2  × 2 
These fractions are really the same:
^{1}/_{2}  ^{2}/_{4}  ^{4}/_{8}  
=  = 
Find pairs of equivalent fractions as fast as you can.
Find the fraction which is not equivalent to the others.
Adding Fractions
december 2009
To add fractions, firstly, we have to make sure the bottom numbers (the denominators) are the same. Then, we add the top numbers (the numerators) and put the answer over the same denominator.
Example:
1  +  1  =  1 + 1  =  2 
—  —  ——  —  
4  4  4  4 
Fractions
november 2009
A fraction is part of an entire object. A fraction consists of two numbers separated by a line: The numerator (the top number) tells how many fractional pieces there are, the denominator tells how many pieces an object is divided into.
The fraction 3/8 tells us that we have three pieces and the whole object is divided into eight pieces.
Activities:
Activities
(Activities and support material about fractions)
Games:
Worksheets:
Division
November 2009
There are four terms in a division: The dividend (the number that is being divided), the divisor (the number that the dividend will be divided by), the quotient (the number of times the divisor will go into the dividend) and the remainder (the number that is less than the divisor and is too small to be divided by the divisor to form a whole number).
In the division 7 : 3 = 2 R = 1
7 is the dividend; 3 is the divisor; 2 is the quotient and 1 is the remainder.
Game: Connect four
Problem solving
October 2009
There are three baskets. Each basket holds 2 pears and 3 apples.
a. How many fruits are there in each basket?
b. How many fruits are there altogether?
c. How many apples are there altogether?
Answers: a._____________ b. _______________ c.______________
Properties of multiplication
October 2009
There are four properties involving multiplication:
 Commutative Property: When two numbers are multiplied together, the product is the same regardless of the orders of the multiplicands. For example: 3 . 4 = 4 . 3
 Associative Property: When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors. For example: (2 . 3) . 5 = 2 . (3 . 5)
 Multiplicative Identity Property: The product of any number and one is that number. For example: 4 . 1 = 4
 Distributive Property: The product of a number and a sum is equal to the sum of the individual products of the addens and the number.
For example: 4 . (3 + 6) = 4 . 3 + 4 . 6
Practice:
Addition, subtraction and multiplication
October 2009
Properties of addition:
 Commutative property: When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4
 Associative Property: When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (2 + 3) + 4 = 2 + (3 + 4)
Subtraction is removing some objects from a group.
The meaning of 53=2 is “Three objects are taken away from a group of five objects and two objects remain”.
There are three terms in a multiplication problem: the multiplicand, the multiplier and the product. The multiplicand and the multiplier are the factors. The result of multiplying the multiplicand by the multiplier is the product.
A multiplication problem may be written vertically:
38754
x 2
77508
In this multiplication: 38754 is the multiplicand, 2 is the multiplier and 77508 is the product. 38754 and 2 are the factors.
Forms of a number
October 2009
We have different forms of writing a number:
 Standard form: shows the numbers the way we usually write them. For example: 458
 Word form: shows the numbers written as all words. For example: four hundred and fiftyeight.
 Place Value: shows the place value of each digit. For example: 4 hundreds, 5 tens, 8 units.
 Expanded form (or Expanded Notation): shows the number written as the sum of the value of its digits. For example: 400 + 50 +8
Place Value
September 2009
Numbers have digits:
Each digit is a different place value. But… what does “Place Value” mean?
Place Value is the value of a digit in a number.
Look at this chart:
The number 1,342,365 has 1 millions, 3 hundred thousands, 4 ten thousands, 2 thousands, 3 hundreds, 6 tens and 5 units (or ones in American English).
Now, try this exercises:
What number might I be?
 Are you in between 100 and 300? = No
 Are you an odd number? = Yes
 Are you less than 500? = Yes
 Are you greater than 350? = Yes
 Are you greater than 450? = No
 Are you less than 400? = Yes
 Are you in between 360 and 370? = No
 Are you in between 380 and 390? = Yes
 Are you more than 384? = No
What numbers could I be? __________
Decimals
Decimal numbers have digits after the decimal point. Each digit is a different place value. The first digit after the decimal point is the tenths place; the second, the hundredths place; the third, the thousandths place; the four, the ten thousandths place…
E.g., in the number 0.6482 there are 6 tenths, 4 hundredths, 8 thousandths and 2 ten thousandths.
profe me encanta xao
is 385 numers
You are wrong. Try it again.
the numbers could be 381,382 and 383.
382 is not an odd number.
the numbers could be three hundred and eighty three
That’s true, but there is another number.
the numbers could be 381,382 and 383
382 is not an odd number. The other numbers are right.
1150
2330
3120
4140
5154
6231
7345
8655
9222
No, you are wrong. Try it again.
the numbers coud be three hundred and eighty three
Yes, but there is another possible number.
maestra kreo ke es el numero 382
The number can’t be 382 because it isn’t an odd number. Try again. Write in English, please
the numbers could be 381 and 383
I am glad to have good
That’s great.
I wanted to say I am glad to have good
los números son:
El 381 y el 383
That’s correct. But you have to write in English, please.
puede ser el numero 397
You have to write in English. The number can’t be 397. Try again.
The numbers are 381 and 383
Very good, Christopher!
teacher on Where are the exercises?
the numbers are 381 and 383
Very good, Javier.
answer: a 3 + 2=5 frits in each asket
answer: b. 5 x 3= 5 is a total fruit
answer:c. 3 x 3= 9 apples are
Answer b is incorrect.
Revise your spelling, some letters are missing.
a) five fruit
b) fifteen fruit
c) nine apples
a) five fruits
b) fifteen fruits
c) nine apples
Very good, Lourdes.
a,5 b,15 c,9
That’s right, Daniel.
a)five
b)fiveten
c)nine
a)five
b)fifteen
b)nine
I’m sorry for putting bad I did not remember
the numbre fifteen ok?
hola Myriam somos Elena y Margarita y no te escribimos en ingles por que nos salen cosas muy raras y no te enfades heee.
Bueno nosotras tenemos una cosa para ti pero hasta el ultimo dia de cole te lo daremos marga y yo