Statistics
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
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
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
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
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
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.
Adding and subtracting fractions with unlike denominators
Firstly, you have to find the Lowest Common Multiple of the denominators, and then… (listen to the video)
Exponents
The result of raising a number (the base) to a power (the exponent) is the same number that would be obtained by multiplying the base number together the number of times that is equal to the exponent. Example: 34= 81 is equivalent to 3 x 3 x 3 x 3 = 81. In this example, the base is 3 and the exponent is 4. Some facts about exponents:
- Zero raised to any power is zero (e.g. 05 = 0)
- One raised to any power is one (e.g. 15 = 1)
- Any number raised to the zero power is one (e.g. 70 = 1)
- Any number raised to the first power is that number (e.g. 71 = 7
Squaring a number
An exponent is a number that tells how many times the base number is used as a factor. For example, 32 indicates that the base number 3 is used as a factor 2 times. To determine the value of 32, multiply 3 x 3 which would give the result 9. 32 (two squared) = 3 x 3 = 9 Squares indicate that the exponent has a value of two. The term square comes from the geometrical shape that has the same width and length. To find the area of a square you would multiply the width times the length.
The cube of a number
Cubes indicate that the exponent has a value of three. The term cube comes from the geometrical shape that has the same width and length and height. To find the volume of a cube you would multiply the width times the length times the height. For example, 43 indicates that the base number 4 is used as a factor 3 times. To determine the value of 43, multiply 4 x 4 x 4 which would give the result 64. 43 (four cubed) = 4 x 4 x 4 = 64. Write multiplication expressions using exponents Evaluate exponents
Factors
november 2010
A factor is a number that divides another number without a remainder, that’s to say, the remainder of the division is 0.
For example: 2 is a factor of 14, because 14 : 2 = 7, and the remainder is 0.
14 is a multiple of 2, so 2 is a factor of 14.
We can calculate all factors of a number:
The factors of 16 are: 1, 2, 4, 8, 16.
Prime and composite numbers
A prime number is a number that has only two factors: 1 and itself.
2, 3, 5, 7, 11, 13, 17 and 19 are prime numbers.
A composite number has more than two factors.
4, 6, 8, 9, 10, 12, 14, 15, 16, 18 and 20 are composite numbers.
The number 1 are neither prime nor composite, because it has only one factor. And the number 2 is the only prime that is even.
Practise on factors, multiples, prime and composite numbers.
Common factors
A common factor is a number that is a factor of two or more given numbers.
Example:
| The factors of 12 are 1, 2, 3, 4, 6 and 12 |
| The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30 |
Then the common factors are those that are found in both numbers:
- Notice that 1,2,3 and 6 appear in both lists.
- So, the common factors of 12 and 30 are: 1, 2, 3 and 6.
Highest common factor
It is simply the largest of the common factors. In our previous example, the largest of the common factors is 6, so the Highest Common Factor (or greatest common factor) of 12 and 30 is 6.
You can:
- find all factors of both numbers,
- then select the ones that are common to both, and
- then choose the largest.
Multiples
november 2010
To get multiples of a whole number, we will multiply this whole number by some other whole numbers.
For example, the multiples of the whole number 4 are: 4, 8, 12, 16, 20, 24, 28, … , because 4 x 1 = 4, 4 x 2 = 8, 4 x 3 = 12, …
Multiplying 4 by 7 gives 28, so 28 is a multiple of 4.
Do you feel confident? Try this quiz
Now, try this game: Firstly, choose the target number and then you must collect only the numbers that are multiples of the target number. Catch as many multiples as possible.
Lowest common multiple
A commom multiple is a number that is a multiple of two or more numbers:
The common multiples of 3 and 4 are 0, 12, 24, …
The lowest common multiple (or least common multiple) (LCM) of two or more numbers is the smallest common multiple (different from 0) of these numbers.
Decimals
october 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
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 thirty-four AND nine hundred eighty-seven thousandths. This number can also be pronounced Two hundred thirty four point nine hundred eighty-seven.
Place value of decimals
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 ten-thousandths place which is five in this example.
Therefore, there are six tenths, four hundredths, nine thousandths, and five ten-thousandths in the number 0.6495.
Ordering decimals
Guess the decimal number
Indentify decimals on a number line
Whole numbers
september 2010
Combined operations:
A standard order must be followed when dealing with combined operations:
1. Do all operations inside parentheses.
2. Multiply or divide from left to right.
3. Add or subtract from left to right.
Integers
may 2010
An integer is a whole number that can be either bigger than 0 (called positive) or smaller than 0 (called negative).
Every integer has an absolute value, which is its distance from zero.
You can visualize positive and negative integers using the number line:
Adding integers
If both of the integers are negative, add their absolute values and prefix the result with a negative sign:
(-3) + (-2) = (-5)
If one of the integers is negative, subtract the absolute value of it from the other number and prefix the result with the sign of the integer with the greater absolute value.
(-5) + (+6) = (+1)
(-16) + (+4) = (-12)
Practice: Adding negative numbers
Play this game:
Percentages
april 2010
How to calculate the percentage of a number:
Firstly, multiply the number by the percentage.
And then, divide the answer by 100.
How to determine the percentage:
Firstly, divide the smaller number by the bigger number.
Secondly, multiply the result by 100.
Finally, follow the answer with the % sign.
Practice
Fractions, decimals and percents
Finding a percent of a quantity
Exponents
february 2010
The result of raising a number (the base) to a power (the exponent) is the same number that would be obtained by multiplying the base number together the number of times that is equal to the exponent.
Example: 34 = 81 is equivalent to 3 x 3 x 3 x 3 = 81.
In this example, the base is 3 and the exponent is 4.
Some facts about exponents:
- Zero raised to any power is zero (e.g. 05 = 0)
- One raised to any power is one (e.g. 15 = 1)
- Any number raised to the zero power is one (e.g. 70 = 1)
- Any number raised to the first power is that number (e.g. 71 = 7)
Squaring a number
february 2010
An exponent is a number that tells how many times the base number is used as a factor. For example, 32 indicates that the base number 3 is used as a factor 2 times. To determine the value of 32, multiply 3 x 3 which would give the result 9.
Squares indicate that the exponent has a value of two. The term square comes from the geometrical shape that has the same width and length. To find the area of a square you would multiply the width times the length.
The cube of a number
february 2010
Cubes indicate that the exponent has a value of three. The term cube comes from the geometrical shape that has the same width and length and height. To find the volume of a cube you would multiply the width times the length times the height.
For example, 43 indicates that the base number 4 is used as a factor 3 times. To determine the value of 43, multiply 4 x 4 x 4 which would give the result 64.
Write multiplication expressions using exponents
Multiples
january 2010
We obtain the multiples of a number multiplying this number a certain number of times.
Multiples of 2: 2, 4, 6, 8, 10, 12….
Multiples of 3: 3, 6, 9, 12, 15…
Lowest Common Multiple
january 2010
The Lowest Common Multiple (LCM) of several numbers is the smallest number which is multiple of each.
Example: What are some multiples of both 4 and 6?
Set of multiples of 4 = {4, 8, 12, 16, 20, 24, 28, 32, …}
Set of multiples of 6 = {6, 12, 18, 24, 30, 36,…}
12 is multiple of both 4 and 6. Another multiple of both is 24. Therefore, 12 and 24 are called common multiples of 4 and 6. But 12 is smaller than 24, then 12 is the Lowest Common Multiple (LCM).
Factors
january 2010
The factors, or divisors, of a number are the positive numbers into which the number can be divided.
The divisors of 12 are: 1, 2, 3, 4, 6, 12.
Highest Common Factor
january 2010
The Highest Common Factor (HCF), of several numbers is the largest number into which these numbers can be divided.
Set the divisors of 12 = {1, 2, 3, 4, 6, 12}
Set the divisors of 16 = {1, 2, 4, 8, 16}
2 and 4 are common factors of both 12 and 16.
4 is the Highest Common Factor because 4 is larger than 2.
Lowest Common Multiple and Higher Common Factor
Angles
November 2009
An angle is formed by two rays with the same vertex. It’s mesured with a protractor.
Place Value of decimals
October 2009
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…
For example, in the number 0.6482 there are 6 tenths, 4 hundredths, 8 thousandths and 2 ten thousandths.
Polygons
A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.
A regular polygon is a polygon whose sides are all the same legth and whose angles are all the same.
Fractions
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 and support material about fractions)
Presentations
(from the page http://www.teachingideas.co.uk)
Equivalent Fractions:
Ordering Fractions:
Simplifying Fractions:
Mixed and Improper Fractions:
Prime numbers
A prime number has only two factors: 1 and itself.
For example: 11 is a prime number because it has only two factors: 1 and 11.
Composite numbers
A number that has more than two factors is a composite number.
For example: 12 is a composite number. The factors of 12 are: 1, 2, 3, 4, 6, 12.
Watch this video:
Practice prime and composite numbers in this link:
Los números decimales
Los números decimales están formados por una parte entera y un parte decimal separadas por una coma:
Cuando la unidad se divide en diez partes iguales, cada parte es una décima.
Si la unidad se divide en cien partes iguales, cada parte es una centésima.
Si la unidad se divide en mil partes iguales, cada una de las partes es una milésima.
Si la unidad se divide en diez mil partes iguales, cada parte será un …
Ahora, ved este vídeo sobre los números decimales:
La división de decimales
(1 de diciembre de 2008)
En la siguiente imagen podéis ver un ejemplo de los diferentes casos de división de decimales que hemos visto hoy en clase:
Casos de división de decimales
Haz clic en este enlace, observa los ejemplos y realiza divisiones por la unidad seguida de ceros:
División por la unidad seguida de ceros
En el siguiente enlace encontrarás ejemplos de divisiones de decimales y actividades variadas:
Myriam Sánchez
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Tofol
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ME HA GUSTADO MUCHO,GRACIAS POR TU AYUDA.
ESPERO QUE AGAS MÀS PARA LOS DEMÀS
ADIOS
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the result of the problem is:
the number is 4.972
That’s not the result. Try again.