Ratios

= = =RATIOS=

What is ratio?
Ratio is a way of comparing amounts of something. It shows how much bigger one thing is than another. For example: Ratio is the number of **parts** to a mix. The paint mix is 4 parts, with 3 parts blue and 1 part white. The order in which a ratio is stated is important. For example, the ratio of screenwash to water is 1:10. This means for every 1 measure of screenwash there are 10 measures of water. Mixing paint in the ratio 3:1 (3 parts blue paint to 1 part white paint) means 3 + 1 = 4 parts in all.
 * Use 1 measure screen wash to 10 measures water
 * Use 1 shovel of cement to 3 shovels of sand
 * Use 3 parts blue paint to 1 part white

3 parts blue paint to 1 part white paint = is ¾ blue paint to ¼ white paint. If the mix is in the right proportions, we can say that it is in the correct ratio.

http://www.bbc.co.uk/skillswise/numbers/wholenumbers/ratioandproportion/ratio/factsheet.shtml

Here is a simple video introducing ratios.
= = media type="youtube" key="grpqwi1cTyA" height="345" width="420"

But lets look at something more mathematical. =media type="youtube" key="eT1yYqmjHPY" height="345" width="420"=

Simplifying ratios
We can often make the numbers in ratios smaller so that they are easier to compare. You do this by dividing each side of the ratio by the same number, the highest common factor. This is called **simplifying.**
 * Example:**

In a club the ratio of female to male members is 12:18 Both 12 and 18 can be divided by 2. 12 ÷ 2 = 6 18 ÷ 2 = 9

To make the ratio simpler again, we can divide both 6 and 9 by 3 6 ÷ 3 = 2 9 ÷ 3 = 3
 * So a simpler way of saying 12:18 is 6:9.**

These are all **equivalent ratios**, they are in the same proportion. All these ratios mean that for every 2 female members in the club there are 3 males: 12:18 6:9 2:3 2:3 is easier to understand than 12:18!
 * So a simplest way of saying 12:18 is 2:3**.

=media type="youtube" key="H1EW3V-LAts" height="345" width="420"= = = =Ratios.=

Click [|Ratios] for a simple introduction to ratios and practise problems. This site has various ratio problems for you to try.

http://www.bbc.co.uk/skillswise/numbers/wholenumbers/ratioandproportion/ratio/index.shtml or simply click on the following link [|BBC Ratios]
 * Go to the following site and practise doing various ratio questions, games and tests.**

=Games= =All about ratios= [|Simple ratios] Which rows below have the same ratio of **Doll : Camera?** [|This link will also take you other various ratio games and activities. There are 8 in total]
 * ==A== ||~ [[image:http://math.rice.edu/%7Elanius/images/turq.gif width="27" height="27" align="middle"]][[image:http://math.rice.edu/%7Elanius/images/turq.gif align="middle"]] ||~ [[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg align="middle"]][[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg align="middle"]][[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg align="middle"]] ||
 * ==B== ||~ [[image:http://math.rice.edu/%7Elanius/images/turq.gif align="middle"]][[image:http://math.rice.edu/%7Elanius/images/turq.gif align="middle"]][[image:http://math.rice.edu/%7Elanius/images/turq.gif align="middle"]] ||~ [[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg align="middle"]][[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg align="middle"]][|Paper pool] ||
 * ==C== ||~ [[image:http://math.rice.edu/%7Elanius/images/turq.gif align="middle"]] ||~ [[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg align="middle"]][[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg align="middle"]] ||
 * ==D== ||~ [[image:http://math.rice.edu/%7Elanius/images/turq.gif align="middle"]][[image:http://math.rice.edu/%7Elanius/images/turq.gif align="middle"]][[image:http://math.rice.edu/%7Elanius/images/turq.gif align="middle"]][[image:http://math.rice.edu/%7Elanius/images/turq.gif align="middle"]] ||~ [[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg align="middle"]][[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg align="middle"]] ||
 * ==E== ||~ [[image:http://math.rice.edu/%7Elanius/images/turq.gif align="middle"]][[image:http://math.rice.edu/%7Elanius/images/turq.gif align="middle"]] ||~ [[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg align="middle"]][[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg align="middle"]][[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg align="middle"]][[image:http://math.rice.edu/%7Elanius/images/bwcamera.jpg width="28" height="28" align="middle"]] ||

=Paper Pool: Analyzing Numeric and Geometric Patterns= The interactive paper pool game provides an opportunity for students to develop their understanding of ratio, proportion, greatest common denominator and least common multiple. This investigation includes student resources for the Paper Pool project, preparation notes, answers, and a holistic-by-category scoring rubric with guidelines for how it can be used to assess the project. Samples of two students' work and a teacher's comments accompany the suggested rubric.

Individual Lessons
[|Lesson 1 - Paper Pool Game] The paper pool game provides an opportunity for students to develop their understanding of ratio, proportion, greatest common divisor, and least common multiple. [|Lesson 2 - Explore More Tables] The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. [|Lesson 3 - Look for Patterns] The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. [|Lesson 4 - Going the Distance] The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. [|Paper Pool]

=[|Stem and Leaf Plot]= [|Stem and Leaf Plots]

[]

=[|Median]= [|Median]

[] Explore median as the middle value of an ordered data set. Learn how to calculate and interpret mean values. Interactive plotter – enter data series, see the plot. Option to turn into a game – get a random data set in stem-and-leaf form, try to work out the mean, median and mode.

=USING MATHS IN THE REAL WORLD EXAMPLE:=

A "Concrete" Example
Concrete is made by mixing cement, sand, stones and water.

You can multiply all values by the same amount and you will still have the same ratio. 10:20:60 is the same as 1:2:6 So if you used 10 buckets of cement, you should use 20 of sand and 60 of stones. || Example: if you have just put 12 buckets of stones into a wheelbarrow, how much cement and how much sand should you add to make a 1:2:6 mix? Ley us lay it out in a table to make it clearer: You can see that you have 12 buckets of stones but the ratio says 6. That is OK, you simply have twice as many stones as the number in the ratio ... so you need twice as much of **everything** to keep the ratio. Here is the solution: And the ratio 2:4:12 is the same as 1:2:6 (because they show the same //**relative**// sizes) //Why are they the same ratio? In the **1:2:6** ratio there is 3 times more Stones as Sand (6 vs 2), and in the 2:4:12 ratio there is **also** 3 times more Stones as Sand (12 vs 4) ... similarly there is twice as much Sand as Cement in both ratios.// //That is the good thing about ratios. You can make the amounts bigger or smaller and so long as the **relative** sizes are the same then the ratio is the same.// So the answer is: add 2 buckets of Cement and 4 buckets of Sand. //(You will also need water and a lot of stirring....)// http://www.mathsisfun.com/numbers/ratio.html
 * [[image:http://www.mathsisfun.com/numbers/images/concrete-pouring.jpg width="200" height="150"]] || A typical mix of cement, sand and stones is written as a ratio, such as 1:2:6.
 * ~  ||~ Cement ||~ Sand ||~ Stones ||
 * ~ Ratio Needed: || 1 || 2 || 6 ||
 * ~ You Have: ||  ||   || 12 ||
 * ~  ||~ Cement ||~ Sand ||~ Stones ||
 * ~ Ratio Needed: || 1 || 2 || 6 ||
 * ~ You Have: || 2 || 4 || 12 ||

1500 : 2000
 * RATIOS IN ART**
 * If you want to draw a horse at 1/10th the normal size, you need to **multiply all sizes by 1/10th**. ||
 * [[image:http://www.mathsisfun.com/numbers/images/scale-horse.jpg width="371" height="185"]] || Example: this horse in real life is 1500mm high and 2000 mm long, so the ratio of its height to length is
 * [[image:http://www.mathsisfun.com/numbers/images/scale-horse.jpg width="371" height="185"]] || Example: this horse in real life is 1500mm high and 2000 mm long, so the ratio of its height to length is
 * What is that ratio when you draw it?** ||