# Ratio, Proportion & Rate of Change for Kids

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Knowing how to work with proportions, ratios and rate of change is a useful skill to have in everyday situations as well as being important in a number of jobs and career situations especially in scientific, mathematic, engineering, business finance and accountancy arenas.

After you have a good understanding of Ratio, Proportions and Rate of Change you should be able to:

- understand relative quantities and sizes
- use proportions in real life situations such as recipes
- work out percentage increases or decreases to a value
- work out simple financial interest calculations
- understand and solve problems rates of change e.g. speed

Check out our high quality resource links below which are a tremendous list of games, activities, videos and worksheets which will give you the best possible start in understanding ratios, proportions and rate of change in your quest for math stardom!

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### "Ratio and Proportion" video notes ages 7 - 11

In these video notes, you learn about 'Calculating size - scaling up and down' (where a model maker scales creations up and down) , 'football scoring percentages challenge' (how many goals children score out of ten worked out as a percentage) and 'using maths to understand food journeys' (an organic farm in Southern England....Read More

### "Equivalent Fractions" activity ages 7 - 11

This BBC activity is all about Equivalent Fractions which, although not identical to equivalent ratios, they are treated mathematically in virtually identical ways. Help Dick and Dom outwit Mrs. Death and steal the Icing on the Cake of Death by completing a number of tests and activities. Your first task is to give each of the four....Read More

### "Ratio Blaster" game ages 9 - 12

In this game, you need to try and find equal ratios. Your cannon has a changing number on it and you are allowed to blast any ratio that is the same as your cannon number. See if you can maximise your number of hits whilst minimising the misses. You get to blast your way....Read More

### "Ratio Martian" game ages 9 - 12

In this game, the Martian loves eating ratios. Various numbers come at him and you must ignore the items that are not ratios and eat the ones that are. You score a hit for each correct ratio eaten or a miss for not eating a ratio or for eating something that is....Read More

### "Ratio Stadium" game ages 9 - 12

In this game, you propel a bike around the track by matching equivalent ratios. You are shown a ratio and you must select an equivalent one out of the four shown. Be quick, because as soon as you answer (correctly or incorrectly) the next question pops up. This is all about speed and accuracy. If you are fast and inaccurate you will be....Read More

### "Ratio Rumble" activity ages 9 - 14

In this activity, you must follow the recipe and knock out the potions in the correct ratio as shown. Choose your character and play! Try and see if you can maximise your bonuses. There is a health bonus, multiplier bonus, speed bonus and bomb bonus. There are 18 levels to play, see how many you can....Read More

### "Ratio, Proportion and Variable Dunk Tank" activity ages 10 - 11

In this game show activity presented by Harry, there are multiple choice questions and a mini-game to earn points. The more points you earn gives you the chance to send the animals into the dunk tank. You are given examples of ratios (e.g. popcorn required at the movies, pizzas for people etc.). One of the 'targets' shows a video about....Read More

### "Bike Proportions" game ages 10 - 13

In this game you need to solve a proportion equation with 'x' as the variable. Just use cross multiplication and then divide. Try and answer as quickly and as accurately as you can. For each question you get right, you propel the bike forward at speed. Get one wrong and you slow down. Answer slowly and you are not....Read More

### "Proportions" Video Notes ages 10 - 12

In these Video Notes, you travel back in time to buy a cinema ticket but must pay a proportional price based on the average monthly income. You can solve the equation using cross multiplying. Then try the Quiz which....Read More

### "Ratio Pairs 2" activity ages 10 - 12

In this activity, there are 12 cards and you must find six matching pairs of equivalent ratios. See how quickly you can match them. The cards stay face up if you have got the match....Read More

### "Equivalent Ratio Pairs" activity ages 10 - 11

In this activity, there are 12 cards. The aim is to find six matching pairs of equivalent ratios. See how quickly you can match them. The cards disappear to show part of a photograph. Match all 6....Read More

### "Understanding Ratio" activity ages 10 - 11

In this activity you get to analyze a model to learn about ratios. Follow the worksheet and use the computer based activity link. Click on new problem and then enter the ratios of the yellow counters to the whole, the whole to the yellow counters, the yellow to red and finally the red to yellow. Remember....Read More

### "RoboWorks Ratios" Activity ages 10 - 11

In this activity, you need to help Spark build robots by selecting the robot kit with the correct answer to some ratio questions. For example, some different coloured shapes are shown and you are....Read More

### "Mrs. Varughese Roadrunner Speed" Video Notes ages 10 - 11

In these Video Notes, Mrs. Varughese asks a question to determine the average speed of a roadrunner if it can run 54 miles in 4 hours. She....Read More

### "Tangrams and Ratios" Video Notes ages 10 - 11

In these Video Notes activity, you are shown how to make a tangram with scissors and card. The ratios of various areas as you move along....Read More

### "Rates" Quiz ages 10 - 11

There are 5 ratio questions in this Quiz, each with four possible multiple choice answers (A-D). Select the best answer in each case. If you need a hint, click on the 'Hint' link at the bottom of each question. When you have answered all 5 questions, click on 'Check It'. Ignore....Read More

### "Mr. Hardesty Ratio of Dollars" Video Notes ages 10 - 11

In these Video Notes, it is explained that Leya exchanged 50 US Dollars and received 90 Canadian Dollars in return. Mr Hardesty shows you how to fill out a ratio table to determine the number of Canadian....Read More

### "Mr. Hardesty Reading Rates comparison" Video Notes ages 10 - 11

In these Video Notes, Mr. Hardesty explains that Felisa read 60 pages of a book in 3 days then 90 pages in 6 days. He poses the question whether the reading rates in these two cases are constant. He....Read More

### "Roboworks Ratios" Activity ages 10 - 11

In this activity, you must build a robot by choosing equivalent ratios. You are given a ratio in the Robot Maker machine and there are four robot kit parts on the right hand side but only one has an equivalent ratio (or equivalent fraction) which you must select. When you have....Read More

### "Mrs. Varughese Car Gas Calculation" Video Notes ages 10 - 11

In these Video Notes, Mrs. Varughese poses the question how far can a family car travel on 10 gallons of gas if it drives a family 105 miles using 3 gallons of gasoline. She works this out using....Read More

### "Ratio and Proportion" video notes ages 11 - 16

In this activity, there are various informative videos related to ratio and proportion including 'Building a Supercross course', 'Calculations using wood fuel as a renewable energy source', 'Ink colours for printing' , 'Planning and Setting up a Fairground' and 'Using maths to....Read More

### "Ratio and Proportion" Quizzes ages 11 - 13

In this topic, there is an introductory video and three quizzes. Ratios are used in the video in terms of calculating the number of computer support engineers, hair colouring mixtures in a salon and a concrete mix for building foundations. In the Quizzes,....Read More

### "Ratios" activity ages 11 - 16

In this activity, the use of ratios is explained. You are tested with a paint mixing problem (how much yellow to red paint is required to make a certain shade of orange). Then an example with money is explained. You are tested once more with a question relating to map enlargement. In the Revision Notes the following topics are described....Read More

### "Ratios" Revision Notes ages 11 - 16

In these Revision Notes, you are shown how to write a comparison in the form of a ratio. Examples of animal ratios are used to illustrate this (cats to dogs and a question on the ratio of sheep to cows). Also there is a worked example on the sharing of money and a question related to the ratios of left handed to right handed pupils.....Read More

### "Ratios" activity ages 11 - 12

In this activity, you are introduced to ratios of soft drinks (orange juice to ginger ale). An example is given then you can try out the interactive juice ratio machine by adding various amounts of orange juice and ginger ale to make punch to the specified quantities in the test questions. Then there are further test questions with....Read More

### "Exploring Proportions" activity ages 11 - 12

In this activity you get to change (increase or decrease) the sizes of three 2D plane figures (square, circle, triangle). Click one of the three shapes and it is duplicated. You then have to make the proportion of the two shapes hit the changing goal e.g. 100/180 by making the bottom shape larger or smaller. When you think it is....Read More

### "Solve Proportions" video notes ages 11 - 12

In these Video Notes you are given the definition of a proportion in terms of equivalent ratios. Then you are taken through an equation which you are shown how to solve in order to find the variable 'n'. The usual method of cross products and then division solves the equation. The solution is checked at the end by....Read More

### "Ratio and Proportion" activity ages 11 - 14

In this activity, the principle of equivalent ratios is explained by first using diluted orange juice and then money. You are asked three questions about sharing money. Then scaling is demonstrated and tested using a model boat. Following this, map scales of 1 to 30,000, 1 to 35,000 and 1 to 20,000 are given with some test questions.....Read More

### "Scaling Similar Triangles" activity ages 11 - 16

In this great learning activity, there are two triangles . The second triangle has been scaled from the first. On the 'Proportional Sides' tab the scale factor is shown on the left hand side and this can be modified by dragging the red sphere horizontally. You can modify the side lengths AC, AB or BC by dragging the sliders in the top....Read More

### "Thinking Blocks" activity ages 11 - 14

The aim of this activity is to model and solve word problems relating to ratios and proportions. There are various models to learn about ('find the missing quantity', 'find the total or difference', 'use the total or difference to find a quantity', 'work with part/total ratios', 'work with ratios that compare three quantities', 'apply....Read More

### "Ratios" Activities ages 11 - 12

These interactive training activities, based on the average U.S. math curriculum but worthwhile learning worldwide, help teach you about ratios . There are 2 videos - 'Introduction to Ratios' and 'Ratios as fractions'. There is 1 interactive....Read More

### "Ratio Word Problems" Activities ages 11 - 12

These highly informative interactive training activities, based on a a typical American math curriculum (but useful for anyone)help you to understand ratios. There are 5 videos - 'Ratio word problem - boys to girls', 'Ratio word problem - centimeters to kilometers', 'Solving ratio problems with tables example 1', 'Solving ratio problems....Read More

### "Rates" Activities ages 11 - 12

These interactive training activities, which utilise the U.S. math curriculum explain all about rates of change / unit rates . There are 2 videos - 'Solving unit rate problem' and 'Solving unit price problem'. There is 1 interactive....Read More

### "Exploring Rate, Ratio and Proportion" Activity ages 11 - 14

In this interactive, the aim is to scale the original ratio (in orange) as close as possible to the target ratio (shown in blue). You can choose a scale of 1x, 2x, 3x, 4x or 5x. Only one of these is correct. Then choose if the final scaled ratio is equal to or not equal to the target. Keep clicking 'Next' or 'New' for more questions. In....Read More

### "3 term Ratios" Activity ages 11 - 14

In this interactive, you are developing some photos and you need to keep the red, green and blue (RGB) ratios the same in the two adjacent pictures. In Activity1, enter proportionally higher or lower values for the 3 colours and see if you can get all 3 photos to match. You can enable hints at the top left hand side to help if you get....Read More

### "Rates" Activities ages 12 - 13

These interactive training activities, which use the typical U.S. math curriculum describe uses of rates of change / unit rates . There are 3 videos - 'Rate problem using fractions', 'unit cost problem using fractions' and 'Finding average speed or rate'. There is 1 ....Read More

### "Identifying Proportional Relationships" Activities ages 12 - 13

These interactive training activities, which are based on the standard United States math curriculum, explain all about proportional relationships . There are 6 videos - 'Introduction to proportional relationships', 'Proportionality between side length and perimeter', 'Testing whether area is proportional to side length', 'Identifying....Read More

### "Constructing Proportions" Activities ages 12 - 13

These interactive training activities, which use the typical U.S. math curriculum describe uses of constructing proportions . There are 4 videos - 'Writing proportions' , 'Solve a proportion with unknown variable', 'Solve a proportion with unknown variable word problem' and 'Constructing equations from proportions to solve problems'.....Read More

### "Biscuit Factory Ratios" Activity ages 12 - 14

In this activity, you have the chance to learn about factors, multiples and ratios by inspecting some gears at a biscuit factory. At the beginning, choose the faster mode or slower mode then click 'Start'. You are taken through a quick tutorial by the master baker and then when you are ready , click 'Start' to experiment with different....Read More

### "Measures - Scaling Up" Activity ages 12 - 15

In this activity, you investigate scaling up various shapes and look at the changes in areas and see if there is a relationship between the scale factor and the area increase. You are first taken through a tutorial about what constitutes similar shapes. Then you must scale up some squares, rectangles and triangles yourself and fill in....Read More

### "Measures - Scaling Down" Activity ages 12 - 15

In this activity, you investigate scaling down various shapes and look at the decreases in areas to look for a correlation between the scale factor and the area reduction. Follow the notes which explain some of the theory and afterwards you must scale down some squares, rectangles and triangles yourself and fill in the corresponding....Read More

### "Flossville Town Park" Activity ages 12 - 14

In this activity, the aim is to design a town park using lots of mathematical skills including scaling. The map scale is 1 unit=10 metres and some of the tasks (e.g. Place and Size the Pond) need you to do some proportional....Read More

### "Windjammer Environmental Center Area Design" Activity ages 12 - 14

The aim is to design an environmental center using lots of mathematical skills including scaling. The map scale is '1 unit=6 feet' and some of the tasks (e.g. 'Place and Size the Garden in the Windjammer Center') require proportional....Read More

### "Graphing and Analyzing Proportional Relationships" Activities ages 13 - 14

These interactive training activities, which use the typical U.S. math curriculum describe uses of constructing proportions . There are 5 videos - 'Comparing rates', 'Representing and comparing rates', 'Graphing proportional relationships example', 'Graphing proportional relationships example 2', 'Graphing proportional relationships....Read More

### "Free Ride Bicycle Gears" activity ages 14 - 17

In this activity, try experimenting on 'Free Ride' to get used to how the bike works. Choose different gear ratios (by selecting different front and back gears on consecutive pedals) and see how far you travelled each time. Read the instructions tab carefully before you go too far! Once you have done a little experimentation, choose a....Read More

### "Ratios and Unit Rates" Activities ages 15 - 17

In this interactive tutorial activity, you first learn about ratios by comparing cups of water to cups of rice. You have to answer questions about the ratios and proportions for rice servings and rice to water amounts. Click on 'Continue' to carry on further in the tutorial. Then there are similar questions for 'Cheesy Macaroni Feast'....Read More

### "Trig Mini Golf" Activity ages 15 - 16

In this interactive activity ,Activity1, play crazy mini golf by answering trigonometric ratio questions and moving your golf ball towards the flag in the hole! You will need to know about tangents, sines and cosines to get these questions correct. The more correct answers you give, the harder your golf swing! There are 4 holes to....Read More

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