Ratio Picasso Grades: 3 rd 5 th grade Program Duration: 60 Minutes Program Type: Lab Program Description Kids mix up different ratios of paint colors to produce varying shades of rose or blue, and reproduce a work of art using the equivalent ratios they have created. Louisiana GLEs: Science 3 rd Grade 1 Ask questions about objects and events in the environment (e.g., plants, rocks, storms) (SI-E-A1) 4 Predict and anticipate possible outcomes (SI-E-A2) 6. Use the five senses to describe observations (SI-E-A3) Math 3.NF. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Science 4 th Grade Grade 1 Ask questions about objects and events in the environment (e.g., plants, rocks, storms) (SI-E-A1) 4 Predict and anticipate possible outcomes (SI-E-A2) 7. Use the five senses to describe observations (SI-E-A3) Math 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n a)/(n b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.2 6 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Math 5 th Grade 5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Key Terms: Ratio: A comparison of two numbers. We generally separate the two numbers in the ratio with a colon (:). Sci-Port: Louisiana's Science Center Ratio Picasso Page 1 of 14
Connections to Permanent Exhibits: These exhibits are located in the Go Figure cluster of The Space Center, 2 nd floor. Magic Abacus: Did you arrange the blocks so each line equaled 10? Did you discover a new pattern? Circular Logic: What was your first step in solving this problem? 3-D Tic Tac Toe: Grab a friend or two and play this unique Tic Tac Toe game. Did you discover the magic position? Language of Logic Mural: Who was famous for his deductive reasoning? What are some tools of logic? Web Resources: Pablo Picasso-Painting, Quotes and Biography-PabloPicasso.org http://www.pablopicasso.org/index.jsp This website provides images of Picasso s paintings and a narrative about the painting. There is a tab entitled Different Art Periods that provides you with an explanation about what the artist was doing at that time. You cand also find a list a list of Picasso s quote, fun facts and video documentaries about Picasso. Algebra: Operations: Ratio and Proportions-Regents Prep School http://www.regentsprep.org/regents/math/algebra/ao3/lratio.htm This is a one page tutorial on What is a ratio? and it provides examples, problem and solution. Historic Figures: Picasso-BBC http://www.bbc.co.uk/history/historic_figures/picasso_pablo.shtml This is a short summary of Picasso s life. Online Color Mixing Palette for Painters-About.com http://painting.about.com/library/blpaint/blcolormixingpalette1.htm This allows children to click on two colors and see what color they make. Students could then be asked to determine the ration of primary colors in the final color. colors) Sagwa Online Coloring-PBS Kids http://pbskids.org/sagwa/color/paint/index_paint.html Have students play with online coloring and mixing colors while painting online at PBS. Math Tools-The Math Forum @ Drexel http://mathforum.org/mathtools/index.html This is the home page for Math Tools. Here you can search the catalog for all types of lessons on various math concepts by grade level. Pre-Visit Activities Have students visit the following sites and do activities within the sites: Fractions Before coming to Sci-Port introduce your students to fractions using this Fraction website developed by BBC- Skillwise. Show the students the short video on how fractions are used and then play the Fractions of Something Game. With this game you can demonstrate the following concepts using a pizza, a person, a glass of water or a piece of chocolate. You would want to use your computer and either an LCD projector or a Smartboard for this lesson. A fraction is a part of a whole As the denominator increases the quantity decreases Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 2 of 14
As the numerator increases with the same denominator the quantity increases The relationship between the fractional parts of a whole Reducing fractions The component of this lesson can be found at the following link: http://www.bbc.co.uk/skillswise/topic/fractions Another Fraction Lesson-All About Fractions This is a fraction lesson developed by Cynthia Lanius of Rice University. This is a series of computer interactives that can be done with your class. You would want to use your computer and either an LCD projector or a Smartboard for this lesson. On this page there is a Teachers Notes section. The components of the lesson are listed below: Introduction More Practice Part 2-Equivalent Fractions More Practice Part 3-Equivalent Fractions More Practice These interactives may be found at the following website: http://math.rice.edu/~lanius/fractions/index.html Post-Visit Activities All About Ratios This would be a great follow to the Sci-Port Ratio Picasso program. Using the interactivities on this All About Ratios page developed by Cynthia Lanius of Rice University School Mathematics. You would want to use your computer and either an LCD projector or a Smartboard for this lesson. On this page there is a Teachers Notes section. The components of this lesson are listed below: Same Ratio Dolls : Cameras Same Ratio Fish : Atom Different Ratio Spider : Lizard Different Ratio Dots : Stars Two Dolls for Every One Camera Three Atoms for Every Two Fish How Many Spiders Do You Have? Which Way Gives More Pizza? Problem Solving-Famous Texas Chili Quiz These interactives may be found at the following website: http://math.rice.edu/~lanius/proportions/rate.html Ratio and Proportion After coming to Sci-Port, follow-up the discussion of ratios with your students to fractions using this Ratio and Proportion website developed by BBC-Skillwise. Show the students the short video on how ratios are used and then play the Ratio and Proportion. Then using either the quizzes on-line or the following worksheets reinforce the understanding of ratios. Caution: If you use the quizzes on-line some of the questions have a British cultural emphasis, for example instead of $ and snooker instead of pool, etc. The component of this lesson can be found at the following link: http://www.bbc.co.uk/skillswise/topic/ratio-and-proportion Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 3 of 14
Ratio and Proportion Worksheets Level A 1. If there are 6 diesel cars sold to every 3 petrol cars, is it the same proportion as 2 diesel cars to every 1 petrol car? A) No B) Yes 2. Each hour a vet usually sees 4 cats, 1 dog and 5 rabbits. Choose the correct way of writing this as a ratio. A) 4:1:5 B) 1:5:4 C) 5:4:1 3. 7 out of 10 women prefer Brand A moisturiser and the other 3 prefer Brand B. Choose how this should be written as a ratio of Brand A to Brand B. A) 7:3 B) 07:10 C) 03:10 4. The instructions on a bottle of orange juice concentrate says to a mix of one part of squash with three parts of water. Choose the correct way of writing this as a ratio. A) 3:1 B) 1:3 C) 1:4 5. An extra used in a TV show is paid $100 for 2 days of work on the show. How much would the extra earn for 4 days work? A) $250 B) $400 C) $200 Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 4 of 14
6. In a keep fit class there are 9 women and 3 men. Is the ratio of women to men... A) 4:1 B) 1:3 C) 3:1 7. A dog training lead adjusts 2 ways, to 160cm or 80cm. Choose the simplest way of writing this as a ratio. A) 2:1 B) 16:8 C) 160:80 8. Sarah and Winston buy the same brand of T-shirt from different stores. Sarah pays $8 and Winston pays $4. Choose the simplest way of writing this as a ratio. A) 2:4 B) 2:1 C) 8:4 9. There are 9 sheep in a farming show. There are only 3 sheep pens. If the sheep are divided equally between the pens what is the ratio of sheep to each sheep pen? A) 3:3 B) 1:3 C) 3:1 10. An old dolphin in a seaworld aquarium catches three times as many fish as a young dolphin at feeding time. The young dolphin catches 8, how many fish does the old dolphin catch? A) 24 B) 64 C) 16 Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 5 of 14
Level B 1. You have a $10 card for your mobile phone. If you have used $6 of your credit, what is the ratio between what you have spent and what you have left in credit? A) 10:6 B) 3:2 C) 4:6 2. If 10 minutes talk-time costs $2, how much will 7 minutes cost? A) $1.40 B) $1.04 C) $1.34 3. You use a mobile phone to send a text message with 160 characters, and receive a reply of 40 characters. What is the simplest ratio between the number of characters in the two messages? A) 160:40 B) 16:4 C) 4:1 4. A survey shows that on average students spend 9 hours a week playing video games and 3 hours e-mailing. What is the ratio between the two? A) 9:3 B) 3:1 C) 1:3 5. If you play 3 games of pooland it costs you $6, would it cost you $16 for 8 games? A) Yes B) No Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 6 of 14
6. While you're playing pool you achieve a maximum break of 147. Your friend's highest break is 49. What is the ratio between the breaks? A) 147:49 B) 3:1 C) 1:3 7. The pool hall has given you a $40 prize for your 147 break. You decide to share it with your friend in the ratio 3:1. How much will you give your friend? A) $10 B) $11 C) $9 8. Your friend spends 10 hours a week swimming and 5 hours a week weight training. Choose the simplest way of writing this as a ratio of swimming to weight training. A) 10:5 B) 5:1 C) 2:1 9. Sessions in the swimming pool cost $10 for 5, how much will it be for 20 sessions? A) $30 B) $20 C) $40 10. A swimming pool is 20m wide and 50m long. What is the simplest ratio of the pool's width to its length? A) 1:10 B) 20:50 C) 2:5 Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 7 of 14
Level C 1. The coach fare to a theme park costs $21 for 3 people, what would be the cost for 6 people? A) $42 B) $63 C) $140 2. In a theme park the roller coaster is six times more popular than the big swingboat. How would you write this as a ratio? A) 1:6 B) 6:1 C) 6:6 3. The entry price for an adult is $10 and the ratio between the prices for adults and children is 5:4. How much is the cost for a child? A) $10 B) $4 C) $8 4. If 800 children a day ride on the roller coaster, but another 200 are turned away because they're not tall enough. What proportion of the total number of children are turned away? A) Half are turned away B) One quarter are turned away C) One fifth are turned away 5. Burger meals are available in 3 sizes: regular, large and extra-large. They are ordered in a ratio of 2:3:5. Out of 10 ordered how many are extra large? A) 3 B) 5 C) 2 Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 8 of 14
6. Out of the 800 children who go on the roller coaster each day, 20 try to eat a burger during the ride. What is the simplest way of saying this as a ratio? A) 800:20 B) 80:2 C) 40:1 7. Standing in line for toilets is always time-consuming. The average wait for males is 3 minutes, and for females it's 9 minutes. Is the ratio between the waiting times 1:3? A) Yes B) No 8. You stand in line in the open for an hour for a ride. It rains for 45 minutes of the time you are waiting, and the sun shines for 15 minutes. What is the simplest form of the ratio of the number of minutes of rain to sun? A) 4:1 B) 45:15 C) 3:1 9. You find out that of 36 people on the bus home from the theme park the ratio of people who felt ill after the scariest ride to people who felt fine was 1:2. How many people felt ill? A) 12 B) 6 C) 18 10. You asked 36 people whether they would make a return visit to the theme park. 18 said 'yes', 12 said ' no' and 6 said 'not sure'. What is the simplest way of writing this as a ratio? A) 18:12:6 B) 3:2:1 C) 1:2:3 Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 9 of 14
Answers Level A 1. If there are 6 diesel cars sold to every 3 petrol cars, is it the same proportion as 2 diesel cars to every 1 petrol car? The correct answer is: B. Yes Did you divide 3 into both numbers, giving 2:1, or use a different method? 2. Each hour a vet usually sees 4 cats, 1 dog and 5 rabbits. Choose the correct way of writing this as a ratio. The correct answer is: A. 4:1:5 The ratio can't be made simpler - there isn't a number that will divide into 4, into 1 and into 5. 3. 7 out of 10 women prefer Brand A moisturiser and the other 3 prefer Brand B. Choose how this should be written as a ratio of Brand A to Brand B. The correct answer is: A. 7:3 7 women go for Brand A while 3 women go for Brand B. So the ratio is 7:3 4. The instructions on a bottle of orange juice concentrate says to a mix of one part of squash with three parts of water. Choose the correct way of writing this as a ratio. The correct answer is: B. 1:3 1 part squash to 3 parts water, so the ratio is 1:3 5. An extra used in a TV show is paid S100 for 2 days of work. How much would the extra earn for 4 days of work? The correct answer is: C. $200 The extra gets paid $100 for 2 days, so double the amount for 4 days = $200 6. In a keep fit class there are 9 women and 3 men. Is the ratio of women to men... The correct answer is: C. 3:1 The ratio is 9 women : 3 men, dividing both numbers by 3 gives 3 : 1, so the correct answer is 3:1 7. A dog training lead adjusts 2 ways, to 160cm or 80cm. Choose the simplest way of writing this as a ratio. The correct answer is: A. 2:1 Did you do the 'simplifying' on paper or in your head? 8. Sarah and Winston buy the same brand of T-shirt from different stores. Sarah pays $8 and Winston pays $4. Choose the simplest way of writing this as a ratio. The correct answer is: B. 2:1 $8 to $4 - both numbers can be divided by 4, giving 2:1. 9. There are 9 sheep in a farming show. There are only 3 sheep pens. If the sheep are divided equally between the pens what is the ratio of sheep to each sheep pen? The correct answer is: C. 3:1 9 sheep: 3 pens. Both numbers can be divided by 3, giving a ratio of 3:1 10. An old dolphin in a seaworld aquarium catches three times as many fish as a young dolphin at feeding time. The young dolphin catches 8, how many fish does the old dolphin catch? Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 10 of 14
The correct answer is: A. 24 The young dolphin catches 8 fish while the old dolphin catches 3 times as many. So 3 times 8 = 24 Level B 1. You have a $10 card for your mobile phone. If you have used $6 of your credit, what is the ratio between what you have spent and what you have left in credit? The correct answer is: B. 3:2 You can take $6 from $10 to leave $4, so that the ratio is 6:4, which simplifies to 3:2 2. If 10 minutes talk-time costs $2, how much will 7 minutes cost? The correct answer is: A. $1.40 You can divide $2 by 10 to find out the cost of one minute. $2 divided by 10 is 20p. So 7 minutes will be 7 times 20p = $1.40. The correct answer is $1.40 3. You use a mobile phone to send a text message with 160 characters, and receive a reply of 40 characters. What is the simplest ratio between the number of characters in the two messages? The correct answer is: C. 4:1 4:1 is the simplest way of showing the ratio 160:40 4. A survey shows that on average students spend 9 hours a week playing video rooms, and 3 hours e-mailing. What is the ratio between the two? The correct answer is: B. 3:1 The simplest ratio is always the best, and 9 and 3 can both be divided by 3 to make 3:1. The simplest way of showing the ratio is 3:1 5. If you play 3 games of pool and it costs you $6, would it cost you $16 for 8 games? The correct answer is: A. Yes To find out the cost of one game of pool you can divide $6 by 3 which is $2. So for 8 games it would be 8 times $2 which is $16. 6. While you're playing pool you achieve a maximum break of 147. Your friend's highest break is 49. What is the ratio between the breaks? The correct answer is: B. 3:1 The simplest way of showing 147:49 is 3:1. Did you notice that both numbers can be divided by 49? 7. The pool hall has given you a $40 prize for your 147 break. You decide to share it with your friend in the ratio 3:1. How much will you give your friend? The correct answer is: A. $10 First work out how many parts the ratio has by adding the 3 and 1, which makes 4. So to find the amount you will give your friend, you divide the $40 by 4 to find one part. $40 divided by 4 = $10. You will give your friend $10. 8. Your friend spends 10 hours a week swimming and 5 hours a week weight training. Choose the simplest way of writing this as a ratio of swimming to weight training. The correct answer is: C. 2:1 The simplest way of showing the ratio 10:5 is by dividing both numbers by 5 to make 2:1 9. Sessions in the swimming pool cost $10 for 5, how much will it be for 20 sessions? Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 11 of 14
The correct answer is: C. $40 You can divide $10 by 5 to find out the cost of one session. $10 divided by 5 is $2. So for 20 sessions it would be 20 times $2 which is $40. The correct answer is $40 10. A swimming pool is 20m wide and 50m long. What is the simplest ratio of the pool's width to its length? The correct answer is: C. 2:5 You can divide 20 and 50 by 10 to give 2:5, which is the simplest form of the ratio. Level C 1. The coach fare to a theme park costs 21 for 3 people, what would be the cost for 6 people? The correct answer is: A. 42 To find out the cost for 6 people you can either multiply the cost for 3 by 2, or you can find out cost for one person ( 21 divided by 3 is 7) and multiply it by six (6 times 7 = 42). 2. In a theme park the roller coaster is six times more popular than the big swingboat. How would you write this as a ratio? The correct answer is: B. 6:1 3. The entry price for an adult is 10 and the ratio between the prices for adults and children is 5:4. How much is the cost for a child? The correct answer is: C. 8 The ratio is 5:4, and the adult price is 10. 10 is twice 5, so to find the cost for a child you double 4 to make 8 4. 800 children a day ride on the roller coaster, but another 200 are turned away because they're not tall enough. What proportion of the total number of children are turned away? The correct answer is: C. One fifth are turned away The ratio is 800:200, which is the same as 8:2, which is the same as 4:1. That means there are 5 parts to the ratio. Of the five parts one part is turned away. One part of five is the same as one fifth. 5. Burger meals are available in 3 sizes: regular, large and extra-large. They are ordered in a ratio of 2:3:5. Out of 10 ordered how many are extra large? The correct answer is: B. 5 The ratio shows you that out of each 10 meals purchased, 2 are regular, 3 are large and 5 are extra-large. 6. Out of the 800 children who go on the roller coaster each day, 20 try to eat a burger during the ride. What is the simplest way of saying this as a ratio? The correct answer is: C. 40:1 The ratio is 800:20 which is the same as saying 80:2, which is the same as 40:1, which is the simplest way of writing the ratio. 7. Queuing for toilets is always time-consuming. The average wait for males is 3 minutes, and for females it's 9 minutes. Is the ratio between the waiting times 1:3? The correct answer is: A. Yes The ratio can be shown as 3:9, but 3 and 9 can both be divided by 3, so the simplest way of showing the ratio is 1:3 Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 12 of 14
8. You queue in the open for an hour for a ride. It rains for 45 minutes of the time you are waiting, and the sun shines for 15 minutes. What is the simplest form of the ratio of the number of minutes of rain to sun? The correct answer is: C. 3:1 To find the simplest form of the ratio 45:15, you can divide by 5 to make 9:3, and then by 3 to make 3:1 Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 13 of 14
9. You find out that of 36 people on the coach home the ratio of people who felt ill after the scariest ride to people who felt fine was 1:2. How many people felt ill? The correct answer is: A. 12 To work this one out you need to add together the 1 and 2, which makes 3 parts to the ratio. To find the number of people who felt ill you divide the 36 by 3 to make 12. So 12 people felt ill, and twice as many - 24 - felt fine. 10. You asked 36 people whether they would make a return visit to the theme park. 18 said 'yes', 12 said ' no' and 6 said 'not sure'. What is the simplest way of writing this as a ratio? The correct answer is: B. 3:2:1 The simplest way of writing 18:12:6 is to divide each number by 6 to give the ratio 3:2:1 Sci-Port: Louisiana's Science Center TRGRatioPicasso.docx Page 14 of 14