One of India s most prestigious chefs the legendary Neerav Gorasia has a world famous recipe for traditional Indian Butter Chicken. Neerav is preparing this recipe to publish in his latest Indian Cuisine Guide, and he has to use a certain amount of ingredients. Neerav isn t very good at maths, but he knows how much of each ingredient he needs as a percentage. If he must use 2 kilograms of ingredients in total, help Neerav figure out how many grams Q1! of each ingredient he needs. The first one has been done for you. Neerav s Succulent Butter Chicken 45% Chicken 15% Tomato Puree 10% Garlic 5% Diced Lemons 7% Yogurt 1% Ginger Paste 4% Honey 2% Salt 2% Pepper 6% Cream 3% Mustard Oil Neerav s Succulent Butter Chicken 0.45 2000=900g Chicken Tomato Puree Garlic Diced Lemons Yogurt Ginger Paste Honey Salt Pepper Cream Mustard Oil This exercise continues on the next page...
Q2 Neerav has decided that it would be a good idea to write quantities as fractions as well. Help him out by completing the conversions (the first has been done for you). Make sure you reduce your answers to their simplest forms. Neerav s Succulent Butter Chicken 45% Chicken 15% Tomato Puree 10% Garlic 5% Diced Lemons 7% Yogurt 1% Ginger Paste 4% Honey 2% Salt 2% Pepper 6% Cream 3% Mustard Oil Neerav s Succulent Butter Chicken 45% = 45 100 = 9 20 Chicken Tomato Puree Garlic Diced Lemons Yogurt Ginger Paste Honey Salt Pepper Cream Mustard Oil This exercise continues on the next page...
Traditional culture is very important in all parts of India. Until British colonial rule ceased in India in 1947, many Indians banded together in tribes and groups to maintain their cultural heritage by partaking in traditional Indian activities, such as establishing villages that had specific Indian hierarchies. While most of these groups fell apart after India became independent, some of these feudal societies still unofficially exist. Q1 One of India s most famous feudal systems was known as the Zamindari System, and was notably active in the 18 th Century. The society s hierarchy can be seen in the pyramid below. In Sindh, during the 1750s, there was 1 Zamindar, with the population of every level of the hierarchy increasing tenfold (x10). a) What is the population of the Mirza tribe (Zamindar x 10)? Zamindar Q2 Q3 Read the information below and answer the following questions. Mirza - Prince Nawab High Nobleman Ryots - Peasants b) What is the population of the Nawab tribe? c) What is the population of Ryots? d) What is the total Sindhi population? What fraction of the total Sindhi population was the single Zamindar? What percentage of the total Sindhi population was peasantry?
Q4 Read the information below and answer the following questions. In India, due to malnutrition and disease because of population growth, many Indians are very unhealthy. A portion of the Indian population participated in a well-being survey. The results are presented above in the infographic. Each symbol represents 20,000 Indians; the lightly coloured symbol represents 20,000 Indians who are sick. a) How many Indians were surveyed? b) What fraction of the surveyed population are not in good health according to the results? Present the answer as a non-simplified fraction, then reduce it by dividing by the highest common factor of both numerator and denominator. c) What percentage of the population is healthy?
Mahatma Gandhi (full name Mohandas Karamchand Gandhi) was an Indian political activist. His inspiring efforts using peaceful protests and non-violent resistance helped free India from the clutches of the British Raj. There were many moments throughout his life that are considered to be significant events in India s struggle for independence. Q1 Using the information below, answer the following questions. Year Event Fraction of Lifespan Used a) How many years did Gandhi live for? b) Fill in the two blank columns in the table by determining how much of Gandhi s life had passed when each of the events in the table took place. The first two have been done for you. Present the information as a fraction of Gandhi s total life (simplify when possible) and also as a percentage (rounding to the nearest percent). Use the lines below for working space if you need.!???: Percentage of Lifespan Used 1869 Mohandas Karamchand Gandhi is born. 0 0% 1883 Gandhi gets married. 1885 Ganhi s first child is born. 1888 Gandhi travels to London to study. 1893 Gandhi travels to South Africa. 1894 Gandhi helps find the Natal Indian Congress. 1922 Gandhi is imprisoned for 6 years for treason. 1930 Gandhi leads the Salt March. 1948 Gandhi is assassinated.
Q2 Mohandas Gandhi s father, Karamchand, remarried four times. Tragically, his other wives died during childbirth. Putlibai, his fourth wife, gave birth to Mohandas. Later, Mohandas and his wife, Kasturbai, conceived five children. One of the children died during birth. What percentage of Karamchand s family did not survive the act of childbirth? Q3 Although Karamchand has other family members excluding those given, only include the members mentioned in your final percentage. Gandhi was not a very successful lawyer, but went onto change the lives and minds of a nation. One of his law professors said that in order to be successful in his profession, he needed to win 60% of his cases. How many cases did he need to win if he fought 30? Tip
Firstly, thank you for your support of Mighty Minds and our resources. We endeavour to create highquality resources that are both educational and engaging, and results have shown that this approach works. To assist you in using this resource, we have compiled some brief tips and reminders below. About this resource This Mighty Minds Fundamentals Lesson focusses on one subtopic from the NAPLAN Tests and presents this skill through a theme from the Australian Curriculum (History, Science or Geography). This lesson is also targeted at a certain skill level, to ensure that your students are completing work that is suited to them. How to use this resource Our Fundamentals Lessons are split into two main sections, each of which contain different types of resources. The student workbook contains The main title page; and The blank student worksheets for students to complete. The teacher resources section contains This set of instructions; The Teacher s Guide, which offers information that may be needed to teach the lesson; The Item Description, which gives a brief overview of the lesson and its aims, as well as extension ideas; The student answer sheets, which show model responses on the student worksheets to ensure that answers to the questions are clear; The teacher s answer sheets, which provide a more detailed explanation of the model responses or answers; and Finally, the end of lesson marker. We suggest that you print the student workbook (the first set of pages) for the students. If students are completing this lesson for homework, you may also like to provide them with the student answer pages. Feedback and contacting us We love feedback. Our policy is that if you email us with suggested changes to any lesson, we will complete those changes and send you the revised lesson free of charge. Just send your feedback to resources@mightyminds.com.au and we ll get back to you as soon as we can.
Fractions and Percentages Fractions and Percentages are types of numbers which represent parts of a whole. They are different ways of representing numbers. Fractions are generally used in situations where there are operations to be done on numbers smaller than 1. Fractions Fractions have a numerator (the number on top) and a denominator (the number on the bottom). The numerator represents the number of parts that are present and the denominator tells us how many of 3 those parts make up a whole. For example, with the number 4 the numerator 3 tells us that there are 3 parts present, and the number 4 tells us that 4 parts would make up a whole. This means that three-fourths of something are present. Percentages A percentage is a way of expressing a number as a fraction of 100. The percentage symbol (%) is a more simple way of expressing parts of 100. For instance, 69% is equivalent to 69 or 69 out of 100 parts. 100 To convert a percentage to a decimal, divide the number before the percentage symbol by 100. e.g. 86% = 0.86. 150% = 1.5. If given a percentage, to determine a quantity, convert the percentage to a decimal (divide by 100) and then multiply that decimal by the total quantity. For example, to find 80% of a 5kg weight, the calculation would be 80 5 = 4kg. 100 If students are asked to find how much of something a percentage is, i.e. 30% of 2000, then they should find 10% (divide by 10 = 200) and then multiply by 3, as 3 10% = 30%. Therefore 30% of 2000 would be 600. Converting To convert a fraction to a percentage, you first need to divide the numerator by the denominator, which will result in a decimal. For example, 3 4 = 0.75. Multiplying this decimal by 100 will give you the percentage value: 100 0.75 = 75 = 75%. Therefore the equivalent decimal for the fraction 3 is 0.75. 4 This teaching guide is continued on the next page...
...This teaching guide is continued from the previous page. Improper Fractions Although percentages and fractions are normally used to represent a number up to one whole i.e. 100 1 100, 1 or 100% both fractions and percentages can be used to represent top heavy numbers numbers greater than one. For instance, 2.1 could be written as 21: this is called an 21 10 improper fraction. The equivalent percentage would be 210% ( can also written as 210 or 210%). 10 100 An improper fraction can also be written as a Mixed Number. 210 For example, with the improper fraction 100 (simplified to 21 over 10), the denominator will go into the numerator twice. When the numerator is divided by the denominator, the whole number is written down, and next to it is written the remainder in the original fraction format. This is the Mixed Number format. 21 21 1 i.e. is two lots of 10, 2 x 10= 20 and 1 remainder so = 2. 10 10 10 Simplifying fractions Fractions should be simplified (reduced) if the denominator and numerator both have a common divisor. Divide both the numerator and the denominator by the Highest Common Factor (HCF) to show the fraction in a reduced/simplified form. i.e. 26 = 13 (GCD = 2). 30 15 Instruct students that if the numerator is ever 0, then there is no need to write down a denominator. The answer is simply 0. This is because when you divide zero into parts you still have nothing.
Item Description Please note: any activity that is not completed during class time may be set for homework or undertaken at a later date. Neerav s Butter Chicken, Population Problems and Gandhi Activity Description: This lesson contains three activities that have been designed to allow students to practise simplifying fractions, differentiating between a fraction s numerator and denominator, and convert between percentages, fractions and decimals. In the first activity, Neerav s Butter Chicken, students will need to determine what quantities of ingredients are required in a traditional Indian chicken recipe by converting between percentages and real values. In the second activity, Population Problems, students will need to interpret a feudal pyramid and use a new term (tenfold) to obtain information. They will then have to use this information to calculate fractional and percentage data. The third activity, Gandhi, is themed around Mohandas Gandhi, and students will need to interpret a timeline-based table to calculate Gandhi's age during certain events and then determine how far Gandhi was through his life when the aforementioned events occurred. The subsequent questions extend the students application of converting word problems to percentage and fraction values. Purpose of Activity: To develop students understanding of converting between fractions, decimals, and percentages. Their knowledge of colonial and contemporary India will also be broadened through the theme of the task. KLAs: Mathematics, History CCEs: Interpreting the meaning of pictures/illustrations (α5) Observing systematically (α53) Calculating with or without calculators (Ф16) Applying a progression of steps to achieve the required answer (Ф37) Explaining to others (π26) Suggested Time Allocation: This lesson is designed to take approximately one hour to complete 20 minutes per activity. This Item Description is continued on the next page...
Item Description continued This Item Description is continued from the previous page. Neerav s Butter Chicken, Population Problems and Gandhi Teaching Notes: Before beginning, introduce the students to the concept of converting between fractions and percentages using the Teacher s Guide. Emphasize the importance of decimals as a sort of middle step when converting between the fractions and percentages. The first activity, Neerav s Butter Chicken, allows students to improve their conversion skills. After familiarizing the class with the basics of percentages, allow them to start the first activity. After 15 minutes, check through the answers and emphasize how important it is to ensure that the number before the percentage sign is being divided by 100, and not 10 or 1000 i.e. 95% = 0.95, not 9.5 or 0.095. The second activity, Population Problems, requires students to interpret an infographic and a block of text. Fully explain the concept of something increasing tenfold i.e. multiplying by 10. Allow them to finish the second activity and ensure that they are absorbing all the historical information. The third activity, Gandhi, allows students to consolidate their conversion skills by applying them to real life problems. Students should be able to understand what is meant by the table in the third activity: if not, assist them. After 8 or so minutes of silent work, encourage the students to get together in groups and discuss their results. After several minutes of this, go through the answers. Any questions that are not finished during the lesson can be completed as homework to consolidate what has already been learnt. Ask the students what they know about Mohandas Gandhi. Ensure they know that Mahatma is actually a title: many individuals believe that his first name was Mahatma. Talk to the students about the controlling regime of the British Raj and why Gandhi s resistance was such a significant cornerstone (because of it s nonviolent approach). Follow Up/ Class Discussion Questions: What was Gandhi s most significant action that contributed to the Independence of India? How large is the entire population of India? Why might we use infographics to display data? What is the purpose of a feudal system? How does it aim to reach order in a society?
One of India s most prestigious chefs the legendary Neerav Gorasia has a world famous recipe for traditional Indian Butter Chicken. Neerav is preparing this recipe to publish in his latest Indian Cuisine Guide, and he has to use a certain amount of ingredients. Neerav isn t very good at maths, but he knows how much of each ingredient he needs as a percentage. Q1! If he must use 2 kilograms of ingredients in total, help Neerav figure out how many grams of each ingredient he needs. The first one has been done for you. Neerav s Succulent Butter Chicken 45% Chicken 15% Tomato Puree 10% Garlic 5% Diced Lemons 7% Yogurt 1% Ginger Paste 4% Honey 2% Salt 2% Pepper 6% Cream 3% Mustard Oil Neerav s Succulent Butter Chicken 0.45 2000=900g 300g 200g 100g 140g 20g 80g 40g 40g 120g 60g Chicken Tomato Puree Garlic Diced Lemons Yogurt Ginger Paste Honey Salt Pepper Cream Mustard Oil This exercise continues on the next page...
Q2 Neerav has decided that it would be a good idea to write quantities as fractions as well. Help him out by completing the conversions (the first has been done for you). Make sure you reduce your answers to their simplest forms. Neerav s Succulent Butter Chicken 45% Chicken 15% Tomato Puree 10% Garlic 5% Diced Lemons 7% Yogurt 1% Ginger Paste 4% Honey 2% Salt 2% Pepper 6% Cream 3% Mustard Oil Neerav s Succulent Butter Chicken 45% = 45 100 = 9 20 Chicken 3 20 Tomato Puree 1 10 Garlic 1 20 Diced Lemons 7 100 Yogurt 1 100 Ginger Paste 1 25 Honey 1 50 Salt 1 50 Pepper 3 50 Cream 3 100 Mustard Oil This exercise continues on the next page...
Neerav s Butter Chicken Question One: In this item, students were asked to convert a list of ingredient quantities from percentage form into their exact weight, given the total weight of the ingredients used. Students should have calculated how many grams or kilograms of each ingredient are needed when making the recipe with a total of 2kg of ingredients. Ensure that they don t confuse themselves with decimals below 0.1 i.e. 5% = 0.05, not 0.5. Teach students to calculate these conversions by dividing a percentage by 100 in order to obtain the decimal i.e. 50% 100 = 0.5. State that to convert from grams to kilograms, students must divide by 1000, and to convert from kilograms to grams, they must multiply by 1000. Remind students that as kilograms is the original unit of measurement, they can write their answers either as grams (g) or kilograms (kg). Students should always identify the units with either a g or a kg after the answer. The correct responses are given below. Correct Responses: 1. (45 100) x 2000 = 900g/0.9kg 2. (15 100) x 2000 = 300g/0.3kg 3. (10 100) x 2000 = 200g/0.2kg 4. (5 100) x 2000 = 100g/0.1kg 5. (7 100) x 2000 = 140g/0.14kg 6. (1 100) x 2000 = 20g/0.02g 7. (4 100) x 2000 = 80g/0.08kg 8. (2 100) x 2000 = 40g/0.04kg 9. (2 100) x 2000 = 40g/0.04kg 10. (6 100) x 2000 = 120g/0.12kg 11. (3 100) x 2000 = 60g/0.06kg This answer guide is continued on the next page...
...This answer guide is continued from the previous page. Question Two: For this item, students were asked to convert the quantities of ingredients from percentage form to their simplest fraction form. In order to complete this question correctly, students needed to understand that a percentage is actually the percentage divided by 100 (as a fraction). From this, students needed to be able to simplify the fraction, which involves finding the highest common factor. The solutions are shown below. Correct Responses: 1. 45% = 45 / 100 = 9 / 20 2. 15% = 15 / 100 = 3 / 20 3. 10% = 10 / 100 = 1 / 10 4. 5% = 5 / 100 = 1 / 20 5. 7% = 7 / 100 6. 1% = 1 / 100 7. 4% = 4 / 100 = 1 / 25 8. 2% = 2 / 100 = 1 / 50 9. 2% = 2 / 100 = 1 / 50 10. 6% = 6 / 100 = 3 / 50 11. 3% = 3 / 100
Traditional culture is very important in all parts of India. Until British colonial rule ceased in India in 1947, many Indians banded together in tribes and groups to maintain their cultural heritage by partaking in traditional Indian activities, such as establishing villages that had specific Indian hierarchies. While most of these groups fell apart after India became independent, some of these feudal societies still unofficially exist. Q1 One of India s most famous feudal systems was known as the Zamindari System, and was notably active in the 18 th Century. The society s hierarchy can be seen in the pyramid below. In Sindh, during the 1750s, there was 1 Zamindar, with the population of every level of the hierarchy increasing tenfold (x10). a) What is the population of the Mirza tribe (Zamindar x 10)? Zamindar Q2 Read the information below and answer the following questions. Mirza - Prince Nawab High Nobleman Ryots - Peasants 1 x 10 = 10 b) What is the population of the Nawab tribe? 10 x 10 = 100 c) What is the population of Ryots? 100 x 10 = 1000 d) What is the total Sindhi population? 1000+100+10+1 = 1111 There was 1 Zamindar, with 1111 Sindhi in total, therefore: 1 / 1111 of the population is Zamindar. Q3 What fraction of the total Sindhi population was the single Zamindar? What percentage of the total Sindhi population was peasantry? There were 1000 Ryots, with 1111 Sindhi total, therefore (( 1000 / 1111 ) 100 = 90%) 90% of the population was peasantry.
Q4 Read the information below and answer the following questions. In India, due to malnutrition and disease because of population growth, many Indians are very unhealthy. A portion of the Indian population participated in a well-being survey. The results are presented above in the infographic. Each symbol represents 20,000 Indians; the lightly coloured symbol represents 20,000 Indians who are sick. a) How many Indians were surveyed? There are 40 symbols. Each represents 20,000 Indians therefore (40 20,000 = 800,000) 800, 000 Indians were surveyed. b) What fraction of the surveyed population are not in good health according to the results? Present the answer as a non-simplified fraction, then reduce it by dividing by the highest common factor of both numerator and denominator. 5 symbols are lightly coloured, meaning there are (5 20,000) 100, 000 people in poor health of the surveyed population. Therefore, the fraction of sick people in the surveyed population is 100,000 800,000 = 1 8 = 1 / 8 c) What percentage of the population is healthy? We know that 100,000 of the population are not healthy, so there are 800,000 100,000 = 700,000 healthy people in the surveyed population. As a percentage this is ( 700,000 / 800,000 ) 100 = 87.5%
Population Problems Question One: For this item, students were asked to calculate the number of Indians in each level of the Zamindari hierarchy, given that at each level the population increases tenfold. Students should have calculated the population of each tribe by multiplying the previous population by 10, as each population increases tenfold. Correct Responses: a) Population of Mirza tribe = 1 x 10 = 10 b) Population of Nawab tribe = 10 x 10 = 100 c) Population of Ryots = 100 x 10 = 1000 d) Total population = 1000 + 100 + 10 + 1 = 1111. Question Two: In this item, students were asked to calculate the fraction of the population that the Zamindar represented. Students should have calculated what fraction of the population was Zamindar. A model response is given below. Model Response: Fraction = Zamindar population / Total population F = 1 1111 = 1 / 1111 Question Three: Students were asked to calculate what percentage of the total population was made up by peasantry (ryots). A model response is shown below. Model Response: To find the percentage, divide the ryot population by the total population and multiply this by 100. = (Ryot population / total population) x 100 = (1000/1111) x 100 = 90% This answer guide is continued on the next page...
...This answer guide is continued from the previous page. Question Four: In this item, students were provided with an infographic representing the health of a portion of the population of India. Students were told that each symbol represented 20,000 Indians and that the lightly coloured symbols represented citizens who are in poor health. Using the information given, students should have calculated how many citizens were surveyed, the fraction that were in poor health, and the percentage that were in good health. The correct responses and working is provided below. Correct Responses: a) 40 symbols x 20 000 = 800, 000 people of the Indian population were surveyed. b) There were 100, 000 unhealthy citizens and 800, 000 surveyed citizens in total. Highest common factor between 100 000 and 800 000 = 100 000 Therefore 100 000 800 000 = 1 8. c) If 1 8 of the surveyed population are ill, then 7 of the surveyed population are healthy. 8 7 x 100 = 87.5%. 8
Mahatma Gandhi (full name Mohandas Karamchand Gandhi) was an Indian political activist. His inspiring efforts using peaceful protests and non-violent resistance helped free India from the clutches of the British Raj. There were many moments throughout his life that are considered to be significant events in India s struggle for independence. Q1 Using the information below, answer the following questions. Year Event Fraction of Lifespan Used 1894 Gandhi helps find the Natal Indian Congress. 24 / 79!???: 30% a) How many years did Gandhi live for? Percentage of Lifespan Used 1869 Mohandas Karamchand Gandhi is born. 0 0% 1883 Gandhi gets married. 14 / 79 18% 1885 Ganhi s first child is born. 16 / 79 20% 1888 Gandhi travels to London to study. 19 / 79 24% 1893 Gandhi travels to South Africa. 23 / 79 29% 1922 Gandhi is imprisoned for 6 years for treason. 53 / 79 68% 1930 Gandhi leads the Salt March. 61 / 79 77% 1948 Gandhi is assassinated. 1 100% 1948 1869 = 79 years b) Fill in the two blank columns in the table by determining how much of Gandhi s life had passed when each of the events in the table took place. The first two have been done for you. Present the information as a fraction of Gandhi s total life (simplify when possible) and also as a percentage (rounding to the nearest percent). Use the lines below for working space if you need. Percentages: 0 x 100 = 0% 23/79 x 100 = 29% 24/79 x 100 = 30% 14/79 x 100 = 18% 14/79 x 100 = 18% 19/79 x 100 = 24% 53/79 x 100 = 68% 61/79 x 100 = 77% 1 x 100 = 100%
Q2 Mohandas Gandhi s father, Karamchand, remarried four times. Tragically, his other wives died during childbirth. Putlibai, his fourth wife, gave birth to Mohandas. Later, Mohandas and his wife, Kasturbai, conceived five children. One of the children died during birth. What percentage of Karamchand s family did not survive the act of childbirth? Three of Karamchand s wives did not survive childbirth. One of Mohandas children died during birth. Therefore, 4 of Mohandas family members did not survive the act of childbirth. The remaining family include Mohandas father and mother, wife and four children (7 in total). 4 / 4 + 7 = 4 11 100 36.36% Q3 60% of 30 = 0.6 30 = 18 cases Although Karamchand has other family members excluding those given, only include the members mentioned in your final percentage. Gandhi was not a very successful lawyer, but went onto change the lives and minds of a nation. One of his law professors said that in order to be successful in his profession, he needed to win 60% of his cases. How many cases did he need to win if he fought 30? Tip
Gandhi Question One: Students were required to interpret the data in the table and use their knowledge of fractions and percentages to determine how much of Gandhi s life had passed at certain important milestones as a fraction and a percentage. Correct Responses: a) Gandhi lived for 79 years. 1948-1869 = 79 b) The table can be completed by using the number of years since Ghandi s birth that the event took place as the numerator and using 79 (the age he died) as the denominator. Percentages can be calculated by dividing the numerator by the denominator and then multiplying the decimal by 100. Fraction Answer: 0 / 79 = 0. Percentage Answer: 0 x 100 = 0%. Fraction Answer: 14 / 79. Percentage Answer: 14 / 79 x 100 = 18%. Fraction Answer: 16 / 79. Percentage Answer: 16 / 79 x 100 = 20%. Fraction Answer: 19 / 79. Percentage Answer: 19 / 79 x 100 = 24%. Fraction Answer: 23 / 79. Percentage Answer: 23 / 79 x 100 = 29%. Fraction Answer: 24 / 79. Percentage Answer: 24 / 79 x 100 = 30%. Fraction Answer: 53 / 79. Percentage Answer: 53 / 79 x 100 = 68%. Fraction Answer: 61 / 79. Percentage Answer: 61 / 79 x 100 = 77%. Fraction Answer: 79 / 79 = 1. Percentage Answer: 79 / 79 x 100 = 100%. Question Two: Students were required to calculate what percentage of Karamchand s family did not survive the act of childbirth. They were given a passage of information that allowed them to work out the percentage of his family who did not survive. Students were expected to recognise that the term family included grandchildren and previous and current spouses. Model Response: 4 11 mentioned family members survived the act of childbirth. 4 100 36.36%. 11 Question Three: In this item, students were told the percentage of court cases Gandhi had to win in order to be successful (according to his professor) and were asked how many he had to win out of 30. Correct Response: 60% of 30 = 0.6 30 = 18 = Gandhi had to win18 cases to be successful.