2. Students will be allowed to work together to construct a series of probability statements.
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1 Lesson 1 Exploring the use of probability terms Time: 40 mins The Curriculum and syllabus are set down in the two Books: Junior Cert Mathematics Syllabus, Foundation, Ordinary & Higher Level (from 2016 Onwards), An Roinn Oideachais agus Scileanna Junior Cert available to download here Lesson 1: Probability Scale, Probability language; Junior Cert (and Common Introductory Course) Page 15 AIM: To allow students to use accurate language regarding the PROBABILITY SCALE. OBJECTIVES: 1. Students will be allowed to reflect on the differences between probability terms and their position on the probability scale. 2. Students will be allowed to work together to construct a series of probability statements. 3. Students will be allowed discover what needs to happen, in order that probabilities can change. 4. Students will be encouraged to consider probability, with particular reference to global issues and injustice in particular. RESOURCES: 1. A series of accurate probability statements (handout). 2. A blank probability scale. 3. Students maths copy. METHOD: 1. Divide the class into groups of three or four. 2. Distribute handout with probability statements. 3. Distribute probability blank probability scale handout (5 mins.) 4. Ask students to express each probability in fraction form. (5 mins.) 5. Ask students to place probabilities on the probability scale. (5 mins.) 6. Ask students to agree probability terms. Look for words like IMPOSSIBLE, CERTAIN, UNLIKELY, VERY LIKELY (or their equivalents). (10 mins) 7. Get feedback from the class and write up the words on the board. (5 mins) 8. Ask students to write probability sentences, in their own copy and to explain their reasoning to the rest of their group. (5 mins) 9. Underline new terms. These are for memory work (including spelling) and written work on probability questions. Joe MacGabhann for Irish Jesuit Mission Office Page 1 of 10 Development Education Lesson Plans Series
2 Lesson 1 HANDOUT Probability Statements Fact Statement Fraction Word A B C D E F G The population of Syria is 23 Million. 11 million have been displaced There are 4,700,000 people in Ireland of whom 14,000 are refugees. In Ireland 4 of every 1000 children born, will die in infancy In Somalia 105 of every 1000 children born, will die in infancy The population of Sudan is estimated to be 40 million, of whom 34 million suffer food scarcity. In Uganda, the literacy rate for females is 71% Can you come up with your own fact here? If a person is selected, at random from the whole of Syria, what is the probability they are a displaced person If a person is selected at random, in Ireland, what is the probability that that person is a refugee? What is he probability that a child born in Ireland will survive infancy? What is he probability that a child born in Uganda will survive infancy? What is the probability that a person chosen, at random in Sudan, suffers from food scarcity? What is the probability that a girl chosen, at random in Uganda is literate? Probability Scale 0 1 View the world and national population stats here Joe MacGabhann for Irish Jesuit Mission Office Page 2 of 10 Development Education Lesson Plans Series
3 Lesson 2 Exploring the use of the formula to calculate per capita income Time: 2x 40 mins Cross curriculum: Business studies, Geography, CSPE. The Curriculum and syllabus are set down in the two Books Junior Cert Mathematics Syllabus, Foundation, Ordinary & Higher Level (from 2016 Onwards), An Roinn Oideachais agus Scileanna Junior Cert Here Leaving Cert Cert Mathematics Syllabus, Foundation, Ordinary & Higher Level (from 2015 Onwards), An Roinn Oideachais agus Scileanna Leaving Cert Here Lesson 2: Per Capita, Ratio, Proportion AIM: To allow students to use the formula, order results and critique their work. OBJECTIVES: 1. Students will be allowed to calculate per capita income, given GDP and Population, GDP using the formula: Per capita income = Population 2. Students will be encouraged to calculate either value, given the other two. 3. Students will be asked to order their results and group them. 4. Students will be asked to discuss, why these groups are so. RESOURCES: 1. A map of the world, globe. 2. A table of GDP and population figures (handout or these can be googled). 3. A calculator. (computer access) 4. Students maths copy. METHOD: 1. Divide the class into groups of three or four. 2. Distribute handout (or allow time to research figures). (10 mins) 3. Teach method for calculation of per capita Income (10 mins.) 4. Invite students to calculate per capita incomes for the countries on the sheet. (15 mins) Complete handout for homework. 5. Class II 6. Check homework - Invite students to give some of their biggest and smallest answers. Any unusual or surprising answers? (10 mins.) 7. Invite students to find the countries they have calculated on the map\globe and to group them into high, medium and low per capita incomes. (15 mins.) 8. Where are the low per capita income countries. Show them the Map! 9. Ask student to report on their findings (15 mins). Joe MacGabhann for Irish Jesuit Mission Office Page 3 of 10 Development Education Lesson Plans Series
4 Lesson 2 HANDOUT GDP and Population Table Country Population GDP (millions) Per capita US$ Ireland 4,635, ,800,000,000 53,027 United States 322,358,000 17,420,000,000,000 54,039 United Kingdom 64,800, ,000,000,000 4,552 South Africa 54,956,900 35,100,000, France Japan Australia Uganda 26,090,000, Zambia Chad India 1,280,960,000 1,600 Mongolia Mozambique Austria 437,100,000,000 50,690 Columbia Cambodia Mali Ivory Coast latvia Russia Australia Denmark Central African Republic Chad sweden Germany italy Spain Argentina Brasil Bangladesh 159,472, ,600,000,000 1,170 Pakistan Rwanda Nigeria Ethiopia Vientnam Sudan North Korea Joe MacGabhann for Irish Jesuit Mission Office Page 4 of 10 Development Education Lesson Plans Series
5 Lesson 3 To calculate the volume of a cylinder, using the formula: Vol = πr 2 h Time: 40 mins The Curriculum and syllabus are set down in the two Books: Junior Cert Mathematics Syllabus, Foundation, Ordinary & Higher Level (from 2016 Onwards), An Roinn Oideachais agus Scileanna Junior Cert available to download here Leaving Cert Cert Mathematics Syllabus, Foundation, Ordinary & Higher Level (from 2015 Onwards), An Roinn Oideachais agus Scileanna Leaving Cert available to download here Lesson 3: Grain Storage, Area and Volume; Junior Cert, Page 24. Leaving Cert, Page 33. AIMS 1. To calculate the volume of a cylinder, using the formula 2. Apply this in a real situation and use results 3. To further develop work on ratios and percentages. Vol = πr 2 h RESOURCES 1. Calculator 2. Maths copy. 3. Projector to show pictures given above. 4. Handout, with Vincent s story. METHOD 1. Tell the story of farmer Vincent from Zambia. 2. Ask students to calculate the volume of grain required for one meal per day, two meals per day and three meals per day. 3. Students are then asked to calculate the volume required for a meal (500cm3 or 400g) 4. Students are then shown a sample of 400g. Bare in mind that this must be de-husked and ground to make Uglai. 5. The calorific content of maize is 342 calories per 100g, calculate the calorie intake for Vincent s family. Ask students to calculate their calorie intake for one meal per day, two meals per day and three meals per day. 6. Are they getting enough? Within a healthy, balanced diet, a man needs around 2,500calories (10,500kJ) per day to maintain his weight. For a woman, that figure is around 2,000 calories (8,400kJ) per day. Students are asked to discuss this, and report back on the importance of the harvest. 7. These findings are written on the board. And then What is the justice in this? Joe MacGabhann for Irish Jesuit Mission Office Page 5 of 10 Development Education Lesson Plans Series
6 Lesson 3 HANDOUT Vincents Story Vincent is a small subsistence farmer. That is, he grows his own food and he must subsist on this alone. His staple crop is Maze. He can feed his family of eight children, his wife and himself, until the next harvest 200 days hence. This is their only source of nourishment. His wife will make Ugali, a white doughy carbohydrate. To do this she must de-husk the maize, grind it into a flower, mix it with water that she fetched from the well, 2km from her house and finally boil it on her open fire. At the end of each harvest, Vincent fills up his grain store. He has put three marks on the side of his store. He knows, from experience that if he can fill the store to the first mark, there will be enough food for his family to have one meal per day, until the next harvest. 0.8 This mark is at a height of 500cm. If his harvest reaches 1m, his family can have two meals per day. The 1.5m mark will allow for three meals per day. Anything above that can be sold for cash, which can be used for medical bills etc Joe MacGabhann for Irish Jesuit Mission Office Page 6 of 10 Development Education Lesson Plans Series
7 Lesson 4 Population change formula and population growth formula Time: 2 x 40 mins Cross Curriculum: Geography, Biology. Senior, higher level students. The Curriculum and syllabus are set down in the two Books: Junior Cert Mathematics Syllabus, Foundation, Ordinary & Higher Level (from 2016 Onwards), An Roinn Oideachais agus Scileanna Junior Cert available to download here Leaving Cert Cert Mathematics Syllabus, Foundation, Ordinary & Higher Level (from 2015 Onwards), An Roinn Oideachais agus Scileanna Leaving Cert available to download here Lesson 4: Population, Exponential functions, slope, Junior Cert, Page 20 and 31. Leaving Cert, Page 24 and 43. AIMS To reinforce the use of the slope formula in a practical application and introduced to the formula for population growth. OBJECTIVES 1. Students will be able to identify the slope formula, written in different notation. 2. Students will be able to apply this formula to exponential (geometric data) data. 3. Students will be able to identify population growth as an exponential function. 4. Students will discuss, why this is so and why in the developing world, in particular 5. Students will be introduced to the formula for population growth. Previous knowledge, slope formula, use of e and ln (x) functions. RESOURCES 1. Student copybook. 2. Slides, pictures of population growth to be shown to students. 3. Calculators 4. Computer access. Continued overleaf s Joe MacGabhann for Irish Jesuit Mission Office Page 7 of 10 Development Education Lesson Plans Series
8 Lesson 4 Population change formula and population growth formula RESOURCES Students will work in pairs. 1. Revision of the formula (or assumed knowledge), y 2 - y 1 m = x 2 - x 1 with some numeric examples (10 mins) 2. Introduce students to the formula, Population change =. (applicable over a short period of time). Students will need time to work with the notation here. The link with the slope formula must be clearly made. (10 mins) 3. Present students with the graph for population growth. (computer access, for more examples) (10 mins) 4. Ask students to select points on the graph and calculate the rate of growth. (10 mins) [ 1 P(t 2 ) - P(t 1 ). (100) % P(t 1 ) t 2 - t 1 [ Class II 1. Seek feedback from the students as to why the population is increasing and in the developing word in particular. Look here. There to be written in the board. (15 mins) 2. Students are then introduced to the formula and how to manipulate it. Practice work is to apply it with various values. (homework) Joe MacGabhann for Irish Jesuit Mission Office Page 8 of 10 Development Education Lesson Plans Series
9 Lesson 5 Developing Difference tables, linear graphs and equations Time: 3 x 40 mins First year Ordinary level Junior Cert. The Curriculum and syllabus are set down in the two Books: Junior Cert Mathematics Syllabus, Foundation, Ordinary & Higher Level (from 2016 Onwards), An Roinn Oideachais agus Scileanna Junior Cert available to download here Leaving Cert Mathematics Syllabus, Foundation, Ordinary & Higher Level (from 2015 Onwards), An Roinn Oideachais agus Scileanna Leaving Cert available to download here Lesson 5: Difference Table, patterns, Junior Cert (and Common Introductory Course) Page 27 AIM: To allow students develop Difference tables, form information given and the lead on to Linear graphs and then to Linear equations. OBJECTIVES: 1. Students will be complete a difference table, including difference Students will be able to identify a Linear difference table. 3. Students will be able to draw a linear graph, deriving slope and y-intercept from the Difference table. 4. Students will be able to derive a linear equation, from the difference table and from the graph. 5. Students will consider the importance of communication in a developing world situation. RESOURCES 1. Molly s story (Powerpoint or handout) 2. Copy of blank difference table and blank graph 3. Students maths copy. METHOD 1. Students will work on their own for class Tell Molly s story (5 mins), emphasizing and explaining Microfinance and the importance of communications to people in developing areas. 3. Teach how to construct a difference table, as per Molly s example. Ask students to complete the difference table; handout (15 mins.) 4. Students should then be asked to complete several difference tables (5 mins.) Joe MacGabhann for Irish Jesuit Mission Office Page 9 of 10 Development Education Lesson Plans Series
10 Lesson 5 HANDOUT Developing Difference tables, linear graphs and equations RESOURCES ON MOBILE PHONES IN DEVELOPING COUNTRIES 1. How mobile phones are changing the developing world 2. Cell phones could help millions to read 3. Use of mobile phones in education in developing economies 4. Ted Talk Month Total Amount Saved Diff Molly s Story Molly lives in a small rural village in Uganda. Her village does not have electricity. She decides to set up a small business, providing a mobile phone service to her village. She needs to look for finance to purchase the phone and a solar charger. She will require Ugandan Shillings ( 140). There is a micro-finance, run by Trócaire, in her local town. She must be a regular saver. She will need to save half of the loan amount requested, before she will qualify for a loan. She deposits shillings and will save shillings per month. Joe MacGabhann for Irish Jesuit Mission Office Page 10 of 10 Development Education Lesson Plans Series
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