Contextualised task 13 Lakes and Reservoirs of Wales Teaching notes Teachers’ script for PowerPoint presentation The text in the right-hand boxes provides a possible script/set of questions with some possible student responses. However, it is probably preferable to use your own words and elaboration. When questions are asked, time for discussion in pairs/groups should be provided. Ensure that learners are given opportunity to explain their reasoning in response to these questions. All learners need to understand the concepts in order to make progress with the task. Slide 1 Organise the class into pairs or small groups – probably no larger than three. Keep this slide on the screen until you are ready to start the presentation, and while you are handing out the cards. The web link is offered to establish some context. • Has anybody visited any of these reservoirs? • Has anyone been sailing, fishing or walking at these reservoirs? • Which is our nearest? Slide 2 Discuss the information on the cards. A question such as ‘You are given the surface area and volume of what?’ should help to establish that it is the surface area and volume of the water in the reservoirs and lakes. • What do you notice about the information you are given? Have a look through the cards, and find out how many different units of • surface area and how many different units of volume are used on the cards. • What do we need to do to make comparisons? • What units should we use? • Are there any useful conversions that you know? Converting to m2 for the surface area and m3 for the volume would help. 1 Slide 3 You may wish to hand out the formula sheet or keep this slide on the screen while the learners are comparing the cards. Slides 4-8 These cards show five different possible activities. It is for the teacher to choose which of these, and how many, are appropriate for the class. Slide 9 This slide acts as a buffer for teachers. • The next two slides show the information in order. • The conversions are not written in standard form, and they are calculated from the rounded figures given on the cards. • As a result, if you checked the information online, it may not agree exactly with the results on the next two slides. 2 Slide 10 Slide 11 The cards provide opportunities for a number of activities, and some examples are given below. The first two activities will apply to Foundation tier, subsequent activities address content from the Intermediate tier. 1) Reservoir trumps – a game for two or three players a. Divide the cards equally between the 2 or 3 players. b. Decide on which category you will compare the cards – either surface area or water volume. c. As you play the cards, you will have to compare the amounts shown. Note that different units of measurement are often used, as well as standard form. d. The winner is the one who has most cards at the end of a run. e. Repeat the game for the other category. 2) Ordering the cards (and finding correlation) a. Order the cards by surface area from largest to smallest. b. Now look at the cards and check whether they remain in order if you compare them by volume. c. How many cards do you have to move? d. Why might a reservoir with a larger surface area have a smaller volume? e. Is there a correlation between the volume and the surface area of the lakes? How would you find out? 3 3) How many times? (Proportional reasoning, multiplying and dividing using standard form) a. How many of the smallest reservoir would divide into the largest … i) by volume, ii) by surface area? b. Make similar comparisons with other pairs of reservoirs. 4) How much bigger? a. Choose any two cards. b. Find the differences between the surface areas and the volumes. c. Express your answers in standard form. d. Repeat for other pairs of cards. 5) Upper and lower bounds a. Llyn Trawsfynydd and Nant y Moch have volumes of 33,190,000 m3 and 32,564,000 m3 respectively. However, when these figures are rounded to two significant figures, what do you notice? b. Is the same degree of accuracy given for the information in all of the cards? Resources required • Card set 1: Information about the Reservoirs of Wales, cut into cards, and laminated. • Calculators (or spreadsheets). • Formula sheet (part of learning resources). The conversions given are: 1 m3 = 219.97 Imperial Gallons 1 Acre = 4,046.86 m2 1 hectare = 10,000 m2 1 km2 = 1,000,000 m2 4 A summary of the data on the cards is as follows: Name Surface Area (acres) Surface Area (m2) Nominal volume (m³) Nominal volume (Gallons) Lake Vyrnwy 4,540,000 13,000,000,000 Ystradfellte 810,000 180,000 Llyn Clywedog 2,490,000 49,900,000 Llyn Trawsfynydd 4,800,000 7,300,000,000 Nant y Moch 525 Llyn Cefni 860,000 400,000,000 Llyn Alaw (Lily Lake) 3,600,000 1,640,000,000 Llanishen Reservoir 238,000 1,440,909 Llyn Celyn 3,300,000 80,900,000 Llyn Brianne 518 64,000,000 Llyn Brenig 3,723,000 61,500,000 Claerwen 664 10,600,000,000 Caban Coch 2,020,000 7,800,000,000 Llandegfedd Reservoir 434 5,400,000,000 Pontsticill Reservoir 1,412,000 16,000,000 Alwen Reservoir 1,490,000 3,200,000,000 Usk Reservoir 1,160,000 2,700,000,000 Talybont Reservoir 318 11,700,000 5 When organised in order of surface area: When organised in order of volume: Surface Area Nominal volume Nominal volume Name Surface Area (m2) Name (acres) (m³) (Gallons) Llyn Trawsfynydd 4,800,000 Llyn Celyn 80,900,000 Lake Vyrnwy 4,540,000 Llyn Brianne 64,000,000 Llyn Brenig 3,723,000 Llyn Brenig 61,500,000 Llyn Alaw (Lily Lake) 3,600,000 Lake Vyrnwy 59,099,194 13,000,000,000 Llyn Clywedog 49,900,000 Llyn Celyn 3,300,000 Claerwen 664 2,687,113 Claerwen 48,188,574 10,600,000,000 Llyn Clywedog 2,490,000 Caban Coch 35,459,517 7,800,000,000 Nant y Moch 525 2,124,600 Llyn Trawsfynydd 33,186,471 7,300,000,000 Nant y Moch 33,000,000 Llyn Brianne 518 2,096,272 Llandegfedd Caban Coch 2,020,000 24,548,896 5,400,000,000 Reservoir Llandegfedd 434 1,756,336 Pontsticill Reservoir 16,000,000 Reservoir Alwen Reservoir 1,490,000 Alwen Reservoir 14,547,494 3,200,000,000 Pontsticill Reservoir 1,412,000 Usk Reservoir 12,274,448 2,700,000,000 Talybont Reservoir 11,700,000 Talybont Reservoir 318 1,286,900 Usk Reservoir 1,160,000 Llyn Alaw (Lily Lake) 7,455,591 1,640,000,000 Llyn Cefni 860,000 Llyn Cefni 1,818,437 400,000,000 Llanishen Reservoir 1,440,909 Ystradfellte 810,000 Llanishen Reservoir 238,000 Ystradfellte 180,000 Note: The calculations are based on the rounded figures given in the card sets. 6 GCSE Content GCSE Mathematics – Numeracy and GCSE Mathematics GCSE Mathematics only Understanding number and place value • Rounding whole numbers to the nearest 10, 100, 1000, etc. • Understanding place value and decimal places. • Rounding decimals to the nearest whole number or a given number of decimal places. • Rounding numbers to a given number of significant figures Understanding number relationships and methods of calculation • Using the facilities of a calculator, including the constant function, memory and brackets, to plan a calculation and evaluate expressions. • Understanding and using number operations and the relationships between them, including inverse operations and the hierarchy of operations. • Estimating and approximating solutions to numerical calculations. • Interpreting numbers written in standard form in the context of a calculator display. • Expressing and using numbers in standard form with positive and negative powers of 10. Solving numerical problems • Interpretation and use of mathematical information presented in written or visual form when solving problems. • Giving solutions in the context of a problem, selecting an appropriate degree of accuracy, interpreting the display on a calculator and recognising limitations on the accuracy of data and measurements. • Rounding an answer to a reasonable degree of accuracy in the light of the context. Interpreting the display on a calculator. • The upper and lower bounds of numbers expressed to a given degree of accuracy. Understanding and using measures • Standard metric units of length, mass and capacity. • Knowledge and use of the relationship between metric units of length, mass, capacity, area and volume. • Making sensible estimates of measurements in everyday situations, recognising the appropriateness of units in different contexts. • Conversion between the following metric and imperial units: litres – gallons. Processing, representing and interpreting data • Constructing and interpreting scatter diagrams for data on paired variables. • Drawing ‘by eye’ a line of ‘best fit’ on a scatter diagram, understanding and interpreting what this represents. Key: Foundation tier content is in standard text. Intermediate tier content that is in addition to foundation tier content is in underlined text. 7 Learner Outcomes and Assessment (to aid comment-only marking) Reasoning strand Assessment Guidance Learners are able to: Can learners: • Prioritise and organise the relevant steps needed to • Compare the data by converting between metric and complete the task or reach a solution; imperial measures? • Choose an appropriate mental or written strategy and • Compare the data by interpreting numbers expressed in know when it is appropriate to use a calculator; standard form? • Use a scientific calculator to carry out calculations • Choose to organise the data into a table, finding effectively and efficiently using the available range of comparisons by using a consistent unit of measures for function keys; each of surface area and volume? • Identify, measure or obtain required information to • Calculate accurately, choosing