Radiators. Teaching Notes. Contextualised task 17

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1 Contextualised task 17 Radiators Teaching Notes This task focuses on designing a central heating system for a house. Students are presented with a real scenario that requires careful calculations and application of information. Task A: How much space? Outline Students study the plan of a house and calculate the volume of each room. You will need Teachers script PowerPoint Plans How much space? question Markscheme Task 2: How powerful? Outline Students review information and calculate the size of radiator required for each room. You will need Teachers script (continued) PowerPoint (continued) Plans How powerful? question Markscheme Tasks A and B: Teachers script for PowerPoint presentation The text in the right- hand boxes provides a possible script to be read to students. 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 students are given opportunity to explain their reasoning in response to these questions. All students need to understand the concepts in order to make progress with the task. Slide 1 Radiators Keep this slide on the screen until you are ready to start the presentation 1

2 Slide 2 Slide 3 BTU: British Thermal Unit BTU/h: British Thermal Units per hour!""#$ %&'()$*'#+',(*-,'$./01$!"#"$%&'(()&,"$"$%&'(()& *+& *+& -"./01$& 23& 415'(()& 26& 47.0'(()& 97::&;&<.7"'<&;&:7$5"$%& *8& 2=& Some of you will know that energy is usually measured in joules. A British Thermal Unit (BTU) is a unit of energy roughly equivalent to 1055 kilojoules. The BTU is the unit used in heating systems. The output of a radiator is measured in BTUs. The figure describes the number of BTUs produced per hour (BTU/h) When choosing a radiator for a room it is necessary to work out the required BTU/h. Different types of room have different heating needs. This table shows some guide temperatures for various rooms in a house. Slide 4 Slide 5 Slide 6!""#$ %&'()$!"#"$%&'(()& *(+,)-&.&/& 0"$"$%&'(()& *(+,)-&.&/& 1"234-$& *(+,)-&.&5& 6-7'(()& *(+,)-&.&8& 6924'(()& *(+,)-&.&/& :9++&;&<29"'<&;&+9$7"$%& *(+,)-&.&5& * volume in cubic metres!"#$%&"' (")%*$+,-'+-'./012'!"#$%&'(%)*&+',-.+",/' 012' 3)4-56',)%%/' 012' 7")89:-%%&+';)4-56',)%%/' <12' =""8')$"4&' <>2'?"%-+':%""@' 012'!"#$%&"' ()*&"#+"',)'-./01'!"#$#%&'()*$"+,,'$ -./$!01**$#%&'()*$"+,,'$ 23/$ 4#1&056+7(89$*:&*18+,$"+,,$ -3/$ ;1*870$"(8)#"'$ <3/$ 4#$,#6&$(8'%,+&(#8$ -./$ =)(1*7&,>$+?#@*$1##AB$ This table shows how to work out the required BTU/h for different types of room. In this case, volume must be measured in cubic feet. Roughly, how many cubic feet do you think are equivalent to a cubic metre? Why? (There are just over 35 cubic feet in a cubic metre) If a house is well insulated it needs less powerful heating. The BTU/h required for a room is then reduced. The table shows some methods of insulating a house and the percentage reduction in BTU/h in each case. Any reduction is always worked out using the original amount. If a room has double glazed windows and cavity walls, what is the percentage reduction in BTU/h? (20%. Note that there could be some initial confusion about repeated percentage change and the fact that B B 0.8) However, sometimes it is necessary to increase the BTU/h. This table shows the features of a room that require a percentage increase in BTU/h. Again the percentage increase would be worked out using the original amount. If a room has two outside walls and one of them is north- facing, what is the percentage increase needed? (25%) 2

3 Slide 7 N DIAGRAM NOT TO SCALE MEASUREMENTS IN METRES KITCHEN Here is the ground floor plan of a detached house. All the rooms are 2.7 metres high. HALL LIVING ROOM What is the volume of the kitchen in cubic metres? 3.6 DINING ROOM (39.5 m 3 ) There are about 35.3 cubic feet in a cubic metre. What is the volume of the kitchen in cubic feet? (1395 cubic feet) Slide 8 N DIAGRAM NOT TO SCALE 1.5 MEASUREMENTS IN METRES 2.4 BATHROOM 3.1 BEDROOM 3 How would you find the volume of the living room? Here are the rooms on the first floor of the house. All of these rooms are also 2.7 metres high CUPBOARD LANDING 3.6 BEDROOM 1 BEDROOM Task A: How much space? Question Imagine that you are designing the heating system for this house. Work out the volume of each room in cubic feet Living room Dining room Kitchen Hall Landing Bedroom 1 Bedroom 2 Bedroom 3 Bathroom Note that the living room and bedroom 3 are more complex shapes Treat the hall and the landing as cuboids and ignore the stairs Remember Volume of a cuboid = length width height Volume of a prism = area of cross- section length 1 cubic metre is roughly equivalent to 35.3 cubic feet All rooms are 2.7 metres high 3

4 Tasks A and B: Ground Floor Plan DIAGRAM NOT TO SCALE MEASUREMENTS IN METRES DINING ROOM HALL KITCHEN LIVING ROOM N 4

5 Tasks A and B: First Floor Plan N DIAGRAM NOT TO SCALE MEASUREMENTS IN METRES CUPBOARD BATHROOM BEDROOM 3 LANDING 3.6 BEDROOM 1 BEDROOM N 5

6 Task A: Markscheme The information below is intended as a guide only. Full credit Uses a clearly organised approach to list and calculate all volumes in cubic metres, and then converts to cubic feet Hall Kitchen = m 3 = 583 cubic feet (nearest whole number) = m 3 = 1395 cubic feet (nearest whole number) Dining room = m 3 = 1167 cubic feet (nearest whole number) Living room (( ) 2) = m 3 = 1312 cubic feet (nearest whole number) Landing Bathroom Bedroom 1 Bedroom 2 Bedroom ( ) 2.7 = m 3 = 729 cubic feet (nearest whole number) = 9.72 m 3 = 343 cubic feet (nearest whole number) = m 3 = 1235 cubic feet (nearest whole number) = m 3 = 1167 cubic feet (nearest whole number) = m 3 = 735 cubic feet (nearest whole number) Partial credit An otherwise correctly reasoned approach that makes no more than two errors such as: Rounding early within a multi- step calculation Calculation error Leaving the answer in cubic metres Includes the cupboard within the volume of the bathroom or bedroom Using an incorrect length for the landing Limited credit An otherwise correctly reasoned approach that makes more than two errors such as those listed above Finds the volumes of cuboid- shaped rooms correctly but fails to find the correct volume for the living room and/or the third bedroom No credit Any other response 6

7 Task B: How powerful? Question A radiator is going to be placed in each of the nine rooms. Work out the required BTU\h for each room. You will need to use the following information: Room BTU/h Living room Volume 5 Dining room Volume 5 Kitchen Volume 3 Bedroom Volume 4 Bathroom Volume 5 Hall/stairs/landing Volume 3 Feature Reduction in BTU/h Double glazed windows 10% Cavity walls 10% Foam- filled cavity walls 20% Room above 25% Solid floor 10% Feature Increase in BTU/h Two outside walls 15% Three outside walls 40% North- facing external wall 10% French windows 20% No loft insulation 15% (directly above room) Also: The house is detached; There is no double- glazing; There are no French windows; There are no cavity walls; There is loft insulation; The dining room, kitchen and hall have a solid floor. Other rooms do not. 7

8 Task B: Markscheme The information below is intended as a guide only. Full credit Uses a clearly organised approach to list and calculate all BTU/h figures Hall Room above (- 25%), solid floor (- 10%): (- 35%) = awrt* 1137 Kitchen Room above (- 25%), solid floor (- 10%), three external walls (+40%), north- facing wall (+10%): (+15%) = awrt 4813 Dining room Room above (- 25%), solid floor (- 10%), three external walls (+40%): (+5%) = awrt 6127 Living room Room above (- 25%), two external walls (+15%), north- facing wall (+10%): (+0%) = 6560 Landing = 2187 Bathroom Two external walls (+15%) = awrt 1972 Bedroom 1 Three external walls (+40%) = 6916 Bedroom 2 Two external walls (+15%), north- facing wall (+10%): (+25%) = 5835 Bedroom 3 Two external walls (+15%), north- facing wall (+10%): (+25%) = 3675 *awrt answer which rounds to 8

9 Partial credit Finds the BTU/h figure based on repeated percentage change; e.g. for the hall calculates = awrt 1180 OR Finds correct BTU/h for up to seven rooms Limited credit Finds correct BTU/h for between three and six rooms No credit Any other response 9

10 GCSE Content GCSE Mathematics Numeracy and GCSE Mathematics GCSE Mathematics only Understanding number and place value Understanding place value and decimal places; Rounding decimals to the nearest whole number or a given number of decimal places. 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; Knowing how a calculator orders its operations. (Candidates will not be expected to list the key depressions that they have made.) Using calculators effectively and efficiently; Reading a calculator display correct to a specified number of decimal places; Estimating and approximating solutions to numerical calculations. 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. Knowing whether to round up or down as appropriate. Understanding and using measures Simple solid figures: cuboid, prism; Using 2- D representations of 3- D shapes; Conversion between the following metric and Imperial units: m feet; Calculating area of a trapezium, and cross- sectional area of cuboids, prisms and composite solids. Key Foundation tier content is in standard text. Intermediate tier content that is in addition to foundation tier content is in underlined text. Higher tier content that is in addition to intermediate tier content is in bold text. 10

11 Progression in reasoning Identify processes and connections Prioritise and organise the relevant steps needed to complete the task or reach a solution Start with an approach; try it out on some examples; e.g. find the volumes of some rooms that can be approximated as a cuboid Identify some steps towards achieving a solution, not necessarily in sequence; e.g. find all missing dimensions Identify a sequence of steps towards achieving a solution; e.g. find all required lengths and organise them in a way enabling straightforward calculation. Break down composite cross- sectional areas into standard shapes Represent and communicate Use appropriate notation, symbols and units of measurement Explanations are clear both orally and in writing, using some mathematical vocabulary; e.g. correct units are stated in solutions A wider range of appropriate mathematical vocabulary is used in explanations. Arguments are supported with evidence; e.g. correct units are stated throughout a multi- step calculation Orally and in writing: use mathematical vocabulary precisely; e.g. correct units are used throughout a multi- step calculation. Symbols are used precisely; e.g. the roughly equivalent to symbol ( ), the equals symbol (=) applied correctly when rounding. Review Select and apply appropriate checking strategies Students check their entry of calculations on the calculator screen Students compare results for the volume of each room, checking results if they seem to contradict each other Students have a sense of the expected magnitude of the BTU/h for each room. They act immediately if a result contradicts what they expect. 11