Module 5: Session plan Group: ____________________________________________________________ Tutor: ____________________________________________________________ Location: ____________________________________________________________ Aims • Develop and/or consolidate numeracy skills around decimals, relevant to participants’ roles in the NHS. • Prepare for typical questions from the Level 1 National Certificate in Adult Numeracy. Outcomes Participants will: • discuss and use decimals in the context of money, metric measures and other examples N2/L1.4 • read, interpret and calculate with decimals N2/L1.5 • round numbers, including decimals, as appropriate N2/L1.7 • relate decimals to participants’ own experience and work role. Activity and time Icebreaker 5 minutes Tutor activity Learner activity • Activity 1: Percentages and • Activity 1 in pairs. fractions dominoes (N2/L1.3). • Use extension dominoes for some participants if appropriate. Introduction • Briefly discuss what participants 15 minutes have done since last session. • Show Module 2 slides 2–3 giving objectives for the session. – what are decimals? (brainstorm): – wholes and parts – decimal point – base 10 (?). • Identification of examples of decimals in work roles. • Contribute and respond. • Contribute and respond. • Offer suggestions. 147 module 5 Activity and time Tutor activity Getting a feel • Slide 4: Discussion of decimals and for place application of strategies used when value comparing amounts of money with 20 minutes other examples. • Activity 2: Ordering decimals. • Activity 2(a): Using number line(s) as a visual approach to this activity. Discussion of and/or practice with identifying some of the sequences of decimals on number lines. Calculating •Activity 3: Calculating with with decimals decimals. 25 minutes • Group discussion of strategies and identification of ‘top tips’. • Summary of key points to remember when calculating with decimals (slides 5 and 6): - line numbers up for +, -, ÷ - for ×, calculate and then decide position of decimal point. Decimals and large numbers 20 minutes Break 15 minutes 148 module 5 • Group discussion of using decimals to describe large numbers: - millions (slides 7 and 8) - thousands (slide 9). • Identify examples from everyday/working life. • Activity 4:Working confidently with large numbers. • Note: these are the same cards as Module 4, Activity 7. Learner activity • Contribute and respond. • Activity 2 in threes. • Activity 2(a): mark decimals from Activity 2 onto lines (for relevant sequences). • Activity 3 in pairs/threes using mini-whiteboards. • Check answers with calculators. • Contribute and respond. • Contribute and respond. • Use numbers from Activity 4 to practise writing large numbers in decimal form. Activity and time Rounding: ‘to the nearest . . .’ 20 minutes Rounding with decimals: ‘to 1 dp’ 25 minutes Tutor activity • Discussion:What is rounding? When do we use it? • Activity 5: Rounding. • Use shaded cards as extension for more confident participants. • Plenary to discuss activity and answers. • Summary about rounding (slide 10) and estimating (slide 11): when do we use them? • Discussion of approach(es) when rounding using slide 12: what are these numbers to the nearest 10 and to 1 dp respectively? • Identify the ‘deciding position’. • Rounding up (5 or more); rounding down (less than 5). Learner activity • Contribute and respond. • Activity 5 in threes. • Contribute and respond. • Discussion of rounding with decimals, including terminology ‘to 1 dp’ etc. • Examples of visual ways to think about rounding: • Place values (slide 13): where would we write 21.45 on the chart? • Number lines (slide 14): what number does the arrow show? • Discuss rounding each of these examples to the nearest 1/10, to the nearest whole number, etc. • Activity 6 in pairs/threes. • Activity 6: Rounding with decimals: metric measures (‘to the nearest. . .’). • Provide measuring equipment if possible (kitchen and bathroom weighing scales and measuring containers) as a practical alternative to the number lines. • Discussion of examples from work • Contribute and respond. when participants need to round to specific degrees of accuracy. 149 module 5 Activity and time Practice 20 minutes Summary 15 minutes Resources/aids: Tutor activity Learner activity • Discuss individual tasks and • Choose which of priority areas for practice. Activities 7 or 8 to complete as practice in • Offer Activities 7 and 8 as practice the session or at home. if required: • Activity 7: Practice with • Practice test questions in rounding (‘to the nearest. . .’). pairs (or offer as practice • Activity 8: Rounding with at home). decimals (‘to 1 dp’). • Individual/pair practice of • Practice test questions. priority areas. • And/or: • practice on areas covered so far identified as needing further practice. • Revisit session objectives (slide 3). • Reflect on session and identify areas for further • Feedback, comments and practice. questions. • Programme journal (slide 15). • Agree independent • Discuss opportunities to apply learning task. skills to work and everyday life. • Discuss individual tasks and opportunities for practice (slide 16). • Module PowerPoint presentation • Activity cards: Activity 1, Activity 3, Activity 4 (Module 4: Activity 7), Activity 5 • Activities: 2, 2(a), 6, 7, 8 • Practice test questions: Decimals • programme journals • flipchart and markers • small whiteboards and pens • calculators • measuring equipment (if required for Activity 6): kitchen scales, bathroom scales, measuring jugs, etc • any supplementary materials. 150 module 5 Assessment evaluation Individual learning planning Learner Skills Activity/ resources Evaluation (where next?) 151 module 5 Module 5 Teacher’s notes Icebreaker Use Activity 1: Percentages and fractions dominoes as an icebreaker. Ask participants in pairs or threes to match the percentages and their equivalent fractions to make a domino chain. Use extension dominoes for more confident participants if appropriate. Introduction • Discuss what participants have done since the last session. • Did they have opportunity to apply the work on handling large numbers at work? What skills practice have they done? Are there any bits (or questions) in particular that are causing difficulty? • Outline the aims and objectives of the module (show slides 1–3). Lead a group discussion: ‘What are decimals?’ (What do we know about them?) Draw out concepts like the decimal point separating ’wholes’ from parts, links to fractions, base 10 (each column is 10 times bigger than the one to its right). Encourage participants to identify contexts in their work roles when they come into contact with or use decimals. Getting a feel for place value Use slide 4 to lead a discussion about which of the numbers is bigger and what strategies participants used when deciding. Use this to extend/reinforce a mathematically sound understanding of the concept of place value (without talking in technical terms). If appropriate, encourage participants to see how they can apply their understanding of money/metric measures to help them in comparing decimal numbers. (eg 14.06 or 14.6: what would 14.6 be in money terms? Which is bigger?) Activity 2: Ordering decimals Ask participants to work in pairs or threes to order the groups of decimals. Activity 2(a): Use the number lines provided on the supplementary sheet to give participants the opportunity to compare the decimals from Activity 2 visually. Relate this back to the work done in Module 2 on metric measures and reading measurements. 152 module 5 Calculating with decimals Ask participants to work in pairs or threes on Activity 3: Calculating with decimals, working out the answers to the questions using mini-whiteboards and checking their answers with calculators. Encourage them to discuss and compare how they tackled the calculations and to identify some ‘top tips’ for calculating with decimals.To help with this, they may wish to sort the cards according to the type of calculation each shows. Make clear that you will discuss these as a whole group afterwards to share ideas and approaches. In the plenary, discuss strategies used and elicit the key points to remember about calculating with decimals. Use slides 5 and 6 to summarise these: lining up decimal points for +, - and ÷ for ×, work out calculation and then decide on position of decimal point. Decimals and large numbers Use slides 7 and 8 to lead a group discussion about using decimals to describe large numbers. How much is 1.3 million when written out in full? Use slide 9 to extend this to thinking about using decimals to describe thousands. How much is 123.5 thousand? (Relate to house prices, which are often written in the form 120k.) Encourage the understanding that the number before the decimal point (to the left) shows the whole millions (or thousands), while the numbers after the point are those bits that are less than a million (or thousand). Encourage participants to identify examples from everyday/working life. Relate this back to the work done in Module 4 on working with large numbers. If appropriate, ask participants in pairs to estimate the number of staff who undertook training for each quarter from the chart on slide 9. If appropriate, ask participants to use Activity 4 to practise writing large numbers in decimal form: eg 37,500 = 1,250,000 = 37.5k or 37.5 thousand 1.25 million Note: these are the same cards as Module 4, Activity 7. Rounding Lead a group discussion: what is rounding? When do we use it? Encourage participants to identify examples from working and everyday life. Ask participants in threes/small groups to do Activity 5: Rounding (cards), working out the scenarios described and, if appropriate, grouping them into sub-groups by type of question. Emphasise that part of the purpose of the activity is to help identify those types of questions involving rounding that participants are each confident with – and also to provide opportunity to share and compare strategies – so to only do the questions they feel they can. 153 module 5 The three final (shaded) cards can be used only with those participants who are more confident, if appropriate. In the plenary, discuss this activity and the answers they got. Were any confusing? If so, why? Use slides 10 and 11 to summarise ideas about when to use rounding (slide 10) and estimating (slide 11). Use slide 12 to lead a discussion of approach(es) when rounding ‘to the nearest 10 (100 etc)’ and ‘to 1 (or 2) decimal places (dp)’. Reinforce the idea that it doesn’t matter how many digits there are: only a couple of numbers will be significant depending on the place value to which you are rounding, and reinforce the importance of identifying the number in the ‘deciding position’ (if you are rounding to the nearest 10, it will be the next number to the right – the units – that will be in ‘deciding position’). Check that participants are happy with the idea of rounding up for 5 or more and rounding down for below 5. Draw the analogy between rounding for whole numbers and rounding decimals. Participants may, or may not, be familiar with the terminology and notation ‘to 1 dp’ so make sure you explain this if necessary. Encourage them to draw on their commonsense maths knowledge to help them with 2 dp (money: £ and pence) and 3 dp (metric measures: m and km). Slides 13 and 14: explore examples of visual ways to think about rounding. Discuss rounding each of these examples to the nearest 1/10, to the nearest whole number, etc: Place values (slide 13): where would we write 21.45 on the chart? How do we know where to place it? Where is the first decimal place (1 dp)? etc. Number lines (slide 14): what number does the arrow show? What would it be to 1 dp? And to the nearest whole number? Activity 6: Rounding with decimals – metric measures (‘to the nearest. . .’) Using Activity 6, ask participants to work in pairs or threes to explore rounding metric measures ‘to the nearest. . .’. If possible, provide measuring equipment (weighing scales and measuring containers) as a practical alternative (or in addition) to the number lines. Otherwise, ask the participants to use the number lines in Activity 6 to mark the given measures and work out the rounded amounts. Encourage participants to identify situations in which they are involved in measuring (and/or recording measurements) to specific degrees of accuracy. What are these? What accuracy do they typically round to? Why do they do this? How important is the degree of accuracy? If appropriate, discuss what degree of accuracy these represent in terms of decimal places. Practice Use this time for participants to either: • practise priority areas for them (individually/in pairs) or • try some of the practice test questions in pairs. Encourage participants to decide which to try now and which to do at home before the next session. (Best to do the ones that they are less confident about in the session so they can get support and suggestions to move them through any problems). Explain that you will, however, review the questions in the next session and discuss any questions that participants were unsure about. 154 module 5 Offer participants Activity 7: Practice with rounding (‘to the nearest. . .’) and Activity 8: Rounding with decimals to do in pairs or at home, deciding which to do now and which to do at home. Encourage participants to identify areas from this or previous sessions that they would like to practice further (use programme journals to help review this). Offer Practice test questions: Decimals. Summary • Revisit the session objectives (slide 3) and reflect on how the session went. • Encourage the group to identify any aspects they are still unsure about/want to practise further and encourage them to use the free resources available to do this (slide 16) between sessions. • Encourage each participant to reflect on what worked well for them as individuals, and to think about which strategies/information helped them most in understanding, remembering or learning more about decimals. • Encourage participants to identify opportunities to relate what they have learnt to their work context/role between sessions eg noting when they come across/use decimals, noticing links between decimals and measurements/measuring equipment around them. • Encourage participants to record relevant information on a Programme journal. Some suggestions for further information and practice (if required) www.bbc.co.uk/skillswise/numbers/fractiondecimalpercentage/comparing/decimalspercentages www.bbc.co.uk/skillswise/numbers/wholenumbers/whatarenumbers/rounding www.keyskills4u.net supporting Level 1 – Carrying out calculations section: Calculations involving money Rounding answers. www.keyskills4u.net at Level 1 – Carrying out calculations section: Rounding answers. www.keyskills4u.com at Level 2 – Carrying out calculations section: Decimals and percentages Fractions, decimals and percentages. 155 module 5 _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ 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_________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ 160 module 5 _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ 161 module 5 Module 5: Activity 1 Percentages and fractions dominoes 1% 1 5 10% 3 4 50% 1 4 100% 1 100 20% 1 10 75% 1 2 25% 1 162 module 5 Extension dominoes 163 module 5 20% 2 5 40% 1 10 75% 4 5 80% 1 2 25% 3 5 60% 1 Module 5: Activity 2 Ordering decimals £16.40 £1.64 £14.60 £1.46 £16.04 £14.06 1.65 km 1.56 km 1.06 km 1.05 km 0.56 km 0.65 km 63.5 kg 56.3 kg 65.3 kg 36.5 kg 35.6 kg 53.6 kg £41.63 £40.36 £403.60 £416.30 2.20 m 1.95 m 2.02 m 2.22 m 1.59 m 0.250 kg 0.2 kg 0.5 kg 0.52 kg 0.3 kg £1,206.25 £1,315.70 £351.40 £351.62 25.4 cm 2.54 cm 29.2 cm 2.9 cm 20.5 cm 2.009 kg 1.950 kg 1.762 kg 2.090 kg 2.900 kg 164 module 5 Module 5: Activity 2(a) Ordering decimals Supplementary sheet 165 module 5 Module 5: Activity 3 Calculating with decimals (a) A patient needs to drink a minimum of 2 litres of fluid each day. If they’ve drunk 1.35 litres already so far, how much more do they need to drink? (b) Four nurses share a flat with rent costing £125 per week. (c) The interest on a loan of £1,500 is £427.61 (d) The VAT on an item of equipment costing £1,500 is £262.50 (e) A care worker earns £1,120.09 He pays £245.75 in tax and N.I. (f) Saline solution comes in 0.5 litre bottles. (g) Patients have an energy drink that is served in 0.3 litre glasses. (h) A hospital care worker’s hourly wage is £6.75 (i) A total of 1.4 litres of IV fluid are used in 7 hours. (j) Three hospital workers share a £6.48 taxi fare between them as equally as they can. What is the total amount owed? How much does he receive in his net pay? How many litres are needed for 6 patients? How much is this per hour? How much does each pay? How much is the total cost? How many litres are there in 5 bottles? How much does she earn for 8 hours? How much do they each pay? 166 module 5 Module 5: Activity 4 Decimals and large numbers 55,000 550,000 125,000 375,000 37,500 3,750 12,500 5,500,000 3,750,000 15,500 2,460,000 25,500 15,000,000 255,000 1,250,000 2,046,000 2,550,000 3,075 246,000 1,025 1,550,000 167 module 5 Module 5: Activity 5 Rounding Without using a calculator, estimate: 3.725 × 8. A nurse buys a new television, costing £254.54 before VAT. She calculates the VAT to be £44.5445. How much will she pay for the television? How much is £99.99 to the nearest £? Without using a calculator, estimate: 5.209 × 4.3. A care assistant buys items costing £4.21, Without using a calculator, estimate: 1.864 £0.91 and £1.21. × 0.9. Estimate the total cost. Joe converts €20 to £ using a calculator. The calculator displays the answer as: 13.7835975. How much money is this? A minor procedure costs £50, to the nearest £1. What is the largest amount of money it could actually cost? An item costs £20 to the nearest £. What is the cheapest it could actually cost? A patient’s weight to the nearest kilogram is 70 kg. What is the heaviest they could actually weigh? 168 module 5 Module 5: Activity 6 Rounding with decimals Metric measures Use the measuring equipment provided or the number lines below to help you work out what these metric measures are to the nearest amount indicated. 1.25 kg to the nearest 100 g 2.75 kg to the nearest 100 g 0.85 kg to the nearest 100 g 0.37 litres to the nearest 100 ml 0.125 litres to the nearest 100 ml 0.575 litres to the nearest 100 ml 63.2 82.5 28.4 40.7 kg kg kg kg to to to to the the the the nearest nearest nearest nearest kg kg 10 kg 10 kg Can you identify any situations when you need to record measurements to a particular degree of accuracy? 169 module 5 Module 5: Activity 7 Practice with rounding Part I: Round the following numbers to the nearest 10 (a) 78 (b) 24 (c) 45 (d) 234 (e) 89 (f) 12 (g) 149 (h) 2,192 (i) 3,199 (j) 6,501 Part II: Round the following numbers to the nearest 100 (a) 89 (b) 120 (c) 350 (d) 124 (e) 309 (f) 2,108 (g) 2,592 (h) 3,588 (i) 6,907 (j) 8,652 170 module 5 Module 5: Activity 8 Rounding decimals (1) Round each of these to the nearest whole number. (a) 14.7 (b) 13.1 (c) 7.4 (d) 3.8 (e) 15.07 (f) 21.55 (g) 0.89 (h) 16.03 (i) 1.128 (j) 249.5 (2) Round each of these to 1 decimal place (1 dp). (a) 32.72 (b) 12.35 (c) 17.203 (d) 1.891 (e) 2.992 (f) 16.224 (g) 0.891 (h) 12.336 (i) 1.0065 (3) Round the numbers from question 2 to 2 decimal places (2 dp). 171 module 5 Module 5: Practice test questions Decimals (1) A sari uses 3.85 metres of material.The material costs £6.98 per metre.Which of these methods of estimating the cost of material is most accurate? (a) 3 × 6 (b) 4 × 7 (c) 4 × 6 (d) 3 × 7 (2) A payslip shows a hospital worker’s weekly pay of £218.99.What is this amount to the nearest £10? (a) £200 (b) £210 (c) £219 (d) £220 (3) A baby weighs 4.781 kg on an electronic scale.What is the weight of the baby correct to 1 kg? (a) 4 kg (b) 4.7 kg (c) 4.8 kg (d) 5 kg (4) A floor tiler works out the cost in pounds of tiling a kitchen floor. His calculator display shows this: 67.8055.What is the cost to the nearest penny? (a) £67.00 (b) £67.80 (c) £67.81 (d) £80.55 (5) A customer’s order at a takeaway shop comes to £10.20. He only has £10. He cancels one bag of prawn crackers, which cost £1.50. How much is the new bill? (a) £8.50 (b) £8.70 (c) £9.30 (d) £9.70 172 module 5 (6) A care worker is paid £6.20 an hour. He works for 39 hours a week.Which of these is the closest estimate of his pay for the week? (a) £6 × 30 (b) £7 × 30 (c) £6 × 40 (d) £7 × 40 (7) A playgroup leader is paid £5.20 per hour. Her payslip shows she earned £119.60 last week.Which calculation gives the number of hours she worked? (a) 5.20 × 119.6 (b) 119.6 ÷ 5.20 (c) 119.60 ÷ 52 (d) 5.20 ÷ 119.6 (8) In one year, 5 471 patients received blood transfusions. How many is this to the nearest 100? (a) 5,000 (b) 5,400 (c) 5,470 (d) 5,500 (9) 29 376 patients went into A&E last year. How many is this to the nearest ten? (a) 29,300 (b) 29,370 (c) 29,380 (d) 29,400 (10) 64 241 people attended a regional hospital last year.What is this number rounded to the nearest thousand? (a) 64,000 (b) 64,200 (c) 64,240 (d) 65,000 (11) The funding for Ward A in a hospital last year was £5.72 million.This amount of money is? (a) £5,720,000 (b) £57,200,000 (c) £572,000,000 (d) £5,720,000,000 (12) A report states that 10.4 thousand people have undergone a clinical procedure with a success rate of 95%. How many people have had the procedure? (a) 1,400 (b) 10,400 (c) 14,000 (d) 900 173 module 5 Module 5: Activities Answers Activity 2: Ordering decimals 1(a) 1(b) 1(c) £1.46 0.56 35.6 £1.64 0.65 36.5 £14.06 1.05 53.6 £14.60 1.06 56.3 £16.04 1.56 63.5 2(a) 2(b) 2(c) £40.36 1.59 0.2 £41.63 1.95 0.250 £403.60 2.02 0.3 £416.30 2.20 0.5 2.22 0.52 3(a) 3(b) 3(c) £351.40 2.54 1.762 £351.62 2.9 1.950 £1 206.25 20.5 2.009 £1 315.70 25.4 2.090 29.2 2.900 £16.40 1.65 65.3 Activity 3: Calculating with decimals (a) 0.65 litres (b) £31.25 each per week (c) £1,927.61 (d) £1,762.50 (e) £874.34 (f) 2.5 l (g) 1.8 l (h) £54 (i) 0.2 litres (j) £2.16 Activity 5: Rounding 4 × 8 = 32 £300 £4 + £1 + £1 = £6 £13.78 £50.49 £100 5 × 4 = 20 2×1=2 £19.50 70.49 kg 174 module 5 Activity 6: Rounding with decimals – metric measures 1.25 kg to the nearest 100 g 2.75 kg to the nearest 100 g 0.85 kg to the nearest 100 g 1 kg 300 g 2 kg 800 g 900 g or or or 1.3 kg 2.8 kg 0.9 kg 0.37 litres to the nearest 100 ml 0.125 litres to the nearest 100 ml 0.575 litres to the nearest 100 ml 400 ml 100 ml 600 ml or or or 0.4 litres 0.1 litres 0.6 litres 63.2 82.5 28.4 40.7 63 83 30 40 kg kg kg kg to to to to the the the the nearest nearest nearest nearest kg kg 10 kg 10 kg kg kg kg kg Activity 7: Rounding Part II (a) 100 (b) 100 (c) 400 (d) 100 (e) 300 (f) 2,100 (g) 2,600 (h) 3,600 (i) 7,000 (j) 8,700 Part I (a) 80 (b) 20 (c) 50 (d) 230 (e) 90 (f) 10 (g) 150 (h) 2,190 (i) 3,200 (j) 6,500 Activity 8: Rounding decimals (1) (a) 15 (b) 13 (c) 7 (d) 4 (e) 15 (f) 22 (g) 1 (h) 16 (i) 1 (j) 250 175 module 5 (2) (a) 32.7 (b) 12.4 (c) 17.2 (d) 1.9 (e) 3.0 (f) 16.2 (g) 0.9 (h) 12.3 (i) 1.0 (3) (a) 32.72 (b) 12.35 (c) 17.20 (d) 1.89 (e) 2.99 (f) 16.22 (g) 0.89 (h) 12.34 (i) 1.01 Practice test questions (1) b (2) d (3) d (4) c (5) b (6) c (7) b (8) d (9) c (10) a (11) a (12) b 176 module 5
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