NAP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Cairns State High School

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1 NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. airns State High School 1

2 Please note: any activity that is not completed during class time may be set for homework or undertaken at a later date. Q1 QS Skill Development Lesson: Numeracy ctivity Description: In the first activity, students are required to answer questions relating to the calculation of the ody diposity Index. In the second activity, students are asked to answer questions related to staff reimbursement for private car usage in the course of employment. The third activity asks students to answer questions based on a graph that contains average Gross Domestic Product growth rates over time. Purpose of ctivity: The aim of this activity is to improve students ability to comprehend data in different forms and use the information provided to respond to questions. Es: Interpreting the meaning of tables, diagrams, maps or graphs (α6) Translating from one form to another (α7) ompiling lists/ statistics (α12) Graphing (π15) alculating with or without calculators (Ф16) Substituting into formulae (Ф19) Setting out/ presenting/ arranging/ displaying (π20) omparing, contrasting (β29) Reaching a conclusion which is consistent with a given set of assumptions (θ33) Extrapolating (θ35) pplying a progression of steps to achieve the required answer (Ф37) Searching and locating items/ information (α52) Suggested Time llocation: This lesson is designed to take approximately an hour to complete 20 minutes per activity. Teaching Notes: Once students have completed each question, go through the answers as a class. Encourage students to volunteer their answers and discuss the model responses together to maximise understanding of the questions and skills required. 2

3 The ody diposity Index (I) approximates human body fat percentage. Unlike the ody Mass Index (MI), it is not based on body weight and gives an actual estimate of body fat percentage. n adult s I is calculated using the formula: I= Hip circumference (cm) 18 Height 1.5 (m) Healthy body fat percentage varies depending on age and gender. These ranges are summarised in the tables below. Men ge Underweight Healthy Overweight Under 8% 8 19% Over 19% Under 11% 11 22% Over 22% Under 13% 13 25% Over 25% Women ge Underweight Healthy Overweight Under 21% 21-33% Over 33% Under 23% 23 35% Over 35% Under 24% 24 36% Over 36% Item 1 alculate the I for a man whose hip circumference is 0.98m and height is 193cm. Is he underweight, healthy or overweight? Make sure you show all your steps clearly and round your answer to one decimal point. 3

4 n easy way for people to determine whether they are over- or underweight is to represent the healthy body fat percentage range graphically. The following two items require you to construct such a graph for women aged Item 2 The first step in constructing a chart is to complete a table of values. omplete the table below using the I formula to find hip circumference. Round to one decimal place. I I = 21% I = 33% rea Height (m) 1.5 Hip circumference (cm) 71.6 Height (m) 1.5 Hip circumference (cm) Item 3 Now, construct a graph to illustrate the data points above. Use the graph paper provided on the next page. The graph has to be accurate (take special notice of units and scales) and encourage meaningful interpretation by readers (use of labels is required). ou should place height on the horizontal axis and hip circumference on the vertical axis. 4

5 I for Women ged

6 The ody diposity Index (I) approximates human body fat percentage. Unlike the ody Mass Index (MI), it is not based on body weight and gives an actual estimate of body fat percentage. n adult s I is calculated using the formula: I= Hip circumference (cm) 18 Height 1.5 (m) Healthy body fat percentage varies depending on age and gender. These ranges are summarised in the tables below. Men ge Underweight Healthy Overweight Under 8% 8 19% Over 19% Under 11% 11 22% Over 22% Under 13% 13 25% Over 25% Women ge Underweight Healthy Overweight Under 21% 21-33% Over 33% Under 23% 23 35% Over 35% Under 24% 24 36% Over 36% Item 1 alculate the I for a man whose hip circumference is 0.98m and height is 193cm. Is he underweight, healthy or overweight? Make sure you show all your steps clearly and round your answer to one decimal point. Hip circumference = 98cm Height = 1.93m I = (98/ ) 18 I = 18.55% Therefore, he is healthy. 6

7 n easy way for people to determine whether they are over- or underweight is to represent the healthy body fat percentage range graphically. The following two items require you to construct such a graph for women aged Item 2 The first step in constructing a chart is to complete a table of values. omplete the table below using the I formula to find hip circumference. Round to one decimal place. I I = 21% I = 33% rea Height (m) Hip circumference (cm) Height (m) Hip circumference (cm) Item 3 Now, construct a graph to illustrate the data points above. Use the graph paper provided on the next page. The graph has to be accurate (take special notice of units and scales) and encourage meaningful interpretation by readers (use of labels is required). ou should place height on the horizontal axis and hip circumference on the vertical axis. 7

8 I for Women ged

9 Marking Scheme Unit One: Short Response Es Present in Unit: 6 Interpreting the meaning, tables, diagrams, maps or graphs 15 Graphing 16 alculating with or without calculators 19 Substituting into formulae 20 Setting out/ presenting/ arranging/ displaying 37 pplying a progression of steps to achieve the required answer Item 1 Students were required to calculate the I of a man using information supplied to them. The correct response, as well as marking criteria, is provided below. orrect response: Hip circumference = 98cm Height = 1.93m I = (98/ ) 18 I = 18.55% Therefore, he is healthy. The response shows the correct working and answers. The response shows some correct working and the answers are correct. The response shows the correct working and there is one error in the answers. OR The response shows no working and the answers are correct. N Response is unintelligible or does not satisfy the requirements for any other grade. O No response has been made. Item 2 Students were required to calculate the hip circumference using a table of values, whereby the height and I were given. The correct responses, as well as marking criteria, are provided on the following page. 9

10 Marking Scheme Unit One: Short Response orrect Response: I I = 21% I = 33% rea Height (m) Hip circumference (cm) Height (m) Hip circumference (cm) The response shows the correct answers. The response shows four out of five correct answers. One value in each table is correct. OR ll values in one table are correct. D One value is correct. N Response is unintelligible or does not satisfy the requirements for any other grade. O No response has been made. Item 3 Students were required to construct a graph to illustrate the data points found in the table above. Students were instructed that the graph had to be both accurate as well as being able to be easily interpreted by a reader for it to be successful. marking criteria and the correct response are show on the pages overleaf. 10

11 Marking Scheme Unit One: Short Response The graph has height on the horizontal axis, hip circumference on the vertical axis and plots all points correctly. The related points have been joined. The axes, curves, and areas above, below and in between the curves are labelled appropriately. The graph has height on the horizontal axis, hip circumference on the vertical axis and plots almost all points correctly. The related points have been joined. The axes, curves are labelled appropriately. OR The graph has height on the horizontal axis, hip circumference on the vertical axis and plots all points correctly. The axes and curves are labelled appropriately. The graph has height on the horizontal axis, hip circumference on the vertical axis and plots most points correctly. The related points have been joined. OR The graph has height on the horizontal axis, hip circumference on the vertical axis and plots most points correctly. The axes and curves are labelled appropriately. D The graph has height on the horizontal axis, hip circumference on the vertical axis and plots most points correctly. N Response is unintelligible or does not satisfy the requirements for any other grade. O No response has been made. 11

12 Marking Scheme Unit One: Short Response Model response: 12

13 The journalists from the Daily Tribune newspaper are required to use their own cars to complete any travel that is needed to and from the locations of stories. The newspaper then reimburses them for this use. Staff are required to keep track of the kilometres they drive and record these amounts in a log book each week. The logbook for the most recent week is below. Mileage Log: Monday 16/7 Sunday 22/7 Name Date Total kilometres (including return) Origin Destination Return to origin? (/N) ndrew Ross 16/7 32 Northport Sophia Lane 16/7 16 East Malden Sophia Lane 17/7 43 Roderick N ob Smith 17/7 13 rookwood Laura Watt 17/7 27 Mitcham ndrew Ross 18/7 53 Raynes Park N Tanya Marsh 18/7 19 Morden Sophia Lane 18/7 103 Vauxhall Tanya Marsh 18/7 47 Southfields N Laura Watt 19/7 92 ollier s Wood ob Smith 19/7 14 arnham ndrew Ross 20/7 63 Weybridge Sophia Lane 20/7 24 ddlestone Laura Watt 20/7 26 Windsor Tanya Marsh 20/7 33 Richmond N Tanya Marsh 21/7 11 Worcester Park ob Smith 22/7 26 Shepperton 13

14 Item 1 Which destination is the furthest away from the office? The amount that staff are reimbursed for each trip is calculated according to their car s engine size and the distance travelled. This information is contained in the table below. Reimbursement is calculated on a per trip (including return) basis. For example if someone has a 1000 cc car and covers 120 km in one trip, they would receive: (100-40) ( ) 0.07 = $66.20 Engine size (cc) ase reimbursement (per km) dditional amounts ents per km c Within 40 km of office 1601 cc c Over 40 km up to 100km 4c per km 2001cc c Over 100 km 7c per km c Item 2 If Sophia has a 1800 cc car, what can she expect to be paid for her mileage covered in the week 16/7 22/7? 14

15 Item 1 Which destination is the furthest away from the office? Raynes Park is 53 km away. Vauxhall is 103/2 = 51.5 km away because it is a return journey. Raynes Park is therefore the furthest destination from the office. The amount that staff are reimbursed for each trip is calculated according to their car s engine size and the distance travelled. This information is contained in the table below. Reimbursement is calculated on a per trip (including return) basis. For example if someone has a 1000 cc car and covers 120 km in one trip, they would receive: (100-40) ( ) 0.07 = $66.20 Engine size (cc) ase reimbursement (per km) dditional amounts ents per km c Within 40 km of office 1601 cc c Over 40 km up to 100km 4c per km 2001cc c Over 100 km 7c per km c Item 2 If Sophia has a 1800 cc car, what can she expect to be paid for her mileage covered in the week 16/7 22/7? Trip 1 (16 km) = = $8.80 Trip 2 (43 km) = (43-40) 0.04 = $23.77 Trip 3 (103 km) = (100-40) ( ) 0.07 = $59.26 Trip 4 (24 km) = = $13.20 Total = $ $ $ $13.20 = $

16 Marking Scheme Unit Two: Short Response In this unit, students were required to answer several questions relating to staff reimbursement for private car use in the course of employment, based on information provided of travel and destinations over a specific time period. Es Present in Unit: 6 Interpreting the meaning of tables, diagrams, maps or graphs 16 alculating with or without calculators 19 Substituting into formulae 37 pplying a progression of steps to achieve the required answer Item 1 Students were required to name the furthest destination from the office using the information provided in the staff travel log book. The correct response and marking criteria are shown below. The response shows the correct answer and working. The response shows the correct answer and no working. The response shows correct working by identifying that the return journey distances need to be divided by two, but does not provide the correct answer. N Response is unintelligible or does not satisfy the requirements for any other grade. O No response has been made. orrect response: Raynes Park is 53 km away. Vauxhall is 103/2 = 51.5 km away because it is a return journey. Raynes Park is therefore the furthest destination from the office. Item 2 Using the information in the table that included reimbursement rates broken down by car engine size and the distance travelled from the office, students were asked to calculate how much Sophia, the owner of a 1800 cc car, can expect to be paid for her mileage in the week 16/7 22/7. The correct response is shown below. orrect response: Trip 1 (16 km) = = $8.80 Trip 2 (43 km) = (43-40) 0.04 = $23.77 Trip 3 (103 km) = (100-40) ( ) 0.07 = $59.26 Trip 4 (24 km) = = $13.20 Total = $ $ $ $13.20 = $

17 Marking Scheme Unit Two: Short Response Item 3 Students were provided with an equation for measuring engine displacement in cubic centimetres. The equation included bore, stroke and the diameter of the engine s cylinders as the variables in the equation. Students were required to use this information to calculate the stroke of Sophia s car. The correct response and a marking criteria are provided below. The response shows the correct answers and working. The response shows correct answers with limited working. OR The response shows one correct answer with correct working. The response shows incorrect answers but shows correct working. OR The response shows one correct answer with limited working N Response is unintelligible or does not satisfy the requirements for any other grade. O No response has been made. orrect response: 1800 = (π/4) stroke 4 stroke = 1800 / (π 9.052) stroke = 1800 / stroke = 7.00 cm Item 4 Using the same information as in Item 4, students were required to find an answer relating to engine displacement if additional cylinders were added. The correct response is provided below. orrect response: The displacement per cylinder is the same, so it is easy enough to find the displacement per cylinder and multiply by how many cylinders there are. Displacement = Displacement (6/4) Displacement = = 2700 cm 17

18 car s engine displacement measured in cubic centimetres (cc or cm3) is calculated using the following formula: π Displacement cc = bore (cm)2 stroke (cm) number of cylinders 4 The bore of an engine is the diameter of its cylinders. The stroke is the distance the pistons travel up and down in the cylinders. Item 3 We know Sophia s car has a 1800 cc engine (this is the displacement). If you measure the bore as 9.05 cm and there are 4 cylinders, what is the stroke? Round your answer to two decimal places. Item 4 How many cubic centimetres would the engine displace if two additional identical cylinders were added? Round your answer to the nearest cubic centimetre. 18

19 car s engine displacement measured in cubic centimetres (cc or cm3) is calculated using the following formula: π Displacement cc = bore (cm)2 stroke (cm) number of cylinders 4 The bore of an engine is the diameter of its cylinders. The stroke is the distance the pistons travel up and down in the cylinders. Item 3 We know Sophia s car has a 1800 cc engine (this is the displacement). If you measure the bore as 9.05 cm and there are four cylinders, what is the stroke? Round your answer to two decimal places. π Displacement cc = bore (cm)2 stroke (cm) number of cylinders = (π/4) stroke 4 stroke = 1800 / (π 9.052) stroke = 1800 / stroke = 7.00 cm Item 4 How many cubic centimetres would the engine displace if two additional identical cylinders were added? Round your answer to the nearest cubic centimetre. The displacement per cylinder is the same, so it is easy enough to find the displacement per cylinder and multiply by the number of cylinders. Displacementnew = Displacementold (6/4) Displacementnew = = 2700 cm3 19

20 Gross Domestic Profit (GDP) is a measure of a country s income. The column graph below depicts average GDP growth for 11 countries in the periods and verage GDP Growth (%) UK New Sweden Zealand US France ustralia anada Italy Japan razil hina ountry Statistics reveal characteristics about data. asic statistical measures include: Mean = (sum of all values)/(number of values). Mode = The most common value in a dataset. Median = The middle value of a dataset given by the value at the position (n+1)/2 where there are n values in ascending or descending order. If the middle number given by the formula ends with 0.5, the median is the average (mean) of the two middle numbers. Range = The difference between the maximum and minimum values in a dataset. Use this information and the information in the graph to answer the multiple choice questions on the following page. 20

21 Item 1 Which country experienced the largest change in growth rate between the two periods? D ustralia Japan United Kingdom razil Item 2 The mean, mode, median and range of GDP growth rates are: D Mean = 4.1%, Mode = 3.9%, Median = 3.7%, Range = 5.6%. Mean = 3.2%, Mode = 2.2%, Median = 2.5%, Range = 7.9%. Mean = 3.6%, Mode = 2.2%, Median = 2.95%, Range = 7.9%. Mean = 2.9%, Mode = 3.9%, Median = 4.2%, Range = 6.3%. Item 3 The increase in the average GDP hinese growth rate from the period to the period is predicted to continue but by half as much as the previous year. What is the predicted average GDP growth rate for ? D 4.8% 11.5% 10.55% 10.6% Item 4 Which country had the most stable average growth rate between the period from 1966 to 1985 and the period from 1986 to 2005? D US Sweden New Zealand ustralia Item 5 Which of these statements is false? D The United Kingdom had the lowest growth rate from 1966 to If all countries started on a GDP of $ million USD, New Zealand would be the only one that ends on a GDP of $ million USD. Three countries had higher average growth in compared to hina was the fastest growing country in

22 Item 1 Which country experienced the largest change in growth rate between the two periods? D ustralia Japan United Kingdom razil Item 2 The mean, mode, median and range of GDP growth rates are: D Mean = 4.1%, Mode = 3.9%, Median = 3.7%, Range = 5.6%. Mean = 3.2%, Mode = 2.2%, Median = 2.5%, Range = 7.9%. Mean = 3.6%, Mode = 2.2%, Median = 2.95%, Range = 7.9%. Mean = 2.9%, Mode = 3.9%, Median = 4.2%, Range = 6.3%. Item 3 The increase in the average GDP hinese growth rate from the period to the period is predicted to continue but by half as much as the previous year. What is the predicted average GDP growth rate for ? D 4.8% 11.5% 10.55% 10.6% Item 4 Which country had the most stable average growth rate between the period from 1966 to 1985 and the period from 1986 to 2005? D US Sweden New Zealand ustralia Item 5 Which of these statements is false? D The United Kingdom had the lowest growth rate from 1966 to If all countries started on a GDP of $ million USD, New Zealand would be the only one that ends on a GDP of $ million USD. Three countries had higher average growth in compared to hina was the fastest growing country in

23 Marking Scheme Unit Three: Multiple hoice In order to successfully answer the comprehension questions within this unit, students needed to read and interpret a table containing average Gross Domestic Product growth rates data for various countries. Es Present in Unit: 6 Interpreting the meaning of tables or diagrams or maps or graphs 12 ompiling lists/ statistics 16 alculating with or without calculators 19 Substituting into formulae 29 omparing/contrasting 35 Extrapolating 52 Searching and locating items/information Item 1 Students had to identify which country experienced the largest change in growth rate between the two periods. The correct response is shown below. orrect response: D. razil Item 2 Students had to identify the mean, mode, median and range of GDP growth rates. The correct response is shown below. orrect response:. Mean = 4.1%, Mode = 3.9%, Median = 3.7%, Range = 5.6%. Item 3 Students had to identify the predicted average GDP growth rate for The correct response is shown below. orrect response: % Item 4 Students had to identify the country with the most stable average growth rate between and The correct response is shown below. orrect response:. US 23

24 Marking Scheme Unit Three: Multiple hoice Item 5 Students had to identify which one of four statements was false. The correct answer is shown below. orrect response:. If all countries started on a GDP of $ million USD, New Zealand would be the only one that ends on a GDP of $ million USD. 24 Powered by TPDF (