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Assessing Understanding of Place Value and Decimals (with Answers) 1 6351 The 3 stands for 3 hundreds a) 635 The 3 stands for 3 Tens B) 635 200 The 3 stands for 3 Ten thousands Answers 2 0.137 The 3 stands for 3 Hundredths a) 0.3 The 3 stands for 3 Tenths B) 0.340 the 3 stands for 3 Tenths c) 0.613 The 3 stands for 3 Thousandths 3 Write in figures: a) Three hundred and seventy 370 b) Six hundred thousand and eighty two 600 082 4 Write in words as you would say it: a) 7040 b) 130 000 c) 0.39 Seven thousand and forty One hundred and thirty thousand Point three nine (not point thirty nine) Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson. 1 5 Add ten: a) 4796 4806 b) 0.15 10.15 6 Add one hundred: a) 23 627 23 727 b) 19 740 19 840 7 Add one tenth: a) 4.273 4.373 b) 3.9 4 8 Subtract one hundred: a) 783 b) 50 000 683 49 900 Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson. 2 9 a) 30 40 This number is 38 Give the next answers as decimals b) 6 7 This number is 6.8 c) . 3.7 This number is 3.8 3.74 d) 17 e) 18 17.65 This number is his number is about 5 . 6 5.2 This number is f) 9 his number is about . This number is about is 10 9.3 Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson. 3 10 This meter counts the people going into a rugby match. 0 6 3 9 9 After one more person has gone in the meter will read: 0 6 4 0 0 11 The number that is 3 less than 26 000 is 25 997 12 For the answer to a maths problem Sandra got 3.70 and Billy got 3.7 Is there any difference between the answers? No 3.70 means 3 ones plus 7 tenths and 0 hundredths. And 3.7 means 3 ones plus 7 tenths. So they are the same. Why? Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson. 4 13 a) Draw a ring around the bigger of the two numbers: 0.65 or 0. 7 5 hundredths is less than 1 tenth. So 6 tenths plus 5 hundredths is less than 7 tenths. Why is it the bigger? b) For each pair, draw a ring around the bigger number. i 30 100 or 30 095 ii 8.55 or 8.5 iii 3.06 or 3.5 14 Six tenths as a decimal is 0.6 a) How would you write as decimals: i four hundredths 0.04 ii eleven thousandths 0.011 iii eleven tenths 1.1 b) Four tenths is the same as ……………. hundredths a) Write down any number between: 15 b) i 3000 and 4000 ii 3100 and 3200 iii 0.3 and 0.4 iv 0.31 and 0.32 eg eg eg eg 3467 3109 0.378 0.3156 How many different numbers could you write which lie between 0.31 and 0.32? An infinite number. 16 Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson. 5 This is 1 square unit a) The area shaded is 1.3 square units. a) b) The area shaded is 1.43 square units. 1.06 square units. c) b) The area shaded is c) Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson. 6 17 Multiply by ten a) 30 3 b) 4.17 41.7 Multiply by one hundred c) 21 700 217 3.2 320 f) 5.7 0.057 h) 16 d) Divide by one hundred e) 14 1400 Divide by twenty g) 1.2 24 0.8 18 Draw a ring around the one in each pair that gives the bigger answer. a) 8 x 4 or 8 4 b) 8 x 0.4 or 8 0.4 c) 0.8 x 0.4 or 0.8 0.4 Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson. 7 19 a) Add 357 + 984 b) 12.4 + 2.7 1412 – 675 d) 9.34 – 5.28 = 15.1 1341 c) Subtract = 4.06 737 20 a) 30 x 400 = 12 000 b) 5 x 0.2 = 1 c) 0.2 x 0.4 = 0.08 d) 80 ÷ 4 = 20 e) 80 ÷ 0.4 = 200 21 a) b) Draw a ring around the number nearest in size to: i 167 100 67 170 150 200 ii 3.9 4 40 3 30 1 iii 0.17 0.1 10 0.2 20 0 Draw a ring around the number nearest in size to the answer. (Do not work out the answer.) i 2.9 x 7 0.002 0.02 0.2 2 20 200 ii 0.29 x 7 0.002 0.02 0.2 2 20 200 iii 59 ÷ 180 0.003 0.03 0.3 3 30 300 Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson. 8 22 Draw a ring around the calculation you would need to do to find the answer. a) The price of mince is $8.75 for each kilogram. What is the cost of a packet of mince that weighs 0.58 kg? b) c) 8.75 + 0.58 0.58 ÷ 8.75 8.75 ÷ 0.58 0.58 – 8.75 8.75 – 0.58 0.58 x 8.75 The cost of a large bag of rice weighing 12.5 kilograms is $10.95 What should be the price of one kilogram of rice? 12.5 + 10.95 10.95 ÷ 12.5 12.5 ÷ 10.95 10.95 – 12.5 12.5 – 10.95 10.95 x 12.5 My car can go 11.8 kilometres on each litre of petrol on a motorway. How many kilometres can I expect to travel on 25.65 litres? 11.8 + 25.65 25.65 ÷ 11.8 11.8 ÷ 25.65 25.65 – 11.8 11.8 – 25.65 25.65 x 11.8 Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson. 9 Assessing Understanding of Place Value and Decimals Determining Level of Attainment Level 1 Description of Item Numbers Level Place-value in whole 3a, 10, 13bi, 15ai, numbers up to 15aii, 17a thousands 2 Decimals – tenths 3 Decimals – hundredths, thousandths etc 4 5 6 Criterion for Level Attainment 2a, 9b, 13biii, 16a, 21aii 2b, 9c, 11, 13a, 14ai, 15aiii, 15aiv, 16b 7a, 7b, 9d, 9e, 16c, 17b, 17c, 21aiii, 21bi, 22c Decimals – relation with adjacent place on left Decimals- more complex relations between places. Decimals as the result of division; infinite number of decimals 4/6 3/5 5/8 6/10 1b, 14aiii, 14b, 17d, 17f, 20e 4/6 15b, 17g, 17h, 21biii 3/4 Attainment for 12 year olds π Percentage 0 17% 1 17% 2 22% 3 20% 4 9% 5 9% 6 6% Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson. 10