Estimation The ability to estimate is a valuable skill which needs constant practice. The Estimation Units help to develop the skills of estimation over a range of topics. Students come to the understanding that estimation is a guide, not the correct answer. Students estimate length, area, time, groups and answers to algorithms involving the four operations. They use rounding to assist in operations. There are two assessment pages and an activity page. 61 Targeting Maths © Blake Publishing 2012. Middle Primary Estimation Unit 1 Area Length Time Groups Content Descriptions Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. © Australian Curriculum, Assessment and Reporting Authority 2012 Proficiency Strands Understanding: • An estimate is a guide, not the correct answer. Fluency: • Estimate • Estimate • Estimate • Estimate • Estimate area in square centimetres. lengths and heights up to 2 metres. time for regular daily tasks. the number in a group given a model. the number in a group without a model. BLM Content • materials needed for each BLM 1.1 Area – estimate; using cubic centimetres; find actual measurements. • cubic centimetres 1.2 Body parts – using hand spans, arm spans, finger spans, feet to measure length. 1.3 Lengths and heights – estimate the heights and lengths of everyday objects, given a model to compare. 1.4 Time – estimate the time it takes to do everyday tasks and plan a timetable accordingly. 1.5 Groups with a model – study how big the model is to enable estimation of the group. 1.6 More groups – estimating large numbers; groups of. 1.7 Assessment • centicubes 1.8 Activity – use estimation and place value to place house numbers. Problem solving: • Use estimation as a checking method. Reasoning: • Use known lengths as a guide in estimation. • Use known groups as a guide in estimation. Language estimate, calculate, guess, rounding off, time, actual, hand span, arm span, nearest, groups Materials blank paper, rulers, metre rulers, pencils, centicubes or Base 10 materials 62 Targeting Maths © Blake Publishing 2012. Remember Before starting ensure each student: • has a sharp pencil — B or 2B. • develops the habit of checking. • understands that an estimate is different from an exact answer. * Estimation Unit 1 Additional Activities Answers • 1 Actual answers a 28 b 28 2 4 • • • Students find other ways to measure objects, eg using marbles, toothpicks, pencils, etc. Use estimation wherever possible in the classroom. eg “Estimate how many people are buying their lunch today.” Encourage estimating answers to all algorithms before the actual answers are worked. The estimation can be recorded in the margin. Hold an ‘Estimation Afternoon’. Each pupil writes one quesion. eg How many stairs to the upstairs classrooms? How many palings on the front fence? Children work in teams to write estimations for all answers and then work out actual answers. BLM 1.1 c 22 d 38 BLM 1.2 Teacher check BLM 1.3 Approximate answers 1 a 2 m 10 cm b c 1 m 50 cm d 2 a 4 m b c 4 ½ m d 3 a 1 m 75 cm b c 45 cm d 1 1 3 3 2 1 m 20 m 70 m ½m m 20 m 20 cm cm cm cm BLM 1.4 Teacher check BLM 1.5 1 2 3 4 5 6 15 40 50 50 14 30 stars blobs hashes diamonds hearts triangles BLM 1.6 1 b 100 2 b 63 3 b 56 c 20 c 10r3 c 4r8 d 10 d 6r3 d 7 e 4 e 7 e 28 f 2 f 21 f 14 BLM 1.7 1 a 16 b 12 2 a 2 m b 2 m c 1 m 3 b 70 4 a to brush teeth c eat breakfast e dry a cup 5 your hand-span b wash a hat d iron a shirt BLM 1.8 Teacher check 63 Targeting Maths © Blake Publishing 2012. Area Estimation 1.1 Name Date 1 Estimate how many 1 cm cubes it would take to cover the following shapes. Then find the actual number. a b 7 8 2 2 4 3 4 Estimate ___________ Actual ___________Estimate ___________ Actual ___________ c d 4 4 2 4 2 3 3 3 2 1 Estimate ___________ Actual ___________Estimate ___________ Actual ___________ 2 Estimate and then find the actual number of ‘tens’ that it would take to cover the following shape. a Estimate ___________ Actual ___________ 64 Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. Understanding: An estimate is a guide, not the correct answer. Fluency: Estimate area in square centimetres. Targeting Maths © Blake Publishing 2012. Body Parts Estimation 1.2 Name Date 1 Use parts of your body to measure the items listed. Estimate first, and then find the actual answer. Add some items of your own to the list. Object Hand span Estimate Actual Arm span Estimate Actual Finger span Estimate Actual Your foot Estimate Actual a desk b school bag c story book d whiteboard e door width f metre ruler g h Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. Fluency: Estimate lengths and heights up to 2 metres. 65 Targeting Maths © Blake Publishing 2012. Lengths and Heights Name 1 Estimation 1.3 Date Dan is 200 cm tall. Dan How tall is:a Toby? ____________ 2 b Yani? ____________ c Henry? ____________ d Elli? ____________ b the garage? c the tree? ____________ ____________ d the ladder? ____________ b the path? ____________ d the rake? ____________ The flagpole is 6 metres tall. How tall is:a the house? ____________ 3 The snake is 2 m long. About how a the rope? long is: ____________ 66 c the mat? ____________ Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. Understanding: An estimation is a guide, not the correct answer. Fluency: Estimate lengths and heights up to 2 metres. Reasoning: Use known lengths as a guide in estimation. Targeting Maths © Blake Publishing 2012. Time Name 1 2 Estimation 1.4 Date Estimate how long it takes you to do the following things. Compare your answers with those of your classmates. a brush your teeth ______________ beat lunch ______________ c travel to school ______________ dget dressed ______________ e tie your shoelaces ______________ f complete your homework ______________ g pack your bag ______________ hsharpen your pencil ______________ Josie Bigge is at home during the holidays. Estimate minutes or hours for her to: a make her bed __________________ b have breakfast c do the cleaning __________________ d clean the car e do the shopping __________________ f have lunch g watch TV __________________ h answer emails i go jogging __________________ j have dinner k read a chapter __________________ l have a shower the time it takes in __________________ __________________ __________________ __________________ __________________ __________________ Make up Josie’s timetable of chores according to your estimates of the time she takes. _________ wake, shower and dress _________ make her bed _________ breakfast _________ do the cleaning _________ do the shopping _________ return home – have a cup of tea _________ clean the car _________ have lunch _________ watch TV _________ answer email _________ go jogging _________ have dinner _________ read 3 Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. Understanding: An estimation is a guide, not the correct answer. Fluency: Estimate time for regular daily tasks. 67 Targeting Maths © Blake Publishing 2012. Groups with a Model Name 1 5 Date stars. 2 10 10 hashes ##### ##### 4 20 3 Estimate how many are here. ______________ Estimate how many are here. ______________ Estimate how many are here. ______________ 4 triangles 68 ######################### ######################### hearts 6 Estimate how many are here. ______________ diamonds 5 Estimate how many are here. ______________ blobs 3 Estimation 1.5 Estimate how many are here. ______________ Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. Understanding: An estimation is a guide, not the correct answer. Fluency Estimate the number in a group given a model. Reasoning: Use known groups as a guide to estimation. Targeting Maths © Blake Publishing 2012. More Groups Name 1 Date Estimate the number of stars in the box and answer the following questions. * ** * * * * * * * Estimation 1.6 * ** * ** * ** * ** * ** * ** * ** * ** * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * a Estimate __________ b Actual total __________ c How many groups of 5? __________ d How many groups of 10?__________ e How many groups of 25? __________ f How many groups of 50?__________ 2 Estimate the number of circles and answer the following questions. a Estimate __________ b Actual total __________ c How many groups of 6? __________ d How many groups of 10?__________ e How many groups of 9? __________ f How many groups of 3? __________ 3 Estimate the number of squares and answer the following questions. a Estimate __________ b Actual total __________ c How many groups of 12?__________ d How many groups of 8? __________ e How many groups of 2? __________ f How many groups of 4? __________ Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. Fluency: Estimate the number in a group without a model. 69 Targeting Maths © Blake Publishing 2012. Assessment • Estimation Date Name 1 Estimation 1.7 Estimate how many 1 cm cubes it will take to cover these shapes. Check your answer by using the cubes. a b Estimate __________ Actual __________ Estimate __________ Actual __________ 2 The ceiling is 3 metres high. About how high is the: a top of the door? ___________________ b top of the board? ___________________ c top of the bookshelf? ___________________ 3 Estimate how many stars are in the box and then count them to give the actual answer. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * a Estimate ____________ 4 Which would take less time? a to brush your teeth or eat dinner b to walk a kilometre or wash a hat c to eat breakfast or vacuum the house d watch a half-hour show or iron a shirt e clean a pair of shoes or dry a cup 5 If you measured a room with your step, your hand-span and your foot, which one would have the most to count? Why? ____________________________________________________________________________________________ ____________________________________________________________________________________________ 70 Targeting Maths © Blake Publishing 2012. b Actual total ____________ _________________________ _________________________ _________________________ _________________________ _________________________ Activity • Estimation Name Estimation 1.8 Date Complete the following a Estimate the area of the grid below ______________________ b Trace your hand on the cm grid paper below and shade it in. Estimate its area. ______________________ c Calculate the area of your hand using the cm squares ______________________ d Estimate the area of the grid paper not shaded in. ______________________ 2 With a partner calculate how long it takes to: a jump 10 times. _______ b write your name. _______ c count to twenty by 2s. _______ 1 3 Now estimate how many times you can do these things in a minute. a jump 10 times. b write your name. Estimate ________ actual ________ Estimate ________ actual ________ c count to twenty by 2s. Estimate ________ actual ________ 71 Targeting Maths © Blake Publishing 2012. Middle Primary Estimation Unit 2 Rounding Addition Subtraction Multiplication Mixed operations Content Descriptions Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. © Australian Curriculum, Assessment and Reporting Authority 2012 Proficiency Strands Understanding: • Rounding can be used as an estimation strategy. • An estimate is a guide, not the correct answer. Fluency: • Round numbers to the nearest 10, 100 and 1 000. • Round numbers to the nearest 10 000. • Estimate answers to addition, subtraction and multiplication problems. Problem solving: • Pose questions and solve problems. Reasoning: • Use known facts to consider if estimates are reasonable. BLM Content • materials needed for each BLM 2.1 Rounding – round numbers to the nearest 10, 100 and 1 000, and consider if the estimate of addition algorithms is reasonable. 2.2 Rounding to ten thousand – round numbers to the nearest ten thousand. • coloured pencils 2.3 Estimating addition – use rounding to estimate the total of 3 digit numbers. 2.4 Estimating subtraction – use rounding to estimate the difference between two 3-digit numbers. 2.5 Estimating multiplication – use rounding to estimate the cost of different items for a party. 2.6 Operations – estimate answers to different algorithms using the 4 different operations; use a calculator to find the actual answer and then discuss if the estimate provided is reasonable. • calculators 2.7 Assessment Language estimate, round, total, difference, multiply, tens, hundred, thousands, ten thousands Materials coloured pencils, calculators 72 Targeting Maths © Blake Publishing 2012. Remember Before starting ensure that each student: • has a sharp B or 2B pencil. • develops the habit of checking. • reads questions twice to avoid simple mistakes. * Estimation Unit 2 Additional Activities • • • Use shopping catalogues, have children go on a shopping spree. Students can select items and then estimate the cost of their total shopping bag. Students estimate the number of children in the school. Ask children to make a general estimation and then gather the numbers of children in each class. Round the numbers to the nearest ten and total the results. They can then compare this result with the exact number of children enrolled in the school, and consider if their estimates were reasonable. Children investigate the result of adding or subtracting two odd numbers and two even numbers. Test this out on a variety of numbers to determine if the result is consistently odd or even. Encourage children to consider this information when estimating answers. Will the actual result be odd or even? Do the same for adding and subtracting a mixture of even and odd numbers. Answers 20 60 40 200 800 900 3 000 5 000 2 000 no yes b 40 f 20 c 80 g 40 d 20 h 60 b 300 f 700 c 500 g 300 d 100 h 700 b e h b f c f i c 6 000 2 000 8 000 yes yes 7 000 9 000 6 000 yes d no BLM 2.2 1 a 20 000 b 20 000 c 70 000 d 80 000 e 40 000 f 50 000 g 70 000 h 80 000 i 30 000 2 a 50 000 b 50 000 c 40 000 3 Red: 55 000, 57 030, 55 001, 59 500, 55 999, 63 234 Blue: 53 067, 54 030, 50 002, 46 310, 52 103, 51 987 4 a 70 000 b 70 000 c 20 000 d 160 000 BLM 2.3 1 b c d e f 300 900 300 500 600 + + + + + 300 700 300 300 300 = = = = = 600 1 600 600 800 900 400 + 300 = 700 600 + 200 = 800 900 + 300 = 1 200 700 + 200 = 900 500 + 400 = 900 600 + 300 = 900 400 + 200 = 600 700 b 800 1 000 f 1 000 1 400 j 800 c 600 g 300 d 900 h 800 BLM 2.4 1 2 a b c d e f a d 3 a 800 – 800 – 700 – 400 – 900 – 900 – 600 400 600 300 400 200 200 400 500 = 500 = 400 = 500 = 200 = 500 = 400 b 100 e 400 b 300 c 500 BLM 2.5 BLM 2.1 1 a e i 2 a e i 3 a d g 4 a e 2 a b c d e f g 3 a e i 1 2 3 a c e a a $5.00 $1.00 × 9 = $9.00 90 × 9 = $8.10 $38.10 240 b 160 b 70 × 8 = $5.60 d 80 × 8 = $6.40 f $1.00 × 4 = $4.00 c 350 d 810 BLM 2.6 1 a b c d e f g h i j est 400 est 400 est 180 est 50 est 900 est 500 est 270 est 300 est 1 100 est 800 actual 380 actual 415 actual 162 actual 49.3 actual 921 actual 525 actual 261 actual 298.6 actual 1 076 actual 819 BLM 2.7 a 500 b 100 a 4 000 b 15 000 a 30 000 b 50 000 a 300 + 600 = 900 c 80 × 5 = 400 5 a False b True d True 6 a 170 b 50 7 a $600 b $160 8 a $500 1 2 3 4 c c c b 1 500 4 000 70 000 1 000 – 400 = 600 c True 73 Targeting Maths © Blake Publishing 2012. Rounding Estimation 2.1 Name Date 1 Round the following numbers to the nearest 10. a 15 ____________ b 42 ____________ c 82 ____________ d 22 ____________ e 55 ____________ f 19 ____________ g 39 ____________ h 63 ____________ i 35 ____________ 2 Round the following numbers to the nearest 100. a 152 ____________ b 310 ____________ c 450 ____________ d 30 ____________ e 750 ____________ f 721 ____________ g 267 ____________ h 683 ____________ i 888 ____________ 3 Round the following numbers to the nearest 1 000. a 3 267 ____________ b 5 555 ____________ c 7 136 ____________ d 4 500 ____________ e 2 230 ____________ f 8 917 ____________ g 1 644 ____________ h 7 896 ____________ i 6 499 ____________ 4 Estimates to the following questions have been given. State whether this is a reasonable estimate or not, and give a reason for your answer. a 263 + 342 = estimate = 500 Reasonable? Yes/No Why? _____________________________________________________________ b 489 + 362 = estimate = 800 Reasonable? Yes/No Why? _____________________________________________________________ c 177 + 446 = estimate = 600 Reasonable? Yes/No Why? _____________________________________________________________ d 336 + 541 = estimate = 800 Reasonable? Yes/No Why? _____________________________________________________________ e 162 + 192 = estimate = 400 Reasonable? Yes/No Why? _____________________________________________________________ f 98 + 335 = estimate = 400 Reasonable? Yes/No Why? _____________________________________________________________ 74 Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. Understanding: Rounding can be used as an estimation strategy. Fluency: Round numbers to the nearest 10, 100 and 1 000. Reasoning: Use known facts to consider if estimates are reasonable. Targeting Maths © Blake Publishing 2012. Rounding to Ten Thousands Name 1 Estimation 2.2 Date Round to the nearest ten thousand. b 24 265 ___________ a 15 487 ___________ d 84 554 ___________ e 36 344 ___________ g 74 999 ___________ h 82 501 ___________ c 67 648 ___________ f 45 001 ___________ i 25 000 ___________ 2 Draw arrows and write the number to round the numbers below to the nearest ten thousand. When rounding numbers to the nearest ten thousand, such as 25 000, round up for a 5 in the thousands. 40 000 Remember When rounding to the nearest ten thousand, look at the number in the thousands place. 50 000 a 45 000 b 45 500 c 44 999 3 Colour the numbers that round to 60 000 red and the numbers that round to 50 000 blue. 55 000 59 500 57 030 55 999 54 030 46 310 55 001 63 234 53 067 50 002 52 103 51 987 4 The following table provides the daily attendance to the Melbourne Cricket test between England and Australia. Round the figures to the nearest ten thousand and then make a total estimate of crowd attendance. Attendance Round to the nearest 10 000 Day 1 67 149 a Day 2 68 733 b Day 3 19 889 c Using the rounded numbers, estimate the total attendance over three days d Number and place value: ACMNA029 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. Understanding: Rounding can be used as an estimation strategy. Fluency: Round numbers to the nearest 10 000. Estimate the total of two numbers. 75 Targeting Maths © Blake Publishing 2012. Estimating Addition Estimation 2.3 Name Date 1 Estimate the answers of the following addition algorithms by rounding each number first. a 117 + 238 b 289 + 327 = c 878 + 650 = d 289 + 289 = e 482 + 324 = f 645 + 331 = = 100 + 200 2 Use rounding to estimate a reasonable answer to these addition algorisms. 687 700 a 388 +220 +200 +292 900 d 679 +224 e 514 +224 +367 + b 608 +202 + +312 +325 + f 635 + c 887 + g 388 +197 + 3 For the following addition algorithms, colour the better estimate. a 332 + 397 = 600 700 b 542 + 327 = 800 900 c 222 + 397 = 500 600 d 437 + 498 = 900 800 e 777 + 234 = 900 1 000 f 432 + 588 = 1 000 900 g 244 + 102 = 300 400 h 533 + 251 = 800 900 i 987 + 398 = 1 300 14 000 j 109 + 684 = 700 800 76 Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. Understanding: An estimate is a guide, not the correct answer. Fluency: Estimate answers to addition, subtraction and multiplication problems. Targeting Maths © Blake Publishing 2012. Estimating Subtraction Name 1 Estimation 2.4 Date Round these numbers to the nearest hundred and then estimate the difference. a d 798 – 332 432 – 165 b _________ e _________ 832 – 426 c _________ 937 – 367 f _________ 742 – 213 _________ 922 – 435 _________ 2 Round these numbers to the nearest hundred and estimate the difference. Colour the most reasonable answer. a 976 b 732 c 842 d 677 e 807 – 432 – 555 – 342 – 288 – 369 3 500 100 600 500 500 600 200 500 400 400 Estimate the answer to these word problems. Explain how you worked out your answer. aThere are 832 cars parked in the bThere are 587 students at Hillville Bellington shopping car park. Public School. 189 primary students 231 cars are parked on the top went to the district athletics level. Estimate how many cars are carnival, and 127 students went on parked on the remaining two levels. an excursion to the zoo. Estimate how many students remained at school? Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. Understanding: An estimate is a guide, not the correct answer. Fluency: Estimate answers to addition, subtraction and multiplication problems. 77 Targeting Maths © Blake Publishing 2012. Estimating Multiplication Name Estimation 2.5 Date Mia needs to buy a few extra items for her party. She is on a strict budget, so she needs to estimate how much it is going to cost before she does her shopping. She has found these items at super low prices! soft drink 92c Super sale mini chips 67c party pies 85c each 1 pack of balloons 95c chocolate bar 81c cup cakes 99c each Round the following prices, and estimate how much it will cost to buy: a 5 cans of soft drink 92c b 8 packs of mini chips $1·00 5× 67c 5× 8× d 8 chocolate bars × c 9 cup cakes 8× e 9 party pies × 99c × × × f 4 packs of balloons × × × 2 What is the total estimate of the cost of the party? _____________________ 3 Estimate the result by rounding the first factor to the nearest ten. a 37 × 6 c 73 × 5× 78 40 × 6 = = b 42 × 4 × = d 94 × 9 × = Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. Understanding: An estimate is a guide, not the correct answer. Fluency: Estimate answers to addition, subtraction and multiplication problems. Targeting Maths © Blake Publishing 2012. Operations Estimation 2.6 Name 1 Date Estimate the answers to the following number problems. Use your calculator to find the actual answer. Consider if your estimate is reasonable. Question Estimate—(show how you got your estimate) Actual Answer Was your estimate Reasonable? Explain a 163 + 217 b 514 – 99 c 27 × 6 d 148 ÷ 3 e 398 + 523 f 912 – 387 g 29 × 9 h 896 ÷ 3 i 378 + 202 + 496 j 642 + 389 – 212 Number and place value: ACMNA0291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. Understanding: An estimate is a guide, not the correct answer. Fluency: Estimate answers to addition, subtraction and multiplication problems. 79 Targeting Maths © Blake Publishing 2012. Assessment • Estimation Estimation 2.7 Date Name 1 Round the following numbers to the nearest 100. a 455 ____________ b 132 ____________ c 1 460 ____________ 2 Round the following numbers to the nearest 1 000. a 4 314 ____________ b 15 330 ____________ d 3 500 ____________ 3 Round the following numbers to the nearest 10 000. a 25 788 ____________ b 47 364 ____________ c 65 000 ____________ 4 Estimate the following algorithms by rounding first. Pay close attention to the sign. a 345 c 78 __________ b 967 __________ – 439 × 5 + 641 __________ __________ 5 The following items were for sale on an online shop. A Snakes and Ladders $22 __________ __________ B Toy front load washer $65 C Watch $123 D Camcorder $287 Use rounding to help you estimate the following answers and then state whether the total given is true or false. a A + B is about $80 _____________ b C + D is about $410 _____________ c B + D is about $360 ____________ d A + C is about $150 _____________ 6 Estimate the difference in cost between the following items. Use the back of the sheet for working out. a D and C ______________________ b B and C ______________________ 7 Estimate the cost of buying the following items. Use the back of the sheet for working out. a 5 watches ____________ b 8 Snakes and Ladders ____________ 8 Estimate the cost of buying all four items. Was your estimate reasonable? Explain. Estimate 80 Targeting Maths © Blake Publishing 2012. Why my estimate is reasonable.
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