PREFACE.

Transcription

1 PREFACE Solve Non-Routine Real World Mathematics Problems is a series of six primary level activity books aimed to develop vital thinking, reasoning, communication, application and metacognitive process skills. Through activity-based learning and novel word problems with real-world contexts, this series of books strives to help students understand mathematical concepts better through visualisations, simulations and representations, while supporting exploration and experimentation, as well as provide a suitable platform for students to develop critical 21 st century competencies. Varied Activities with a Purpose The authors ensured the questions are fun and interesting, taking care to include everyday settings and scenarios. Such question types are current and relevant, and provide students with a more immersive learning experience. The vivid, beautifully illustrated drawings in the lower level books also provide the younger students with interesting colouring activities. Solutions Detailed step-by-step working show students how to solve the problems. Enhanced resources available Learning Discussion notes for selected activities that provide hints or more background information on certain questions. Teacher notes for all activities that provide teachers or parents with additional teaching resources.

2 CONTENTS Use spatial visualisation and logical reasoning to solve problems Activity 1 : Surface Area... 1 Activity 2 : Volume and Surface Area... 3 Activity 3 : Squares and Area... 5 Use logical reasoning and number sense to solve problems Activity 4 : The Farmers Market... 7 Read, interpret and analyse information Activity 5 : Profit and Loss... 9 Activity 6 : Calculator Patterns Activity 7 : Puzzle Scrolls (1) Analyse and understand statistics Activity 8 : Weather or Not Solve problems involving time and make decisions based on particular criteria Activity 9 : Wilderness Explorer Use strategic thinking to solve problems Activity 10 : Changing Lockers Activity 11 : Cycle Days Activity 12 : Puzzle Scrolls (2) Use spatial visualisation, logical and proportional reasoning and the ability to solve problems with fractions and percentage Activity 13 : Office Hours Activity 14 : At the Office Activity 15 : Out of Office Use patterns and logical reasoning to determine numbers in spatial arrangements Activity 16 : Number Patterns... 31

3 Identify and use number understandings Activity 17 : Magic Squares Activity 18 : Sudoku Activity 19 : Alphametic Puzzles Analyse and use information in word problems Activity 20 : At the Shops Activity 21 : The Plant Nursery Activity 22 : On the Farm Activity 23 : Beading Activity 24 : Library Activity 25 : The Commuter Train Use strategic thinking to solve problems Activity 26 : Fisherman s Wharf Use spatial visualisation and measurement to solve problems Activity 27 : Making Designs Activity 28 : Squares and Rectangles Activity 29 : Designer Squares Interpret and organise information in series of interrelated statements and to use logical thinking to find solutions Activity 30 : Travelling to Australia...59 Activity 31 : Distance Activity 32 : Cost Use logical reasoning and an ability to visualise a sequence of events so as to use number patterns to solve problems Activity 33 : Prospect Plains Organise data and use number understanding to solve problems Activity 34 : Money Matters Activity 35 : Scoring Points Activity 36 : Puzzle Scrolls (3)... 71

4 Use logical reasoning, fractions and measurement to solve problems Activity 37 : Riding to Work Activity 38 : Bike Tracks Activity 39 : Puzzle Scrolls (4) Analyse information and use proportional and logical reasoning to solve problems Activity 40 : Farm Work Activity 41 : Farm Produce Activity 42 : Selling Fish Use logical reasoning and measurement to solve problems Activity 43 : Rolling Along Activity 44 : Balancing Out Activity 45 : Christmas Shopping Activity 46 : Calendar Calculations Use spatial visualisation, logical reasoning and measurement to solve problems Activity 47 : Distance Travelled Activity 48 : Taking Time Activity 49 : Puzzle Scrolls (5) Organise data and use an understanding of numbers to solve problems Activity 50 : Soccer Records Analyse information and use proportional reasoning to solve problems Activity 51 : Building Houses Use logical reasoning and mathematical understanding to solve problems Activity 52 : Running Races Solutions...S1 S17

5 Name: Class: Date: Activity 1 SURFACE AREA Learning Objective: To use spatial visualisation and logical reasoning to solve problems 1 (a) Some 2-m long wooden blocks with 10 cm by 20 cm rectangular ends are going to be stacked to form a set of garden stairs with 5 steps. If all the exposed surface area except the bottom and the ends set into the garden wall are painted with lacquer, what area will be painted? garden wall (b) When the builder puts the steps together, he decides to paint all the outer surfaces before assembling the steps in order to prolong the life of the stairs. What area does he actually paint? 2 (a) Some 1 cm 3 cubes are stacked to form a 3 by 3 by 3 cube as shown. One cube from the centre of each face is removed. If all of the exposed faces are painted red, what is the surface area of the solid that has been painted? 1 Activity 1

6 (b) Will the surface area to be painted change if there is a hole through the centre of the cube? What will the new surface area be? 3 (a) Now imagine a 4 by 4 by 4 cube. Remove a square of cubes from the centre of each face. What will the surface area of this solid be? (b) What will the new surface area be if there is a hole in the centre of this cube? 4 (a) If you have a cube and remove a square of cubes from the centre of each face, what will the surface area be? (There are 2 possibilities.) (b) What will the surface area be if there is a hole through the centre of the cube? 2 Activity 1

7 Name: Class: Date: Activity 2 VOLUME AND SURFACE AREA Learning Objective: To use spatial visualisation and logical reasoning to solve problems 1 Some cubes with sides measuring 2 cm long have been arranged to make the solid as shown below. (a) What is the surface area of the solid? (b) What is the volume of the solid? (c) If you add one more block to the upper surface of every block, what will the new surface area and volume be? Surface area: Volume: 3 Activity 2

8 2 Here is a plan of a solid made from a number of cubes with 3-cm sides. The squares show where the cubes are and the numbers show how many cubes are at each place. (a) Get the number of cubes you will need and make the solid. Use this model to work out the surface area and volume of the solid Surface area: Volume: (b) Work out the surface area and volume of the solids shown by these plans. The size of the cubes is written below each plan. (i) cm cubes Surface area: Volume: (ii) cm cubes Surface area: Volume: (iii) cm cubes Surface area: Volume: 4 Activity 2

9 Name: Class: Date: Activity 3 SQUARES AND AREA Learning Objective: To use spatial visualisation and logical reasoning to solve problems A 10 cm 2 B 1 The area of the small square in this tangram is 10 cm 2. (a) What is the area of one of the three smallest triangles? (b) What is the area of parallelogram A? (c) What is the area of triangle B? 5 Activity 3

10 Activity 1: SURFACE AREA 1 (a) steps = 2 m 0.2 m = 0.4 m 2 rises = 0.1 m 2 m = 0.2 m 2 ends = 0.1 m 0.2 m = 0.02 m m m m 2 = 0.62 m 2 area painted = m 2 = 3.1 m 2 (b) Surface area of one wooden block: 2 m 0.2 m = 0.4 m m 2 m = 0.2 m m 0.2 m = 0.02 m 2 (0.4 m m m 2 ) 2 = 1.24 m 2 Total surface area of five wooden blocks: 1.24 m 2 5 = 6.2 m 2 2 (a) cm 2 = 48 cm cm 2 = 30 cm 2 48 cm cm 2 = 78 cm 2 (b) Yes 78 cm 2 6 cm 2 = 72 cm 2 New surface area will be 72 cm 2. 3 (a) cm 2 = 72 cm cm 2 = 72 cm 2 72 cm cm 2 = 144 cm 2 (b) cm 2 = 24 cm cm 2 24 cm 2 = 120 cm 2 New surface area will be 120 cm 2. 4 (a) If a hole of 1 cm 1 cm cube is removed from all six faces: cm 2 = 144 cm cm 2 = 30 cm cm cm 2 = 174 cm 2 If a hole of 3 cm 3 cm cube is removed from all six faces: cm 2 = 126 cm cm 2 = 96 cm cm cm 2 = 222 cm 2 (b) If a 1 cm 1 cm cube is removed from each face, and a hole is made by removing 1 cm 1 cm cubes through all 6 sides 174 cm 2 6 cm 2 + (6 4 1 cm 2 ) = 192 cm 2 If a 3 cm 3 cm cube is removed from each face, and a hole is made by removing 1 cm 1 cm cubes through all 6 sides 222 cm 2 6 cm 2 + (6 4 1 cm 2 ) = 240 cm 2 If a 3 cm 3 cm cube is removed from each face, and a hole is made by removing 3 cm 3 cm cubes through all 6 sides 222 cm 2 ( cm 2 ) = 168 cm 2 Activity 2: VOLUME AND SURFACE AREA 1 (a) cm 2 cm = 600 cm 2 (b) 2 cm 2 cm 2 cm = 8 cm = = cm 3 = 792 cm 3 (c) Extra surface area, which is area of 20 squares cm 2 = 80 cm 2 Total surface area 600 cm cm 2 = 680 cm 2 Extra volume, which is that of 25 cubes (2 cm 2 cm 2 cm) 25 = 200 cm 3 Total volume 792 cm cm 3 = 992 cm 3 2 (a) back view side view 1 side view 2 front view Top view and bottom view are laid out exactly as in the plan above. Number of exposed faces from side view 1 = = 24 faces (side view 1) Number of exposed faces from side view 2 is the same as from side view 1 = = 24 faces Number of exposed faces from the front view = = 19 faces (front view) Number of exposed faces from the back view is the same as from the front view = = 19 faces Number of exposed faces from the top view = = 12 faces (top view) Number of exposed faces from the bottom view is the same as from the top view = = 12 faces Area of 1 square face = 3 cm 3 cm = 9 cm 2 Total surface area = ( ) 9 = 990 cm 2 Sum of all the cubes = 58 Total volume 58 3 cm 3 cm 3 cm = 1566 cm 3 (b) (i) back view side view side view front view Top view and bottom view are laid out exactly as in the above plan. S1