Pages 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 14895 result(s) returned

3.5.1 Try some yourself

Activity 30

Carry out the following calculations, without your calculator.

  • (a) 3 × (60 + 70).

  • (b) (3 × 60) + 70.

  • (c) (70 − 60) ÷ 5.


  • Author(s): The Open University

    License information
    Related content

    Copyright © 2016 The Open University

3.4 Did I make a rough estimate to act as a check?

When using a calculator many people have ‘blind
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

Try some yourself

Question 1

Which of these triangles are similar?

2.7 Rotational symmetry

There is another kind of symmetry which is often used in designs. It can be seen, for instance, in a car wheel trim.

Look at the trim on the left. It does not have line symmetry but
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

2.1 Geometric shapes – triangles

This section deals with the simplest geometric shapes and their symmetries. All of the shapes are two-dimensional – hence they can be drawn accurately on paper.

Simple geometric shapes are studied in mathematics partly because they are used in thousands of practical applications. For instance, triangles occur in bridges, pylons and, more mundanely, in folding chairs; rectangles occur in windows, cinema screens and sheets of paper; while circles are an essential part of wheels, gears a
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

Try some yourself

Question 1

Find γ and δ in the following diagrams produced by a ship's navigator.

Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

2.2 Direct proportion

In a recipe the quantity of each ingredient needed depends upon the number of portions. As the number of portions increases, the quantity required increases. The quantity per portion is the same. This is called direct proportion. The quantity is said to be directly proportional to the number of portions. If 2 potatoes are required for one portion, 4 will be required for two portions etc. A useful method for direct proportion problems is to find the quantity for one and multiply by the
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

1.2.1 Try some yourself

Activity 1

A friend is painting the inside walls of a garage. So far she has used a 2 litre tin of emulsion paint and covered an area of 9 m2. She needs some more paint. How much more would you advise her to
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

1.1 Introduction

Ratios crop up often in official statistics. The government wants the teacher–pupil ratio in schools to be increased to one teacher to thirty pupils or less. The birth rate has fallen: the ratio of children to women of child bearing age has gone down. It used to be 2.4 to 1, and now it is 1.9 to 1. Predictions for the ratio of working adults to retired adults is disturbing. Predictions are, that by 2030 the ratio will be two working adults to every retired person, instead of three to one no
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

1.2.2 Content

School mathematics curricula often focus on lists of content objectives in areas like number, arithmetic, statistics, measurement, geometry, trigonometry, and algebra. A typical list of content objectives might contain over one hundred objectives to be introduced or revisited and learned each year. These can be seen as hierarchical in nature but many textbooks do not attempt to organise the objectives in ways that enable the bigger underpinning ideas to become apparent to the pupils. In addit
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

5 Approaches to problem solving

You should not expect always to be able to read a problem and then just write down the answer. When you are faced with a written mathematical question or problem to solve, read it carefully. It is important that you get to grips with the question in two ways: first, that you absorb the information given; and second, that you find out what the question is really asking. Your solution will link the two. This method can be summarised by the following questions.

    Author(s): The Open University

    License information
    Related content

    Copyright © 2016 The Open University

Environment: LA River
Who killed the river that runs through Los Angeles? Did you even know there was a river? Using a mix of archive and new footage , this album tells the fascinating story of a city that has ignored the benefits of its river for decades. Now waking up to the fact that it could be a green belt with more acreage than all of Central Park, river activists are fighting developers to bring back nature to central Los Angeles. Up till now the city conquered the threat of floods by concreting over the river
Author(s): The OpenLearn team

License information
Related content

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

Mediating Change: Culture and Climate Change
Every generation faces challenges that previous generations could scarcely imagine. Twenty years ago, few people were talking about climate change, now it's one of the most hotly-contested areas in politics. How do artists, writers, musicians and broadcasters respond when a new subject appears that is as large and significant as this? What kind of novels, plays, paintings, sculptures, movies and music begin to emerge? ‘Mediating Change’ is a four-part series, chaired by BBC Radio 4’s Que
Author(s): The OpenLearn team

License information
Related content

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

Studying mammals: Food for thought
Who were our ancestors? How are apes and humans related? And where does the extinct Homo erectus fit into the puzzle? In this free course, Studying mammals: Food for thought, we will examine culture, tool use and social structure in both apes and humans to gain an understanding of where we come from and why we behave as we do. This is the tenth course in the Studying mammals series. Author(s): Creator not set

License information
Related content

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

Living without oil
Crude oil is currently our most important global source of energy. It is vital in the manufacture of many modern materials. But the worlds supply of oil is finite, its price is unstable and our reliance on oil has damaging environmental consequences. This free course, Living without oil, explains why developing alternatives to oil is an essential and urgent task for humanity.
Author(s): Creator not set

License information
Related content

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

Exploring philosophy: faking nature
Commercial exploitation of nature, such as mining, fracking, or generating hydro-electric power, often damages the way the natural environment looks. What if the environment could be restored to exactly how it looked before? Would that mean that no damage had been done, that the natural environment was as valuable as it had been before the commercial exploitation? This free course, Exploring philosophy: faking nature, examines ‘the restoration thesis’, and provides an insight into philosophi
Author(s): Creator not set

License information
Related content

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

2.8 End of course question

Question 12

The writer and campaigner George Monbiot wrote the following (in The Guardian Weekly, 10 February 2000): 'Every time someone in the West switches on a kettle, he or she is helpting to flood Banglades
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

1.8 End of section questions

Question 5

2.3 Citizens in conversation with nature and experts

Before leaving office in 2008, Sir David King (the ex-Chief Scientific Advisor to the UK Government) introduced an ethical code for scientists. This drew particularly on his experience in working across the scientific–political divide on issues of climate change. The code comprises three attributes of scientific endeavour: rigour, representation and responsibility (Author(s): The Open University

2.2 Environmental pragmatism: positioning expert support

I believe that the principal task for an environmental pragmatism is not to reengage the … debates in environmental ethics but rather to impress upon environmental philosophers the need to take up the largely empirical question of what morally motivates humans to change their attitudes, behaviours, and policy preferences toward those more supportive of long-term environmental sustainability.

(Light, 2002, p. 446)


Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

Pages 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745