Вписанные и центральные углы. Вписанный и описанный четырехугольник.

Интеллектуальная математическая игра для 8 класса

«Своя игра»

Правила игры:

В игре принимают участие 3 команды.

Игра состоит из 3 раундов.

Задача каждой команды набрать как можно больше баллов. Для этого необходимо правильно ответить на вопросы в игре. Каждый вопрос имеет свою стоимость. Вопросы выбирает капитан команды.

Если команда не отвечает на выбранный вопрос, то право ответа переходит к следующей команде.

Известные

математики

Slide 2-Category Selection

This slide is the main game board. You go here to begin the game, and you return here after each Question/Answer slide. This is where the “contestant” selects one of the five categories and a dollar value for the question. The higher the value, the more difficult the question. When you open this slide, the categories appear one at a time, and the dollar values appear at random with an accompanying laser beep. Here’s how it works: if the contestant selects the first category for $300, you would click on the $300 text under

Углы

Окружность

вписанная

Окружность

описанная

Веселые

вопросы

100

100

100

100

100

200

200

200

200

200

the 1st category (i.e., the 3rd dollar box in column one). As a result, the corresponding Question/Answer slide will automatically appear. Once the question, and then the answer, for that slide have been shown, you will click on the arrow in the bottom right of that slide to return to this main slide. When you return to this slide, the dollar amount for the box you selected will have changed from white to blue to show that that particular question has already been used. Below, you will see how to tailor the game for your particular categories.

300

300

300

300

300

To tailor this slide, follow these instructions:

Five different categories are used in the game. The category names appear at the top of the columns on this slide and on the five associated Question/ Answer slides (one for each dollar value). Rather than changing all of these separately, you will use the Replace command to change each placeholder category name only once.

400

400

400

400

400

1. Under Edit , choose Replace

• Type the placeholder name for category 1 as shown in the pop-up at the right. Type in your category name (e.g., Mixed Numbers) under Replace with:
• Type the placeholder name for category 1 as shown in the pop-up at the right.
• Type in your category name (e.g., Mixed Numbers) under Replace with:

The Replace pop-up should now look like the one on the right, only with your category name.

• The Replace pop-up should now look like the one on the right, only with your category name.

• Click the Replace All button to make the changes.
• Click the Replace All button to make the changes.

You will then see this pop-up

• You will then see this pop-up

• Click the OK button. This replaces the six occurrences of the specified placeholder category name with your category name. After this, the top of the slide will look like this:
• Click the OK button. This replaces the six occurrences of the specified placeholder category name with your category name. After this, the top of the slide will look like this:

Notice that in this case, “Mixed Numbers” doesn’t fit on the line. To fix this, simply click on the text right before the “N” and press Backspace followed by Enter. Now it’s on two lines:

2. Now, repeat Step 1 for the remaining four category placeholder names:

Slide 2-Category Selection

This slide is the main game board. You go here to begin the game, and you return here after each Question/Answer slide. This is where the “contestant” selects one of the five categories and a dollar value for the question. The higher the value, the more difficult the question. When you open this slide, the categories appear one at a time, and the dollar values appear at random with an accompanying laser beep. Here’s how it works: if the contestant selects the first category for $300, you would click on the $300 text under

Числа

Логические

задачи

Веселые

вопросы

Известные

математики

the 1st category (i.e., the 3rd dollar box in column one). As a result, the corresponding Question/Answer slide will automatically appear. Once the question, and then the answer, for that slide have been shown, you will click on the arrow in the bottom right of that slide to return to this main slide. When you return to this slide, the dollar amount for the box you selected will have changed from white to blue to show that that particular question has already been used. Below, you will see how to tailor the game for your particular categories.

500

500

500

500

To tailor this slide, follow these instructions:

Five different categories are used in the game. The category names appear at the top of the columns on this slide and on the five associated Question/ Answer slides (one for each dollar value). Rather than changing all of these separately, you will use the Replace command to change each placeholder category name only once.

1. Under Edit , choose Replace

• Type the placeholder name for category 1 as shown in the pop-up at the right. Type in your category name (e.g., Mixed Numbers) under Replace with:
• Type the placeholder name for category 1 as shown in the pop-up at the right.
• Type in your category name (e.g., Mixed Numbers) under Replace with:

The Replace pop-up should now look like the one on the right, only with your category name.

• The Replace pop-up should now look like the one on the right, only with your category name.

• Click the Replace All button to make the changes.
• Click the Replace All button to make the changes.

You will then see this pop-up

• You will then see this pop-up

• Click the OK button. This replaces the six occurrences of the specified placeholder category name with your category name. After this, the top of the slide will look like this:
• Click the OK button. This replaces the six occurrences of the specified placeholder category name with your category name. After this, the top of the slide will look like this:

Notice that in this case, “Mixed Numbers” doesn’t fit on the line. To fix this, simply click on the text right before the “N” and press Backspace followed by Enter. Now it’s on two lines:

2. Now, repeat Step 1 for the remaining four category placeholder names:

4

Slide 3-Question/Answer (Cat1, $100)

This slide is the first Question/Answer slide. It corresponds to Category 1 for $100. Once you have followed the instructions on Slide 2 to replace category name placeholders with your actual categories, the text “Cat1” on this slide will be replaced with your 1 st category name.

When you click on Category 1 for $100 on the main slide, this slide opens automatically, with the Question appearing at the top. (Note: On TV Jeopardy, the contestant is actually shown an

answer and is asked to offer a related question. Since this concept is sometimes difficult to understand and implement, this PowerPoint version shows a question followed by the corresponding answer.)

One way to play the game in class is to set up three teams. For each round, have one person from each team stand up as contestants. Have one pick the category and dollar value; click on that box and then ready the question that appears. Call on the first contestant that raises his or her hand for the answer. If they are correct, their team gets corresponding points or dollars (e.g., 1 point for each $100). If the first contestant misses the question or does not answer quickly enough, his or her team loses the corresponding points. Then, offer the question to the remaining two contestants in order of their raised hands. After the question has been answered correctly, or after all three contestants miss it, or after no contestant wants to try, return to the main slide by clicking on the yellow arrow. The current contestants then sit down, and the game moves to the next round.

Note that this Jeopardy game does not have a Double Jeopardy question.

Архимед .

To tailor this slide, follow these instructions:

You are now ready to put in your questions and answers, but you might want to go ahead and save this file first, using Save As and giving it a new name—one that makes sense for this particular Jeopardy game (e.g., Fractions Jeopardy ).

• If your Question is short, simply double click on the word “Question” and type in your specific question (e.g., “50% of 150” or “Capitol of France”). If the text you enter will not fit on one line, there’s room for two lines at this font size. If you need more room, reduce the font size by triple clicking on the text and using the Font Size selector in the toolbar. In some cases, your question may need a drawn figure or graphic. You can use PowerPoint features to draw the figure you need or to insert graphics. A few examples are show below.
• Double click on the word “Answer” and type in your answer in the same way.
• Do the same steps to tailor the remaining Question/Answer slides, remembering to make questions of higher dollar value more difficult. Also remember to save your work.

Example Questions:

7

Чьи слова. «Делай лишь то, что

впоследствии не огорчит тебя и

не принудит раскаиваться.»

Пифагор .

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

10

Ее знакомство с математикой

произошло в 8 лет,

так как стены ее комнаты

были оклеены листами

с записями лекций по математике

профессора Остроградского.

Кто она?

Софья Ивановна Ковалевская

– первая женщина-профессор математики.

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

10

Именно этому ученому

принадлежат слова

«Математика- царица всех наук.

Арифметика-царица математики».

Карл Фридрих

Гаусс.

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

10

Именно этот учебник был первой в России

энциклопедией математических знаний.

По нему учился М.В. Ломоносов,

называвший его «вратами учености».

Именно в нем впервые на русском языке

введены понятия «частное»,

«произведение», «делитель».

Назовите учебник и его автора.

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

«Арифметика». Л.Ф.Магницкий .

10

Крышка стола имеет четыре угла.

Один из них отпилили.

Сколько стало углов?

Пять.

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

10

Какое число нужно

увеличить в 15 раз и

получить 15.

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

1

10

Сумма каких двух

натуральных чисел равна

из произведению?

2+2=2*2

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

10

Две монашки пошли в церковь

и прошли 60 вёрст.

Сколько вёрст прошла каждая,

если они шли с одинаковой скоростью.

60

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

10

Врач прописал больному 3 пилюли,

чтобы он принимал их по

одной через каждый полчаса.

На сколько по времени

больному хватит этих пилюль?

на 1 час.

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

10

Найти :

3 0 0

C

B

6 0 0

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

19

Найти : АВ

А

Окр.( О, r) , АВ- касательная. ОА = 5 см, ОВ = 3 см.

B

О

АВ =4 см

Х Найти :

С

70˚

А

80˚

В

140˚

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

АС = 140˚

19

Найти :

А

C

О

30˚

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

АС = 60˚

19

Какими двумя цифрами

оканчивается произведение

1*2*3*4*5*6*7*8*9*10*11*12*13?

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

Двумя нулями.

19

Угол A четырехугольника

ABCD , вписанного в

окружность,

равен 100 о . Найдите угол C  

80

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

19

Два угла вписанного в окружность

четырехугольника равны 80 о и 60 о .

Найдите больший из оставшихся углов

120

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

19

Угол B четырехугольника ABCD ,

вписанного в окружность, равен 70 о .

Найдите угол D .

110

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

19

В четырехугольнике ABCD , вписанном в окружность, угол A равен 75 о , угол B равен 90 о . Найдите разность двух других углов  

15

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

19

Меньшая сторона прямоугольника

равна 5 см. Угол между диагоналями

равен 60 о . Найдите радиус описанной

окружности

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

5

19

Боковые стороны трапеции,

описанной около окружности,

равны 2 и 4.

Найдите среднюю линию трапеции

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

3

19

В четырехугольник ABCD

вписана окружность, AB = 11, CD = 17.

Найдите периметр четырехугольника

56

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

19

Периметр четырехугольника,

описанного около окружности,

равен 20, две его стороны равны 4 и 5.

Найдите большую из

оставшихся сторон.

6

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

19

В четырехугольник ABCD

вписана окружность, AB = 11,

BC = 10 и CD = 15. Найдите

четвертую сторону четырехугольника

Welcome to Power Jeopardy

© Don Link, Indian Creek School, 2004

You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.

16

19