Задания по математической грамотности PISAметодическая разработка по алгебре (5, 8 класс)

The context is occupational. The question belongs to the change and relationships content area, which involves understanding fundamental types of change and recognising when they occur in order to use suitable mathematical models to describe and predict change.

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Задания по математической грамотности PISA
методическая разработка по алгебре (5, 8 класс)

Асель Мансуровна планирует в отпуск полететь отдыхать в Стамбул на самолете авиакомпании «Turkish Airlines».

Она узнала, что в салон самолета можно взять ручную кладь весом не более 5 кг. Также в стоимость билета входит 1 место багажа весом 15 кг.

Если у пассажира несколько мест багажа, то на каждое из них нужно оформить дополнительное багажное место. Дополнительное место для одного предмета весом до 15 кг стоит 1500 сомов. Если предмет весить больше 15 кг, то каждый лишний килограмм нужно заплатить еще по 350 сомов, при этом вес округляется в большую сторону килограмма.

В день вылета Асель Мансуровна приехала в аэропорт по раньше и взвесила каждый предмет своего багажа.

14 кг 900 г 2 кг 900 г 1 кг 700 г 3кг 200 г

Какие два предмета может взять с собой в салон самолета Асель Мансуровна?

Заполните в таблице варианты выбора предметов Асель Мансуровны.

Ручная кладь (багаж, который можно взять с собой в салон самолета)

Асель Мансуровна решила взять с собой в салон самолета рюкзак и ноутбук. Как поступить Асель Мансуровне с остальным багажом?

Характеристика вопроса 1

Область математического содержания: Количество

Контекст: Личная жизнь.

Мыслительная деятельность: Формулирование

Описание задания – сравнение величин, округление величин, сложение нескольких величин.

Уровень сложности :2.

Формат ответ: краткий ответ

Ответ полный – два верных заполнения «коробка и ноутбук», «рюкзак и ноутбук» – 2б.

Ответ частичный – один из приведенных верных ответов – 1 балл.

Ответ не верный – если приведены другие варианты решения – 0 баллов

Характеристика вопроса 2

Область математического содержания: Количество

Контекст: Личная жизнь.

Мыслительная деятельность : Рассуждение

Описание задания – умение выполнять вычислительные операции с величинами, числами, выполнять сравнение и округление величин, предположить результат.

Уровень сложности :3.

Формат ответ: развернутый ответ

Ответ полный – «Сдать в багаж», «оформить дополнительное багажное место за 1500 сомов» – 2 б.

Объяснение 1: Чемодан весит до 15 кг, его можно сдать в багаж бесплатно. Коробка весит меньше чем 15 кг, можно оплатить дополнительное место за 1500 сомов.

Объяснение 2: Коробку можно сдать в багаж бесплатно, а чемодан сдать в багаж за 1500 сомов.

Ответ частичный – «Сдать в багаж чемодан и коробку», а объяснение неполное, но не содержит неверного суждения. – 1 балл.

Ответ не верный – если приведены другие варианты решения – 0 баллов

Задание «Наша спортивная семья»

Все члены семьи Мамасадыковых – дедушка, бабушка, мама, папа, а также дети Алия, Самат и Тимур – участвовали в эстафете. Бабушка пробежала 60 м, Алия 200 м, мама в 25 раз больше, чем бабушка, а Самат пробежал в 5 раз больше, чем Алия. Дедушка пробежал в 2 раза больше, чем мама, а Тимур в 5 раз и папа в 10 раз больше, чем Самат.

Кто их членов семьи пробежал больше всех остальных? Опиши свое решение

Подпиши каждый столб диаграммы, используя данные из решения задачи. Кто на каком месте по расстоянию пробега этапов эстафеты.

Характеристика вопроса 1

Область математического содержания: Измерение и зависимости

Контекст: Общественная жизнь.

Мыслительная деятельность: Процедуры размышления

Описание задания – нахождение и сравнение величин.

Уровень сложности :2.

Формат ответ: развернутый ответ

Ответ полный – Папа пробежал больше всех расстояние этапа эстафеты 10000м, так как он пробежал больше в 10 раз, чем Самат. А Самат пробежал в 5 раз больше, чем Алия– 2б.

Ответ частичный – Папа – 1 балл.

Ответ не верный – если приведены другие варианты решения – 0 баллов

Характеристика вопроса 2

Область математического содержания: Измерение и зависимость

Контекст: Общественная жизнь.

Мыслительная деятельность : Рассуждение и зрительное представление информации

Описание задания – умение выполнять вычислительные операции с величинами, числами, выполнять сравнение величин, предположить результат на предложенной диаграмме.

Уровень сложности :3.

Формат ответ: развернутый ответ

Ответ полный – Оранжевый – это папа, так как он самый высокий, голубой – Самат, красный – это дедушка, зеленый – этой Тимур, синий – мама, серый – это Алия и желтый – это бабушка – 2 б.

Объяснение: Просчитав расстояние пробега каждого из участника эстафеты из этой семьи, можно на диаграмме расположить следующие столбцы.

Ответ частичный –Частичное распределение столбцов – 1 балл.

Ответ не верный – если приведены другие варианты решения – 0 баллов

Задание «Любимое блюдо»

Бегимай решила приготовить манты. Для этого написала список продуктов и их количество. После исследования цен в супермаркетах, составила таблицу, куда выписала цены по каждому наименованию продукта.

8 sinf matematika pisa test

This picture shows a new design Josh printed onto paper.

How will the design appear on the t-shirt?

QUESTION LEVEL 2: WHICH FORMULA?

A radio station has 10 free tickets to a concert to give away. Each listener may send in one email requesting a ticket. Emails are received from 1200 listeners. Emails are then selected at random one at a time until all tickets are given away.

Question

The first 9 tickets have been given away. John’s email has not been selected. What is John’s chance of winning the last ticket? John’s chance = 1 in .

Type answer here:

QUESTION LEVEL 3: WHICH FORMULA?

Steph and Jawad run their own businesses.

Steph makes greeting cards and sells them at a market each Sunday.

Jawad is a gardener

Question

Jawad’s total charge for a gardening job is:

• a fixed charge of 20 zeds plus
• an hourly charge of 30 zeds per hour.

Write a formula that shows how Jawad’s total charge, C, relates to, h, the number of hours he spends on a job?

NOTE: PISA questions often refer to situations that take place in the fictional country of Zedland, where the Zed is the unit of currency.

Type answer here:

QUESTION LEVEL 4: AGE OF MOTHERS

This graph shows the percentage of births in Zedland for two years (1960 and 2000), according to the mother’s age at the time of birth.

For example, in 1960, 16% of the births were to mothers in the 30-34 age group.

NOTE: PISA questions often refer to situations that take place in the fictional country of Zedland.

Question

Is each of the following statements about the graph true or false?

Click “True” or “False” for each statement.

Statement	True or False?
Approximately one quarter of the births in 1960 were to mothers aged 25-29.	True False
There were fewer mothers who gave birth aged 15-19 in 2000 than in 1960.	True False
In 1960, the median age of mothers who gave birth was in the 20-24 age group.	True False

QUESTION LEVEL 5: SUN ROOM

The diagrams show the plans for a sun room. It will be built onto the wall of a house.

The four walls of the sunroom are square clear glass panels.

The roof is made using

• four clear glass panels, trapezium in shape, all the same size
• one tinted glass panel, half a regular octagon in shape.

Question

The edge AB of one of the roof panels is shown on the diagrams.:

What is the actual length of AB? (in metres)

Type answer here:

QUESTION LEVEL 6: FILL A ROOM COMPETITION

To raise money for a school fete, a competition is held.

Students must guess the number of bags of plastic beads that would be needed to fill a classroom.

Each bag holds 100 litres of beads.

Question

One kilolitre of beads fills one cubic metre.

Show by your working that the volume of one bag of beads is 0.1 cubic metres.

Type answer here:

Mathematics questions

MATHEMATICS QUESTION (LEVEL 1) THE CORRECT ANSWER IS: (B)

Question level

Students at Proficiency Level 1 can answer questions involving familiar contexts where all relevant information is present and the questions are clearly defined. They are able to identify information and to carry out routine procedures according to direct instructions in explicit situations. They can perform actions that are obvious and follow immediately from the given stimuli.

Nature of the task

Identify the reflection of an abstract image

The context is occupational. The question belongs to the space and shape content category, which encompasses a wide range of phenomena that are encountered everywhere in our visual and physical world: patterns, properties of objects, positions and orientations, representations of objects, decoding and encoding of visual information, navigation and dynamic interaction with real shapes as well as with representations.

Mathematical Process

The process is employing mathematical concepts, facts, procedures and reasoning because the individual has to apply mathematical concepts, facts, procedures, and reasoning to solve mathematically-formulated problems to obtain mathematical conclusions.

Scoring

Full credit: B. (graphic)

No credit: Other responses or missing.

MATHEMATICS QUESTION (LEVEL 2) THE CORRECT ANSWER IS:

1191 OR WORKING THAT SHOWS 1 ÷ 1191

Question level

Students at Proficiency Level 2 can interpret and recognise situations in contexts that require no more than direct inference. They can extract relevant information from a single source and make use of a single representational mode. Students at this level can employ basic algorithms, formulae, procedures, or conventions. They are capable of direct reasoning and literal interpretations of the results. PISA considers Level 2 a baseline level of mathematics proficiency at which students begin to demonstrate the kind of skills that enable them to use mathematics in ways that are considered fundamental for their future development.

Nature of the task

Calculate conditional probability of an event

The context is societal. The question belongs to the uncertainty and data content category, which includes recognising the place of variation in processes, having a sense of the quantification of that variation, acknowledging uncertainty and error in measurement, and knowing about chance.

Mathematical process

The process is formulating situations mathematically because the individual has to recognise and identify opportunities to use mathematics and then provide mathematical structure to a problem presented in some contextualised form.

Scoring

Full credit: 1191 or working that shows 1 ÷ 1191

No credit: Other responses or missing.

MATHEMATICS QUESTION (LEVEL 3) THE CORRECT ANSWER IS:

AN EXPRESSION THAT SHOWS AN UNDERSTANDING OF THE RELATIONSHIP BETWEEN TOTAL CHARGE, FIXED CHARGE, HOURLY CHARGE AND HOURS (E.G., C = 30H +20; C = 20 + H x 30)

Question level

Students at Proficiency Level 3 can execute clearly described procedures, including those that require sequential decisions. They can select and apply simple problem-solving strategies. Students at this level can interpret and use representations based on different information sources and reason directly from them. They can develop short communications reporting their interpretations, results and reasoning.

Nature of the task

Create a correct formula in a context based on a linear relationship between fixed and variable costs

The context is occupational. The question belongs to the change and relationships content area, which involves understanding fundamental types of change and recognising when they occur in order to use suitable mathematical models to describe and predict change.

Mathematical process

The process is formulating situations mathematically because the individual has to recognise and identify opportunities to use mathematics and then provide mathematical structure to a problem presented in some contextualised form.

Scoring

Full credit: An expression that shows an understanding of the relationship between total charge, fixed charge, hourly charge and hours

Partial credit: An expression that shows an understanding of the relationship between total charge, hourly charge and hours [omits fixed charge]

No credit: Other responses or missing.

MATHEMATICS QUESTION (LEVEL 4) THE CORRECT ANSWER IS:

TRUE, TRUE, FALSE IN THAT ORDER

Question level

Students at Proficiency Level 4 can work effectively with explicit models for complex, concrete situations that might involve constraints or call for making assumptions. They can select and integrate different representations, including symbolic ones, linking them directly to aspects of real-world situations. Students at this level can use well-developed skills and reason flexibly, with some insight, in these contexts. They can construct and communicate explanations and arguments based on their interpretations, arguments and actions.

Nature of the task

Determine accuracy of statements about grouped data represented by comparative bar graph

The context is societal. The question belongs to the uncertainty and data content category, which includes recognising the place of variation in processes, having a sense of the quantification of that variation, acknowledging uncertainty and error in measurement, and knowing about chance.

Mathematical process

The process is employing mathematical concepts, facts, procedures and reasoning because the reader has to recognise and identify opportunities to use mathematics and then provide mathematical structure to a problem presented in some contextualised form.

Scoring

Full credit: Three correct responses: True, True, False in that order

No credit: Fewer than three correct responses or missing.

MATHEMATICS QUESTION (LEVEL 5) THE CORRECT ANSWER IS:

2.236 OR 2.24 OR 2.2 OR √5.

Question level

Students at Proficiency Level 5 can develop and work with models for complex situations, identifying constraints and specifying assumptions. They can select, compare, and evaluate appropriate problem solving strategies for dealing with complex problems related to these models. Students at this level can work strategically using broad, well-developed thinking and reasoning skills, appropriate linked representations, symbolic and formal characterisations, and insight pertaining to these situations. They can reflect on their actions and formulate and communicate their interpretations and reasoning.

Nature of the task

Use information from scale drawings and Pythagoras’ Theorem to show how an actual length is found

The context is societal. The question belongs to the space and shape content area, which encompasses a wide range of phenomena that are encountered everywhere in our visual and physical world: patterns, properties of objects, positions and orientations, representations of objects, decoding and encoding of visual information, navigation and dynamic interaction with real shapes as well as with representations.

Mathematical process

The process is employing mathematical concepts, facts, procedures and reasoning because the reader has to recognise and identify opportunities to use mathematics and then provide mathematical structure to a problem presented in some contextualised form.

Scoring

Full credit: 2.236 or 2.24 or 2.2 or √”5″

Partial credit: 2 [Uses scale correctly but not Pythagoras]

No credit: Other responses or missing.

MATHEMATICS QUESTION (LEVEL 6) THE CORRECT ANSWER:

SHOWS THAT 100 LITRES IS EQUIVALENT TO 0.1 M3.

Question level

Students at Proficiency Level 6 can conceptualise, generalise and utilise information based on their investigations and modelling of complex problems. They can link different information sources and representations and flexibly translate between them. Students at this level are capable of advanced mathematical thinking and reasoning. They can apply this insight and understanding along with a mastery of symbolic and formal mathematical operations and relationships to develop new approaches and strategies for attacking novel situations. Students at this level can formulate and precisely communicate their actions and reflections regarding their findings, interpretations, arguments, and the appropriateness of these to the original situations.

Nature of the task

Use metric information about volume and capacity to show that a quantity of litres is equivalent to a fraction of a cubic metre

The context is personal. The question belongs to the quantity content area, which involves understanding measurements, counts, magnitudes, units, indicators, relative size, and numerical trends and patterns. Aspects of quantitative reasoning – such as number sense, multiple representations of numbers, elegance in computation, mental calculation, estimation and assessment of reasonableness of results – are the essence of mathematical literacy relative to quantity.

Mathematical process

The process is employing mathematical concepts, facts, procedures and reasoning because the individual has to apply mathematical concepts, facts, procedures, and reasoning to solve mathematically-formulated problems to obtain mathematical conclusions.

Scoring

Full credit: Working shows that 100 litres is equivalent to 0.1 m3.

No credit: Other responses or missing.