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Fractional Thinking: Engaging Activity for Concept Exploration

This activity stimulates critical thinking by posing questions on fractions & operations, encouraging students to create unique questions. Ideal for warm-up and reflection, it offers opportunities for varied skill levels & self-assessment.

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Fractional Thinking: Engaging Activity for Concept Exploration

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  1. Situation Choose the activity(ies) that best suit your students’ learning needs Use this short activity to get students to think about the information in a question . Ideal for the beginning of the lesson Warm up Four questions that encourage students to think about alternative questions using the same information What are the possibilities? Four questions that require students to use higher order thinking skills in order to consider question alternatives Thinking harder Opportunities to use the same approach in different contexts Some more to try Students can assess what they still need to learn and the grade they are working at. Reflection Content covered Print so students can learn the key points. Take home or work in pairs. Test yourself cards

  2. Situation – Content covered Reflection

  3. Situation – Warm up Answers 1. Which 2 fractions divide to give an integer? 2. Add the first 3 fractions in the list. 3.Square root the product of the last 3 fractions in the list. 4. Make up a simple question using these fractions.

  4. Situation – What are the possibilities? 1. What different fractions can you make by adding, subtracting, multiplying and dividing these fractions? 2. (5 marks) 3.Make up a mark scheme for this question. 4. Write your own exam question about this situation. Question 3 Three kinds of marks can be given: B for something being correct, irrespective of method M for carrying out a correct step A for a correct answer Question 4 Use the prompts button below to help students who are unfamiliar with this style of question Use the thinking prompts button to help students be more creative with their questions. Thinking prompts Answer Prompts

  5. Situation – Thinking harder Answers 1. 2. Two pairs of the fractions multiply to give the same answer. What are those pairs? 3. Two of the fractions divide to give 0.36. Which two? 4. Which two fractions have a difference of ?

  6. Situation – Some more to try Answers 1. 64 27 Combine these 4 numbers with mathematical operators to make a true statement. 2. Unit fractions are fractions with a numerator of 1. The Egyptians used to write non unit fractions as the sum of unit fractions. For example Write as the sum of unit fractions. 3. • Which of the above have recurring decimal equivalents? • Which of the above have integer reciprocals?

  7. Situation – Reflection Click below the button to reveal the grades I can D C C B B • Self assess • Find or write some evidence to support your assessment • Write down your next steps • You may wish to use the Test Yourself cards.

  8. These cards have the things you may need to learn in order to do fraction questions. Copy down the ones YOU need or ask your teacher for a printout. Situation – Test yourself cards

  9. Situation – Answers for Warm-up

  10. Situation – Answers for What are the possibilities? 1. Using the fractions in the box some possibilities include: Q2. and Q3. 4. The exam questions would normally be a selection of ‘testing techniques’ which do not need to have any connection with each other. Consideration of whether they should merit 1, 2 or 3 marks could be an extension task. Possible exam questions, in addition to those in Warm-up question 4, are: [2 marks grade C] [2 marks grade B]

  11. Situation – Answers for Thinking harder 1. 2. 3. 4.

  12. Click on the question to reveal the solution Situation – Answers for Some more to try 1. 64 27 Arrange these 4 numbers to make a true statement. 2. Unit fractions are fractions with a numerator of 1. The Egyptians used to write non unit fractions as the sum of unit fractions. For example Write as the sum of unit fractions. 3. • Which of the above have recurring decimal equivalents? • Which of the above have integer reciprocals?

  13. Situation – Prompts Think of a really obvious question Think of a really easy question Think of a really boring question Think of a really short question Think of a really hard question Think of a really strange question

  14. Situation – Thinking prompts Could I make a question with fractions in it? Is there a question that would involve the number 90? Is there a question that would mean adding some of the numbers? Is there a question that would mean dividing? Could I make a question with an answer less than 1? Could I make a question worth 2 marks? Could I make a question worth 5 marks? Is there a question that would involve multiplication?

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