1. Integers BAA* Content covered Situation Some more to try Reflection Test yourself cards Thinking harder What are the possibilities? Warm up Choose the activity(ies) that best suit your students’ learning needs. A short activity to get students thinking about the information in a question – ideal for the beginning of the lesson Four questions to encourage students to think about alternative questions using the same information Four questions to encourage students to use higher order thinking skills to consider question alternatives Three more questions to practise the same approach in different contexts An opportunity for students to assess and reflect on their progress, including the grade they are working at Key points which can be printed and used at home or in pairs in the classroom

2. Integers BAA* Reflection Situation – Content covered AIntegersUnderstand and use negative indices AIntegersUnderstand and use fractional indices AIntegersUnderstand and use surds A*IntegersRationalise the denominator of a surd A*IntegersSolve problems involving surds

3. Integers BAA* Answers Situation – Warm up √2√3√53√22√32√25√23√5 8  8  27  27  16  16  9  (9  )³ 1.Evaluate 8  2.√50 can be simplified to one of the expressions in the box above. Which one? 3.The product of two of the expressions in the box above is 15. Which two? 4.Make up a simple question using the expressions in the box above.

4. Integers BAA* Prompts Thinking prompts Thinking prompts Answers Situation – What are the possibilities? √2√3√53√22√32√25√23√5 8  8  27  27  16  16  9  (9  )³ 1.What integers can you make from these expressions? 2.Simplify fully (√5 − √3)(√5 + √3) (4 marks) √2 3.Make up a mark scheme for this question. 4.Write your own exam-style 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 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.

5. Integers BAA* Situation – Thinking harder Answers √2√3√53√22√32√25√23√5 8  8  27  27  16  16  9  (9  )³ 1.Which three expressions multiply to give an answer of 48? 2.How else could you write 3  and (3  ) 3 3.Arrange all 16 expressions in order of size without using a calculator. 4.What would be the value of 16 -  and 8 -  ?

6. Integers BAA* Answers Situation – Some more to try 1. (√3 + √7) (3√7 – 2√3)(2√7 + 5√3)(4√3 – 5√7) Simplify fully (√3 + √7)(3√7 – 2√3) 3. √50 √8 √32 √200 2. 8 −  16 −  9 −  27 −  Add these 4 expressions, simplifying fully. Which of these is the largest?

7. Integers BAA* Situation – Reflection 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. 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. A A A* A Click below the button to reveal the grades. I can  Understand and use negative indices Understand and use fractional indices Understand and use surds Rationalise the denominator of a surd Solve problems involving surds

8. Integers BAA* These cards contain some of the key terms and skills you will need to answer questions involving surds and indices. Copy down the ones you need or ask your teacher for a printout. These cards contain some of the key terms and skills you will need to answer questions involving surds and indices. Copy down the ones you need or ask your teacher for a printout. What is a surd? What does a surd look like? A way of expressing exactly the square root of a non-square number It is the square root of a non-square number, e.g. √2 Calculate √2 × √2How do you rationalise a denominator? 2 Multiply both top and bottom of a fraction by a surd to make the denominator an integer. What do you do with a negative power?What does a fractional power mean? The reciprocal, e.g. 3 -2 = 1/3 2 A root, e.g. power of  means square root What order do you calculate the numerator and denominator of a power? What does a power of  mean? It doesn’t matter Power of  means cube root Situation – Test yourself cards

9. Integers BAA* Situation – Answers for Warm up 1.2.82842712… 2.5√2 3.3√5 and √5 4.Possible simple questions include: –Which two expressions add to give an answer of 8√2? [answer 3√2 and 5√2] –Which two expressions multiply to give an answer of 8? [answer 8  and 8  ] –Which expression is equal to 8? [answer 16  ] –Which expression has the smallest value? [answer √2]

10. Integers BAA* Situation – Answers for What are the possibilities? 1.Using the expressions in the box some possible integers include: 6 = √2 × 3√2 81 = (9  )³ × 27  120 = 16  × 3√5 × √5 2. and 3. (√5 − √3)(√5 + √3) = √5√5 + √5√3 − √3√5 − √3√31 mark = 5 + √15 − √15 − 3 1 mark = 21 mark 2/√2 = √21 mark 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: –Simplify fully √2(√3 + 3√5) [2 marks, grade A] –Rationalise the denominator of [4 marks, grade A*] –Evaluate 27  [2 marks, grade A]

11. Integers BAA* Situation – Answers for Thinking harder 1.16 , √3 and 2√3 2.√3 and 3√3 3.√2, √3, 16  = 8 , √5, 2√2, 27  = 9 , 2√3, 8 , 3√2, 3√5, 5√2, 16 , 27 , (9  )³ 4. , 

12. Integers BAA* 1. (√3 + √7) (3√7 – 2√3)(2√7 + 5√3)(4√3 – 5√7) Simplify fully (√3 + √7)(3√7 – 2√3) 3. √50 √8 √32 √200 2. 8 −  16 −  9 −  27 −  Add these 4 expressions, simplifying fully. Which of these is the largest? 15 + √21 16 −  21√2 Situation – Answers for Some more to try Click on the question to reveal the solution.

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

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