Integers BAA*

Content coveredContent covered

Situation

Some more to trySome more to try

ReflectionReflection

Test yourself cardsTest yourself cards

Thinking harderThinking harder

What are the possibilities?What are the possibilities?

Warm upWarm 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

Integers BAA*

ReflectionReflection

Situation – Content covered

AIntegers

Understand and use negative indices

AIntegers

Understand and use fractional indices

AIntegers

Understand and use surds

A*Integers

Rationalise the denominator of a surd

A*Integers

Solve problems involving surds

Integers BAA*

AnswersAnswers

Situation – Warm up

√2 √3 √5 3√2 2√3 2√2 5√2 3√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.

Integers BAA*

PromptsPrompts Thinking promptsThinking prompts

AnswersAnswers

Situation – What are the possibilities?

√2 √3 √5 3√2 2√3 2√2 5√2 3√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 3Three 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 4Use 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.

Integers BAA*

Situation – Thinking harder

AnswersAnswers

√2 √3 √5 3√2 2√3 2√2 5√2 3√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- ?

Integers BAA*

AnswersAnswersSituation – 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?

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

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

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?

2Multiply 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 = 1/32 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

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]

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√3 1

mark= 5 + √15 − √15 − 3 1 mark= 2 1 mark

2/√2 = √2 1 mark4. 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]

5 2

3 2

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. ,

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.

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…

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?