Surds – Thursday 26th September 2013

Today’s Lesson Objectives:

To be able to demonstrate that I can rationalise surds

To be able to recognise square numbers and apply rules of surds

Copy the date, title and LO. Ensure that your literacy is correct!

Register Challenge: Tell me one thing that you have learnt this term.

Starter: Look through your book carefully. 1) Add targets from all of your homework's.2) Make sure that you have copied my target into the back of your book.3) Look at all of my green comments and mark them with a red pen to ensure that I know that you have read them.Extension: can you complete the timetable grid?

Mark in red, total results, results at the back of your book

– with a target!

Grade Objective

A* · Rationalise the denominator, and e.g. write (√18 +10) ¸ √2 in the form p + q√2

A* · Write surds as multiples of irrational numbers . √8 in the form 2√2

A*· Give the final answer to an appropriate degree of accuracy following an analysis of the upper and lower bounds of a calculation

A · Calculate with positive, negative and fractional indices and combinations of these.

A · Use index laws to write expressions for integer, negative, and fractional powers and powers of a power

A· Use index laws to simplify and calculate numerical expressions involving powers, eg (2³ x 2⁵) ÷ 2⁴, 4⁰, 8^–2/3

B · Be able to write very large and very small numbers presented in a context in standard form

B · Calculate with standard form with and without a calculator.

B · Use calculators to explore exponential growth and decay

C · Find the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) of two numbers

C · Convert between ordinary and standard form representations

C

· Understand ‘reciprocal’ as multiplicative inverse, knowing that any non-zero number multiplied by its reciprocal is 1 . Find the reciprocal of a number given as a fraction or decimal

C · Use index laws to calculate with squares and cubes

C

· Use index laws to simplify and calculate the value of numerical expressions involving multiplication and division of integer powers, and powers of a power

D · Check calculations by rounding, eg 29 ´ 31 » 30 ´ 30

D · Be able to find the square, square root, cube and cube root of any number with or without a calculator as appropriate

D · Find the prime factor decomposition of positive integers and write in index form

D · Know the effects that a change of place value has on a calculation. E.g. 13.5 / 0.5 = 135 / 5

D · Multiply and divide by any number between 0 and 1

D· Multiply and divide decimal numbers by whole numbers and decimal numbers (up to 2 d.p.), eg 266.22 ¸ 0.34

D · Use brackets and the hierarchy of operations (BIDMAS)

D · Use index notation for integer powers of 10

The Big Quiz:

Could you tackle these?

Why Surds? Learning Outcomes

I can rationalise surds using multiplication and division rules and square

number knowledge

I can expand surds and simplify the resulting

answer

Review

There are 2 basic identities:

• The first one:

The Second One:

• Note – There are no simple identities for adding and subtracting surds:

• in most cases, something like this can't be simplified!

Whiteboard Check:

Independence & Review

Simplifying Surds:

• To simplify a surd, you have to find the largest perfect square that divides x.

• Above, that was 36. • You then separate the two to get something of the

form. • Sometimes this isn't easy – • If you can't immediately find the largest factor,

then, it's a good idea to get rid of smaller factors to simplify the problem.

Copy these sums and attempt them independently

Independence

Copy these sums and attempt them independently

Independence

Copy these sums and attempt them independently

Independence

Peer assessmentPick a box from below to copy and complete in your partner’s

bookToday (name) has

done well at…

Next time (name) does this topic he/she needs to

make sure...

One thing (name) needs to do to improve is...

(Name) has met grade ... today

because…

Grade Objective

A* · Rationalise the denominator, and e.g. write (√18 +10) ¸ √2 in the form p + q√2

A* · Write surds as multiples of irrational numbers . √8 in the form 2√2

A*· Give the final answer to an appropriate degree of accuracy following an analysis of the upper and lower bounds of a calculation

A · Calculate with positive, negative and fractional indices and combinations of these.

A · Use index laws to write expressions for integer, negative, and fractional powers and powers of a power

A· Use index laws to simplify and calculate numerical expressions involving powers, eg (2³ x 2⁵) ÷ 2⁴, 4⁰, 8^–2/3

B · Be able to write very large and very small numbers presented in a context in standard form

B · Calculate with standard form with and without a calculator.

B · Use calculators to explore exponential growth and decay

C · Find the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) of two numbers

C · Convert between ordinary and standard form representations

C

· Understand ‘reciprocal’ as multiplicative inverse, knowing that any non-zero number multiplied by its reciprocal is 1 . Find the reciprocal of a number given as a fraction or decimal

C · Use index laws to calculate with squares and cubes

C

· Use index laws to simplify and calculate the value of numerical expressions involving multiplication and division of integer powers, and powers of a power

D · Check calculations by rounding, eg 29 ´ 31 » 30 ´ 30

D · Be able to find the square, square root, cube and cube root of any number with or without a calculator as appropriate

D · Find the prime factor decomposition of positive integers and write in index form

D · Know the effects that a change of place value has on a calculation. E.g. 13.5 / 0.5 = 135 / 5

D · Multiply and divide by any number between 0 and 1

D· Multiply and divide decimal numbers by whole numbers and decimal numbers (up to 2 d.p.), eg 266.22 ¸ 0.34

D · Use brackets and the hierarchy of operations (BIDMAS)

D · Use index notation for integer powers of 10

Resources