Monday 4th July – Rationalising – when there is a surd on the denominator of a fraction

Monday 4th July – Rationalising – when there is a surd on the denominator of a fraction

LEARNING OBJECTIVE: Discover a method for 'getting rid of' a denominator that includes a surd.

SUCCESS CRITERIA: You will be able to rationalise a surd, ensuring that there is no surd in the denominator

STARTER: Watch and Listen carefully to this video (NB You will have to logon to iRodillian to play this video) it last 9mins and 15 seconds

LESSON: Have a go at Question 6 & 7 on page 196 – Check answers as you complete each question from Page 614.

I any students are struggling with these try taking them through this PowerPoint.

PLENARY: Check answers to questions. Get some feedback on their confidence – students use five finger feedback with me – they hold fingers up to show their confidence – 0 fingers – can't do it, five fingers – easy peasy!!

 
 

  

Weds June 29th – Dealing with Surds when we have to expand brackets

LEARNING OBJECTIVE: Develop skills in manipulating and simplifying surds when we have brackets involved

SUCCESS CRITERIA: You will be able to expand a bracket containing at least one surd and then simplify the expression to its simplest form

STARTER

Find the value of a that makes each of these surd statements true

√5 x √a = 10	√6 x √ a =12
√10 x 2√a = 20	2√6 x 3√a = 72
2√a x √a = 6	3√a x 3√a = 54

 

LESSON: Work through this Mymaths Lesson up to the loop cards game.

Have a go at the questions in Ex 7K page 195 – don't give up straight away they are A* questions!!

PLENARY: Checking Answers around the room, then Have a go at question 7 on page 197

Tuesday 28th June- Simplifying Surds continues

LEARNING OBJECTIVE: To understand how you can split a number into a multiple of a square number to help simplify it in surd form

SUCCESS CRITERIA: You will be able to simply a surd

STARTER: Watch this Video on Simplifying Surds

LESSON: Have a go at Question 6 on page 193 of text book. Check your answers when completed before moving on to question 7 onwards

EXTENSION
QUESTIONS

PLENARY: Checking answers and five finger feedback on confidence.

Remind homework due to be completed by Thursday

  

Mon June 27th – More work on Simplifying surds

LEARNING OBJECTIVE: Using knowledge of square numbers, simplify surds

SUCCESS CRITRIA: You will be able to simplify a surd using your knowledge of square numbers and the rules of surds

SURDS RULES

√a x √b = √ab	√(a/b) = √a/√b
a√c +b√c = (a+b) √c	a√c - b√c = (a –b)√c

 
 

STARTER: Using the rules of surds simplify the following WITHOUT using your calculator

√3 x √2	√5 x √6	√3 x √12
√14 / √2	√25 / √5	5√2 - 3√2
6√3 + 2√3	7√8 + 3√8	3√3 + √12

 
 

LESSON: Work through Ex 7j page 192 of Higher H GCSE Text book for 30 mins

Use the following examples to show how to simplify surds using a knowledge of square numbers.

√72,    √162,    √250,    √162

Now have a go at Question 6 on page 193 – Check answers, if all OK continue with q7 onwards

EXTENSION
QUESTIONS

PLENARY: Checking answers and five finger feedback on confidence.

Remind homework due to be completed by Thursday

Thurs 23rd June - SURDS

LEARNING
OBJECTIVE: To discover what rational number is, what an irrational number is and what a surd is, and learn how to simplify surds

SUCCESS
CRITERIA: You will be able to explain the difference between an irrational number and an irrational number and understand what a surd is and how to simplify an expression including surds.

STARTER: Use your calculator to find the following

√1, √2, √3 , √4, √5, √6, √7, √8, √9, √10, √11, √12, √13, √14, √15, √16

Can you put the answers into two distinct groups and explain what those groups are: - Discussion about Rational and Irrational numbers.

LESSON: Irrational Numbers, Rational Numbers. Work through this MyMaths Lesson with Students giving time to answers question screens.

Work through these questions

Check answers with students

EXTENSION QUESTIONS

PLENARY: recap rules of surds with some examples on IWB to simplify

Weds June 22nd – Module 5 Maths – Reading Scales

LEARNING OBJECTIVE: Discover how to read and interpret scales

SUCCESS CRITERIA: You will be able to read and interpret the values from lots of different scales

STARTER: Use this interactive resource to get students reading information live from Different scales

Then use this Interactive Scales resources which is harder.

LESSON Work through Ex 17a page 361 & 362. DONT FORGET TO INCLUDE THE UNTIS IN YOUR ANSWERS

PLENARY: Checking answers, looking at interactive scales again to confirm understanding

Weds June 22nd – Fractions as Decimals

LEARNING OBJECTIVE: By converting fractions to decimals understand the difference between a terminating and a recurring decimal. Plus discover how to convert a Recurring Decimal back into a fraction

SUCCESS CRITERIA: You will understand the difference between terminating and recurring decimals and be able to convert a recurring decimal back into a fraction

KEYWORDS: Recurring Decimal, Terminating Decimal, a rational number

STARTER: Using your calculator convert these fractions into decimals

1/3 = 0.33333	2/5 = 0.4
2/11 = 0.181818...	3/13 = 0.230769230769231
5/6 = 0833333	7/8 = 0.875
5/12 = 0.4166666	7/15 = 0.466666

 
 

Which are recurring decimals, which are terminating decimals.

LESSON: How to convert a recurring decimal into a fraction: Work through this MyMaths Lesson Screens 1 to 5 ONLY

Have a go at these questions

PLENARY: Checking answers then answer this question

Put these fractions in order from smallest to largest just by looking at them DO NOT USE A CALCULATOR_ Use your instinct

4/7    7/20    1/12    3/11    7/80

Now check your answers by converting them to decimals using your calculators

Tues June 21st – Fractions Problems and Expressing one quantity as a fraction of another

LEARNING OBJECTVIE: To apply skills in Multiplying and dividing fractions to solve problems and Learn how to express one quantity as a fraction of another quantity

SUCCESS CRITERIA: You will be able to solve fractions problems involving multiplying, dividing and reciprocals and also be able to express one quantity as a fraction of another.

STARTER: You have 10/12 mins to solve these problems , Check answers with Students

8.		4 x 2/3 = 2 2/3
9.		3 x 2 ¾ = 6 9/4 = 8 ¼
10.		6 x 2 1/4 =12 6/4 = 13 ½
11.		6 ÷ 1 ¾ = 6 x 4 /7 = 24/7 = 3 3/7, 3 tops and 3/7 yards left
12.		a. 2 b. ½ c. 4 ÷ 2 ½ = 4 x 2/5 = 8/5 = 1 3/5 d. 6 x ¾ = 18/4 = 4 ½

   
 

LESSON: Show examples on IWB of how to express one quantity as a fraction of another

Eg. 35/40 in a test,

45 mins of an hour,

6 hours of a day

6 hours of a week

15 mm of a metre

45, 000 voters in a town of 80,000

REMEMBER: If values are in different units change the larger units to the smaller units

Work through these questions

PLENARY: Which is the bigger fraction 12 mins of one hour or 18 hours of 1 week, SHOW ALL YOUR WORKING

Thurs – June 16th – Multiplying and Dividing Fractions

LEARNING
OBJECTIVE: To revise Multiplication and Division of fractions and understand what is meant by the reciprocal of a number

SUCCESS
CRITERIA: YOU will be able to solve problems involving multiplication & division of fractions and understand and use the reciprocal of a number or fraction.

STARTER: Multiply Fractions Rap, Dividing Fractions hip-hop style

Have a go at these fractions sums:

4/5 x 3/7	3/8 X 4/11	2/3 ÷ 3/5
7/8 ÷ 3/7	3 ½ ÷ 2 ¼	12 ¾ ÷ 2 ⅖

LESSON: Use answers to above questions to revise methods for multiplication and division of fractions including mixed numbers

What is a reciprocal

Now Work through These Questions

Extension Questions

PLENARY:

Which is Bigger 2 ⅗ x 1½ or 2 ⅗ ÷ 1½

This is a test Blog

This is my Lesson

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Tuesday 14th June – nth term of Difficult Sequences

LEARNING OBJECTIVE: To discover how to find the nth term of difficult sequences

SUCCESS CRITERIA: You will be able to find the nth term of difficult sequences

LESSON:

Hand out the First Sequence Worksheets –Double Sided

Check Answers from Ans grid provided

If anyone finishes hand out the Second Sequences Worksheet (these are very difficult and they might need these hints)

HINTS:

• With a fractions sequence look at the sequence on the numerator and find the nth term and then the look at the answer is the sequence on the denominator.
  
• Remember any integer can be written as a fraction by using a denominator of 1
  

If anyone is really stuck or completes the work, use ex 25E on page 549 of higher text Book

PLENARY: Give students 5 minutes to check solutions with each other.

Weds June 15th – Adding and Subtracting Fractions

LEARNING OBJECTIVE: To revise methods of adding fractions and use them to solve fraction problems

SUCCESS CRITERIA: You will be able to solve fraction addition and subtraction problems

STARTER: Adding Fractions Song, now solve these problems

4/5 + ¾

4/5 – 3/4

5/8 + 1/3

5/8 – 1/3

 
 

LESSON: Use the answers to the above problems to revise fractions

Now have a go at these problems

PLENARY: Check all Answers then have a go at this problem:

3¾ -(1½ + ⅗)     

Mon June 13th The nth term of a sequence

KEYWORDS: sequence, term-to-term, nth term, linear sequence

Level D: write the terms of a sequence or a series of diagrams given the nth term

Level C: write the nth term of a linear sequence or a series of diagrams

LEARNING
OBJECTIVE: use the nth term and find the nth term of a linear sequence

SUCCESS
CRITERIA: Solve nth term problems

STARTER: Have a go at these two questions

Write down the first five terms of the sequence whose nth term is: n+3 n + ½ 5n – 3 n2 +3 n2-5 4n2 n/(n+11)

Aisha writes down the sequence 2, 6, 10, 14 She says the nth term is n + 4. Is she correct? Give a reason for your answer.

  
 

LESSON: Reminder on what the nth term means and how to find the nth term of a linear sequence. Use this lesson if needed (screens 4,5,6 & 7)

Work through these questions

PLENARY: Check Answers regularly throughout the lesson;

Have a go at these questions

 
 

  
 

  
 

   

Weds June 8th More HCF – LCM and Factor Trees

LEARNING OBJECTIVE: To use HCF, LCM, Prime Numbers in problems and be able to express a number as a product of its prime factors.

SUCCES CRITERIA: You will be able to solve HCF,LCM and Prime number problems and be able to express any number as a product of its prime factors

STARTER:

1. Write down all the prime numbers between 20 and 40
   
2. Which of these numbers are NOT prime numbers? Explain your answers
   
3. Two prime Numbers lie between 80 and 90. Find their sum and their difference
   

LESSON: Prime numbers and factor trees using index notation. LCM using VENN Diagrams

Complete all these questions (or continue if you started them yesterday)

Then complete these questions, Extension Questions

PLENARY:

1. Here are three numbers: 36 42 and 49. Give a reason why each number could be the odd one out.
   
2. Helen is training for a triathlon.
   

She plans to run every 2 days, swim every 4 days and cycle every 5 days. Today she ran swam and cycled.

How many days will it be before she next runs, swims and cycles on the same day?

Tuesday June 6th – LCM’s and HCF’s

LEARNING OBJECTIVE: To understand and solve LCM and HCF problems

SUCCESS CRITERIA: You will be able to solve LCM and HCF problems:

Level C	Find The LCM of two simple numbers Find the HCF of two simple numbers Write a number as a product of its prime factors
Level B	Find the LCM of two or more numbers Find the HCF of two or more numbers

STARTER:

1. Find the common factors of 42 and 70 and write down the Highest Common Factor
   
2. Find the LCM of the following sets of numbers
   
   1. 36, 45 and 54
      
   2. 14, 56 and 84
      
   3. 60, 75 and 90
      

LESSON: Remind students of what is meant by Lowest common Multiple and Highest Common Factor using questions above.

LCM Lesson, HCF Lesson if needed. Indian Method

Questions

1. The HCF of two numbers if 7. Give a possible pair of numbers
   
2. The HCF of three number is 15. Give a possible set of three numbers.
   
3. Find the LCM of the following sets of numbers
   
   1. 6 and 8
      
   2. 5 and 9
      
   3. 12 and 20
      
   4. 2, 3 and 5
      
   5. 6, 18 and 24
      
   6. 3,4 and 7
      
4. Tracy says that the LCM of 24 and 60 is 12. Is she correct? Explain your answer
   

More questions on Worksheet

PLENARY: Checking answers together, discussion on answers

June 7th 2011 – Your Maths Lesson Blog

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Mr Sp8