Mathematics: Simplifying Ratios and Mathematical Anagrams

1. Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Real life cross/curricular links? Where are we in our journey? Which ones are you using? PLT Skills LESSON OBJECTIVES Always aim high! We are learning to: • Finding connections between different words. (Which PLT skills?) • Accurately write ratios in their simplest form. (Grades E-C) AUTHOR www.mistrymaths.co.uk

2. Which ones are you using? BRAIN IN GEAR Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills EXAMPLE DITDIONA can be rearranged to make ADDITION TASK Work out the following Mathematical anagrams: Odd Multiply Prime EXTENSION Develop your own Mathematical anagrams as above as a creative thinker.

3. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager STARTER PLT Skills TASK 2 3 ÷ Write as a single power: 8 ÷ 8 Write as a single power: 5 x 5 Find: 10% of £71 1) 2) 4) 3) 4 5 3 7 2 8 Write 0.4 as a percentage Find 80% of 30m 5) 6) 7) of £120 2 2 2 3t + 18t = 4t + 16t = t + 34t EXTENSION 5 6 Expand and simplify: 4t(t + 4) – 3t(t – 6) -

4. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills Simplifying Ratio : means ‘to’ in Mathematics EXAMPLES Express the following ratios in their simplest form: 15kg : 20kg 20p : £1 3 : 6 (c) (a) (b) ÷5 ÷5 ÷3 ÷3 3kg : 4kg 1 : 2 20p : 100p ÷20 ÷20 1p : 5p (d) A room is divided into a kitchen and dining area in the ratio 5:2. What fraction is the (i) kitchen and (ii) dining area? (e) 5 2 (i) (i) Kitchen = Dining area = Ratio of orange : green? 7 7 8 : 10 ÷2 ÷2 4 : 5

5. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills Simplifying Ratio EXTENSION (GRADE C) TASK 1 (GRADE E) TASK 2 (GRADE E) Write each of the following ratios of quantities in its simplest form. a)£5 to £15 b)£24 to £16 c)125g to 300g d)40 minutes: 5 minutes e) 34 kg to 30 kg f) £2.50 to 70p g)3 kg to 750 g h) 50 minutes to 1 hour i)1 hour to 1 day j)12 cm to 2.5 mm k)1.25 kg : 500 g l)75p : £3.50m) 4 weeks : 14 days 1) June wins three-quarters of her bowls matches. She loses the rest. What is the ratio of wins to losses? 2)Three brothers share some cash. The ratio of Mark’s and David’s share is 1 : 2 The ratio of David’s and Paul’s share is 1 : 2 What is the ratio of Mark’s share to Paul’s share? Express each of the following ratios in its simplest form. a) 6 : 18 b) 15 : 20 c) 16 : 24 d) 24 : 36 e) 20 to 50 f) 12 to 30 g) 25 to 40 h) 125 to 30 i)15 : 10 j)32 : 12 k)28 to 12 l)100 to 40m)0.5 to 3 n)1.5 to 4 o)2.5 to 1.5 p)3.2 to 4 TASK 3 (GRADE D) 1) A length of wood is cut into two pieces in the ratio 3 : 7. What fraction of the original length is the longer piece? 2) Jack and Thomas find a bag of marbles that they share between them in the ratio of their ages. Jack is 10 years old and Thomas is 15 years old. What fraction of the marbles did Jack get? 3) Dave and Sue share a pizza in the ratio 2 : 3. They eat it all. a) What fraction of the pizza did Dave eat? b) What fraction of the pizza did Sue eat? 4) The recipe for a pudding is 125 g of sugar, 150 g of flour, 100 g of margarine and 175 g of fruit. What fraction of the pudding is each ingredient?

6. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills Simplifying Ratio MINI-PLENARY 1) Work out the ratio of colours below in their simplest form. Blue : Green : Pink 6 : 2 : 4 3 : 1 : 2 2) The mixture of red paint to blue paint is 4:6. Write each part as a fraction. 6 4 Blue = Red = 10 10 2 3 Blue = Red = 5 5

7. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager • LINK BACK TO OBJECTIVES • Accurately write ratios in their simplest form. What grade are we working at? DISCOVERY PLT Skills

8. PLENARY ACTIVITY The ratio 8:10 Simplifies to 4:5 TRUE FALSE Stand Up Remain Seated

9. PLENARY ACTIVITY The ratio 50p:£1 Simplifies to 50:1 TRUE FALSE Stand Up Remain Seated

10. PLENARY ACTIVITY The ratio 3:2 Can be written as and 3 2 2 3 TRUE FALSE Stand Up Remain Seated

11. What grade are we working at? Where are we in our journey? What have you learnt? Draw your brain In your brain, write or draw everything you can remember about writing ratios in their simplest form. It can be a skill or a reflection, or something else that might be prominent in your brain.

12. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? Plenary Activity How well do you understand the task? . I fully understand I don’t understand I nearly understand www.mistrymaths.co.uk

13. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? Plenary Activity WWW (What Went Well) EBI (Even Better If) On your post it notes… Think about how you can improve your work. www.mistrymaths.co.uk