Compare fractions, decimals and percentages Grade 4 Compare fractions, decimals and percentages Compare quantities by calculating equivalent fractions, decimals and percentages If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl.org.uk

Lesson Plan Lesson Overview Progression of Learning Objective(s) Compare quantities by calculating equivalent fractions, decimals and percentages Grade 4 Prior Knowledge Number line Inequality signs Common F, D, P conversions Division Duration Allow at least 60 minutes for this lesson. Resources Print slides: 6, 10, 12, 16, 18, 24 Equipment Progression of Learning What are the students learning? How are the students learning? (Activities & Differentiation) Standard conversions fraction, decimal, percentage Show students slide 4 and 5. These conversions should be familiar and all students should be able to easily convert by memory or process. 5 Method for conversion between fraction, decimal and percentage Give students slide 6 printed. They need to complete the grid and make notes on the method for conversion. Using slides 7, 8 & 9 take one conversion at a time to review the method. Give students slide 10 printed to apply these conversion methods. 15 Method for conversion (more complex) between fraction, decimal and percentage Give students slide 12 printed. Using slides 13, 14, & 15 review how to do more complex conversions. This includes fraction to decimal where you cannot make an equivalent fraction with denominator 100 and need to use the method of division. Give students slide 16 printed – further practice Comparing numbers in contextualised problems Give students slide 18. Allow students to attempt the question on their own for 2 minutes. Review question together and model answer. Stress the importance of making a conclusion where asked to do so. Comparing numbers in OCR exam questions (from specimen papers) Give students slide 24. This is an exam questions related to objective. Students need to use notes from lesson to answer the questions. Ensure that all steps are shown. Relate to mark scheme. 10 Next Steps Assessment PLC/Reformed Specification/Target 4/Ratio, Proportion and Rates of Change/Comparing Fractions, Decimal and Percentages

Key Vocabulary Fractions Decimals Percentages

Fractions, decimals and percentages There are three different ways of writing exactly the same number; as a fraction, decimal or percentage. Here are some examples: 1 2 = 0.50 = 50% 1 4 = 0.25 = 25% 18 100 = 0.18 = 18%

Fractions, decimals and percentages Here are some common fractions, decimals and percentages you need to know Fraction Decimal Percentage 1 2 0.5 50% 1 4 0.25 25% 1 3 0.333333….. 0. 3 33. 3 % 3 4 0.75 75% 1 5 0.2 20% 1 10 0.1 10%

How to compare decimals, fractions and percentages 0.54 0.03 75% 8% 4 10 7 25 Student Sheet 1

How to compare decimals, fractions and percentages 54 100 27 50 54% 0.54 = out of 100 x 100 3_ 100 3% 0.03 out of 100 x 100

How to compare decimals, fractions and percentages 75% 75 100 3 4 0.75 = out of 100 ÷ 100 8% 8 100 2 25 0.08 = out of 100 ÷ 100

How to compare decimals, fractions and percentages 4 10 40 100 40% 0.4 = numerator ÷ 100 7 25 28 100 28% 0.28 = numerator ÷ 100

Compare decimals, fractions and percentages – Now you try … 1) Write 26% as fraction and decimal 0.56 as percentage and fraction in its simplest form 0.03 as percentage and fraction in its simplest form 2/5 as percentage and decimal 2) Order the following numbers, smallest first 0.23, ¼, 24% Student Sheet 2

Compare decimals, fractions and percentages – Now you try … 1) Write 26% as fraction and decimal 0.56 as percentage and fraction in its simplest form 0.03 as percentage and fraction in its simplest form 2/5 as percentage and decimal 2) Order the following numbers, smallest first 0.23, ¼, 24% 26/100 = 13/50 0.26 56% 56/100 = 14/25 3% 3/100 40% 0.4 0.23 0.24 0.25

Fractions, decimals and percentages Change the fractions into decimals: 1) 3 8 2) 5 6 Order the following numbers from lowest to highest: 40% 0.38 1 4 68% 0.3 1 8 Change the following decimals into fractions: 0.65 = 0.08 = 0.1 = 0.51 = Student Sheet 3

Fractions, decimals and percentages Change the following fractions into decimals: 1) 3 8 2) 5 6 Is the same as 3÷8 Is the same as 5÷6 3 is a recurring decimal =0.8 3 0 . 3 7 5 8) 3 .0 0 0 - 0 3 0 - 2 4 6 0 - 5 6 4 0 - 4 0 8x3=24 8x7=56 8x5=40 0 . 8 3 3….. 6) 5 .0 0 0 - 0 5 0 - 4 8 2 0 - 1 8 - 1 8 2 6x8=48 6x3=18

Fractions, decimals and percentages Change the following decimals into fractions: 0.65 = 0.08 = 0.1 = 0.51 = 𝟔𝟓 𝟏𝟎𝟎 𝟖 𝟏𝟎𝟎 𝟏𝟎 𝟏𝟎𝟎 𝟓𝟏 𝟏𝟎𝟎 = 𝟏𝟑 𝟓𝟎 = 𝟒 𝟓𝟎 = 𝟐 𝟐𝟓 = 𝟏 𝟏𝟎 The digits of the decimal make the numerator of a fraction Two decimal places make a fraction over one hundred which is the denominator. Fractions can then be simplified by dividing the numerator and denominator by the same factor

Fractions, decimals and percentages Order the following numbers from lowest to highest: 40% 0.38 1 4 68% 0.3 1 8 Convert all numbers in to decimals: 0.40 0.38 0.25 0.68 0.3 0 0.125 Now you can order the numbers from lowest to highest: 0.125 0.25 0.30 0.38 0.40 0.68

Fractions, decimals and percentages Convert 11 4 in to a decimal. Order the following numbers from lowest to highest: 0.18 28% 1 3 0.08 0.3 70% 1 10 Insert either of the following symbols to make each statement correct: =, ≠, <, >, ≤, ≥ – 8 + 4 6 (ii) 82% 82 100 (ii) 4 5 81% Order the following numbers from highest to lowest: -140 234 -130 187 120 -98 Convert the following fraction 4 9 into a decimal Student Sheet 4

Fractions, decimals and percentages Convert 11 4 in to a decimal. Order the following numbers from lowest to highest: 0.18 28% 1 3 0.08 0.3 70% 1 10 Insert either of the following symbols to make each statement correct: =, ≠, <, >, ≤, ≥ – 8 + 4 6 (ii) 82% 82 100 (ii) 4 5 81% Order the following numbers from highest to lowest: -140 234 -130 187 120 -98 Convert the following fraction 4 9 into a decimal =2.75 0.08 𝟏 𝟏𝟎 0.18 28% 0.3 𝟏 𝟑 70% < = < 234 187 120 -98 -130 -140 0.444 = 0. 4

Problem solving and reasoning In a quiz, competitors get 6 points for answering a question correctly and lose 5 points if they answer incorrectly. In the first round Sam answered all three questions correctly, his score was 18. In the same round Jay answered two questions correctly and one question incorrectly. What was his score? If Carl answered one question incorrect and two questions correctly. What is his score? Three students completed their end of term maths assessment. Amy scored 36 60 Tom answered 62% of his test correctly. Farah’s test score was equivalent to 0.58. Out of the three students who achieved the highest score? Circle each card that shows more than a half. 𝟔 𝟖 𝟑𝟔% 𝟑 4 0.34 0.55 𝟑 𝟔 𝟕𝟎% Celine has £48 to spend on food and clothes. She wants to spend more on food. Should she spend 3/8 or 0.4 of her money on food? Ben, Jake and Rachel have solved a problem. Ben’s answer is 0.33, Jake’s answer is 1/3 and Rachel’s answer is 6/20. The correct answer is 0.29. Whose answer is closest to the correct answer? Student Sheet 5

Problem solving and reasoning In a quiz, competitors get 6 points for answering a question correctly and lose 5 points if they answer incorrectly. In the first round Sam answered all three questions correctly, his score was 18. In the same round Jay answered two questions correctly and one question incorrectly. What was his score? If Carl answered one question incorrect and two questions correctly. What is his score? As Jay answered 2 questions correctly he gets 6 points for every correct answer 6 + 6 =12 He then answers one questions incorrectly, so 5 points must be deducted 12 – 5 = 7 Jay has a total score of 7 As Carl answered 2 questions incorrectly he has to deduct five for each incorrect answer -5 - 5 points = - 10 . He answered one question correctly which is 6 points -10 + 6 = - 4 Carl has a total score of -4

Problem solving and reasoning Three students completed their end of term maths assessment. Amy scored 36 60 Tom answered 62% of his test correctly. Farah’s test score was equivalent to 0.58. Out of the three students who achieved the highest score? In order to compare their test results all numbers need to be converted into percentages. Amy’s result 36 60 = 6 10 = 60 100 = 60% ÷6 x10 Farah’s result 0.58 = 58% Tom achieved the highest percentage of 62% therefore he achieved the highest result.

Problem solving and reasoning Circle each card that shows more than a half. 𝟔 𝟖 𝟑𝟔% 𝟑 4 0.34 0.55 𝟑 𝟔 𝟕𝟎% More than a half is any value which is greater than 0.50 Which decimal values are greater than 0.50? Start by changing fractions and percentages into decimals. 36% = 0.36 70% = 0.70 𝟔 𝟖 = 𝟑 𝟒 = 0.75 𝟑 𝟔 = 0.50

Problem Solving and Reasoning Celine has £48 to spend on food and clothes. She wants to spend more on food. Should she spend 3/8 or 0.4 of her money on food? If she spends 3/8 on food => 3/8 x £48 = £18 If she spends 0.4 on food => 0.4 x £48 = £19.20 She should spend 0.4 of her money on food

Problem Solving and Reasoning Ben, Jake and Rachel have solved a problem. Ben’s answer is 0.33, Jake’s answer is 1/3 and Rachel’s answer is 6/20. The correct answer is 0.29. Whose answer is closest to the correct answer? Ben => 0.33 Jake => 1/3 = 0.3333333333… Rachel => 6/20 = 3/10 = 0.3 0.29 < 0.3 < 0.33 < 0.33333333…. Rachel’s answer is closest.

Exam Question – Specimen Papers Student Sheet 6

Exam Question – Specimen Papers