Ordering numbers Grade 3 Compare and order positive and negative integers, decimals and fractions, including using the symbols =, ≠, <, >, ≤, ≥ 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 and order positive and negative integers, fractions, decimals and percentages, including using the symbols =, ≠, <, >, ≤, ≥ Grade 3 Prior Knowledge Number line Inequality signs Common F, D, P conversions Duration Allow at least 40 minutes for this lesson. Resources Print slides: 4, 6, 12, 14, 18 Equipment Progression of Learning What are the students learning? How are the students learning? (Activities & Differentiation) Ordering positive and negative integers Give students slide 4 printed. Students complete questions with the help of a the number line if needed. Encourage students to draw their own number line in exams if they think will help (especially with addition / subtraction questions). 5 Ordering numbers between 0 and 1. Show students slide 5 – comparison of fractions, decimals and percentages. Give students slide 6 printed. Students to attempt independently the various questions. Use slides 7 to 11 to review the solutions. Discuss which the standard conversions students should know but also how to convert so that they can apply to any number. Give students slide 12 – further practice. 15 Ordering integers and non integers in contextualised problems Give students slide 14. 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. 10 Ordering integers and non integers in OCR exam questions (from specimen papers) Give students slide 18. This includes 3 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. Next Steps Assessment PLC/Reformed Specification/Target 3/Number/Ordering numbers

Key vocabulary Ordering Positive Negative Decimal Fraction Integer More than Less than

Positive & Negative Integers Order the following numbers from highest to lowest: -4 2 0 -3 7 -1 6 Order the following numbers from highest to lowest: -8 21 13 -1 -32 17 Insert either of the following symbols to make each statement correct: =, ≠, <, >, ≤, ≥ 5 3 -2 6 2 -1 7 -7 Student Sheet 1

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 0.5 50% 25% 1 3 33. 3 % 0.75 1 5 10% Change the following decimals into fractions: 0.65 = 0.08 = 0.1 = 0.51 = Order the following numbers from lowest to highest: 40% 0.38 1 4 68% 0.3 1 8 Change the fractions into decimals: 1) 3 8 2) 5 6 Insert either of the following symbols to make each statement correct: =, ≠, <, >, ≤, ≥ 0.75 3 4 4% 0.4 4-9 -1 2 5 0.39 Student Sheet 2

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%

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 Insert either of the following symbols to make each statement correct =, ≠, <, >, ≤, ≥ 0.75 3 4 4% 0.4 4-9 -1 2 5 0.39 Definitions of signs: = Equal to ≠ Not equal to < Less than > Greater than ≤ Less than or equal to ≥ Greater than or equal to 3 4 can be written as 75% which is the same as 0.75 = < 4% can be written as 4 100 = 0.04 0.4 is the same as 0.40 < 4 - 9 = -5 > 2 5 = 20 50 = 40 100 =0.40

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 3

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% Student Sheet 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 two questions incorrectly and one question 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 the same form- we will change them into a percentage. 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

Exam Questions – Specimen Papers Student Sheet 5

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers Student Sheet 5

Exam Questions – Specimen Papers