Understand and use standard form for very large and very small numbers Grade 4 Standard Form Understand and use standard form for very large and very small numbers 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) Understand and use standard form for very large and very small numbers Grade 4 Prior Knowledge Place value Index rules Duration Allow 60 minutes to cover this objective and to get sufficient student practice time. Resources Print slides: 4, 9, 12, 15, 19, 21 Equipment Calculator Progression of Learning What are the students learning? How are the students learning? (Activities & Differentiation) How to write numbers in standard form Give students slide 4 printed. Show how to convert big numbers into standard form using slide 5. Students to then practice 5 conversions. Show how to convert small numbers into standard form using slide 7. Students to then practice 5 conversions. 10 How to multiply when numbers in standard form Give students slide 9 printed. Demonstrate method using slide 10. Students then complete independent practice. How to divide when numbers in standard form Give students slide 12 printed. Demonstrate method using slide 13. Students then complete independent practice. 5 How to add / subtract when numbers in standard form Give students slide 15 printed. Demonstrate method using slide 16. Explain how the method changes when powers are not the same - easier to convert to normal numbers and then back to standard form at the end of the calculation. Students then complete independent practice. 15 Using standard form in contextualised problems Give students slide 19 printed. Students to attempt independently. Collectively review the answers on slide 20. Understand and use standard form for very large and very small numbers in OCR exam questions (from specimen papers) Give students slide 21. 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 to show how the marks are allocated. Next Steps Assessment PLC/Reformed Specification/Target 4/Number/Standard Form

Key Vocabulary Power Index notation Standard index form Scientific notation

Writing Numbers in Standard Form 700000 91000 3230000 4580000 12140000 3000000 0.0000023 0.000035 0.0025 0.00000006 0.00000789 0.00000000124 Student Sheet 1

How to write big numbers in standard form To write in standard form we must have a number between 1 and 10 x 10 to the power of a number Move the point to get a number between 1 and 10 The index number should represent the number of spaces we moved the decimal point 3 000000 . . = 3 x 10 6 Write the decimal point at the end first (it will be moved) This number should be between 1 and 10

Now you try writing numbers in standard form Write the following numbers in standard form 700000 91000 3230000 4580000 12140000 7 x 10⁵ 9.1 x 10⁴ 3.23 x 10⁶ 4.58 x 10⁶ 1.214 x 10⁷

How to write small numbers in standard form Write 0.0000023 in standard form. We use a negative power when converting small numbers to SF Move the point to get a number between 1 and 10 and count the jumps back to the original decimal place The index number should represent the number of jumps from new decimal place to original decimal place . 0.0000023 = 2.3 x 10 ¯6 This number should be between 1 and 10

Now you try writing small numbers in standard form 0.000035 0.0025 0.00000006 0.00000789 0.00000000124 3.5 x 10 ¯⁵ 2.5 x 10 ¯³ 6 x 10 ¯⁸ 7.89 x 10 ¯⁶ 1.24 x 10 ¯⁹

Multiply in Standard Form DEMO PRACTICE (4 x 108) x (5 x 10⁴) (3x 102) x (7 x 105) (9 x 10⁹) x (3 x 10-5) (6 x 10⁴) x (3 x 102) (4 x 10) x (3 x 10⁴) Student Sheet 2

How to multiply using standard form Remember the rules for multiplying indices (4 x 108) x (5 x 10⁴) 4 x 108 x 5 x 104 Multiply Numbers Multiply Powers of 10 4 x 5 x 108 x 104 ADD powers = 20 x 1012 ÷10 x10 NOT Standard Form = 2.0 x 1013

Now you try multiplying using standard form (3x 102) x (7 x 105) (9 x 10⁹) x (3 x 10-5) (6 x 10⁴) x (3 x 102) (4 x 10) x (3 x 10⁴) 2.1 x 10⁸ 2.7 x 10⁵ 1.8 x 10⁷ 1.2 x 106

Divide in Standard Form DEMO PRACTICE (44 x 108) ÷ (4 x 10⁴) (45x10⁷)÷(9x 10²) (36x10⁵)÷(4x 10⁹) (33x10⁷⁸)÷(11x 10⁹) (60x10²)÷(6x 10⁹) Student Sheet 3

How to divide using standard form (44 x 108) ÷ (4 x 10⁴) Divide numbers Divide Powers of 10 44 ÷4 108 ÷ 104 subtract powers = 11 x 10⁴ x10 ÷10 NOT Standard Form = 1.1 x 10⁵

Now you try dividing using standard form 5 x 10⁵ (45x10⁷)÷(9x 10²) (36x10⁵)÷(4x 10⁹) (33x10⁷⁸)÷(11x 10⁹) (60x10²)÷(6x 10⁹) 9 x 10¯⁴ 3 x 10⁶⁹ 1 x 10¯6

Add / Subtract in Standard Form DEMO PRACTICE (5 x 104) + (3 x 10⁴) (2.53 × 10 ⁹) + (7.61 × 10⁸) (2.86 × 10³) + (7.55 × 10⁶) (2.24 × 10²) + (9.92 × 10²) (1.35 × 10 ¯⁸) + (6.82 × 10 ¯⁸) (1.53 × 10¯³) - (2.41 × 10¯⁴) (8.22 × 10 ¯⁴) - (8.33 × 10 ¯⁵) (2.75 × 10 ¯⁴) - (4.89 × 10 ¯⁷) (4 x 109) - (3 x 105) Student Sheet 4

How to add/ subtract using standard form 5 x 10⁴ If the powers are the same you can just add the big numbers and keep the powers the same! + 3 x 10 ⁴ _______________ 8 x 10 ⁴ If the exponents are not the same convert the numbers to whole numbers and then add / subtract 4 x 10⁹ _______________ - 3 x 105 4000000000 = 3.9997 x 10⁹ - 300000 _______________ 3999700000

Now you try adding/ subtracting using standard form (2.53 × 10 ⁹ ) + (7.61 × 10⁸ ) (2.86 × 10³ ) + (7.55 × 10⁶ ) (2.24 × 10² ) + (9.92 × 10² ) (1.35 × 10 ¯⁸ ) + (6.82 × 10 ¯⁸ ) (1.53 × 10¯³ ) - (2.41 × 10¯⁴ ) (8.22 × 10 ¯⁴ ) - (8.33 × 10 ¯⁵ ) (2.75 × 10 ¯⁴ ) - (4.89 × 10 ¯⁷ )

Now you try adding/ subtracting using standard form (2.53 × 10 ⁹ ) + (7.61 × 10⁸ ) (2.86 × 10³ ) + (7.55 × 10⁶ ) (2.24 × 10² ) + (9.92 × 10² ) (1.35 × 10 ¯⁸ ) + (6.82 × 10 ¯⁸ ) 3.291 × 10⁹ 7.552860 × 10⁶ 1.216 x 103 8.17 × 10 ¯⁸ (1.53 × 10¯³ ) - (2.41 × 10¯⁴ ) (8.22 × 10 ¯⁴ ) - (8.33 × 10 ¯⁵ ) (2.75 × 10 ¯⁴ ) - (4.89 × 10 ¯⁷ ) 1.289 × 10¯³ 7.387 × 10 ¯⁴ 2.74511 × 10 ¯⁴

Contextualised Problems Q1: Dinosaurs lived between 65 million years ago, in a time known as the Mesozoic Era. Write this in standard form. Q2: Light travels at a constant, finite speed of 186,000 miles per second. Using standard form multiply this by (1.3 x 10⁵). Q3: A super rocket is going to travel from Earth to Jupiter and then to the Kuiper Belt. If the distance from earth to Jupiter is 2.9x1010m and from Jupiter to the Kuiper Belt is 9.9 x 109m. What is the total distance it will travel? If its speed is 100m/s how long will the journey take? Student Sheet 5

Problem Solving and Reasoning Dinosaurs lived between 65 million years ago, in a time known as the Mesozoic Era. Write this in standard form. 6.5 x 107 Light travels at a constant, finite speed of 186,000 miles per second. Using standard form multiply this by (1.3 x 10⁵). 2.418 x 1010 A super rocket is going to travel from Earth to Jupiter and then to the Kuiper Belt. If the distance from earth to Jupiter is 2.9x1010m and from Jupiter to the Kuiper Belt is 9.9 x 109m What is the total distance it will travel? 3.89 x 1010 If its speed is 100m/s how long will the journey take? 3.89 x 10⁸ seconds

Exam Questions – Specimen Papers Student Sheet 6

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers