1. 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
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2. 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

3. Key Vocabulary Power Index notation Standard index form
Scientific notation

4. Writing Numbers in Standard Form
700000
91000
Student Sheet 1

5. 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 x 10 6
Write the
decimal point at the end first (it will be moved)
This number should be between 1 and 10

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

7. How to write small numbers in standard form
Write 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 .
= 2.3 x 10 ¯6
This number should be between 1 and 10

8. Now you try writing small numbers in standard form
3.5 x 10 ¯⁵
2.5 x 10 ¯³
6 x 10 ¯⁸
7.89 x 10 ¯⁶
1.24 x 10 ¯⁹

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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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
= x 10⁹
_______________

17. 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 )

18. 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
× 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
× 10 ¯⁴

19. 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

20. 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

21. Exam Questions – Specimen Papers
Student Sheet 6

22. Exam Questions – Specimen Papers

23. Exam Questions – Specimen Papers

24. Exam Questions – Specimen Papers