Download Standard form

Grade 4
Standard Form
Understand and use standard form for very large and
very small numbers
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Lesson Plan
Lesson Overview
Objective(s)
Understand and use standard form for very large and very small numbers
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
Grade
Equipment
4
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.
10
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.
10
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.
10
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
3000000
700000
91000
3230000
4580000
12140000
0.0000023
0.000035
0.0025
0.00000006
0.00000789
Student Sheet 1
0.00000000124
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
3.000000 .
=
3 x 10 6
Write the
decimal point
at the end first
This number should
(it will be
be between 1 and 10
moved)
The index number
should represent
the number of
spaces we moved
the decimal point
Now you try writing numbers in
standard form
• Write the following numbers in standard form
7 x 10⁵
700000
9.1 x 10⁴
91000
3230000
3.23 x 10⁶
4.58 x 10⁶
4580000
1.214 x 10⁷
12140000
How to write small numbers in
standard form
Write 0.0000023 in standard form.
Move the point to get a
number between 1 and 10 and count the
jumps back to the original decimal place
6
.
=
2.3
x
10
¯
0.0000023
This number should
be between 1 and 10
We use a negative
power when
converting small
numbers to SF
The index number
should represent
the number of
jumps from new
decimal place to
original decimal
place
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
(4 x 108) x (5 x 10⁴)
PRACTICE
(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
Remember
form
the rules
for
multiplying
indices
Multiply Powers of 10
(4 x 108) x (5 x 10⁴)
4 x 108 x 5 x 104
Multiply Numbers
4x5
÷10
NOT
Standard
Form
= 20 x
x 108 x 104
ADD powers
1012
x10
= 2.0 x 1013
Now you try multiplying using
standard form
(3x 102) x (7 x 105)
2.1 x 10⁸
(9 x 10⁹) x (3 x 10-5)
2.7 x 10⁵
(6 x 10⁴) x (3 x 102)
1.8 x 10⁷
(4 x 10) x (3 x 10⁴)
1.2 x 106
Divide in Standard Form
DEMO
(44 x 108) ÷ (4 x 10⁴)
PRACTICE
(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
44 ÷4
= 11 x
NOT
Standard
Form
÷10
Divide Powers of 10
108 ÷ 104
10⁴
= 1.1 x 10⁵
subtract powers
x10
Now you try dividing using
standard form
(45x10⁷)÷(9x 10²) 5 x 10⁵
(36x10⁵)÷(4x 10⁹) 9 x 10¯⁴
(33x10⁷⁸)÷(11x 10⁹) 3 x 10⁶⁹
(60x10²)÷(6x 10⁹) 1 x 10¯6
Add / Subtract in Standard Form
DEMO
(5 x 104) + (3 x 10⁴)
PRACTICE
(2.53 × 10 ⁹) + (7.61 × 10⁸)
(1.53 × 10¯³) - (2.41 × 10¯⁴)
(2.86 × 10³) + (7.55 × 10⁶)
(8.22 × 10 ¯⁴) - (8.33 × 10 ¯⁵)
(2.24 × 10²) + (9.92 × 10²)
(2.75 × 10 ¯⁴) - (4.89 × 10 ¯⁷)
(4 x 109) - (3 x 105)
(1.35 × 10 ¯⁸) + (6.82 × 10 ¯⁸)
Student Sheet 4
How to add/ subtract using
standard form
If the powers are the same
5 x 10⁴
you can just add the big
⁴
+_______________
3 x 10
numbers and keep the
powers the same!
8 x 10 ⁴
If the exponents are not the same convert
the numbers to whole numbers and then
⁹
4 x 105
add / subtract
- 3 x 10
_______________
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 ) 3.291 × 10⁹
(2.86 × 10³ ) + (7.55 × 10⁶ ) 7.552860 × 10⁶
(2.24 × 10² ) + (9.92 × 10² ) 1.216 x 103
(1.35 × 10 ¯⁸ ) + (6.82 × 10 ¯⁸ ) 8.17 × 10 ¯⁸
(1.53 × 10¯³ ) - (2.41 × 10¯⁴ ) 1.289 × 10¯³
(8.22 × 10 ¯⁴ ) - (8.33 × 10 ¯⁵ ) 7.387 × 10 ¯⁴
(2.75 × 10 ¯⁴ ) - (4.89 × 10 ¯⁷ ) 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