Transcript Chapter 1 - Whole Numbers

Whole Numbers
MNU 2-02a
MNU 2-03a
www.mathsrevision.com
Place Value
Scales
Addition and Subtraction
Multiplying & Dividing by 10,100,1000
Multiplying by a Single Digit
Dividing by a Single Digit
Multiplying & Dividing by 20, 300 etc..
Rounding to nearest 10,100,1000
Estimating Answers
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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MNU 2-02a
MNU 2-03a
1. 35 + 45
2. Calculate 10% of 1000
3. What is the name of
the shape will this net make.
4. Calculate the value of the
missing angle.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
34o
Whole Numbers
Place Value
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Learning Intention
1. We are learning the value
of a digit given its place in
a numbers.
Success Criteria
1. Understand the value of a
digit given it place in a
number.
2. Be able solve simply problems
involving place value.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Place Value
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MNU 2-02a
MNU 2-03a
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Place Value
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MNU 2-02a
MNU 2-03a
Place Value Sheet
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Place Value
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MNU 2-02a
MNU 2-03a
Now try
Exercise XX
Ch1 (page XX)
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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MNU 2-02a
MNU 2-03a
1. 19 + 32
2. Calculate 10% of 50
3. What is the name of
the shape will this net make.
4. 2 680
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Reading Scales
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Learning Intention
1. We are learning the value
of a digit given its place in
a numbers.
Success Criteria
1. Understand the value of a
digit given it place in a
number.
2. Be able solve simply problems
involving place value.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Liquid Volume
S4
Reading Scales
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How much liquid in the jug ?
Litres
Count the number of small divisions
2
1litre 5
= 1000ml
Each division is worth
1
1 litre ÷ 5 =
0
1000ml ÷ 5 =
200ml x 4 = 800ml
16-Jul-15
Compiled by Mr. Lafferty Maths Dept.
200ml
Liquid Volume
S4
Reading Scales
www.mathsrevision.com
How much liquid in the jug ?
Litres
2
1
0
Count the number of small divisions
1litre 5
= 1000ml
Each division is worth
1 litre ÷ 5 =
1000ml ÷ 5 =
200ml x 7 = 1400ml or 1.4 litres
16-Jul-15
Compiled by Mr. Lafferty Maths Dept.
200ml
Liquid Volume
S4
Reading Scales
How much liquid in the jug ?
www.mathsrevision.com
( Careful different scale)
Litres
2
1
Count the number of small divisions
1litre 4
= 1000ml
Each division is worth
1 litre ÷ 4 =
0
1000ml ÷ 4 =
250ml x 7 = 1750ml or 1.75 litres
16-Jul-15
Compiled by Mr. Lafferty Maths Dept.
250ml
Weight & Scales
S4
Reading Scales
Calculate the weight each arrow is pointing at?
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120g
0
100g
Count the number of small divisions
5
200g
300g
500g 400g
Each division is worth
280g
100 ÷ 5 = 20g
540g
16-Jul-15
Compiled by Mr. Lafferty Maths Dept.
Weight & Scales
S4
Reading Scales
Calculate the weight each arrow is pointing at?
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80g
0
Count the number of small divisions
200g
5
400g
Each division is worth
600g
1kg 800g
200 ÷ 5 = 40g
720g
1kg 20g
16-Jul-15
Compiled by Mr. Lafferty Maths Dept.
Whole Numbers
Reading Scales
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MNU 2-02a
MNU 2-03a
Reading Weights
Reading different scales
Scale Sheet
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Reading Scales
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MNU 2-02a
MNU 2-03a
Now try
Exercise XX
Ch1 (page XX)
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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MNU 2-02a
MNU 2-03a
1. 37 + 174
2. Calculate 10% of 80
3. What is the name of
the shape will this net make.
4. 4 520
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Addition and Subtraction
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Learning Intention
1. We are learning the
importance of layout when
doing addition and
subtraction.
16-Jul-15
Success Criteria
1. Using and understanding
layout for addition and
subtraction.
2. Be able to solve simple
problems involving addition
and subtraction.
Created by Mr. Lafferty Maths Dept.
www.mathsrevision.com
Are there any
Whole
Numbers
errors in these
MNU 2-02a
MNU 2-03a
sums. Addition and Subtraction
There are many reasons why pupils do not get
the correct answer to addition and subtraction sums.
23
+9
23
9
23 + 9
54 - 8
54
-8
8
-54
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Addition and Subtraction
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Proper layout
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Addition and Subtraction
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MNU 2-02a
MNU 2-03a
Now try
Exercise XX
Ch1 (page xx)
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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MNU 2-02a
MNU 2-03a
Make up your own
addition subtraction
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Created by Mr. Lafferty Maths Dept.
Whole Numbers
Multiply by 10, 100, 1000
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MNU 2-02a
MNU 2-03a
Learning Intention
1
16-Jul-15
We are learning how to
multiply and divide simple
whole numbers by 10, 100,
1000.
Success Criteria
1. Understand the simple rules
to multiply and divide simple
whole numbers.
2. Be able do simple calculations.
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Multiply by 10, 100, 1000
MNU 2-02a
MNU 2-03a
www.mathsrevision.com
For this section you need to know your tables
To multiply by 10, 100, 1000
To multiply by 10 simply add a zero to the number
To multiply by 100 simply add 2 zero’s to the number
To multiply by 1000 simply add 3 zero’s to the number
Example : Multiply 36 by 10, 100, 1000.
Guess
36 rule
x 10 = 360
for 1000
16-Jul-15
36 x 100 = 3600
Created by Mr. Lafferty Maths Dept.
36 x 1000 = 36000
Whole Numbers
Multiply by 10, 100, 1000
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Example : A box of crisps contain 48 packets.
How many in 100 boxes ?
48 x 100 = 4800
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Divide by 10, 100, 1000
MNU 2-02a
MNU 2-03a
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Try and
To Divide by 10, 100, 1000
write down
rule forTo divide by 10 remove a zero from the number
100, 1000
To divide by 100 remove 2 zero’s from the number
To divide by 1000 remove 3 zero’s from the number
Example : Divide 54000 by 10, 100, 1000.
54000÷ 10 = 5400
54000 ÷ 100 = 540
54000 ÷ 1000 = 54
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Divide by 10, 100, 1000
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Example : A box contains 1000 cups. How
many boxes are needed to hold 7000 ?
7000 ÷ 1000 = 7
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Units of Length
Converting Measurements
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MNU 2-11b
MNU2-11c
MTH 3-11b
×1000
Kilometres
(km)
×100
metres
(m)
1000
100
centimetres
(cm)
10
16-Jul-15
Created by Mr. Lafferty Maths Dept.
×10
millimetres
(mm)
Units of Length
Converting Measurements
MNU 2-11b
MNU2-11c
MTH 3-11b
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Examples
Convert 2m to cm :
2 x 100 = 200 cm
Convert 4km to m :
4 x 1000 = 4000 m
Convert 34cm to mm : 34 x 10 = 340 mm
Convert 50cm to m :
16-Jul-15
50 ÷ 100 = 0.5 m
Created by Mr. Lafferty Maths Dept.
Weight & Scales
S4
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Kilograms
16-Jul-15
x 1000
grams
2kg
2 x 1000
2000g
1.5kg
1.5 x 1000
1500g
grams
÷ 1000
Kilograms
3000g
3000 ÷ 1000
3kg
1500g
1500 ÷ 1000
1.5kg
Compiled by Mr. Lafferty Maths Dept.
Converting Weights
MNU 2-11b
MNU2-11c
MTH 3-11b
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Examples
Convert 4 kg to g :
4 x 1000 = 4000 g
Convert 9 kg to g :
9 x 1000 = 9000 g
Convert 2000 g to kg : 2000 ÷ 1000 = 2 kg
Convert 5000 g to kg : 5000 ÷ 1000 = 5 kg
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Multiply & Divide by 10, 100, 1000
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Now try
Exercise 3 & 4
Ch1 (page 13)
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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MNU 2-02a
MNU 2-03a
1. 39.7 - 22.3
2. Calculate 25% of 824
3. What is the name of
the shape will this net make.
4. Calculate the value of the
missing angle.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
34o
Whole Numbers
Multiplying by a single number
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Learning Intention
1
We are learning how to do
multiply by a single digit.
Success Criteria
1. Remember your tables.
2. Apply appropriate layout
and working for multiplying
by a single digit.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
www.mathsrevision.com
Are there any
Whole
Numbers
errors in these
MNU 2-02a
MNU 2-03a
sums. Addition and Subtraction
There are many reasons why pupils do not get
the correct answer to multiplication sums.
23
x9
16-Jul-15
23
9
Created by Mr. Lafferty Maths Dept.
23 x 9
Whole Numbers
Multiplying by a single number
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
To be able to multiply by a single digit you need to
know your tables.
Examples
16-Jul-15
746
3276
x2
1492
1
x8
26208
264
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Multiplying by a single number
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Example :
A palette holds 164 tins of paint.
How many tins in 8 palettes.
164
x8
1312
53
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Multiplying by a single number
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Now try Exercise 5
Ch1 (page 15)
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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MNU 2-02a
MNU 2-03a
1. 324 + 79
2. Calculate 10% of 200
3. What is the name of
the shape will this net make.
4. Calculate the value of the
missing angle.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
123o
Whole Numbers
Dividing by a single number
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Learning Intention
1
16-Jul-15
We are learning how to do
divide by a single digit.
Success Criteria
1.
Created by Mr. Lafferty Maths Dept.
Apply appropriate layout
and working for dividing by a
single digit.
www.mathsrevision.com
Are there any
Whole
Numbers
errors in these
MNU 2-02a
MNU 2-03a
sums. Addition and Subtraction
There are many reasons why pupils do not get
the correct answer to division sums.
586 ÷ 9
16-Jul-15
586 9
Created by Mr. Lafferty Maths Dept.
15 4
4 3
9 586
Whole Numbers
Dividing by a single number
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MNU 2-02a
MNU 2-03a
Use the following layout for dividing by a single digit.
Examples : 732 ÷ 8
950 ÷ 5
7 32
2 1
8 58 5 6
16-Jul-15
9 50
2
5 47 50
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Dividing by a single number
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MNU 2-02a
MNU 2-03a
Example :
A carton can hold 6 eggs.
How many cartons are needed
for 5436 eggs.
906
6 5436
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Dividing by a single number
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MNU 2-02a
MNU 2-03a
Example :
Copy and complete.
544
7 3808
1853
5 9265
1239
6 7434
652
8 5216
952
4 3808
2336
3 7008
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Dividing by a single number
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Now try Exercise 7
Ch1 (page 17)
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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MNU 2-02a
MNU 2-03a
1. 76 - 54
2. Calculate 75% of 400
3. What is the name of
the shape will this net make.
4. Calculate the value of the
missing angle.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
36o
Whole Numbers
Multiply or Divide by 20,300,4000
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Learning Intention
1
16-Jul-15
We are learning how to
divide by 20, 300, 4000
etc using our knowledge so
far.
Success Criteria
1. Understand the two step
process to multiply or
divide by 20, 300 etc…
2. Show all working.
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Multiply or Divide by 20,300,4000
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
By combining our knowledge so far of
“multiplying / dividing by 10, 100, 1000”
and
“multiplying / dividing by a single digit”
we can do harder calculations.
We use a TWO step process.
Example 1 : Calculate 20 x 52
20 can be written as 2 x 10 so we have : 2 x 10 x 52 =
Step 1 : 10 x 52 = 520
16-Jul-15
Step 2 : 2 x 520 = 1040
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Multiply or Divide by 20,300,4000
MNU 2-02a
MNU 2-03a
www.mathsrevision.com
Example 2 : Calculate 44 x 30
30 can be written as 10 x 3 so we have : 44 x 10 x 3 =
Step 1 : 44 x 10 = 440
Step 2 : 440 x 3 = 1320
Example 3 : Calculate 300 x 35
300 can be written as 3 x 100 so we have : 3 x 100 x 35 =
Step 1 : 100 x35 = 3500
16-Jul-15
Step 2 : 3500 x 3 =10500
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Multiply or Divide by 20,300,4000
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Example 4 : Calculate 16000 ÷ 200
Since 200 divide by 100 then divide by 2:
16000 ÷ 100 ÷ 2 =
Step 1 : 16000 ÷ 100 = 160
Step 2 : 160 ÷ 2 = 80
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Multiply or Divide by 20,300,4000
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Example 5 : Calculate 120000 ÷ 6000
Since 6000 divide by 1000 then divide by 6:
120000 ÷ 1000 ÷ 6 =
Step 1 : 120000 ÷ 1000 = 120
Step 2 : 120 ÷ 6 = 20
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Multiply or Divide by 20,300,4000
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Now try Exercise 8
Ch41 (page 19)
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
1. 39 x 2
2. Calculate 50% of 750
3. What is the name of
the shape will this net make.
4. Calculate the value of the
missing angle.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Rounding to nearest 10, 100 and 1000
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Learning Intention
1. We are learning to round
numbers to the nearest 10,
100 and 1000.
Success Criteria
1. Understand the rules for
rounding to the nearest
10, 100, 1000.
2. Apply rules to problems.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Rounding to nearest 10, 100 and 1000
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
To round to the nearest 10 : look at the units digit:
- If it is a 0, 1, 2, 3, 4
leave the 10’s digit as it is.
- If it is a 5, 6, 7, 8, 9
round the 10’s digit up by 1.
To round to the nearest 100 : look at the tens digit:
- If it is a 0, 1, 2, 3, 4
leave the 100’s digit as it is.
- If it is a 5, 6, 7, 8, 9
round the 100’s digit up by 1.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Rounding to nearest 10, 100 and 1000
MNU 2-02a
MNU 2-03a
www.mathsrevision.com
To round to the nearest 1000 : look at the hundreds digit:
- If it is a 0, 1, 2, 3, 4
leave the 1000’s digit as it is.
- If it is a 5, 6, 7, 8, 9
round the 1000’s digit up by 1.
Example : Round 3467 to the nearest 10, 100, 1000
The nearest 10
: 3467
The nearest 100 : 3467
- look at
The nearest 1000 :3467
- look at
16-Jul-15
3470
3500
the tens digit :
the hundreds digit:3000
- look at the units digit :
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Rounding to nearest 10, 100 and 1000
MNU 2-02a
MNU 2-03a
www.mathsrevision.com
Example : Round 18 565 to the nearest 10, 100, 1000
The nearest 10
: 18 565 - look at the units digit :18 570
The nearest 100 : 18 565 - look at the tens digit : 18 600
The nearest 1000 :18565 - look at the hundreds digit:19 000
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Rounding to nearest 10, 100 and 1000
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Now try Exercise 9
Ch1 (page 21)
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
1. 67 x 7
2. Calculate 20% of 400
3. What is the name of
the shape will this net make.
4. Calculate the value of the
missing angle.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
42o
Whole Numbers
Using Rounding to Estimate Answers
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Learning Intention
1. We are learning how
estimate answer by
rounding.
16-Jul-15
Success Criteria
1. Remember how to round
numbers to a whole
number.
2. Estimate the answer to a
difficult calculation using
easier whole numbers.
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Using Rounding to Estimate Answers
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
It is very important when solving problems that we have
a rough idea of the answer we are expecting.
Example :
Mentally estimate the answer to 42 x 49
Easiest way, is to round the two numbers first
40 x 50 = 400 x 5 = 2000
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Using Rounding to Estimate Answers
MNU 2-02a
MNU 2-03a
www.mathsrevision.com
Example :
Mentally estimate the answer to 104 x 19
Easiest way, is to round the two numbers first
100 x 20 = 1000 x 2 = 2000
Example :
Mentally estimate the answer to 878 ÷ 27
Easiest way, is to round the two numbers first
900 ÷ 30 = 90 ÷ 3 = 30
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Whole Numbers
Using Rounding to Estimate Answers
www.mathsrevision.com
MNU 2-02a
MNU 2-03a
Now try Exercise 10
Ch1 (page 22)
16-Jul-15
Created by Mr. Lafferty Maths Dept.