|
Sums |
|
|
|
To use the resources of this chapter you must first register |
|
|
CONTENTS |
|
|
ITEM |
|
TYPE |
|
NUMBER |
|
| Working with sums |
|
Workout |
|
33 slides |
|
| Sums |
|
Library |
|
11 questions |
|
|
|
Once you have registered, you can work through the slides one by one.
The workout comprises a series of sides that guide you systematically through the topic concept by concept, skill by skill. The slides may be used with or without the support of a tutor. The methodology is based on problem-solving that advances in logical succession by concept and difficulty. The student is presented with a problem or series of questions, and the next slide presents the fully-worked solution. To use the material you must sign-in or create an account.
blacksacademy.net comprises a complete course in mathematics with resources that are comprehensive.
|
|
|
|
SAMPLE FROM THE WORKOUT |
| Showing American English version |
SLIDE 1 - QUESTION 1 |
 |
|
SLIDE 2 - SOLUTION |
 |
|
|
SAMPLE FROM THE LIBRARY |
| Showing American English version |
QUESTION [difficulty 0.1] |
 |
|
SOLUTION |
 |
|
|
DEPENDENCIES |
|
|
|
|
CONCEPTS |
|
|
|
|
LEV. |
|
|
Double digit sums in column form
|
|
344.1 |
|
|
Three digit sums in column form
|
|
344.1 |
|
|
Mental calculations - additions with number bonds
|
|
344.3 |
|
|
Counting on and carrying forward
|
|
344.5 |
|
|
Sums with carrying forward 1
|
|
344.6 |
|
|
Method: carrying a digit forward
|
|
344.8 |
|
|
Larger sums
|
|
344.9 |
|
|
Carrying forward digit larger than 1
|
|
344.9 |
|
|
Subtraction sums in column form
|
|
345.1 |
|
|
Method: borrow one and add one
|
|
345.3 |
|
|
Internalisation of thought processes - thinking aloud
|
|
345.3 |
|
|
Double sums and subtractions
|
|
345.6 |
|
|
Number puzzles with sums
|
|
345.8 |
|
|
Coins, monetary values
|
|
346.0 |
|
|
Bills, money calculations with decimal quantities
|
|
346.2 |
|
|
Pounds and pence, or dollars and cents ...
|
|
346.2 |
|
|
Money calculations and bills with multiple quantities
|
|
346.8 |
|
|
Larger bills
|
|
347.0 |
|
|
Word problems with money and bills
|
|
347.2 |
|
|
|
|
RAW CONTENT OF THE WORKOUT |
|
| To make use of this chapter, please first register. Then you can work through the slides one by one. |
|
| What is provided here is the raw text of the workout. Most of the information is contained in the image files, which are not included with this text. The text may appear deceptively short. (The content overall of blacksacademy.net is vast.) Any in-line questions appear as a question mark [?]. This text is provided only as an indication of the overall quantity of material contained in the chapter. To use the material you must sign-in or create an account. |
|
| * |
|
|
Working with sums
SLIDE 1
Example
Exercise
?
?
?
?
?
?
SLIDE 2
?
?
?
?
?
?
SLIDE 3
Fill in the missing numbers
? ?
? ?
SLIDE 4
? ?
? ?
SLIDE 5
When we add 7 to 8, we count on to the second row of the counting square
Therefore, when we add 7 and 8 in a column, we must carry forward the ten:
SLIDE 6
?
?
?
?
?
?
SLIDE 7
?
?
?
?
?
?
SLIDE 8
We keep a tally of what we are doing by carrying a digit.
Notes for tutors
The 1 that is carried forward is shown as a small 1 above the unit 3. This 1 is then added in the next column.
Another 1 is carried forward and added to the 5.
These marks must be included by the learner in a sum. The digit carried forward must not be placed anywhere on the page, but must be close to the final number, as in the example. These digits should be smaller than the digits in the final answer, so as not to be confused with them.
If the student is putting the little digits anywhere on the page, this indicates that he/she does not fully understand the sum.
SLIDE 9
?
?
?
?
?
?
SLIDE 10
SLIDE 11
Subtraction example
The minus to the right indicates that we are subtracting
Exercise
?
?
?
?
SLIDE 12
?
?
?
?
SLIDE 13
Example
Here we encounter a problem, because 8 is bigger than 2.
But we can subtract 8 from 12. Therefore, we take a ten from the top number and add a ten to the bottom number.
This is shown by adding marks to the sum.
We say, borrow one and add one.
Notes for tutors
The alternative method of knocking down the 5 to 4 in this example is not preferred here.
The student should be encouraged to say aloud, borrow one and add one as the sum is made, and then to say this internally.
Internalisation of thought processes, the ability to talk to oneself while problem-solving, is essential to effective problem-solving at all levels. Children in fact begin to learn speech not by talking to others, but by talking to themselves. Students should be encouraged to articulate their thought processes.
SLIDE 14
?
?
?
?
?
?
SLIDE 15
?
?
?
?
?
?
SLIDE 16
By making sums, find the following
?
?
?
?
?
?
?
?
?
?
SLIDE 17
?
?
?
?
?
?
?
?
?
?
SLIDE 18
Fill in the missing numbers
?
?
SLIDE 19
?
?
SLIDE 20
?
£
?
?
£
?
? £
?
? £
?
? £
?
SLIDE 21
?
£ 0.60
?
£ 0.08
? £ 0.63
? £ 0.33
? £ 0.32
SLIDE 20 B
?
$
?
?
$
?
? $
?
? $
?
? $
?
SLIDE 21 B
?
$ 0.75
?
$ 0.06
? $ 0.66
? $ 0.41
? $ 0.36
SLIDE 22
Complete the following bills by writing all sums in pounds and then finding the total.
? Potatoes £1.27
Carrots 95 pence
Onions 58 p
Beans One pound twenty-five pence
? Avocado 90 pence
Apples £1.15
Cucumber 85p
Tomatoes One pound five pence
SLIDE 22 B
Complete the following bills by writing all sums in dollars and then finding the total.
? Potatoes $1.27
Carrots 95 cents
Onions 58 ’
Beans One dollar twenty-five cents
? Avocado 90 cents
Apples $1.15
Cucumber 85’
Tomatoes One dollar five cents
SLIDE 23
? £
Potatoes 1.27
Carrots 0.95
Onions 0.58
Beans 1.25
Total 4.05
? £
Avocado 0.90
Apples 1.15
Cucumber 0.85
Tomatoes 1.05
Total 3.95
SLIDE 23 B
? $
Potatoes 1.27
Carrots 0.95
Onions 0.58
Beans 1.25
Total 4.05
? $
Avocado 0.90
Apples 1.15
Cucumber 0.85
Tomatoes 1.05
Total 3.95
SLIDE 24
Complete the following bills
? £
Magazine 1.20
Newspaper 1.53
Chocolate 0.75
Crisps 0.82
Total
? £
Bus journey 1.50
Train fare 8.95
Entrance fee 4.99
Coffee 1.18
Cake 2.69
Total
SLIDE 24 B
Complete the following bills
? $
Magazine 1.20
Newspaper 1.53
Chocolate 0.75
Crisps 0.82
Total
? $
Bus journey 1.50
Train fare 8.95
Entrance fee 4.99
Coffee 1.18
Cake 2.69
Total
SLIDE 25
? £
Magazine 1.20
Newspaper 1.53
Chocolate 0.75
Crisps 0.82
Total 4.30
? £
Bus journey 1.50
Train fare 8.95
Entrance fee 4.99
Coffee 1.18
Cake 2.69
Total 19.31
SLIDE 25 B
? $
Magazine 1.20
Newspaper 1.53
Chocolate 0.75
Crisps 0.82
Total 4.30
? $
Bus journey 1.50
Train fare 8.95
Entrance fee 4.99
Coffee 1.18
Cake 2.69
Total 19.31
SLIDE 26
? At a supermarket I bought a pint of milk for 49 pence, a loaf of bread for 90 pence and wedge of cheese for £1.75. What was my total bill?
? Find the cost of a milk shake at 88 pence, an ice cream at £1.15, a bag of peanuts at 0.75 pence and a fruit bar at £1.45.
SLIDE 27
? £
Milk 0.49
Bread 0.90
Cheese 1.75
Total 3.14
? £
Milk shake 0.88
Ice cream 1.15
Peanuts 0.75
Fruit bar 1.45
Total 4.23
SLIDE 26 B
? At a grocery store I bought a pint of milk for 49 cents, a loaf of bread for 90 cents and wedge of cheese for $1.75. What was my total bill?
? Find the cost of a milk shake at 88 cents, an ice cream at $1.15, a bag of peanuts at 0.75 cents and a fruit bar at $1.45.
SLIDE 27 B
? $
Milk 0.49
Bread 0.90
Cheese 1.75
Total 3.14
? $
Milk shake 0.88
Ice cream 1.15
Peanuts 0.75
Fruit bar 1.45
Total 4.23
SLIDE 28
Find
? Four pencils at 12p each
? Six notepads @ 25p
? Seven books at £3 each
? 5 apples @ £0.50
? Twelve roses at forty pence each
? Three lipsticks at £1.10 each
SLIDE 29
? Four pencils at 12p each is
? Six notepads @ 25p is
? Seven books at £3 each is
? 5 apples @ £0.50 is
? Twelve roses at forty pence each is
? Three lipsticks at £1.10 each is
SLIDE 28 B
Find
? Four pencils at 12’ each
? Six notepads @ 25’
? Seven books at $3 each
? 5 apples @ $0.50
? Twelve roses at forty cents each
? Three lipsticks at $1.10 each
SLIDE 29 B
? Four pencils at 12’ each is
? Six notepads @ 25’ is
? Seven books at $3 each is
? 5 apples @ $0.50 is
? Twelve roses at forty pence each is
? Three lipsticks at 41.10 each is
SLIDE 30
Complete the following bills
? £
12 pencils @ 60p
2 drawing pads @ £2.80
4 brushes @ £1.25
1 eraser @ 70p
Total
? £
4 litres petrol @ £1.25
6 gas cannisters @ 0.90
1 camping stove @ £5.49
3 packets sausages @ £1.20
2 packets burgers @ £2.50
1 frying pan at £8.45
Total
SLIDE 30 B
Complete the following bills
? $
12 pencils @ 60’
2 drawing pads @ $2.80
4 brushes @ $1.25
1 eraser @ 70’
Total
? $
4 litres petrol @ $1.25
6 gas cannisters @ $0.90
1 camping stove @ $5.49
3 packets sausages @ $1.20
2 packets burgers @ $2.50
1 frying pan at $8.45
Total
SLIDE 31
? £
12 pencils @ 60p 7.20
2 drawing pads @ £2.80 5.60
4 brushes @ £1.25 5.00
1 eraser @ 70p 0.70
Total 18.50
? £
4 litres petrol @ £1.25 5.00
6 gas cannisters @ 0.90 5.40
1 camping stove @ £5.49 5.49
3 packets sausages @ £1.20 3.60
2 packets burgers @ £2.50 5.00
1 frying pan at £8.45 8.45
Total 32.94
SLIDE 31 B
? $
12 pencils @ 60’ 7.20
2 drawing pads @ $2.80 5.60
4 brushes @ $1.25 5.00
1 eraser @ 70’ 0.70
Total 18.50
? $
4 litres petrol @ $1.25 5.00
6 gas cannisters @ $0.90 5.40
1 camping stove @ $5.49 5.49
3 packets sausages @ $1.20 3.60
2 packets burgers @ $2.50 5.00
1 frying pan at $8.45 8.45
Total 32.94
SLIDE 32
? I had £423 in my account. I spent £158. How much did I have left?
? At a festival there were 4,320 people. 2,031 were male. How many were female?
? At the end of the month a girl had £125 in a bank account. Wages of £1,218 were then paid in, and she also received a gift of £150 from her mother. How much was in the bank account at the beginning of the next month?
? Before making his latest tweet, Lucky has 832 followers on Twitter. After his tweet, 28 of these people decided to unfollow him, but another 83 people began to follow him for the first time. How many followers did he have after his tweet?
? At the beginning of the week, a store had 25 smartphones in stock. During the week, another two dozen were delivered. 32 were sold. How many smart phones were in stock at the end of the week?
SLIDE 33
?
?
?
?
? 1 dozen = 12
SLIDE 32 B
? I had $423 in my account. I spent $158. How much did I have left?
? At a festival there were 4,320 people. 2,031 were male. How many were female?
? At the end of the month a girl had $125 in a bank account. Wages of $1,218 were then paid in, and she also received a gift of $150 from her mother. How much was in the bank account at the beginning of the next month?
? Before making his latest tweet, Lucky has 832 followers on Twitter. After his tweet, 28 of these people decided to unfollow him, but another 83 people began to follow him for the first time. How many followers did he have after his tweet?
? At the beginning of the week, a store had 25 smartphones in stock. During the week, another two dozen were delivered. 32 were sold. How many smart phones were in stock at the end of the week?
SLIDE 33 B
?
?
?
?
? 1 dozen = 12
|
|
