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Beginning algebra |
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CONTENTS |
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| Working with algebra and symbols |
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Workout |
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40 slides |
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| Beginning algebra |
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Library |
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18 questions |
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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.
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SAMPLE FROM THE WORKOUT |
| Showing American English version |
SLIDE 1 - QUESTION 1 |
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SLIDE 2 - SOLUTION |
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SAMPLE FROM THE LIBRARY |
| Showing American English version |
QUESTION [difficulty 0.1] |
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SOLUTION |
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DEPENDENCIES |
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CONCEPTS |
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LEV. |
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Substituting numbers for letters, plugging in
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382.1 |
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Algebraic equation
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382.5 |
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Letter or symbol as solution to arithmetical operation
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382.5 |
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Solution by one step arithmetical operation
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382.5 |
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Number pyramids and towers
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382.9 |
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Map, mapping (implicit function), rule
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383.1 |
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Identity of rule (identity of function)
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383.3 |
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Inference to unknown quantity
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383.5 |
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Equation as number balance
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384.1 |
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Elementary problems in system of ratios
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384.4 |
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Number chain with rule
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384.9 |
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Hailstone sequence
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385.1 |
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Notion of an unsolved problem
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385.4 |
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Mapping diagram
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385.5 |
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Algebraic rule
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385.7 |
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RAW CONTENT OF THE WORKOUT |
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| 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. |
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Working with algebra
SLIDE 1
Example
When
Exercise
Find
(a) When
(b) When
(c) When
(d) When
(e) When
SLIDE 2
(a) When ,
(b) When ,
(c) When ,
(d) When ,
(e) When ,
SLIDE 3
Example
Plug into
Answer:
Exercise
Plug into
(a)
(b)
(c)
(d)
(e)
SLIDE 4
(a)
(b)
(c)
(d)
(e)
SLIDE 5
Work out
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SLIDE 6
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SLIDE 7
Work out
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SIDE 8
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SLIDE 9
SLIDE 10
SLIDE 11
Example
Rule 1: add 12
Rule 2: multiply by 3
Rule 3: multiply by 2 and add 6
Exercise
Make three rules for the following
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Rule 1 ………………………………………………….
Rule 2 ………………………………………………….
Rule 3 ………………………………………………….
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Rule 1 ………………………………………………….
Rule 2 ………………………………………………….
Rule 3 ………………………………………………….
SLIDE 12
There are many solutions to this problem
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Rule 1 Add 15
Rule 2 Multiply by 4
Rule 3 Multiply by 2 and add 10
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Rule 1 Add 28
Rule 2 Multiply by 5
Rule 3 Multiply by 2 and add 21
SLIDE 13
Example
The two mappings have the same rule.
The rule is: multiply by 2
Exercise
The mappings have the same rule. What is the rule?
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Rule ………………………………………………….
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Rule ………………………………………………….
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Rule ………………………………………………….
SLIDE 14
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Rule Multiply by 3
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Rule Add 8
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Rule Divide by two, divide in half
SLIDE 15
Four cubes of the same size are piled up into a column. The height of the column is 64 cm.
One more cube is added. What is the new height of the column?
SLIDE 16
Height of one cube =
Height of five cubes,
SLIDE 16
Four batteries weigh 48g.
What do five batteries weigh?
SLIDE 17
Weight of one battery is
Weight of five batteries,
SLIDE 18
? 12 boxes of tiles cost £84. What do 7 boxes cost?
? To insure 3 pet cats for a year costs £720. What would it cost to insure 5 cats at the same price?
? A family of 4 fly to Spain. It costs £880. Another family of 6 also wishes to take the same flight. What will cost them?
SLIDE 19
? 12 boxes of tiles cost £84. What do 7 boxes cost?
? To insure 3 pet cats for a year costs £720. What would it cost to insure 5 cats at the same price?
? A family of 4 fly to Spain. It costs £880. Another family of 6 also wishes to take the same flight. What will cost them?
SLIDE 19 B
? 12 boxes of tiles cost $84. What do 7 boxes cost?
? To insure 3 pet cats for a year costs $720. What would it cost to insure 5 cats at the same price?
? A family of 4 fly to Spain. It costs £880. Another family of 6 also wishes to take the same flight. What will cost them?
SLIDE 20 B
? 12 boxes of tiles cost $84. What do 7 boxes cost?
? To insure 3 pet cats for a year costs $720. What would it cost to insure 5 cats at the same price?
? A family of 4 fly to Spain. It costs $880. Another family of 6 also wishes to take the same flight. What will cost them?
SLIDE 20
Find X
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SLIDE 21
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SLIDE 22
2 bears balance 1 pig
1 bear and 1 pig balance 1 cow
? How many pigs balance 10 bears?
? How many cows balance 3 pigs?
? How many bears balance 1 cow and 2 pigs?
SLIDE 23
2 bears balance 1 pig
1 bear and 1 pig balance 1 cow
1 pig
? How many pigs balance 10 bears? Answer: 5
? How many cows balance 3 pigs?
? How many bears balance 1 cow and 2 pigs?
SLIDE 25
In a game
3 cars = 1 house
4 houses = 1 hotel
How many cars is 3 hotels and 3 houses?
SLIDE 26
SLIDES 27 and 28
I am thinking of a number
My number multiplied by 12 is 192
My number multiplied by 15 is 240
What is my number?
Method 1
Method 2
SLIDE 29
This is a number chain.
The rule is .
? Using this rule find the next two numbers.
? Find the next three numbers in the number chain with the rule
? What is the rule for the following number chain?
SLIDE 30
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The rule is
SLIDE 31
A rule of generating a number sequence goes as follows.
If the number is even, divide by 2
If the number is odd, multiply by 3 and add 1
? Generate the first 11 terms starting with the number 5
? Generate the first 12 terms starting with the number 6
? Generate the first 20 terms starting with the number 7
These are called Hailstone sequence.
? What do you observe about each of these number sequences at the end?
SLIDE 32
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? All these sequences end in the cycle
This then repeats infinitely.
SLIDE 33
Hailstone sequence
If the number is even, divide by 2
If the number is odd, multiply by 3 and add 1
We have found the following Hailstone sequences
All these sequences end in the cycle
This then repeats infinitely.
? Do you think all Hailstone sequences will end in the cycle ?
? Generate the first 20 terms of the Hailstone sequence starting with the number 27.
SLIDE 34
? It is not known whether all Hailstone sequences do end in the cycle .
? Starting with 27
The sequence starting with 27 does not end in within the first 20 terms. However, it does come to that cycle eventually.
All numbers up to a million million million have been shown by computers to end in the cycle , but it is still not known whether all Hailstone sequences end in this way.
SLIDE 35
? Continue the sequence
? What is the rule for this sequence?
? Complete this mapping diagram
? Complete the following
SLIDE 36
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? Add 5
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SLIDE 37
? When what is the value of ?
? A rule is given by
Find 3x when
? Complete the following mapping diagram for this rule
SLIDE 38
? When ,
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When ,
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SLIDE 39
? A rule is given by
Complete the following mapping diagram for this rule
? What is the rule for this sequence?
SLIDE 40
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