Flow diagrams and tables with integers
Input, rule and output, and working back with the inverse rule. Numbers below zero: comparing, on the number line, and calculating with signs. Read one part at a time and tap “I know this”. Then test yourself in the quiz.
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Flow diagrams
A flow diagram takes an input, applies a rule and gives an output.
| Input | Rule: × 3 + 2 | Output |
|---|---|---|
| 1 | 1 × 3 + 2 | 5 |
| 4 | 4 × 3 + 2 | 14 |
| 10 | 10 × 3 + 2 | 32 |
Work back to the input with the inverse rule: output 20 → 20 − 2 = 18 → 18 ÷ 3 = 6.
Find the rule: inputs 1, 2, 3 give outputs 6, 11, 16. The outputs go up by 5 each time, so the rule starts with × 5. Test: 1 × 5 = 5, but the output is 6, so add 1. Rule: × 5 + 1. Check: 3 × 5 + 1 = 16.
Functions and tables
A flow diagram is a function: y = 3x + 2. Each input (x) has exactly one output (y). With integers: x = −2 → y = 3 × (−2) + 2 = −4.
Positive and negative
Integers are the numbers …, −3, −2, −1, 0, 1, 2, 3, …: the whole numbers (0, 1, 2, 3, …) and their negatives. Negative numbers are less than 0, like temperatures below freezing.
- On a number line left is always smaller: −7 < −3.
- The opposite of 5 is −5; their sum is 0.
Calculating with integers
| Rule | Example |
|---|---|
| plus a negative = minus | 5 + (−3) = 2 |
| minus a negative = plus | 5 − (−3) = 8 |
| same signs × or ÷ → positive | (−4) × (−3) = 12 |
| different signs × or ÷ → negative | (−4) × 3 = −12 |
- On the number line: adding a positive number moves you right; subtracting a positive number moves you left.
- −3 + (−4) = −7: start at −3 and move 4 to the left.
- −2 − 5 = −7: start at −2 and move 5 to the left.
- −6 + 9 = 3: start at −6 and move 9 to the right.
Think of money: −3 is a debt of R3. If someone takes your debt away, you are better off: −(−3) = +3.
Remember this and test yourself
- Input → rule → output.
- Negative numbers are less than 0.
- Apply the rule in order.
- Left on the number line is smaller.
- Work back with the inverse rule in reverse order.
- Minus a negative = plus.
Write these points in your book. Read them again the night before the test.
Forwards: do the rule. Backwards: undo it in reverse.
Important words
First say the answer yourself, then turn the card over.
Match column A to column B
Tap a word in column A, then its meaning in column B. You can also start in column B.
Now the real quiz!
The quiz has many more questions on this topic. Every question shows straight away whether you are right and explains why.
Take the quiz: Flow diagrams and tables with integers- Let your child work the examples on paper and explain them to you.
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Follows CAPS for Grade 7 Mathematics. Always check your teacher’s notes and textbook too.