Patterns with integers
Finding the rule of a number pattern, and working out far terms with a position 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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Number patterns
- Find the rule: what happens from one term to the next? 3; 7; 11; 15 → +4.
- Patterns can also multiply or divide: 2; 6; 18; 54 → ×3.
- Some grow by a growing step: 1; 2; 4; 7; 11 → +1, +2, +3, +4.
- Patterns can cross 0: −5; −2; 1; 4; … → +3, the next term is 7. 10; 6; 2; −2; … → −4, the next term is −6. Counting down past 0 takes you into the negative numbers.
The position rule
To find a far term (e.g. the 50th), link the term to its position. Pattern 4; 7; 10; 13: term = 3 × position + 1. The 50th term = 3 × 50 + 1 = 151.
The step between terms becomes the number that multiplies the position. Then test the first term to find the extra number.
In Grade 7 we write the rule as Tₙ = 3n + 1, with n the position.
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.
Subtracting an integer
Subtracting an integer is the same as adding its opposite (additive inverse): 6 − 9 = 6 + (−9) = −3 and −2 − (−5) = −2 + 5 = 3.
- When you add, the order does not matter (commutative): (−7) + 10 = 10 + (−7) = 3. You may also group differently (associative): [(−5) + 8] + (−2) = (−5) + [8 + (−2)] = 1.
- Check addition with subtraction: if (−7) + 10 = 3, then 3 − 10 = −7.
- In context: at 06:00 it is −4 °C and by midday it is 9 degrees warmer: −4 + 9 = 5 °C. From −4 °C to 5 °C is a rise of 5 − (−4) = 9 degrees.
Remember this and test yourself
- Find the rule from term to term.
- Negative numbers are less than 0.
- Patterns can add, subtract, multiply or divide.
- Left on the number line is smaller.
- Far terms: link the term to its position.
- Minus a negative = plus.
Write these points in your book. Read them again the night before the test.
Step → multiply; first term → check.
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.
True or false?
Read the question and the answer. Is the answer right? Tap True or False.
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: Patterns 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.