Flow diagrams, tables and formulas
Follow a flow diagram with integers, make a table, find the rule y = ax + b, work back to the input, and use formulas in real life. Read one step, play with it, then tap “I understand this”.
Flow diagrams with integers
A flow diagram takes every input (x) through the rule to an output (y). In Grade 7 the inputs and the numbers in the rule can also be negative: remember the integer rules.
The flow diagram
Change the two operations and watch the outputs.
−2 × 3 = −6 (negative times positive is negative) and −2 × (−3) = 6 (negative times negative is positive).
From table to formula
We can write the rule as a formula: y = ax + b. The number a is how much y changes every time x gets 1 bigger. The number b is y when x = 0.
Table and formula
Change a and b and watch the table and the jump at the bottom.
When x gets 1 bigger, a × x gets exactly a bigger. The + b stays the same, so y jumps by a every time.
Find the rule
- Look at the jump between the y values: that is a.
- Choose one pair from the table, for example x = 1, and work out a × 1.
- What must you add to get to y? That is b.
- Check with another pair from the table.
Which formula?
Look at the table and choose the formula.
Correct: 0Work back to the input
Do you know the output and want the input? Start at the end and do the inverse operations in the reverse order: first the + or −, then the × or ÷.
× 4 + 3 = 31 → back: 31 − 3 = 28, then 28 ÷ 4 = 7. Check: 7 × 4 + 3 = 31 ✓
Work backwards
Find the input.
Correct: 0The last thing that happened to the number must be undone first, like taking off your shoes before your socks.
Formulas in real life
Many things work with a fixed amount plus an amount per unit: a taxi, a phone plan, a burning candle. Substitute the number for x and work out y.
Substitute and calculate
Read the situation and choose y.
Correct: 0Check yourself
- Flow diagram: do the operations in the order of the arrow. Watch out for negative signs.
- Formula y = ax + b: a is the jump in y when x gets 1 bigger, b is y at x = 0.
- Check your rule with a second pair from the table.
- Working backwards: inverse operations in reverse order.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 5 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 3 A4 pagesPractice sheet
- Numbers, Patterns and Algebra8 pages · PDFPaperMemo
- Patterns and algebra8 pages · PDFPaperMemo
Ready for more? The Grade 7 quiz on flow diagrams and functions gives you new questions every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Make a “machine” together: one person says a number (also negative), the other applies a secret rule (like × 3 − 2) and says the answer. Guess the rule and write it as y = …
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 7 Maths. Always check your teacher’s notes and textbook too.