Number sentences, properties and flow diagrams
Balance a number sentence, find the missing number with the inverse operation, calculate cleverly with the properties, and follow and find the rule of a flow diagram. Read one step, play with it, then tap “I understand this”.
Number sentences and the balance
A number sentence like □ + 15 = 42 is like a balance: both sides must weigh the same. The □ is the number we are looking for.
Try and improve
Change your guess until the balance is level.
The inverse operation
Every operation has an opposite that undoes it. Use it to find the □ quickly, and then check by putting your answer back in.
+ and − are inverses · × and ÷ are inverses. □ × 7 = 56 → □ = 56 ÷ 7 = 8. Check: 8 × 7 = 56 ✓
Find the □
Use the inverse operation.
Correct: 0Plus 15 and minus 15 cancel each other out, like walking ten steps forward and then ten steps back. You are back where you started: at the □.
The properties of operations
- Commutative (swap): 6 × 9 = 9 × 6 and 6 + 9 = 9 + 6.
- Associative (group): (25 × 13) × 4 = 13 × (25 × 4) = 1 300.
- Distributive (break up): 7 × 36 = 7 × 30 + 7 × 6.
- They work for + and ×, but not for − and ÷.
Clever calculating
Choose a property and try.
They let you rearrange sums so you can calculate in your head: 25 × 13 × 4 looks hard, but 25 × 4 = 100 and 100 × 13 = 1 300.
Flow diagrams
A flow diagram takes an input, applies the rule to it, and gives an output. With two operations you do them in the order of the arrow.
The flow diagram
Change the two operations and watch the outputs.
Find the rule and work backwards
Look at how much the outputs jump every time the input gets 1 bigger: that is the number you multiply by. Then see what you still need to add. To find an input, work backwards from the end with the inverse operations.
Which rule?
Look at the table and choose the rule.
Correct: 0Work backwards
Find the input.
Correct: 0Check yourself
- A number sentence is a balance: both sides are equal.
- Inverse: + and − undo each other, so do × and ÷. Check by putting the answer back in.
- Commutative, associative and distributive work with + and ×.
- Flow diagram: input → rule → output. The jump in the outputs is the number you multiply by.
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 · 2 A4 pagesPractice sheet
- Numbers, Operations and Patterns7 pages · PDFPaperMemo
- Patterns6 pages · PDFPaperMemo
Ready for more? The Grade 6 quiz on number sentences and flow diagrams 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, the other applies a secret rule (like × 2 + 1) and says the answer. Guess the rule!
- 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 6 Maths. Always check your teacher’s notes and textbook too.