Using a symbol to represent a missing number or operation
🎯 In this topic you will
- Use a symbol to represent a missing number or an operation sign in addition and subtraction calculations.
🧠 Key Words
- symbol
Show Definitions
- symbol: A letter, shape, or sign used in mathematics to represent an unknown number or an operation in a calculation.
Enjoying Number Puzzles
Many people, both young and old, enjoy solving number puzzles. Very young children often begin with simple jigsaws, while adults usually enjoy more challenging puzzles.
Missing Number Puzzles
In this unit, you will learn how to solve missing number puzzles. A symbol can be used to represent a missing number in a calculation.
❓ EXERCISES
1. Write the missing numbers.
a. $15 + 29 =$
b. $35 - 19 =$
c. $\square - 14 = 8$
d. $\square + 6 = 30$
e. $12 + \square = 25$
f. $30 - \square = 16$
👀 Show answer
a. $44$
b. $16$
c. $22$
d. $24$
e. $13$
f. $14$
2. Copy and complete the number sentence.
$5\square + \square5 = 100$
👀 Show answer
$55 + 45 = 100$
3. Write the missing numbers.
a. $1 + 10 + \square = 100$
b. $57 + \square = 120$
c. $50 - \square = 31 + 10$
👀 Show answer
a. $89$
b. $63$
c. $9$
4. In this diagram, the numbers on three circles in a straight line add up to $1000$. Copy and complete the diagram.
👀 Show answer
Top right: $450$
Left middle: $300$
Right middle: $550$
Bottom middle: $400$
5. Find the missing operation signs.
a. $28 \circ 72 = 100$
b. $55 = 70 \circ 15$
👀 Show answer
a. $+$
b. $-$
6. Use the rule to find the missing numbers.
👀 Show answer
a. $55$
b. $50$
7. $\square + \triangle + \circ = 10$. What numbers could they represent?
👀 Show answer
One possible answer: $3 + 4 + 3 = 10$ (many other answers are possible).
🧠 Think like a Mathematician
Use each of the numbers 3, 4, 5, 6 and 7 to complete the cross pattern. The total going across must be the same as the total going down.
You will show you are specialising when you find solutions to the problem.
Method:
- Place the numbers 3, 4, 5, 6 and 7 into the five circles (each number used once).
- Calculate the total across: $\text{left} + \text{centre} + \text{right}$.
- Calculate the total down: $\text{top} + \text{centre} + \text{bottom}$.
- Adjust the positions until the totals match, and record each distinct solution.
- To specialise, look for a rule that guarantees equality (rather than random trial-and-error).
Follow-up Questions:
👀 show answer
Top $=4$, Left $=3$, Centre $=5$, Right $=7$, Bottom $=6$.
Across total $=3+5+7=15$ and down total $=4+5+6=15$.
- If the centre is $5$, then you can use equal-sum pairs $3+7=10$ and $4+6=10$. This gives $2$ choices for which pair is horizontal vs vertical, and $2\times 2$ orders within the pairs, for $2\times 2\times 2 = 8$ solutions.
- If the centre is $7$, then you can use equal-sum pairs $3+6=9$ and $4+5=9$, giving another $8$ solutions.
- Total $=8+8=16$.