Working with special numbers
🎯 In this topic you will
- Use odd and even numbers correctly in problem solving.
- Identify and work with factors and multiples of numbers.
- Recognise and use square numbers.
🧠 Key Words
- even
- factor
- multiple
- odd
- square number
Show Definitions
- even: A number that can be divided by 2 with no remainder.
- factor: A whole number that divides exactly into another number.
- multiple: A number obtained by multiplying a given number by a whole number.
- odd: A number that cannot be divided by 2 exactly.
- square number: A number made by multiplying a whole number by itself.
Working with Special Numbers 🔢
I n this section, we will work with these special numbers.
❓ EXERCISES
1. Mia makes a number using the digits $4$, $5$ and $6$.
The number is even.
The hundreds digit is greater than $4$.
The tens digit is greater than the hundreds digit.
What is Mia’s number? Copy the boxes and write Mia’s number in them.
👀 Show answer
2. Here is a Venn diagram for sorting numbers.
Copy and complete the diagram. Write each of these numbers in the correct place.
$10,\;11,\;12,\;13,\;14,\;15,\;16$
👀 Show answer
Multiples of $2$ only: $10$, $14$.
Outside the circles: $11$, $13$, $15$.
3. Here are four number cards.
$30,\;32,\;33,\;35$
Use each number once to make these statements correct.
a. ⬜ is a multiple of $3$.
b. ⬜ is a multiple of $4$.
c. ⬜ is a multiple of $5$.
d. ⬜ is a multiple of $6$.
👀 Show answer
b. $32$
c. $35$
d. $30$
4. Find two square numbers that have a sum of $100$.
👀 Show answer
5. Copy and complete this sentence.
Every number with a factor of $6$ must also have factors of ⬜, ⬜ and ⬜.
👀 Show answer
6. Pablo writes a $3$-digit number.
All of the digits are odd.
The sum of the digits is $7$.
What is the smallest number Pablo can write? Copy the boxes and write the number in them.
👀 Show answer
7. Ingrid says, “All numbers that end in a $4$ are multiples of $4$.”
Is Ingrid correct? Explain how you know.
👀 Show answer
🧠 Think like a Mathematician
Multiples
You will need these cards:
$0\;1\;2\;3\;4\;5\;6\;7\;8\;9$
Choose a set of multiples, for example multiples of $4$. Now make as many different multiples of $4$ as you can.
You can use each card only once. You may not be able to use all the cards.
Example:
Using the digits, some multiples of $4$ that can be made are: $12$, $40$, $36$, and $8$.
The unused numbers in this example are $5$, $7$, and $9$.
Choose other multiples to investigate.
You will show you are specialising when you find solutions to the problem.
Show possible outcomes
- You might find that multiples of $2$ allow more numbers to be formed than multiples of $5$.
- Some sets, such as multiples of $9$, are harder because fewer digit combinations work.
- Trying different target multiples helps you notice patterns in divisibility.