Connecting 2 ×, 4 × and 8 ×
🎯 In this topic you will
- Build the multiplication tables for 4 and 8.
- Connect the multiplication tables for 2, 4, and 8.
- Count in fours or eights starting from any number.
🔁 Doubling to Find New Tables
W hen you know the multiplication table for 2, you can use it to find other multiplication tables by doubling. You can also use the patterns in the multiples to help you count in twos, fours, or eights starting from any number.
❓ EXERCISES
$1.$ Which multiplication fact is represented below?
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$2.$ What are the next five multiples of $4$? $4, 8, 12, 16, 20,$
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$3.$ Write the missing multiplication facts.
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From $4 \times 3 = 12 \Leftarrow 2 \times 3 = 6$
From $2 \times 5 = 10 \Rightarrow 4 \times 5 = 20$
From $4 \times 4 = 16 \Leftarrow 2 \times 4 = 8$
$4.$ Which multiplication fact is represented below?
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$5.$ Colour all the multiples of $8$.
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$6.$ Write the missing multiplication facts.
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$2 \times 3 = 6 \Rightarrow 4 \times 3 = 12$
From $4 \times 6 = 24 \Rightarrow 8 \times 6 = 48$
From $8 \times 5 = 40 \Leftarrow 4 \times 5 = 20$
$7.$ The term-to-term rule is add $4$. Start at $5$. What are the next five numbers in the sequence?
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$8.$ What is the term-to-term rule in the sequence below? What are the missing numbers?
The term-to-term rule is __________.
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Term-to-term rule: add $8$
🧠 Think like a Mathematician
Investigation:
Zara said that if the term-to-term rule is an even number, then the terms will all be even if the start number is even.
Is Zara’s conjecture correct? How do you know?
Try this on your own by creating a few sequences with:
- An even start number.
- An even term-to-term rule.
- At least five terms in each sequence.
Write down your sequences and look carefully at whether any odd numbers appear.
Reflection: Do you agree with Zara? Explain your reasoning.
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Yes — Zara’s conjecture is correct.
If you start with an even number and keep adding an even number each time, the result will always stay even. This is because:
- Even $+$ even $=$ even
For example:
Start at $4$, add $6$ each time:
$4,\;10,\;16,\;22,\;28$
All the terms are even.
Since every new term is made by adding an even number to an even number, it is impossible for an odd number to appear. Therefore, Zara’s conjecture is always true.