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Number Tricks And Problems With Two Unknowns

Explain 'think of a number' tricks with algebra, and solve two-unknown problems by writing one unknown using the other.

6 micro-lessons

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Algebra Behind a Trick

Track the unknown number through each step of the trick.

Riyaz's trick (Textbook p. 178, Example 11)

Try it first with a few starting numbers. Start with 5: 5 − 3 = 2, × 4 = 8, + 8 = 16. Start with 10: 7, 28, 36. Do you see a link between the start and the answer?

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Akash Said 24

Finding Akash's number, and the chapter's magic trick.

Problem. Akash's final answer was 24. What number did he think of? (Textbook p. 178)

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Make Your Own Trick

Invent a number trick and explain it with algebra.

Create a number trick

Textbook p. 190: Can you make your own such tricks?

Make one trick of either kind:

an 'I predict you get …' trick, where the starting number cancels out, or
a 'tell me your answer and I'll find your number' trick.

List the steps, write the expression after each step (start with x), and explain why the trick works.

Your steps, with the expression after each one*

Start: x

Why does it work?*

Two Unknowns, One Letter

Write one unknown using the other, so there is only one letter.

Example 12 (Textbook p. 179)

Ramesh and Suresh have 60 marbles between them. Ramesh has 30 more than Suresh. How many does each have?

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Marbles, Donkeys and Drinks

Solving three two-unknown problems.

Problem 1. Marbles (p. 179). y + (y + 30) = 60.

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Two Unknowns Practice

Solve by writing one unknown in terms of the other.

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Two numbers add up to 76; one is 3 times the other. The numbers are…

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