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Puzzles And Real Life: Machines, Blobs, Bricks And Giraffes

Turn puzzles, number machines, pictures and stick patterns into equations and solve them.

8 micro-lessons

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Turning Words and Pictures into Equations

Name the unknown, find the equality, write it down.

Phrases into equations (Textbook pp. 181–189)

'The weight is 1 kg more than half its weight' → w = w/2 + 1
'One quarter of a number increased by 9 gives the number' → n/4 + 9 = n
'A number increased by 36 equals ten times itself' → n + 36 = 10n

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Machines and Stick Patterns

Working out machine inputs and stick-pattern positions.

Problem 1 (p. 185, Q4a). This machine adds 3, multiplies by 4 and subtracts 5. An input of 12 gives 55.

What input gives 43?

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A Modelling Checklist

From words or pictures to an equation.

From a puzzle to an equation

1. Pick a letter for the unknown.

2. Write every other quantity using it.

3. Find what is equal: a total, a balance, a machine's output, 180° in a triangle.

4. Write the equation.

5. Solve, and check the answer makes sense: a whole number of sticks? a positive length?

More Machines and the Blobs

Pictures for the questions below.

Machine questions (Textbook pp. 185–186).

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Machines and Blobs

Find machine inputs and hidden dots.

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Machine P (+3, ×4, −5) gives 75. The input is…

Classic Word Puzzles

Five classic 'find the number' puzzles.

Solve the puzzles

Figure it Out, Textbook pp. 181 and 188. For each, write the unknown, the equation, the solution and a check.

I am a 3-digit number. My hundreds digit is 3 less than my tens digit. My tens digit is 3 less than my units digit. My digits add up to 15. Who am I? (p. 181, Q3)
A brick weighs 1 kg more than half its weight. What does it weigh? (p. 181, Q4)
One quarter of a number, increased by 9, gives the same number. What is it? (p. 181, Q5)
A giraffe's height is two and a half metres more than half its height. How tall is it? (p. 188, Q15)
A number increased by 36 is equal to ten times itself. What is it? (p. 188, Q17)

Unknown, equation, solution, check

Let the units digit be u.

Let the weight be w.

The Window and the Triangles

Pictures for the task below.

The window grill (Textbook p. 187, Q8). The window is 34 cm tall. The frame at the top is 3 cm, and the frame at the bottom matches it. There are 5 rods, each 2 cm thick, with equal gaps between them.

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