1 of 39

Continued fractions inquiry

Inquiry Maths

2 of 39

Inquiry Maths

Inquiry prompt

3 of 39

Inquiry Maths

4 of 39

Inquiry Maths

Inquiry prompt

5 of 39

Link to Regulatory cards

Inquiry Maths

6 of 39

Inquiry Maths

7 of 39

Inquiry Maths

8 of 39

Inquiry Maths

Fractions formed from consecutive terms of the Fibonacci sequence.

The continued fraction leads, at the limit, to the reciprocal of the Golden Ratio or the ratio of the shorter side to the longer side of the Golden Rectangle (see the proof in line of inquiry 4).

9 of 39

Alternative prompts

Inquiry Maths

10 of 39

Inquiry Maths

Lines of inquiry

1. Change the prompt

11 of 39

Inquiry Maths

12 of 39

Inquiry Maths

13 of 39

Inquiry Maths

What are the differences between the sequences?

14 of 39

Inquiry Maths

What are the differences between the sequences?

15 of 39

Inquiry Maths

Lines of inquiry

2. Euclid’s algorithm for any rational number

16 of 39

Inquiry Maths

17 of 39

Inquiry Maths

18 of 39

Inquiry Maths

19 of 39

Inquiry Maths

20 of 39

Inquiry Maths

21 of 39

Inquiry Maths

22 of 39

Inquiry Maths

Choose an improper fraction and create your own continued fraction.

Work backwards to check your continued fraction is equivalent to the improper fraction.

23 of 39

Inquiry Maths

Lines of inquiry

3. General form

24 of 39

Inquiry Maths

Examples

25 of 39

Inquiry Maths

Examples

26 of 39

Inquiry Maths

Explore patterns by making up your own examples.

27 of 39

Inquiry Maths

Lines of inquiry

4. Proof

28 of 39

Inquiry Maths

The prompt

29 of 39

Inquiry Maths

30 of 39

Inquiry Maths

Lines of inquiry

5. Irrational numbers

31 of 39

Inquiry Maths

Irrational numbers

32 of 39

Inquiry Maths

Irrational numbers

33 of 39

Inquiry Maths

Irrational numbers

34 of 39

Inquiry Maths

Irrational numbers

35 of 39

Inquiry Maths

Lines of inquiry

6. Square roots

36 of 39

Inquiry Maths

Square roots

37 of 39

Inquiry Maths

Square roots

38 of 39

Inquiry Maths

Square roots

39 of 39

Inquiry Maths