1 of 20

Adding fractions inquiry

Inquiry Maths

Think, pair, share

Ask a question or make a statement about the prompt.

 

2 of 20

 

Inquiry Maths

3 of 20

 

 

 

Inquiry Maths

4 of 20

 

 

 

Inquiry Maths

5 of 20

Inquiry Maths

  1. Find the sum of the fractions in the next two calculations in the sequence.
  2. Describe the patterns and rules you notice.

……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………...................................................................................................................................................

Exploring the prompt

 

6 of 20

Patterns

  • The numerators increase by 2 (5, 7, 9, 11, …)
  • The denominators increase at a faster rate - by 2 more each time (6, 8, 10, …)
  • The sum of the fractions gets smaller each time.

Rules

  • Add the denominators to get the numerator in the sum.
  • Multiply the denominators to get the denominator in the sum.
  • This only works when we use unit fractions (the numerator is one).

Exploring patterns and rules: examples

 

Inquiry Maths

7 of 20

Inquiry Maths

Exploring other patterns

8 of 20

Inquiry Maths

Exploring other patterns 1

 

Change the difference between the denominators.

 

 

  1. Find the sum of the pairs of fraction.
  2. Describe the patterns and rules you notice.

​

……………………………………………

…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….................................................................................................................

9 of 20

Inquiry Maths

Exploring other patterns 2

Change the numerators, but keep them the same.

  1. Find the sum of the pairs of fraction.
  2. Describe the patterns and rules you notice.

​

……………………………………………

…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….................................................................................................................

 

 

 

10 of 20

Inquiry Maths

Exploring other patterns 3

The differences between the two numerators and the two denominators are equal.

  1. Find the sum of the pairs of fraction.
  2. Describe the patterns and rules you notice.

​

……………………………………………

…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….................................................................................................................

 

 

 

11 of 20

Inquiry Maths

Exploring other patterns 4

The difference between the numerator and denominator of each fraction is the same. The first denominator is the same as the second numerator.

  1. Find the sum of the pairs of fraction.
  2. Describe the patterns and rules you notice.

​

……………………………………………

…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….................................................................................................................

 

 

 

12 of 20

Inquiry Maths

Expressing the fractions algebraically

13 of 20

Inquiry Maths

Exploring other patterns 1

 

Change the difference between the denominators.

 

 

  1. Find the sum of the pairs of fraction.
  2. Describe the patterns and rules you notice.

​

……………………………………………

…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….................................................................................................................

14 of 20

Inquiry Maths

Exploring other patterns 2

Change the numerators, but keep them the same.

  1. Find the sum of the pairs of fraction.
  2. Describe the patterns and rules you notice.

​

……………………………………………

…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….................................................................................................................

 

 

 

15 of 20

Inquiry Maths

Exploring other patterns 3

The differences between the two numerators and the two denominators are equal.

  1. Find the sum of the pairs of fraction.
  2. Describe the patterns and rules you notice.

​

……………………………………………

…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….................................................................................................................

 

 

 

16 of 20

Inquiry Maths

Exploring other patterns 4

The difference between the numerator and denominator of each fraction is the same. The first denominator is the same as the second numerator.

  1. Find the sum of the pairs of fraction.
  2. Describe the patterns and rules you notice.

​

……………………………………………

…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….................................................................................................................

 

 

 

17 of 20

Inquiry Maths

Other lines of inquiry

18 of 20

Extending the inquiry

Inquiry Maths

 

(2) Make up fraction patterns using subtraction. Describe the patterns and rules you notice.

 

19 of 20

Extending the inquiry

Inquiry Maths

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(4) This is the Leibniz harmonic triangle. How are the unit fractions arranged? Can you work out the sixth and seventh rows?

The Leibniz harmonic triangle appears as an inquiry prompt on Samia Henaine’s website Math teachers as bridge builders.

20 of 20

Inquiry Maths