#### FRACTIONS NRICH PROBLEM SOLVING TASKS

Where were the cuts and what fraction of the whole cake was each piece? There are lots of ideas to explore in these sequences of ordered fractions. Almost One Age 11 to 14 Challenge Level: The Greedy Algorithm might provide us with an efficient way of doing this. Keep it Simple Age 11 to 14 Challenge Level: When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators? Of course, by their very nature, rich tasks will also provide opportunities for children to work like a mathematician and so help them develop their problem-solving skills alongside this conceptual understanding.

All of the following tasks provide contexts in which to encourage learners to talk about their ideas and to work towards refining their vocabulary. Andy’s Marbles Age 7 to 11 Challenge Level: Helpful preparation for those intending to study a course involving pure mathematics at university. Choose some fractions and add them together. Can you untangle what fractional part is represented by each of the ten numbered shapes? This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

## 242 Matches for fractions

Fractions can refer to objects, quantities or shapes, thus extending their complexity. Circuit Training Age 14 to 16 Challenge Level: Fraction Fascination Age 7 to 11 Challenge Level: Modular Fractions Age 16 to 18 Challenge Level: Teaching Fractions with Understanding: Here is a chance to explore how they could have written different fractions.

We recommend you start by reading nroch article, which problej each group of tasks in turn, outlining further reasons for grouping in this way and explaining why each particular task has been selected. Linked Chains Age 7 to 11 Challenge Level: Folding Squares Age 14 to 16 Challenge Level: Plus or Minus Age 16 to 18 Challenge Level: So, the tasks in this second group are curriculum-linked but crucially also offer opportunities tractions learners to develop their problem-solving and reasoning skills.

# Fractions, Decimals, Percentages, Ratio and Proportion :: Fractions :

The tasks in this group reflect a progression of ideas associated with fractions but crucially also offer opportunities for learners to develop their problem-solving and reasoning skills. Fractions Age 5 to 7 The activities in this feature give you chance to explore fractions. What is the sum of the denominator and numerator? Repeat infinitely many times, and you have the Cantor Set.

Egyptian Fractions Age 11 to 14 Challenge Level: Fair Feast Age 5 to 11 Challenge Level: Forgot the Numbers Age 7 to 11 Challenge Level: The large rectangle is divided into a series of smaller quadrilaterals and triangles. The Egyptians expressed all fractions as the sum of different unit fractions. In a similar way to Paper Halvingthis activity encourages learners to explore fractions as area.

Ratio Sudoku 1 Age 11 to 16 Challenge Level: You can facilitate discussion about not all halves being symmetrical and it would also be fruitful to ask how learners think the task would have been affected if they had been given squared paper rather than plain.

If the length of the black is 1, how could you write the sum of the strips?

# More Fractions Upper Primary :

How long could he make his peaches last for? Matching Fractions Age 7 to 11 Challenge Level: Working on these problems will help you develop a better understanding of fractions, decimals and percentages.

Continued Fractions I Age 14 to 18 An article introducing continued fractions with some simple puzzles for the reader.

Can you fit the tangram pieces into the outlines of the chairs? To rractions this aim, members of the NRICH team work tsks a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths. Fractional Wall Age 7 to 11 Challenge Level: Age 16 to 18 Challenge Level: Learners are invited to halve pieces of paper in different ways and to articulate how they know that they have created halves.

The article Developing a Classroom Culture That Supports A Pronlem Approach to Mathematics offers several practical ideas to help your classroom become a classroom that is based on talk. What were the interesting questions that needed to be asked, and where did they lead?

Keep it Simple Age 11 to 14 Challenge Level: