Teaching fractions
The history of teaching fractions is long and colourful. In 1958 Hartung wrote, "The fraction concept is complex and cannot be grasped all at once. It must be acquired through a long process of sequential development." This sequential development of the fraction concept needs to be well understood if we are to develop widespread access to learning fractions with understanding.
NSW Department of Education and Training, (2003) Fractions, pikelets and lamingtons, (pp. 5)
 | We know that many students experience difficulties in working with fractions. Beyond the algorithmic manipulation of fractions lie the related difficulties of the underpinning concept. The Fractions, pikelets and lamingtons book provides activities for students to develop a conceptual understanding of fractions. It highlights the role of equal parts and collections of parts that form new units. NSW Department of Education and Training 2003
ISBN 0 7313 8278 1 Available from:DETSales
Phone: (02) 9793 3086
Fax: (02) 9793 3242
Product code: 10132
Price: $24.00 |
Pattern block fractions
What are pattern blocks?
Pattern blocks are versatile manipulatives for the mathematics classroom. They include the following shapes: green equilateral triangle, blue rhombus, tan rhombus, orange square, red trapezium and yellow regular hexagon. Activities using these blocks can not only assist students understanding of fractions but also assist with geometric concepts, spatial relationships and pattern awareness. | 
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| Why use pattern blocks to teach fractions?
These activities are designed to make students think about the concept of a fraction rather than just following an algorithmic process or a set of rules for adding or subtracting. The students will explore geometric models of fractions and discover relationships among them. |
Where can you get pattern blocks?
Students should have access to a plentiful supply of pattern blocks. Depending on the activity, one tub is usually enough for three or four small groups. Approximate cost of one tub (250 pieces) is $27 for wood or solid plastic blocks (in 2007). Q Stores and a range of educational suppliers stock pattern blocks. | 
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Recording solutions with pattern blocks
Many of the activities require students to record their solutions. This recording is best left to the students so they can demonstrate their thinking. Explaining how to record may suggest how to solve the problem.
Organising the information is one of the greatest difficulties when recording solutions. Recording in an organised way may lead to other solutions for the same problem. Share the good strategies amongst students.
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| Recording methods may include: - listing the blocks used and the number of each type
- sketching
- leaving the solution (blocks) on display
- tracing blocks (templates are available)
- copying solutions onto paper or into books using pattern block stickers or stamps
- writing explanations
- combinations of the above methods
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Recorded solutions could form part of students' assessment - a work sample indicating whether the outcome had been achieved at that point in time.
Linking pattern block fractions to the syllabus
Syllabus link | Pattern block activity |
NS3.4 Unit 1 Compares, orders and calculates with decimals, simple fractions and simple percentages Students learn about: |
- modelling thirds, sixths and twelfths of a whole object or collection of objects
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 Exploring PBs (pdf - 433KB)
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- placing thirds, sixths or twelfths on a number line between 0 and 1 to develop equivalence
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PB line up (pdf - 423KB)
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- expressing mixed numerals as improper fractions, and vice versa, through the use of diagrams or number lines, leading to a mental strategy
|  Make it (doc - 418 KB)
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- recognising that 1 + 1/2 = 1 1/2
| More than one (doc - 414 KB) Build one whole (pdf - 426 KB) |
- using written, diagram and mental strategies to subtract a unit fraction from 1 eg 1 - 1/3 = 2/3
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PB take-away 1 (pdf - 432 KB)
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- using written, diagram and mental strategies to subtract a unit fraction from any whole number eg 4 - 1/3
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PB take-away 2 (pdf - 434KB)
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- adding and subtracting fractions with the same denominator
eg 5/6 + 3/6
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PB add it (pdf - 433KB)
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NS3.4 Unit 1 Compares, orders and calculates with decimals, simple fractions and simple percentages Students learn to: |
- explain or demonstrate why two fractions are or are not equivalent (Reasoning, Reflecting)
| When using PB take-away 1, PB take-away 2 and PB add it encourage students to work in pairs, explain to a partner or write about how they worked out the Equal column. |
- interpret an improper fraction in an answer
(Applying Strategies)
| PB add it More than one |
NS3.4 Unit 2 Compares, orders and calculates with decimals, simple fractions and simple percentages Students learn about: |
- finding equivalent fractions using diagrams and number lines by re-dividing the unit
| Build a fraction 1 (pdf - 428KB) PB fraction puzzles (pdf - 436KB) PB fraction puzzles solutions
(pdf - 424KB) |
- developing a mental strategy for finding equivalent fractions eg. multiply or divide the numerator and the denominator by the same number
| Build a fraction 2 (pdf - 428KB) PB fraction puzzles PB fraction puzzles solutions |
- multiplying simple fractions by whole numbers using repeated addition, leading to a rule
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PB multiply it (pdf - 433KB)
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NS4.3 Operates with fractions, decimals, percentages, ratios and rates Students learn about: |
- finding equivalent fractions
| PB fraction puzzles |
- expressing improper fractions as mixed numerals and vice versa
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More than one
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| PB add it |
- subtracting a fraction from a whole number
| PB take-away 1 PB take-away 2 |
NS4.3 Operates with fractions, decimals, percentages, ratios and rates Students learn to: |
- recognise and explain incorrect operations with fractions
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But why? (pdf - 433KB)
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Online pattern blocks
 | This online pattern block program can be used to explore the different shapes, their relations and their proportions. By rotating the blocks, students can see the symmetrical properties of them. The real purpose behind the program is to use it as a tool to learn and practice fractions if there are no pattern blocks available. |
