Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M5N03
Numeracy Progression: Interpreting fractions: P6
At this level, students compare and order fractions and mixed numbers with the same and related denominators and demonstrate their understanding of the values of fractions on a number line.
Encourage students to represent, order and compare fractions on a number line including fractions with the same and related denominators and mixed numerals.
Provide opportunities for students to use region models (rectangular models divided in only one direction) such as fraction walls or strips of folded paper to look beyond the partwhole method and make sense of these representations.
Demonstrate the connection between fraction walls and number lines visually, for example, one third of a fraction wall demonstrates one equal part of 3, and a point that is 13 of the distance between 0 and 1.
Move from proper fractions (fractions less than 1) to improper fractions/mixed numbers on number lines. For example, demonstrate how to identify the position of 12, 43 , and 14 on a number line from 0 to 2.
Extend students’ understanding of improper fractions and mixed numbers through skip counting by fractional parts on number lines to demonstrate that when counting by, for example, quarters the number after one would be 54, which is equivalent to 1 and 14.
Extend students’ understanding of equivalent fractions by using parallel number lines of the same length and demonstrating why, for example, 210 and 15 are located at the same position on each number line (both represent the same amount but have different sized parts).
Teaching and learning summary:
 Demonstrate the relationship between improper fractions and mixed numbers when on a number line.
 Encourage students to use knowledge of factors and multiples to compare and order fractions with the same and related denominators including mixed numerals.
Students:
 use both vertical and horizontal number lines to compare the values of a range of fractions
 demonstrate understanding of proper and improper fractions by positioning them on number lines
 compare and order a range of fractions and justify their reasoning with reference to the size of the fractions
 use knowledge of factors and multiples when working with mixed numbers or fractions with related denominators.
Some students may:
 use wholenumber ideas when working with fractions. For example, they use the same reasoning as they do to order 2, 4, 6 and 8 to order the fractions 12 , 14 and 18 without considering the size of each fraction.
 identify 12 as being halfway between any range represented on a number line as they are interpreting ‘half’ as an action instead of a numerical value. For example, marking ‘1’ as half when presented with a number line showing a range of 0 and 2 rather than 0.5.
To address these misconceptions, help students develop ideas of partitioning (sharing equally) and equivalence (different representations of the same amount) which should help bring many of the concepts together. Both improper and proper fractions can be seen as a number that lies between any two whole numbers. By extending the idea that 1 can be partitioned into equalsized parts and denotes a number between 0 and 1, other fractions can be formed and seen as numbers in an extended number system rather than using already known whole numbers separated by a point (3.46) or on top of each other ( 34 ). Thus, an improper fraction may be a part of 2 ones ( 74 ), 3 ones ( 83 ) and so on (numbers that lie between two whole numbers).
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
Learning intention
 We are learning to order and compare fractions around us.
Why are we learning about this?
 Learning about fractions can help with calculating time when cooking, travelling or paying for a bill.
What to do
Task:
1. Choose a fraction 14 , 43 , 25 or 1 34 and write everything you know about this fraction.
2. Represent the chosen fraction on a number line. What is the range of your number line? Ask yourself, where is 0? Where is 1?
3. Find a fraction that is closer to 0 than your fraction. Mark it on your number line. Explain how you know this fraction is less
than your fraction.
Success criteria
I can:
 use my understanding of factors and multiples to compare fractions
 order fractions and place each fraction on the same number line.
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Teaching strategies
A collection of evidencebased teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.

Explicit teaching
Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.
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Questioning
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.
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Classroom talks
Classroom talks enable students to develop language, build mathematical thinking skills and create mathematical meaning through collaborative conversations.
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Feedback
It has been shown that good feedback can make a significant difference to a student’s future performance.
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Teaching resources
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.

Fraction shape puzzles
Students investigate fractions by exploring the colourful world of flags.
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Fraction line up
This is a level 4 number activity from the Figure It Out series. It is focused on ordering fractions, converting improper fractions to mixed fractions and finding equivalent fractions. A PDF of the student activity is included.
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Decimal fractions: Video and teaching guide
Use this video to explore decimal fractions, how they are represented and how we use them in daytoday contexts.
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Assessment
By the end of Year 5, students order and represent, add and subtract fractions with the same or related denominators.

Assessment: Can you find the fraction?
In this assessment task, students use their understanding of improper fractions and equivalence to determine the value of a number.
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Who were the fastest swimmers?
Use this task to assess students’ proficiency in their use of place value to write and order decimals including decimals greater than one.
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