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 part-whole 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.
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Teaching strategies
A collection of evidence-based 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.
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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.
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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 day-to-day 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.
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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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