Expected level of development
Australian Curriculum Mathematics V9: AC9M4N01
Numeracy Progression: Number and place value: P7
At this level, students apply their understanding of fractions and division to divide a whole (rectangle model) into 10 equal pieces. They learn that each piece represents 0.1 or one-tenth of the length of the original whole.
Encourage students to recognise that one whole is equivalent to ten-tenths and use this knowledge to rename other decimals (e.g. 0.15 as fifteen-hundredths or one-tenth and five-hundredths).
By using materials such as bundling sticks, students can represent a whole and then show the multiplicative relationship between the whole and its tenths and hundredths. For example, a bundle of 10 sticks can represent one whole and one stick is therefore one-tenth.
Relate the models of decimals to measurement examples where the relationship between the base unit and part of the unit are shown. For example, 1.5 metres can be demonstrated as one whole metre and five-tenths (or half) of the next unit metre.
Compare the language used for measurement units such as length with those used for money, emphasising that the cents are parts (hundredths) of the next dollar. For example, one dollar and seventy-five cents is one dollar and 75-hundredths of the next dollar.
Teaching and learning summary:
- Support students making connections between fractional language and decimal notation (e.g. tenths and hundredths).
- Emphasise the base ten place value system when working with decimals (one of the larger units is equivalent to ten smaller units and vice versa).
- Recognise the equivalence of fractions and decimals (e.g. half is the same as 0.5 or five-tenths) through the use of correct mathematical language (not zero point five).
- demonstrate their understanding of the base ten system and generalise this understanding to decimals (tenths and hundredths)
- represent decimal fractions (10-tenths and 100-hundredths)
- use decimals in real-life examples for measurement and money and explain how tenths and hundredths are represented.
Some students may:
- use incorrect language to describe a decimal number. Difficulties usually occur because place value is not used when naming numbers and numbers are said as separate digits (e.g. ‘three point four five’). The correct place value language should be used to prevent whole-number thinking (i.e. 3 and 45-hundredths)
- use whole-number thinking to compare the value of fractions and incorrectly believe that a longer number is always larger, for example, they think that 0.342 is larger than 0.4. Support students to use number lines and base 10 materials to compare the two 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.
- We are learning about decimals.
Why are we learning about this?
- Decimals are an important part of our number system.
What to do
1. Create this number expander.
2. Use your number expander to show if these statements are true.
- represent decimals on a number line
- write decimals as common fractions.
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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.
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.Go to resource
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.Go to resource
Classroom talks enable students to develop language, build mathematical thinking skills and create mathematical meaning through collaborative conversations.Go to resource
Providing students with multiple opportunities within different contexts to practise skills and apply concepts allows them to consolidate and deepen their understanding.Go to resource
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.
My decimal number
In this activity, students brainstorm different ways to represent decimal fractions. They will draw on their knowledge of decimal place value and writing decimals using words and symbols.Resource details
Locating decimal fractions
Students read decimals with tenths, count forwards and backwards in tenths, and order decimals with tenths.Resource details
Place value practice: tenths
Students can write decimals in expanded form, and vice versa, and identify a number on a number line marked in tenths in order to develop a deeper understanding of decimal place value.Resource details
Decimals: Tenths and hundredths
A resource containing teaching ideas related to the conceptual meanings of tenths and hundredths, and how they can be represented on both grids and number lines.Resource details
Composition and calculation: hundredths and thousandths
Introduce students to hundredths (and thousandths) using both the partitioning structure and ideas of place value.Resource details
By the end of Year 4, students use their understanding of place value to represent tenths and hundredths in decimal form and to multiply natural numbers by multiples of 10.