Expected level of development
Australian Curriculum Mathematics V9: AC9M6N06, AC9M6N04
Numeracy Progression: Additive strategies: P9, Multiplicative strategies: P9, Number and place value: P9
At this level, students apply knowledge of place value to add and subtract decimals, using digital tools where appropriate. They further develop whole-number multiplication and then strengthen their understanding of decimals by multiplying and dividing decimals and whole numbers. Students multiply by decimals and powers of ten.
Reinforce the idea that place value patterns extend in both directions. Use materials such as MAB: Base Ten Blocks and Cuisenaire rods to demonstrate the multiplicative relationships between the places in the base ten system. Contrast that with the number line to show the relationship between whole numbers and decimals.
Use classroom talks to collaboratively solve number problems that ask students to add and subtract decimals. Build a culture of using estimation before solving as a form of checking calculations, and then ask how close their result was to their estimation. Use questioning to elicit different strategies for addition and subtraction problems to at least hundredths. For example, one student may solve using partitioning, another may use place value parts, while the next may use the inverse relationship between addition and subtraction.
Use number talks in a similar way to solve problems that require multiplicative thinking and solving problems that involve multiplication and division of decimals. Make explicit the effect of multiplying and dividing by 10, 100 and 1,000 in terms of place value. Address and correct misconceptions that the decimal point is shifting.
Provide opportunities to use real-world examples to calculate and solve problems involving decimals, including those that use linear measurements.
Use calculators to solve additive and multiplicative problems that involve decimals. Compare the answer using the calculator with their initial estimation.
Teaching and learning summary:
- Make explicit the use of place value models demonstrating ten times larger than the place to the right, and 110 as large as the place to the left.
- Present mathematical equations to solve problems with large whole numbers and decimals to the hundredths and thousandths.
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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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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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Feedback
It has been shown that good feedback can make a significant difference to a student’s future performance.
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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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Classroom talks
Classroom talks enable students to develop language, build mathematical thinking skills and create mathematical meaning through collaborative conversations.
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Concrete, Representational, Abstract (CRA model)
The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.
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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 through the relationships between various shapes.
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Farm fence fractions
In this lesson, we explore fractions, decimals and perimeter.
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Decimals: Adding and subtracting
In this lesson, students play a board game that draws on their knowledge of adding decimals to tenths, hundredths and thousandths.
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All the digits
This problem requires students to think about place value and the way that standard column multiplication works.
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How do you do it?
This resource offers opportunities for students to discuss their mental calculation strategies and make decisions about the effectiveness and efficiency of different strategies in different contexts.
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The power of 10
This is a level 5 number activity from the Figure It Out series. It is focused on solving division problems involving decimals. A PDF of the student activity is included.
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Getting partial - Multiplying decimals
This unit requires students to apply their number sense about the size of decimals to estimate and calculate the product of decimal fractions.
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Branching out
This is a level 4 number activity from the Figure It Out series. It is focused on multiplying decimals with multiples of ten, and operating on fractions and decimals. A PDF of the student activity is included.
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Spring fever
This is a level 5 number activity from the Figure It Out series. It is focused on solving multiplication and division involving decimals. A PDF of the student activity is included.
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Assessment
By the end of Year 6, students use all four operations with decimals and connect decimal representations of measurements to the metric system.
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Assessment: Interpreting multiplication and division
Use this formative assessment task to help students interpret the meaning of multiplication and division.
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Fundraiser
Students create a budget for a sausage sizzle. Assess student’s proficiency in using four operations.
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