Operating with Decimals

This learning sequence aims to develop student proficiency when adding, subtracting, multiplying and dividing with decimals. A well-developed understanding of place value and number sense is critical for students to flexibly and intuitively operate with decimals. This sequence provides opportunities for students to consolidate their understanding of the continuous nature of the base 10 system and deepen their conceptual understanding about the role of estimation and efficient strategies when adding, subtracting, multiplying and dividing with decimals.

The sequence has been written by teachers for teachers. It has been designed to provide students with rich, engaging learning experiences that address the Victorian Curriculum. The sequence consists of four flexible stages, including suggested learning intentions.

Before you commence this sequence, it is suggested that you ensure your students are familiar with terms and concepts of place value, tenths and hundredths (VCMNA159) and the connection between fractions and decimals. Students should also have had experience using intuitive and flexible computation strategies for whole number (VCMNA156), which includes rounding and estimation.

It will be helpful for students to have first explored the concepts contained in the ‘Fractions to decimals’ and ‘Colour in decimats’ stages of the Keeping it in Proportion: Fractions and Decimals sequence, that focus on comparing and ordering decimals (VCMNA187; VCMNA190) as well as decimal place value (VCMNA189).

You can find support for building students’ understanding of these concepts in the Mathematics Curriculum Companion. The Teaching Context and Teaching Ideas related to content descriptions VCMNA159;  VCMNA189 and VCMNA190 may be particularly useful.

The Mathematics Curriculum Companion provides teachers with content knowledge, suggested teaching and learning ideas as well as links to other resources. Resources are organised by Mathematics strands and sub-strands and incorporate the proficiencies: Understanding, Fluency, Problem Solving and Reasoning. The Companion is an additional resource that you could refer to when you are planning how you might use the sequence in your school.

The sequence highlights opportunities to apply the High Impact Teaching Strategies (HITS), which are a component of the Victorian Teaching and Learning Model. 

The sequence highlights the use of a variety of scaffolding practices to help support students in the learning process, in particular:

• Collaborating
• Convince Me
• Noticing
• Extending

Students should be able to understand and use the following concepts and terms by the end of the learning sequence:

You can find definitions of some of these terms in the F-10 Victorian Curriculum Mathematics Glossary. It is recommended that the explicit teaching of vocabulary occur throughout the learning sequence.

The Literacy in Mathematics section of the Literacy Teaching Toolkit provides several teaching strategies with worked examples demonstrating how teachers can use literacy to support student understanding of mathematical language. A further set of strategies demonstrate how teachers can develop students' literacy skills to support their mathematical problem solving.

Opportunities for formative and summative assessment are identified at different stages of the learning sequence. Look for the 'Assessment Opportunity' icon.

You may want to develop a rubric to assess students’ progress. A range of Formative Assessment resources are available from the Victorian Curriculum and Assessment Authority. This includes a Guide to Formative Assessment Rubrics, a series of modules to support you to develop your own formative assessment rubrics, and sample rubrics across six curriculum areas that demonstrate how you can put formative assessment rubrics into practice in the classroom.

In developing a rubric, you may wish to co-construct assessment criteria with your students. Each stage of the sequence provides sample success criteria for students working at Level 6.

The Victorian Curriculum and Assessment Authority has published annotated work samples that provide teachers with examples of student learning achievement at multiple levels for each strand of the Mathematics curriculum.