# How Big?

Mathematics

Level 5Level 6Level 7 This learning sequence explores measurement and geometry. Throughout the sequence, students are encouraged to estimate and test their estimates. Students transition from measuring and comparing different lengths, masses, capacities, and temperatures of common items to measuring perimeter, area of two-dimensional shapes and area and volume of three-dimensional objects. Students will have opportunities to acquire the knowledge and skills to investigate, demonstrate, classify, and compare.

This sequence provides opportunities for students to explore the metric system and when possible, compare it to the imperial system of units. There is a strong focus within this sequence on supporting students to develop the four mathematical proficiencies set out in the curriculum: Understanding, Fluency, Problem Solving and Reasoning, as well as extend their capacity for critical and creative thinking. Students will move through this learning process at different pace and from differing starting points.

 Big understandings Zero represents the absence of a property being measured. We use numbers to describe the size of an object by selecting a unit and then counting how many of the units (or parts of the unit) match the size object. We can compare two objects by selecting a unit and then comparing how many units match each object. The size of an object doesn’t change when we use a different sized unit to measure it. Estimation supports students to determine the reasonableness of their answer.

This 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 five flexible stages, including suggested learning intentions.

Overview of stages

• 1. It's Estimation Time

Suggested Learning Intentions

• To estimate, measure, and compare different lengths, masses, capacities, and temperatures of common items
• To accurately measure using scaled instruments

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• 3. Do We Have Enough Space?

Suggested Learning Intentions

• To devise the formulas for area of two-dimensional shapes and to make connections to real-life problem applications of these rules
• To solve problems involving the comparisons of lengths and area using appropriate units

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• 5. How Big is That Balloon?

Suggested Learning Intentions

• To compare different lengths, masses, capacities, and temperatures
• To convert between a range of units
• To theorise the volume of a sphere

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• 2. Uncle Jack's Land

Suggested Learning Intentions

• To compare and contrast perimeter and area
• To explain how to convert between units of linear measurement
• To formulate the rules for areas of two-dimensional shapes
• Students explore and define equable shapes

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• 4. Who is Right?

Suggested Learning Intentions

• To articulate the formulae for areas of two-dimensional shapes
• To explain how to convert between units of linear measurement

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• Prior knowledge

Before you commence this sequence, it is recommended that students are familiar with the use of scaled instruments to measure and compare length, mass, capacity, and temperature. Students should be familiar with using metric units of length, mass and capacity to measure, order and compare objects. Students would also benefit from a basic understanding of two-dimensional and three-dimensional shapes.

You can find support for building students understanding of these concepts in The Mathematics Curriculum Companion.

Teaching strategies

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.

This sequence employs the following teaching strategies:

• Concrete manipulatives
• Differentiated teaching
• Student collaboration
• Questioning
• Feedback
• Multiple exposures
• Structured lessons
• Student choice
• Metacognition.

Vocabulary

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

 Estimation Perimeter Compare Area Accuracy Capacity Dimension Volume Width Mass Unit Millimetre Metric Centimetre Imperial Metre Length Kilometre Convert Grams Attributes Kilogram

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. Teacher delivery suggestions in this sequence will help you maximise learning with the activities in this learning sequence.

Assessment

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 student work samples that provide teachers with examples of student learning achievement at multiple levels for each strand of the Mathematics curriculum.

Victorian Curriculum connections

Contents

Level 5

This sequence addresses content from the Victorian Curriculum in Mathematics, Measurement and Geometry, Using units of Measure and Number and Algebra, fractions, and decimals. It is primarily designed for Level 6 but also addresses the following Level 5 content descriptions:

 Content description Stage Mathematics Choose appropriate units of measurement for length, area, volume, capacity and mass (VCMMG195) It's Estimation Time Do We Have Enough Space? How Big is That Balloon? Calculate the perimeter and area of rectangles and the volume and capacity of prisms using familiar metric units (VCMMG196) Assemble your Angles Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (VCMNA188) Playing with Polygons Assemble your Angles Dancing Between the Lines Untangle Polygons and Angles

The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum: Mathematics Level 5:

• Students use appropriate units of measurement for length, area, volume, capacity, and mass.
• Students calculate perimeter and area of rectangles and volume, and capacity of rectangular prisms.

Level 6

This sequence addresses content from the Victorian Curriculum in Mathematics, Measurement and Geometry, using units of measurement and Number and Algebra, fractions, and decimals. It is primarily designed for Level 6, addressing the following content descriptions:

 Content description Stage Mathematics Connect decimal representations to the metric system (VCMMG222) Uncle Jack’s Land How Big is that Balloon? Convert between common metric units of length, mass and capacity (VCMMG223) It’s Estimation Time Uncle Jack’s Land How Big is That Balloon? Solve problems involving the comparison of lengths and areas using appropriate units (VCMMG224) Uncle Jack’s Land Do We Have Enough Space?  Who is Right? Connect volume and capacity and their units of measurement (VCMMG225) How Big is That Balloon? Multiply and divide decimals by powers of 10 (VCMNA216) It’s Estimation Time Uncle Jack’s Land How Big is That Balloon? Solve problems involving addition and subtraction of fractions with the same or related denominators (VCMNA212) It’s Estimation Time Critical and Creative Thinking Consider the importance of giving reasons and evidence and how the strength of these can be evaluated (VCCCTR025) Do We Have Enough Space?  Who is Right? How Big is That Balloon?

The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum: Mathematics Level 6:

• Students relate decimals to the metric system and choose appropriate units of measurement to perform a calculation.
• Students convert between units, recognise the prefixes used in metric measurements, and relate and compare measures and units, including capacity and volume.
• Students solve problems involving length, area, volume, and make connections between capacity and volume.

Level 7

This sequence addresses content from the Victorian Curriculum in Mathematics, Measurement and Geometry, using units of measurement and Number and Algebra, real numbers. It is primarily designed for Level 6, but also addresses the following content descriptions from Level 7:

 Content description Stage Mathematics Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (VCMMG258) It’s Estimation Time Uncle Jack’s Land Do We Have Enough Space?  Who is Right? Critical and Creative Thinking Consider a range of strategies to represent ideas and explain and justify thinking processes to others (VCCCTM040) Do We Have Enough Space?  Who is Right? How Big is That Balloon?

The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum: Mathematics Level 7:

• Students use formulas for the area and perimeter of rectangles.

Learning Progressions

The Numeracy Learning Progressions support teachers to develop a comprehensive view of how numeracy develops over time. You can use the Numeracy Learning Progressions to:

• identify the numeracy capability of your students
• plan targeted teaching strategies, especially for students achieving above or below the age-equivalent expected level in the Victorian Curriculum: Mathematics
• provide targeted feedback to students about their learning within and across the progressions.

The sequence is related to the following progression(s):

 Learning Progression Level 5 Level 6 Level 7 Understanding Units of Measure Identifying the structure of units Identifying the structure of units Converting Units

Click on the Learning Progression to access more detailed descriptions of student learning at each level.