# GM4-6: Relate three-dimensional models to two-dimensional representations, and vice versa. (2023)

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Elaboration on this Achievement Objective

This means students will focus on key characteristics of 3-dimensional models (shape and relationship of faces and surfaces, faces joining at edges and vertices) to create 2-dimensional drawings of those models. Drawings of objects can take the form of isometric projections, plan views or nets. Students should also be able to construct a model from given 2-dimensional drawings, for example build a model using interlocking cubes from the plan views below. Students should be able to create nets for simple polyhedral and closed surfaces by visualising the “unwrapping” of those solids, for example the net for a cube.

Teaching resources for this Achievement Objective ## A Different View

Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

draw different views of three dimensional shapes ## Blocked Plans

Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

interpret plan views of buildings ## Breakfast Biscuits

Level Four

Integrated

Units of Work

This unit seeks to connect learning outcomes across all five content strands, number, geometry, statistics, and measurement. However the context lends itself strongly to use of measurement and statistics.

• Construct nets.
• Measure masses, capacities, lengths, and temperatures using scales and devices.
• Conduct investigations and present results.
• Carry out experiments and systematically record the results. ## Building Boldly

Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

interpret plan views of cube buildings ## Building Specs

Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 activity from the Figure It Out series.A PDF of the student activity is included. ## Building with triangles

Level Four

Geometry and Measurement

Units of Work

In this unit, students will identify the properties of triangles, construct both equilateral and irregular triangles using either ruler and protractor or ruler and compass, and make nets.

• Construct triangles with specified dimensions using two different techniques.
• Design and construct nets for three-dimensional objects.
• Name basic three-dimensional objects, especially those made with equilateral triangles. ## Cantitowers

Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 link geometry activity from the Figure It Out series.

interpret different views of three dimensional buildings ## Castles on the ground

Level Four

Geometry and Measurement

Problem solving activities

Construct 3D shapes from 2D drawings

Describe the symmetries of 3D shapes

Draw 3D shapes on isometric paper

Interpret information and results in context; make conjectures in a mathematical context;

Devise and use problem solving strategies to explore situations mathematically (guess and300 ## Cube Creations

Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 geometry strand activity from the Figure it Out series. A PDF of the student activity is included.

draw three dimensional shapes on isometric paper

make three dimensional shapes from two dimensional pictures ## Cubic Conundrums

Level Four

Integrated

Units of Work

This unit provides a set of learning tasks that integrate across the strands of the Mathematics and Statistics learning area of the New Zealand Curriculum and provide opportunities for assessment of student achievement across those strands. Each session may involve more than one lesson, especially...

Session One
Use systematic approaches to find all the possible outcomes, e.g. tree diagrams, organised lists.

Session Two
Use tables, graphs, and word rules to represent growing patterns.

Session Three
Draw cube models using plan views.

Session Four
Draw cube models using isometric300 ## Cute Cubes

Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

follow geometric instructions to make a cube ## Emergency Shelters

Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 activity from the Figure It Out series.A PDF of the student activity is included. ## Fantastic Folding

Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

follow instructions to make a three dimensional geometric shapes ## Fire Alarm!

Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 geometry activity from the Figure It Out theme series. A PDF of the student activity is included.

interpret a contour map

draw a three dimensional modle

build a scale model ## Hut building

Level Four

Geometry and Measurement

Rich learning activities

The purpose of this activity is to engage students in relating two dimensional projections to a three dimensional perspective in the context of a scale and unit conversion measurement problem. Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

draw a net Level Four

Level Five

Integrated

Figure It Out activities

These are level 4 geometry and level 5 number problems from the Figure It Out series.A PDF of the student activity is included.

solve problems involving division and decimals (Problem 2)

use fractions of two dimensional shapes to solve puzzles (Problem 3) ## Penguin Properties

Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 activity from the Figure It Out series.A PDF of the student activity is included. ## Pyroxene

Level Four

Geometry and Measurement

Rich learning activities

The purpose of this activity is to engage students in evaluating a claim made on the basis of supporting statistics. ## Representing 3D objects in 2D drawings

Level Four

Geometry and Measurement

Units of Work

This unit develops students’ ability to represent three dimensional objects using two dimensional representations.

• Use plans from different viewpoints to represent 3D objects.
• Draw isometric drawings of 3D objects.
• Create nets for polyhedra.
• Interpret the above representations to create a model of the 3D object. ## Solid Understanding

Level Four

Geometry and Measurement

Units of Work

In this unit students make and investigate various solids, including regular and semi-regular polyhedra, and cylinders and cones. They look for patterns in the numbers of faces, edges and vertices.

• Construct models of polyhedra using construction materials, like geoshapes or polydrons.
• Use the terms faces, edges and vertices to describe models of polyhedraand look for relationships between these features.
• Anticipate the features of the solid created when a Platonic solid is truncated300 ## The castle

Level Four

Geometry and Measurement

Problem solving activities

Construct 3-D shapes from 2-D drawings

Describe the symmetries of 3-D shapes

Draw 3-D shapes on isometric paper

Devise and use problem solving strategies to explore situations mathematically (guess and check, use equipment) ## Volumes of Cubes

Level Four

Integrated

Secondary activities

These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (see Related Resources) and may become longer and more involved with subsequent recording/reporting.

• Draw 3D shapes on isometric paper.
• Explore the relationship between edges, faces and vertices of relevant cube structures.
• Explore the relationship between the dimensions of a cube and its volume.
• Interpret drawings of 3D cubes.
• Calculate volume of 3D cube structures. ## X-ray Vision

Level Four

Geometry and Measurement

Figure It Out activities

This is a level 4 geometry strand activity from the Figure It Out series.A PDF of the student activity is included.

draw different views of three dimensional shapes

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