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

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

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

draw different views of three dimensional shapes

Figure It Out activities

Geometry and Measurement

Level Four

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

interpret plan views of buildings

Figure It Out activities

Geometry and Measurement

Level Four

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. In the unit students investigate questions that involve them in experiment design, data...

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.

Units of Work

Geometry and Measurement

Level Four

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

interpret plan views of cube buildings

Figure It Out activities

Geometry and Measurement

Level Four

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

Figure It Out activities

Geometry and Measurement

Level Four

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

Units of Work

Geometry and Measurement

Level Four

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

interpret different views of three dimensional buildings

Figure It Out activities

Geometry and Measurement

Level Four

Construct 3D shapes from 2D drawingsDescribe the symmetries of 3D shapesDraw 3D shapes on isometric paperInterpret information and results in context; make conjectures in a mathematical context;Devise and use problem solving strategies to explore situations mathematically (guess and check, use...

Problem solving activities

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure it Out series.

draw three dimensional shapes on isometric paper make three dimensional shapes from two dimensional pictures

Figure It Out activities

Geometry and Measurement

Level Four

To provide a set of learning tasks that integrate across the strands of the New Zealand Mathematics Curriculum and provide opportunities for assessment of student achievement across those strands. Each session may involve more than one lesson, especially if students need more time to become...

Session OneUse systematic approaches to find all the possible outcomes, e.g. tree diagrams, organised lists.Session TwoUse tables, graphs and word rules to represent growing patterns.Session ThreeDraw cube models using plan views.Session FourDraw cube models using isometric projections.Session...

Number and Algebra

Level Four

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

follow geometric instructions to make a cube

Figure It Out activities

Geometry and Measurement

Level Four

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

Figure It Out activities

Geometry and Measurement

Level Four

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

follow instructions to make a three dimensional geometric shapes

Figure It Out activities

Geometry and Measurement

Level Four

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

interpret a contour map draw a three dimensional modle build a scale model

Figure It Out activities

Geometry and Measurement

Level Four

This interactive learning module supports students to explore how viewpoints and perspective can help to draw a more accurate representation of a three-dimensional object.

Recognising different views of objects. Accurately drawing 2-D representations of 3-D objects. Making a perspective drawing of a 3-D object, applying an understanding of vanishing points.

Student e-Ako

Geometry and Measurement

Level Four

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.

Rich learning activities

Geometry and Measurement

Level Four

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

draw a net

Figure It Out activities

Geometry and Measurement

Level Four

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)

Figure It Out activities

Number and Algebra

Level Five

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

Figure It Out activities

Geometry and Measurement

Level Four

The purpose of this activity is to engage students in evaluating a claim made on the basis of supporting statistics.

Rich learning activities

Geometry and Measurement

Level Four

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 they see whether they can “discover” Euler’s famous formula. By truncating the vertices of the Platonic...

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

Units of Work

Geometry and Measurement

Level Four

Construct 3-D shapes from 2-D drawingsDescribe the symmetries of 3-D shapesDraw 3-D shapes on isometric paperDevise and use problem solving strategies to explore situations mathematically (guess and check, use equipment)

Problem solving activities

Geometry and Measurement

Level Four

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

Secondary activities

Number and Algebra

Level Four

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

Figure It Out activities

Geometry and Measurement

Level Four