Measurement

AO3: Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae.

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How High? and Other Problems

In this unit we use ruler and compass constructions to draw a variety of shapes and to construct angles such as 90°, 60°, 45° and 15°.

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AO2: Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.

AO1: Measure at a level of precision appropriate to the task.

AO4: Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.

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Scale Factors for Areas and Volumes

This unit provides students with the opportunity to discover the effect of a change of length by a given factor on area and volume.

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Round the Track

This unit is about making calculations in the real life situations of athletics.

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Fences and Posts

In this unit a measurement strand objective concerning finding areas of shapes is explored, then a link to the algebra strand is explored.

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A4 Containers

Describe the relationship between the surface area and volume of a container

Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram, use a model)

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Bill's Badge

Construct two intersecting circles where the radius of the second circle is on the circumference of the first.

Use Pythagoras’ theorem to find the area of a rhombus

Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram, use a model)

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Penny's Box

Find the volume and surface area of rectangular prisms

Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram).

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Puck's Girdle

Find the circumference of a circle;

Understand the relationship between changes in the circumference of a circle and changes in the radius.

Devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).

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Tennis Ball Tubes

Use the formula for the circumference and diameter of a sphere to solve a problem

Devise and use problem solving strategies to explore situations mathematically (be systematic, make a model)

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Playdough Balls

compare the volume of a sphere and a cylinder by either measuring or applying a formula.

devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).

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Karen's Tiles

investigate how perimeter changes as area changes

see the relation between area and perimeter for similar shapes

pose questions for mathematical exploration

prove or refute mathematical conjectures

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Peter's Second String

determine the maximum area of a rectangle with a given perimeter

determine the range of areas of a rectangle with a given perimeter

pose questions for mathematical exploration

prove or refute mathematical conjectures

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Dan's Badge

Use area formulas of circles and squares to solve problems

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The measurement of circles and the relationships to be found within them are the focus for this unit. Students investigate a range of circles, each with a different radius, diameter and circumference and assemble this information in their search for relationships.

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Circle Links

This is a level 4 and 5 measurement strand activity from the Figure It Out series.

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Colossal Kiwifruit

This is a level 5 measurement strand activity from the Figure It Out series.

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Round the Bend

This is a level 5 measurement strand activity from the Figure It Out series.

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On the Right Track

This is a level 5 measurement strand activity from the Figure It Out series.

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Gumboot Games

This is a level 5 measurement strand activity from the Figure It Out series.

AO3: Deduce and use formulae to find the perimeters and areas of polygons and the volumes of prisms.

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Square Pegs in Round Holes

Draw a diagram to represent a physical situation for a general case;

Apply Pythagoras’ theorem to a general situation

Devise and use problem solving strategies to explore situations mathematically

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Penny's Box

Find the volume and surface area of rectangular prisms

Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram).

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Playdough Balls

compare the volume of a sphere and a cylinder by either measuring or applying a formula.

devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).

AO2: Convert between metric units, using decimals.

Children

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Ratios

In this unit we use the theme of drinks to develop an understanding of ratios. It is suitable for students working at Level 5 of the curriculum or Stage 8 of the Number Framework. The unit provides a sequence of demonstrations and questions to help guide students' learning. It includes activities that require students to convert between the metric units for capacity, and to use their knowledge of fraction, decimal and percentage conversions. Students use proportional thinking to explore, compare and combine ratios. The unit concludes with a session on rates (a subset of ratios).

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Ratios

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Body Measurements

These exercises and activities are for students to use independently of the teacher to practice number and measurement skills.

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Plentiful Plankton

This is a level 5 measurement strand activity from the Figure It Out series. It also has an achievement objective from the Level 5 Number strategies and knowledge substrand.

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Fat in Foods

This is a level 5 measurement strand activity from the Figure It Out series. It also has an achievement objective from the Level 5 Number strategies and knowledge substrand.

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Television Views

This is a level 5 measurement strand activity from the Figure It Out series. It also has an achievement objective from the Level 5 Number strategies and knowledge substrand.

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Sailing with Maths

This is a level 5 number, measurement, and geometry activity from the Figure It Out theme series.

AO1: Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.

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Measurement Investigations 1

The students will complete a number of practical measuring investigations, with an emphasis on accuracy of measuring and communication of their findings

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Measurement Investigations 2

The students will complete a number of practical measuring investigations, with an emphasis on accuracy of measuring and communication of their findings.

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Body Measurements

These exercises and activities are for students to use independently of the teacher to practice number and measurement skills.

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Little Links

This is a level 4 and 5 measurement strand activity from the Figure It Out series.

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Hot Dogs

This is a level 5 measurement strand activity from the Figure It Out series. It also has an achievement objective from the Level 5 Number strategies and knowledge substrand.

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Average Looking

In this unit we use measurements of our classmates to find the average (means and modes) of our features. We use our findings to create a 3-dimensional "class head" .

AO4: Interpret and use scales, timetables, and charts.

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How long is a slinky?

In this unit students take part in a variety of measurement tasks including measuring the length of a slinky, working out how many slices of tomato will fit around the edge of a pizza and drawing the label from a can accurately.

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How Far?

Calculate using the 24-hour clock and time zones

Devise and use problem solving strategies to explore situations mathematically (make a drawing, be systematic)

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Time Zones

In this unit we introduce and explore time zones and international Date Line.

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Cool Times with Heat

In this unit we use thermometers to investigate questions about temperature. We explore questions relating to cooling patterns, the effect of location on temperature, and the results of mixing of water with different temperatures

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Doing Time

In this activity students will explore activities relating to time.

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Home Run

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

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Gigantic Jumbo

This is a level 3 and 4 measurement activity from the Figure it Out series.

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The Heat is On

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

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Working with Data

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

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Energy Crisis

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

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Cellphone Confusion

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

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Scale of Events

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

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Ways to Go

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

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Time and Tide

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

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Cylinder Collection

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

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Chilling Out

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

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You're All Heart!

These are level 4 number, and measurement problems and level 3 algebra problems from the Figure It Out series.

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When and Weather

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

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Planning the Tramp

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

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Claws!

This is a level 4 measurement and statistics activity from the Figure It Out theme series.

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Melissa's Room

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

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Cosmo's Kennel

This is a level 4 measurement and number activity from the Figure It Out theme series.

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Roundabout Rugby

This is a level 4 probability and masurement activity from the Figure It Out theme series.

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Hitting Four

This is a level 4 measurement and number activity from the Figure It Out theme series.

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Day Trippers

This is a level 4 measurement, geometry, statistics and level 5 number activity from the Figure It Out theme series.

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Time Zones

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

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Queenstown Extravaganza

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

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Measuring Potential

This is a level (3+ to 4+) mathematics in science contexts activity from the Figure It Out series.

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Wind Chill

This is a level (3+ to 4+) mathematics in science contexts activity from the Figure It Out series.

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Tramping against Gravity

This is a level (3+ to 4+) mathematics in science contexts activity from the Figure It Out series.

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Hypothermia

This is a level (3+ to 4+) mathematics in science contexts activity from the Figure It Out series.

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Wind Power

This is a level (3+ to 4+) mathematics in science contexts activity from the Figure It Out series.

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Using Electricity

This is a level (3+ to 4+) mathematics in science contexts activity from the Figure It Out series.

AO3: Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids.

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You Can Count on Squares!

The unit is presented as a scenario that includes five tasks that students engage in and explore to develop mathematical, specifically algebraic, ideas. Although the tasks are built around measurement, they are algebraic to the extent that they require ‘formulae’ to be derived form the geometric situations. It is sufficient at this Level for the students to express these formulae in words rather than in symbols.

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What Goes Around

This unit is made up of five stations which investigate the relationships between the area and perimeters of squares and rectangles. The unit could be taken a series sessions with the whole class or the students could circulate around the stations over the five days.

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Triangles

This unit is around discovering and applying the rule for area of a triangle (area equals half base times height). Students will practice multiplication and division strategies as they calculate areas.

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Fertiliser

Calculate the area of rectangles using m²

Use remainders within the context of a problem

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The Chicken Run

explain the relationship between the area and perimeter of rectangles

use a table to solve a problem

devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, make a table, make a drawing)

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Peter's String

Determine the area of a rectangle with a given perimeter;

Pose questions for mathematical exploration

Make conjectures in a mathematical context

Prove or refute mathematical conjectures

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Volumes of Cubes

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.

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Covering Up

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

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It's a Wrap

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

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Castle Construction

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

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Divide and Prosper

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

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Books in Boxes

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

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Great Gardens

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

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The Big Drip

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

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Ps for Ever

These are level 4 measurement, number and algebra problems from the Figure It Out series.

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Stretching Exercises

These are level 4 number and measurement problems from the Figure It Out series.

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Talk About: Four

These are level 4 measurement and algebra problems from the Figure It Out series.

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Melissa's Room

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

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Cosmo's Kennel

This is a level 4 measurement and number activity from the Figure It Out theme series.

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The Warlord’s Kites

This is an activity based on the picture book The Warlord’s Kites

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The Emperor’s Army

This is an activity based on the picture book The Emperor’s Army

AO2: Convert between metric units, using whole numbers and commonly used decimals.

Children

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Team Puzzles

In this unit students work in co-operative teams of four to complete a puzzle. Each student initially works independently, and then the team jointly puts together the four shapes they have individually made, to complete the puzzle.

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How fast is fast?

This unit is designed to provide students with a measurement context in which to use number operations. In calculating speed from distance and time, they will apply number strategies as they convert between units.

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Spaced Out

In this unit we explore the volume (in cubic units) of our skyscraper constructions and those of others in the class. We investigate the most efficient way to pack cuboids in a confined space and conclude with "water play" as we investigate the relationship between millilitres and cubic centimetres

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How fast is fast?

This unit is designed to provide students with a measurement context in which to use number operations

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Squirt Level 4

This unit explores how the suite of learning objects, "Squirt", can be used to support students’ development of multiplicative thinking. Squirt encourages students to anticipate multiplicative measurement relationships, e.g. three measures of A fit in B, by partially filling a container and imaging how many more squirts will be needed. Since the containers are not always cylindrical it also develops ideas about conservation of volume.

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