# Dynamic Darts

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Purpose

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

Achievement Objectives
GM4-1: Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
S4-1: Plan and conduct investigations using the statistical enquiry cycle: determining appropriate variables and data collection methods; gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends; comparing distributions visually; communicating findings, using appropriate displays.
Student Activity

Click on the image to enlarge it. Click again to close. Download PDF (1547 KB)

Description of Mathematics

While discrete objects (such as people in a room) can be counted, continuous variables (such as length, time, angle, volume, mass, and temperature) can only be quantified (that is, measured) with the aid of a suitable device and unit.
Measurement skills include being able to use devices (for example, a ruler, a jug, a protractor, a thermometer), read scales, estimate, choose appropriate units, interchange units, round, interpret a decimal point, and assess the sensibleness of a result.
Measurement is the basis of most quantifying and most comparing. Confidence in measuring is developed over time, through experiences in many different contexts. Ideally, students extend and develop their skills in response to a need.
In this activity, students need a basis for judging performance. They explore which attributes enable a paper dart to fly further, straighter, or faster, or to stay in the air for longer, and they work together to try to create a “best ever” dart.

Required Resource Materials

paper

measuring equipment (e.g., a tape measure, a stopwatch, a large protractor)

FIO, Technology in Practice, Levels 3+-4+, Dynamic Darts, pages 22 - 24

classmates

Activity

Paper dart designs can be readily found on the Internet. For examples, see:

• www.paperairplanes.co.uk/planes.php
• www.bestpaperairplanes.com

Evaluating the relative flights of the darts requires group consensus on how to measure and record performance.
If the students are measuring flight distance, they will need to define “distance”. The flight paths of the darts are unlikely to be straight. In sporting competitions such as shot put or javelin, the flight distance is measured from the point that the object first touches the ground rather than the object’s final resting point. Discuss the practicality of using this approach in a paper dart competition.
Measuring the speed of a dart is incredibly challenging. Although in theory this could be achieved by measuring speed over a fixed distance, the speed a dart travels is dependent on the force with which it is thrown. The flight path of the dart is unlikely to be perfectly straight, nor will it be level. Discuss these challenges with the students. They should conclude that they are not equipped to deal with this variable.
Straightness of flight could be measured using a centre line (from the throwing point) and measuring the angle of deviation with a large protractor and string.
Students need to decide what degree of accuracy they should aim for. For example, should they measure to the nearest centimetre or to the nearest millimetre? To the nearest second or the nearest tenth of a second? If they are timing flight duration, there will be variation in the reaction times of those doing the timing. Ask three students to time the same flight and compare their times. Discuss the reasons for any differences.
Check that your students are using their measurement equipment correctly.
Discuss how the steps in this activity relate to the statistical enquiry cycle:

• Problem: What is it we are trying to find out? For example, which attributes enable a dart to fly further?
• Plan: How will we collect and record the data to answer our question?
• Data: Collect and record data.
• Analysis: Which darts flew the furthest? What design features do they share?
• Conclusion: What else could we try to make the dart fly further?

Working in groups to investigate modifications develops the key competency participating and contributing.

#### Support for English Language Learners

##### Supporting students with writing a report to explain a process

In Activity Two, question 2 (page 24) students are asked to write a report explaining a process. To support your students, especially English language learners, you could provide (or co-construct) a writing frame to show ways to create such a report (see the example below). Use the frame to co-construct a report, modelling how they can use the frame to write their own reports.
Consider writing a short report yourself (on a similar topic) to help you identify the language demands of this kind of report: the structure of the text, sentence types, language structures (for example, phrases and clauses signalling sequence), and vocabulary.
Some students will be able to write more effectively after presenting their process orally. Students who share a first language other than English will also benefit from opportunities to explain their process in this language.
Example of a writing frame for an explanation of a process

 Section Content My notes My report Introduction Introduce the process.Introduce the three stages. Stage 1 Introduce the first stage.Explain each step in the stage. Stage 2 Introduce the second stage.Explain each step in the stage. Stage 3 Introduce the third stage.Explain each step in the stage. Conclusion Restate the process and the three stages.Explain the final outcome.

Adapt the writing frame to provide different levels of support according to the needs of your students. Some may need just the first column, some the first and second. Some students may benefit from sentence starters or even cloze sentences (gap-fill sentences) in the last column (where they write their first draft).
For information about language for explaining and ideas on how to support students, see Supporting English Language Learning in Primary Schools: A Guide for Teachers of Years 7 and 8, Explaining, pages 50–59.

#### Technology-related student activities

• Construct the model aeroplanes as illustrated in the student booklet to investigate thrust, lift, weight, and drag.
• Research world-record performances for paper darts.
• Hold a school-wide paper-dart-throwing event.

#### Exploring the technology-related context

Technologists use models to test ideas. These can be a relatively inexpensive and safe way to determine whether an idea is feasible. The model can represent a complete product or a component. A new technology may need components that have yet to be invented, and models can reduce development time. From concept design (possibly computer-assisted) and mock-ups through to a prototype, model making is an essential aspect of technological innovation. Paper darts illustrate how models can demonstrate the performance of aircraft designs.
Sometimes, models become products in their own right. Many people enjoy controlling model cars, boats, and trains.

#### Activity One

1. a.–b. Ideas will vary. Darts with narrow, tapered wings are likely to travel further, faster, and straighter. Darts with wide wings are likely to be slower and to stay in the air longer, but they are less likely to travel in a straight line.
2. a.–e. Practical activity.

Activity Two

1. a.–e. Practical activity
2. Practical activity. Reports will vary.
3. It’s not possible to directly compare the improvements made by each group because they were investigating different variables. However, Calvin’s group more than doubled their dart’s flight time (6.5 ÷ 3 = 2.2), while Mali’s group increased flight distance by a rather smaller factor of 1.74 (10.8 ÷ 6.2). So it could be argued that Calvin’s group did better than Mali’s group.

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