Round-up 5 Teachers Guide

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Data collection activities should lead to classification, organisation, summarising and displaying in a variety of ways.

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In the New Wave Maths series, students are introduced to activities that include an element of unpredictably and refine their use of some of the everyday language of chance. Classification skills are developed through a variety of activities. Where practical, students are asked to record and represent data. Students are directed to construct graphs or represent data in a format that is logical and easy to read. Space Students are to recognise shapes as well as visualise, draw and model shapes, locations and arrangements and predict and show the effect of transformations on them. Using their knowledge of shapes, transformations and arrangements, students are able to solve problems and justify solutions.

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Space activities should emphasise the investigation of the features of objects in the environment, including their shape and the effect on them of changes in shape, size and position, and include symmetry and tessellations. The features of objects should be emphasised in space activities. Relationships between three-dimensional shapes and two-dimensional shapes are represented by nets, diagrams and scale models. Sorting and classifying of shapes continues. Angles and directions are related to compass directions.

The New Wave Maths series develops space exploration of the students' own environment and objects within it. By manipulating materials in a variety of ways students learn to observe and describe them in everyday language. Estimation and measuring skills using standard units should be completed. Work in algebra is based on patterns in space and number strands. Relationships between two quantities should be noted when one of the quantities is varied. Where possible, relationship graphs should be used to explain relationships.

Students should be finding ways to explain generalisations in these early stages of development of algebra. There is little algebra covered in the New Wave Maths series; however, teachers should be aware of this outcome, particularly for talented students who may recognise and describe the nature of variation in situations and are able to read, write and understand the meaning of symbolic expressions. They may also write equations and inequalities to describe situations. Number patterns are covered in much of the number work, which in turn leads to the development of algebra.

Technology Calculators are an important technological resource in the teaching and learning of mathematics. The calculator should be used as both an instructional aid and as a computational tool. With the advent of cheaper and more sophisticated calculators there comes a natural deemphasis on written calculations. There is, as a consequence, a reduction in the complexity of written computation work but a clear emphasis on the use of concrete material to improve understanding of concepts to be developed through the New Wave Maths series. Greater emphasis is placed on quick and accurate mental computation.

Mental calculations and calculator use need to be developed as these form the basis of most computational needs of adults in real-life situations. It is strongly recommended that all students use calculators at all Year levels K— The Learning Mathematics Handbook Pre-Primary to Stage Seven Mathematics Syllabus, pages 30 — 31 details where calculators can be used as an instructional aid to:. An emphasis on knowledge of basic addition and multiplication facts and relationships, place value understanding, estimation, checking of results and confidence in applying appropriate calculations is essential.

Computers also have their place in the mathematical learning environment and should be accorded appropriate time. Teachers need to select software which is sufficiently flexible and open-ended to allow students to develop their own ideas and use their initiative.

The computer can be used in problem-solving, investigations, modelling, strategy games, refining ideas, concept development, skill development and gaining factual knowledge. There is still a place for textbooks in the teaching and learning of mathematics. However, emphasis must be placed on the need to use a variety of print materials.

No single text is likely to cater for the interests of all students or cover the mathematics curriculum in full. The New Wave Maths series provides a solid foundation and allows teachers the opportunity to add their own ideas and activities to suit their individual class and students. Assessment Assessment is a critical component of the teaching program and is outlined in The Curriculum Framework, pages — by these points:.

Assessment should provide valid information on the actual ideas, processes, products and values which are expected of students. Assessment should be demonstrably fair to all students and not discriminate on grounds that are irrelevant to the achievement of the outcome. Assessment is a crucial aspect of the mathematics learning process. Assessment provides feedback on individual development to the student, teachers and parents. It provides the information for future teaching.


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All the outcomes of the school mathematics curriculum should be reflected in the assessment process. All assessments should be demonstrably fair, valid and reliable. The fairness of mathematical testing is brought into question by the practice of using one form of test only. Individual students respond to different environments in different ways; therefore the use of a single assessment tool, such as a pencil and paper test, may be valid and reliable but not fair, as the individual may respond better to short-answer questions, extended response questions or other forms of assessment.

Hence, using nonrepresentative sampling of the mathematics curriculum outcomes or narrow sampling methods of assessment may be unfair to many students. It is clearly understood now that conventional forms of tests pencil and paper cannot address all areas of the mathematics curriculum; therefore, additional, not alternative, methods of assessment must be developed. Commercially prepared assessment packages are available from R.

New Wave Maths is not a stand-alone assessment document. Activities may be assessed based on Student Outcome Statements. Teachers will need to be familiar with these to make the appropriate assessments. All activities may be assessed in this way. It is suggested that a random sample of activities only is assessed using Student Outcome Statements to determine progress.

Cross-curriculum Linkages The learning and application of mathematics occurs across all curriculum areas. Literacy skills are developed in the English learning area where language foundations are provided that are essential for the learning of mathematics. Mathematics also provides for the development of language skills. Together, English and mathematics provide the information skills used in activities such as reading the newspaper, information text such as a telephone directory, and preparing and presenting reports.

Spatial and measurement tasks are interwoven in many art activities which may in themselves provide alternative stimulus for the learning of mathematical skills.


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    Design activities and spatial knowledge development are a practical component of the Technology and Enterprise learning area. Activities in this learning area provide a wider diversity of learning opportunities than those provided from the basic mathematics syllabus. The cultural significance of mathematics, its origins and different developments may be explored in the Languages Other than English and Society and Environment learning areas. How to Use the Teachers Notes Unit and student page shown here as a quick reference to the equivalent page in the student workbook.

    Indicators from the Student Outcome Statements have been included as a quick guide. These are directly related to the main activity only. Outcomes relevant to all activities on the student workbook page have been listed as a ready reference.

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    A space for you to record notes relevant to the lesson has been provided. This space could be used for any purpose. Language terms relevant to the workbook page have been listed here. It is preferred these words be introduced before beginning the activity to ensure students have a clear understanding of the terminology used in the activities. The student workbook page is broken into distinct sections. These are each discussed in detail in this section of the teachers notes. The section is stated, followed by the relevant outcome in brackets. Then bullet points are used to guide you through the activity.

    The great thing is that once this information is recorded, when you come to teach the lesson again, these notes will refresh your memory and enhance the smooth running of the lesson. This section is a guide only and you are more than welcome to take from it what you choose, modify it or add your own touches.

    Answers have been provided to assist teachers in marking students' work. Some answers do require a teacher check as they are dependent on the classroom environment and the students in your class. Where possible, all answers are given.

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    The answers for the Challenge activities are generally an example of one possible solution, as many solutions are often possible. Where possible, links to a relevant assessment activity in the R. Suggested activities for consolidation of the main activity on the workbook page have been provided as a guide only. Feel free to use, modify, extend or disregard these as you feel necessary.

    Materials List The following list of suggested materials is a guide only. It is not suggested that they must be purchased or are the only items that may be used. If compiling a set of materials that will both supplement and compliment the teaching program, the following items will assist.

    Some items are required to complete the workbook activities. These are listed in more detail on the relevant page in the teachers notes. Teachers may photocopy and use them with their class es. Record and display data in a pictograph. Identify half turns clockwise and anticlockwise and full turns. Use a balance scale to compare the mass of objects. Identify place value in three-digit numbers.