acinca.wikispaces.comacinca.wikispaces.com/file/view/MYL+maths+unit+plan… · Web viewThroughout this unit, it is expected that students will have ready access to ICTs at whole class,

DEPARTMENT OF EDUCATION AND TRAINING

Unit Plan Mathematics

NT Multiple Year Level Unit Plan

Key Focus Data representation and interpretation Year Level 6 - 9

Teacher Unit 6

Class Duration 5 weeks (Term 3, Wk6 - Wk10)

Unit Outline

In this unit, students apply a variety of mathematical concepts in real-life, lifelike and purely mathematical situations. Through the sub-strand Statistics and Probability students have the opportunities, dependent on year level, to develop understandings of:

Techniques for collecting and recording data Representing data in a variety of forms Interpreting data sets and evaluating effectiveness of data displays Checking and investigating data and data sources, and issues surrounding validity Calculating, using and describing median, mode and range when presenting or interpreting data

Students have opportunities to consolidate knowledge in the following sub-strands: Fractions & Decimals (Unit 5) Using Units of Measurement (Unit 5)

Students have opportunities to revisit knowledge in the following sub-strands: Number & Place Value (Units 1, 2, 3) Patterns & Algebra (Unit 3) Chance (Unit 3) Using Units of Measurement (Unit 2)

C2C adapted with permission by NT DET © The State of Queensland 1 of 16 www.det.nt.gov.au

Throughout this unit, it is expected that students will have ready access to ICTs at whole class, small group and individual levels.

Proficiency strandsThe proficiency strand statements relevant to this unit are:Understanding includes explaining the purpose of statistical measuresFluency includes collecting, recording and interpreting data from various sources effectivelyProblem solving includes interpreting secondary data displays and collecting data from secondary sources to investigate an issueReasoning includes interpreting data displays, evaluating data sources and using statistical knowledge to clarify situations

Curriculum intent: Content descriptions

Year 6 Year 7 Year 8 Year 9

Statistics and ProbabilityData Representation and Interpretation

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables ACMSP147

Interpret secondary data presented in digital media and elsewhere ACMSP148


Identify and investigate issues involving numerical data collected from primary and secondary sourcesACMSP169

Construct and compare a range of data displays including stem-and-leaf plots and dot plots ACMSP170

Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of dataACMSP171

Describe and interpret data displays using median, mean and range ACMSP172


Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes ACMSP206

Explore the variations of means and proportions of random samples drawn from the same population ACMSP293

Investigate the effect of individual data values , including outliers, on the mean and median ACMSP207


Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sourcesACMSP228

Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’ACMSP282

Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread ACMSP283


http://www.australiancurriculum.edu.au/Elements/ACMSP283










http://www.australiancurriculum.edu.au/Curriculum/ContentDescription/ACMSP148

http://www.australiancurriculum.edu.au/Curriculum/ContentDescription/ACMSP147


General capabilities

LiteracyStudents will understand and use: Word knowledge: technical vocabulary and everyday language used in mathematical contexts (See Key Mathematical Language Section) Grammar knowledge: procedural vocabulary (e.g. plot, calculate, evaluate, compare, interpret, describe) Visual knowledge: visual representations (e.g. column graphs, pie charts, dot plots, stem-and-leaf plots, histograms) Text knowledge: conventions and symbols (e.g. x axis, y axis, headings, sub headings)

Numeracy:Students will: Develop the knowledge and skills to use mathematics confidently Apply mathematical understanding in context Develop mental computation strategies

Information and Communication Technology (ICT) capabilityStudents will: Investigate, create and communicate mathematical ideas and concepts using interactive and multimodal technologies Navigate virtual and software environments including learning objects, games and websites

Critical and creative thinking:Students will: Reflection thinking, clarifying concepts and solving problems Reason, evaluate and develop strategies Generate and develop ideas and possibilities

Ethical Behaviour:Students will:

Build a strong personal and socially oriented ethical outlook Explore, develop and apply ethical behaviour in a range of contexts

Intercultural Understanding:Students will:

Value their own cultures, languages and beliefs and those others Understand how personal, group and national identities are shaped and the changing nature of culture Learn and engage with diverse cultures that recognise commonalities and differences, create connections with others and cultivate mutual respect


Cross Curriculum Priorities

Aboriginal and Torres Strait Islander Histories and Cultures:Students will:

Deepen their understanding of the lives of Aboriginal and Torres Strait Islander Peoples through the application and evaluation of statistical data

Asia and Australia’s Engagement With Asia:Students will:

Learn about the understandings and applications of mathematics Develop mathematical understandings in fields such as statistics by drawing on knowledge of and examples from the Asia region. Undertake investigations involving data collection, representation and analysis that can be used to examine issues pertinent to the Asia region

Sustainability:Students will:

Develop abilities in statistics and probability through rich, engaging and authentic contexts Develop the proficiencies of problem solving and reasoning Observe, record and organise data collected from primary sources over time and analyse data relating to issues of sustainability from secondary sources


Supportive learning environment

Differentiation

What do your learners already know, do and value? Where do the learners need and want to be? How do the learners best learn?

Consider the individual needs of all students, including English as an additional language/ dialect, gifted and talented and special needs, and provide learning experiences that are accessible to and respectful of the diversity of students’ cultural backgrounds.Start from where your students are at and differentiate teaching and learning to support the learning needs of all students. Plan and document how you will cater for individual learning needs.

The learning experiences within this unit can be differentiated by increasing the: frequency of exposure for some students intensity of teaching by adjusting the group size duration needed to complete tasks and assessment.

For guided and/or independent practice tasks: student groupings that will offer tasks with a range of complexities to cater for individual learning needs rotational groupings that allow for more or less scaffolding of student learning.

Assessment

How will I check the learners have made progress?Assessment is the purposeful, systematic and ongoing collection of information as evidence for use in making judgments about student learning.Principals, teachers and students use assessment information to support improving student learning. Feedback from evaluation of assessment data helps to determine strengths and weaknesses in students’ understanding.Students should contribute to an individual assessment folio that provides evidence of their learning and represents their achievements over the year. The folio should include a range and balance of assessments for teachers to make valid judgments about whether the student has met the achievement standard. Refer to Year level plan for more assessment information.


Monitoring student learningYear 6

ObservationCollect information about students’ ability to, for example: explore different ways that data

can be presented effectively collect data from sources or

experiments create data representations using

standard conventions

ConsultationConduct interviews with students to collect information about their knowledge and understanding of, for example: gathering information from

unfamiliar data displays validity of secondary data

Student work samplesCollect samples of work which may include: digital records of data displays

created by students worksheets on graphing of data

ACARA – Australian Curriculum Work Samples – Mathematics, Year 6


ObservationCollect information about students’ ability to, for example:

obtain secondary data from a variety of sources

present data effectively in different ways

ConsultationConduct interviews with students to collect information about their knowledge and understanding of, for example:

predicting and making inferences relating to secondary data

mean, median, mode and range

Student work samplesCollect samples of work which may include: worksheet calculating mean,

mode, median and range for data sets

print out of stem and leaf plot created using generator software

Data representation – stem and leaf plots task



ObservationCollect information about students’ ability to, for example: identify situations where data can

be collected compare and analyse data sets

from secondary sources

ConsultationConduct interviews with students to collect information about their knowledge and understanding of, for example: the different ways that data can

be obtained through sampling the effect of individual data values

on the mean and median

Student work samplesCollect samples of work which may include: Data representation – What

makes a safe driver? Task Data representation – Analysing

OHS risks task



ObservationCollect information about students’ ability to, for example: identifying appropriate questions

and issues to examine obtain primary data and

secondary data from a variety of sources

ConsultationConduct interviews with students to collect information about their knowledge and understanding of, for example: describing data using

mathematical terms including ‘skewed’, ‘symmetric’ and ‘bi-modal’

drawing valid conclusions based on findings of data analysis

Student work samplesCollect samples of work which may include: posters of histograms and back-

to-back stem-and-leaf plots Statistics assignment task Interpreting graphs task



http://www.acara.edu.au/curriculum/worksamples/AC_Worksample_Mathematics_9.pdf








Assessing student learning

Year 6 – Year 9

Common task:

Year 6 Year 7 Year 8 Year 9

Assessment task – Data decoder

C2C Unit 4

Assessment task – Basketball scores: mean, median, mode, range

C2C Unit 3

Assessment task - Fair games

C2C Unit 2


Sequencing teaching and learning

What is the sequence of teaching and learning?What do learners already know, do and value? Where do learners need and want to be? How do learners best learn?What will constitute the learning journey?

The relationship between what is taught and how it is taught is critical in maximising student learning.Start with what your students already know and set goals for the next steps for learning. Decide how to provide multiple opportunities for all students to explore and consolidate ideas, skills and concepts by considering how students learn best and by using a variety of teaching strategies.

Teaching strategies & learning experiences - a suggested teaching and learning sequence is outlined below:

Year 6Data representation & interpretation

explore differences between sample data and census data

evaluate sources of data, both digital and non-digital

explore and interpret data displays with two categorical variables

discuss and evaluate appropriateness of data display type

interpret secondary data and identify possible validity and bias issues within secondary data sources


collect, record data and construct stem-and-leaf plots and dot plots

calculate mean, find median and mode and calculate range

interpret data displays including mean, median and mode

investigate an issue by collecting secondary data

identify factors (sample size, sample method, bias) which influence data sets

make informed inferences and predictions base on presented data

Year 8Data representation & interpretation define and identify variables, and

classify as discrete, continuous or categorical

collect data through a variety of different methods including sampling, census and observation, and investigate differences in collection methods

identify factor, including bias, which influence data selection

investigate ways to draw different random samples from the same population

explore variation of means and proportions of random samples drawn from the same population

explore the concept of outliers and clusters, and investigate their effect on data sets


collect data from a variety of primary and secondary sources, with both numerical and categorical variables

construct and interpret histograms, back-to-back stem-and-leaf plots and dot plots

investigate the meaning of ‘skewed’, ‘symmetric’ and ‘bi-modal’

describe the data distribution using appropriate mathematical terms

find, compare and analyse mean, median and a range for sets of data

draw valid conclusions based on data


Key Mathematical Language

categorical data, numerical data, secondary data, graphical display,

axis, data source, variable, identify, record, organise,

evaluate, investigate, interpret, represent, construct, explain,

compare

categorical data, numerical data, secondary data, axis, data source,

stem-and-leaf plot, dot plot, pie chart, mean, median, mode, bias, range, statistics, variable, identify, investigate, construct, compare,

calculate, describe, interpret,

categorical variable, numerical variable, sampling, census,

secondary data, observation, variation, proportion, random,

population, outlier, cluster, mean, median, mode, range, statistics

investigate, explore, identify, calculate

categorical variable, numerical variable, secondary data, sampling

census, observation, population, variation, mean, median, range, spread, outlier, cluster, back-to-back stem-and-leaf plot, dot plot,

histogram, skewed, symmetric, bi-modal, bias, investigate, compare,

describe, interpret


Making judgements

How will I check that the learners have made progress?

Teachers and students use standards to judge the quality of learning based on the available evidence. The process of judging and evaluating the quality of performance and depth of learning is important to promoting learning.Teachers identify the task-specific assessable elements to make judgements against specified standards on evidence.

Achievement standard

YEAR 6By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and

YEAR 7By the end of Year 7, students solve problems involving the comparison, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving percentages and all four operations with fractions and decimals. They compare the cost of items to make financial decisions. Students represent numbers using variables. They connect the laws and properties for numbers to algebra. They interpret simple linear representations and model authentic information. Students describe different views of three-dimensional objects. They represent transformations in the Cartesian plane. They solve simple numerical problems involving angles formed by a

YEAR 8By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in

YEAR 9By the end of Year 9, students solve problems involving simple interest. They interpret ratio and scale factors in similar figures. Students explain similarity of triangles. They recognise the connections between similarity and the trigonometric ratios. Students compare techniques for collecting data in primary and secondary sources. They make sense of the position of the mean and median in skewed, symmetric and bi-modal displays to describe and interpret data.Students apply the index laws to numbers and express numbers in scientific notation. They expand binomial expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment. They sketch linear and non-linear relations. Students calculate areas of shapes and the volume and surface area of right


volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They evaluate secondary data displayed in the media.

Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students list and communicate probabilities using simple fractions, decimals and percentages.

transversal crossing two parallel lines. Students identify issues involving the collection of continuous data. They describe the relationship between the median and mean in data displays. Students use fractions, decimals and percentages, and their equivalences. They express one quantity as a fraction or percentage of another. Students solve simple linear equations and evaluate algebraic expressions after numerical substitution. They assign ordered pairs to given points on the Cartesian plane. Students use formulas for the area and perimeter of rectangles and calculate volumes of rectangular prisms. Students classify triangles and quadrilaterals. They name the types of angles formed by a transversal crossing parallel line. Students determine the sample space for simple experiments with equally likely outcomes and assign probabilities to those outcomes. They calculate mean, mode, median and range for data sets. They construct stem-and-leaf plots and dot-plots.

that data.Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities.

prisms and cylinders. They use Pythagoras’ Theorem and trigonometry to find unknown sides of right-angled triangles. Students calculate relative frequencies to estimate probabilities, list outcomes for two-step experiments and assign probabilities for those outcomes. They construct histograms and back-to-back stem-and-leaf plots.


Lesson Overview

Allocate a short time at the start of each lesson for ‘switching on’ student thinking and reasoning (familiarising), and ‘tuning in’ students (analysing) by promoting the use of mathematical language and revising mental computation strategies.Focussed learning (modelling) involves demonstrating what students need to learn and centres students on specific focus areas. Students may be in instructional groupings.Through guided practise, allow students to work individually or cooperatively. Provide focussed support for individuals needing extra support in reaching their learning goal.Allow students to demonstrate their learning. This may be through evidence from guided practise or may be through a separate assessment task.End each lesson with a reflection of student learning in that lesson, which may be through whole class reflection, group discussion or teacher summary.

Along with the suggested sequence of teaching and learning above, this five week block must also include lessons on the measurement and shape concepts in Unit 4 to allow students opportunities to consolidate their knowledge.

Revisiting of previous concepts - number & place value, money, time – is also included in the lessons. This may be through explicit sessions or incidental opportunities.

Intended Curriculum Weekly Lesson Outline

(Teacher to insert program here)



Differentiation

(Teacher dif ferent iation notes for class)


Resources

CARS AC Year 6 Maths Resources MapCARS AC Year 7 Maths Resources MapCARS AC Year 8 Maths Resources MapCARS AC Year 9 Maths Resources Map

ScootleMaths 300Improve (log on via Scootle)

First Steps in Mathematics: NumberFirst Steps in Mathematics: Measurement

C2C Unit Plans:Year Seven - Unit 2, Unit 3, Unit 4Year Eight - Unit 1, Unit 2, Unit 3Year Nine - Unit 1, Unit 2, Unit 4

References

http://www.australiancurriculum.edu.au/ Australian Curriculum Version 3.0 dated 23 January 2012https://portal.ntschools.net/SITES/LEARNINGLINKS/default.aspxhttp://www.scootle.edu.au/ec/p/homeCopyright © The State of Queensland (represented by the Department of Education and Training)Copyright in this work is owned by or licensed to the State of Queensland (acting through the Department of Education and Training), PO Box 15033 City East QLD 4002 Australia and is reproduced with its permission. No part may be further reproduced in hardcopy form by anyone outside the Northern Territory Department of Education without the express permission of the Queensland Department of Education and Training.


http://www.scootle.edu.au/ec/p/home

https://portal.ntschools.net/SITES/LEARNINGLINKS/default.aspx

http://www.australiancurriculum.edu.au/


http://www.maths300.esa.edu.au/


https://portal.ntschools.net/sites/NTSites/CentralAustralianRemoteSchools/Curriculum%20Resources/Maths/Maths%20Resource%20Maps/Mathematics%20Yearly%20Overviews%20Middle%20Years/CARS%20AC%20Year%209%20Maths%20Resources%20Map.pdf



https://portal.ntschools.net/sites/NTSites/CentralAustralianRemoteSchools/Curriculum%20Resources/Maths/Maths%20Resource%20Maps/Mathematics%20Yearly%20Overviews%20Primary%20Years/CARS%20AC%20Year%206%20Maths%20Resources%20Map.pdf

Documents

acinca.wikispaces.comacinca.wikispaces.com/file/view/MYL+maths+unit+plan… · Web viewThroughout this unit, it is expected that students will have ready access to ICTs at whole class,