mathematics program proforma

8/13/2019 Mathematics Program Proforma

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Sharon Tooney

MATHEMATICS PROGRAM PROFORMA

STAGE:ES1 S1 S2 S3

STRAND:NUMBER AND ALGEBRA

TERM:1 2 3 3

WEEK:1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Whole Number KEY CONSIDERATIONS OVERVIEWOUTCOMESA student: describes mathematical situations using everyday language,actions, materials and informal recordings MAe-1WM uses objects, actions, technology and/or trial and error toexplore mathematical problems MAe-2WM uses concrete materials and/or pictorial representations tosupport conclusions MAe-3WM counts to 30, and orders, reads and represents numbers inthe range 0 to 20 MAe-4NA

Background InformationIn Early Stage 1, students are expected to be able to count to30. Many classes have between 20 and 30 students, andcounting the number of students is a common activity.Students will also encounter numbers up to 31 in calendars.Counting is an important component of number and theearly learning of operations. There is a distinction betweencounting by rote and counting with understanding. Regularlycounting forwards and backwards from a given number willfamiliarise students with the sequence.Counting with understanding involves counting with one-to-one correspondence, recognising that the last number namerepresents the total number in the collection, anddeveloping a sense of the size of numbers, their order andtheir relationships. Representing numbers in a variety ofways is essential for developing number sense.Subitising involves immediately recognising the number ofobjects in a small collection without having to count theobjects. The word 'subitise' is derived from Latin and means'to arrive suddenly'.In Early Stage 1, forming groups of objects that have thesame number of elements helps to develop the concept ofequality.

LanguageStudents should be able to communicate using the followinglanguage: count forwards , count backwards , number before ,

number after , more than , less than , zero , ones , groups of ten , tens , is the same as , coins , notes , cents , dollars . The teen numbers are often the most difficult for students. The orallanguage pattern of teen numbers is the reverse of the usualpattern of 'tens first and then ones'.Students may use incorrect terms since these are frequently heardin everyday language, eg 'How much did you get?' rather than 'Howmany did you get?' when referring to a score in a game.To represent the equality of groups, the terms 'is the same as' and'is equal to' should be used. In Early Stage 1, the term 'is the same

Establish understanding of the language and processes ofcounting by naming numbers in sequences, initially to and

from 20, moving from any starting poin t Count forwards to 10 from a given number Count backwards from 10 to 0Connect number names, numerals and quantities, including

zero, initially up to 10 and then beyond read numbers to at least 10, including zero, and

represent these using objects (such as fingers), pictures,words and numerals

recognise numbers in a variety of contexts, egclassroom charts, cash register, computerkeyboard, telephone (Communicating)

communicate the use of numbers through everydaylanguage, actions, materials and informalrecordings (Communicating)

estimate the number of objects in a group of up to 10objects, and count to check

Subitise small collections of objects recognise the number of objects or dots in a pattern of

objects or dots recognise dice and domino dot patterns

Compare, order and make correspondences betweencollections, initially to 20, and explain reasoning count with one-to-one correspondence make correspondences between collections compare and order numbers and groups of objects use the term 'is the same as' to express equality of

groupsUse the language of money use the language of money in everyday contexts

Learning Across The Curriculum

Cross-curriculum priorities

Aboriginal &Torres Strait Islander histories & cultures Asia & Australias engagement with Asia Sustainability

General capabilities

Critical & creative thinking Ethical understanding Information & communication technology capability Intercultural understanding Literacy Numeracy

Personal & social capability

Other learning across the curriculum areas

Civics & citizenship Difference & diversity Work & enterprise


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CONTENT WEEK TEACHING, LEARNING and ASSESSMENT ADJUSTMENTS RESOURCES

Establishunderstanding ofthe language and

processes ofcounting by

naming numbersin sequences,initially to and

from 20, moving from any starting point

Connect numbernames, numeralsand quantities,including zero,initially up to 10

and then beyond

Subitise smallcollections ofobjects

Compare, orderand makecorrespondencesbetweencollections,initially to 20, and

explain reasoning

Use the languageof money

1-2Rhymes, Songs and StoriesStudents could listen to stories and sing songs and nursery rhymes to develop number concepts egThree Bears, Five Little Ducks, Ten Little Indians, Ten Fat Sausages.It is important to use rhymes that involve counting backwards as well as rhymes that involvecounting forwards, and to use ordinal numbers.

Teachers could also use stories to teach ordinal names by asking questions such as Whathappened second in the story of the Three Little Pigs?

Use animations of songs orpictorial representations tosupport visual learners

3-4CountingStudents should be given frequent opportunities to count forwards and backwards from variousstarting points. Counting experiences could include: rhythmic counting eg 1 2 3 4 5 6 (where the bold numbers are said aloud) counting individually counting off. Students stand as they call their number and when counting backwards students

sit. circle counting. Students sit in a circle and take turns to count particular groups of students eg

the number of students in the class, the students with blue shirts. counting with body percussion to emphasise a pattern eg odd numbers hitting knees, even

numbers with a clap.

Point to visualrepresentations of numbersas students count toreinforce numeralidentification

5Class ShopThe teacher sets up play situations to allow students to explore coins and notes, and use them inshopping contexts. A selection of items could be available with marked prices.Students order the items for sale from least expensive to most expensive.Students role-play buying items at the shop using coins and notes for whole amounts.Students group the items they could buy with a given coin or note.The class shop can vary to include businesses such as hairdresser, butcher, baker, trash andtreasure, office, restaurant, or bookshop.

Begin with limitedcoins/notes and increase asstudents become morefamiliar.

play money, variety ofitems to sell in store

6

Wind Up Toy Race

The teacher sets up some toy races in groups of ten. Students race the toys and order them fromfirst to tenth. They then label them with ordinal cards made by the teacher.Possible questions include: who came first? who came last? what are the words we use to describe where we come in a race?

wind up toys, ordinal

cards

7Peg CardsIn pairs, students are given a set of large numeral cards (eg 0 to 10). The cards are not in order.

numeral cards, pegs


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Students take turns to read the numeral on each card to their partner and attach thecorresponding number of pegs.The cards are then ordered from 0 to 10 across the floor.Extension: Students are asked to select two of the numbers from the floor and count from thesmallest to the largest, or the largest to the smallest.

8ConcentrationStudents are given a set of cards with numbers represented by numerals, pictures, dots, or wordsEG.

variety of cards

9Address BooksStudents collect numbers that relate to themselves and collate them into a book let eg telephonenumbers, addresses, birthdays, ages.These books can be used for discussions about numbers and assessment of writing numerals.

number books, oldphone books,calendars, magazines,catalogues, scissors,glue

10Revision

ASSESSMENT OVERVIEW

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STAGE:ES1 S1 S2 S3


TERM:1 2 3 3

WEEK:1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Addition and Subtraction KEY CONSIDERATIONS OVERVIEWOUTCOMESA student: describes mathematical situations using everyday language,actions, materials and informal recordings MAe-1WM uses objects, actions, technology and/or trial and error toexplore mathematical problems MAe-2WM uses concrete materials and/or pictorial representations tosupport conclusions MAe-3WM combines, separates and compares collections of objects,describes using everyday language, and records usinginformal methods MAe-5NA

Background InformationAddition and subtraction should move from counting andcombining perceptual objects, to using numbers asreplacements for completed counts with mental strategies,to recordings that support mental strategies (such as jump,split, partitioning and compensation).Subtraction typically covers two different situations: 'takingaway' from a group, and 'comparing' two groups (ie finding'how many more'). Students should be confident with takingaway from a group before being introduced to comparingtwo groups. They should be able to compare groups ofobjects by using one-to-one correspondence before beingasked to find out how many more or how many less thereare in a group.In Early Stage 1, addition and subtraction problems shouldbe related to real-life experiences that involve themanipulation of objects.Modelling, drawing and writing mathematical problemsshould be encouraged in Early Stage 1. However, formalwriting of number sentences, including the use of thesymbols +, and =, is introduced in Stage 1.Addition and subtraction should be taught in conjunctionwith each other as the foundation for conceptualunderstanding of their inverse relationship.

LanguageStudents should be able to communicate using the followinglanguage: count forwards , combines with , joins , countbackwards , take away , how many more , all together ,makes .Some students may need assistance when two tenses areused in the one problem, eg 'I had six beans and took awayfour. How many do I have?'The word 'difference' has a specific meaning in this context,referring to the numeric value of the group. In everydaylanguage, it can refer to any attribute.

Represent practical situations to model addition andsharing combine two or more groups of objects to model addition model subtraction by separating and taking away part of agroup of objects use concrete materials or fingers to model and solve simpleaddition and subtraction problems co mpare two groups of objects to determine 'how manymore' use visual representations of numbers to assist withaddition and subtraction, eg ten frames create and recognise combinations for numbers to at least10, eg 'How many more make 10?' describe the action of combining, separating andcomparing using everyday language, eg makes, joins,combines with, and, get, take away, how many more, alltogether- explain or demonstrate how an answer was obtained(Communicating, Reasoning)- apply strategies that have been demonstrated by otherstudents (Problem Solving)- investigate different methods of adding and subtractingused in various cultures, eg Aboriginal and Torres StraitIslander methods involving spatial patterns and reasoning,Asian counting tools such as the abacus (Communicating,Problem Solving) count forwards by ones to add and backwards by ones to

subtract record addition and subtraction informally using drawings,words and numerals










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Represent practicalsituations tomodel additionand sharing

5Hand PrintsIn small groups, students are given a die (numbered 1, 1, 2, 2, 3 and 3), a collection of counters,and a game board made up of two hand prints as shown.

The object of the game is to collect exactly ten counters. In turn, students roll the die, collect thatnumber of counters, and place them on the game board. If the student cannot fit the number ofcounters on their game board, they must remove that number from those on the board.For example, Paulas game board looks like this.

Paula needs to roll a 1 to finish the game. If she rolls a 3, she has to take 3 counters off the board,leaving her with 6 counters .Rabbit Ears PlusThe teacher models making rabbit ears by putting their fists at the sides of their head, saying a

number less than 10 and raising that number of fingers. Students are asked to:- raise two fingers on one hand and three fingers on the other hand. How many fingers are raisedaltogether?- show six rabbit ears. How many fingers have been raised on each hand to make six altogether?- raise two fingers on one hand. How many fingers need to be raised on the other hand to makefour altogether?Students should be encouraged to raise their fingers while their hands are still at the side of theirheads. Then they can check if they have the correct number by looking at and counting theirfingers. Some students may be selected to model and explain their solution eg I made 6 with 5fingers on one hand and 1 more.

Begin with one hand only forstudents struggling to 10.

Use additional hands forstudents requiring extension.

dice, counters, handgame boards

6Ten-frame SubtractionsStudents are shown a ten-frame with some counters on it eg

Possible questions include:- how many counters are on the ten-frame?- how many squares are full/empty?Students are asked to imagine three counters jumping off the ten-frame. Possible questionsinclude:- how many counters are left on the ten-frame?

Begin with a five-frame forstudents struggling to 10.

Students requiring extensioncan begin with a full ten-frame and roll a dice tosubtract counters anddescribe what happened.For addition they can choosefrom number cards facedown on the table and addthe two numbers using

ten-frames, counters,dice, number cards


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- how did you work that out?- how many squares are full/empty?The three counters are then moved off the ten-frame for students to check their answer. Thisactivity encourages students to visualise numbers. It should be repeated with other countercombinations.Ten-frame AdditionsStudents are shown a ten-frame with some counters positioned on it and others beside it eg

Possible questions include:- how many counters are on the ten-frame?- how many counters are off the ten-frame?Students are asked to imagine the th ree counters jumping onto the ten-frame. Possible questionsinclude:- how many counters are there altogether?- how did you work that out?- how many squares are full/empty?The three counters are then moved onto the ten-frame for students to check their answer. Thisactivity encourages students to visualise numbers. It should be repeated with other count ercombinations.

counters on their ten-frameand describe what hashappened.

7Domino CountStudents are given a set of dominoes and are asked to count how many dots are on each side of adomino and then how many dots there are altogether. Students are encouraged to:- work out how many dots there are on each side without counting one at a time- discuss different strategies they could use to work out how many there are altogether.The teacher could ask the students to imagine a domino with four dots on one side and one dot onthe other. They then discuss with students how many dots there are and strategiesthat can be used to find out. The teacher could also pose the problem: There are six dotsaltogether on my domino. How many dots could there be on each side? Students record anddiscuss the possible answers. Some students may require materials such as counters to assist themin solving the problem. Possible questions include:- is there a quicker way to find the answer than counting by ones from one?- is there a quicker or easier way to add?- is that the only possible answer?Combinations to TenStudents are given a container of 10 counters that are all one colour on one side and a differentcolour on the reverse. In pairs, students shake the container and roll the counters onto the floor.Students sort the counters into colour groups, depending on which side the counters land.Students should be encouraged to organise the groups so they can see how many at a quickglance eg

Counters to assist dominocount.

Large print dominoes

Students requiring extensioncan complete activity usingtwo domino

Begin with 5 counters forstudents struggling to 10

For students requiringextension, use additional

dominoes, counters


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Students determine how many counters are, for example, red and how many are yellow. Studentsuse drawings and numerals to record their results.

counters

8Hidden CountersStudents are given a small number of counters to count. The teacher picks up the counters withone hand, puts both hands behind their back, distributes the counters between their two handsand closes their fists. Students are then shown the two closed fists. One hand is opened and thestudents see the number of coun ters in that hand. Students determine how many counters theteacher has in the other hand and explain how they worked it out. The activity is repeated manytimes and the number of coun ters is varied.Variation: Students play this as a game wi th a partner.Comparing TowersIn pairs, Student A rolls a die, collects the corresponding number of interlocking cubes and makes atower. Student B then rolls the die, collects the corresponding number of interlocking cubes andmakes a tower. The two students compare their towers and are asked to determine whose toweris taller. Possible questions include:- how do you know which tower is taller?- how many cubes are in each tower?- how many more cubes are in the taller tower?The student with the taller tower removes the difference and keeps it. The game continues untilstudents have collected up to 30 cubes. Students may also use two or three dice, or dice withnumbers larger than 6.

For students struggling withthe concept, show thecounters in each hand brieflybefore hiding

Encourage students havingdifficulty with concept toplace towers side by side, tomake a direct comparison

More capable studentsshould be encouraged todecide without directcomparison and explain

counters, dice,interlocking blocks

9Selection of above activities revisited

10Revision

ASSESSMENT OVERVIEW


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Sharon Tooney


STAGE:ES1 S1 S2 S3


TERM:1 2 3 3

WEEK:1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Patterns and Algebra KEY CONSIDERATIONS OVERVIEWOUTCOMESA student: describes mathematical situations using everyday language,actions, materials and informal recordings MAe-1WM uses objects, actions, technology and/or trial and error toexplore mathematical problems MAe-2WM uses concrete materials and/or pictorial representations tosupport conclusions MAe-3WM recognises, describes and continues repeating patternsMAe-8NA

Background InformationEarly number learning (including additive and multiplicativethinking) is important to the development of algebraicthinking in later stages.In Early Stage 1, repeating patterns can be created usingsounds, actions, shapes, objects, stamps, pictures and othermaterials.

LanguageStudents should be able to communicate using the followinglanguage: group , pattern , repeat .

Sort and classify familiar objects and explain the basis forthese classifications sort and classify a group of familia r objects into smallergroups recognise that a gro up of objects can be sorted andclassified in different ways- explain the basis for their classification of objects(Communicating, Reasoning)Copy, continue and create patterns with objects anddrawings recognise, copy and continue repeating patterns usingsounds and/or actions recognise, copy, continue and create repeating patternsusing shapes, objects or pictures, eg

, , , , , , , ,...............- create or continue a repeating pattern using simplecomputer graphics (Problem Solving)- recognise when an error occurs in a pattern and explainwhat is wrong (Communicating, Reasoning) describe a repeating pattern made from shapes byreferring to its distinguishing features, eg 'I have made mypattern from squares. The colours repeat. They go red, blue,red, blue, '










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2-3Beginning to Make Repeating PatternsPart AStudents are given a set of counters containing two colours and are asked to put the counters in arow. Some students may create a repeating pattern, while others may not. The intention o f theactivity is to distingui sh between those arrangements that are repeating patterns and those that

are not. Possible questions include:- where do we see patterns?- what comes next in this pattern? How do you know?- which part of the pattern is repeated?- can you describe how to make this pattern?

Use a card with circles on itfor students to placecounters on top of, that havedifficulty making a row ontheir own

counters

4-5Beginning to Make Repeating PatternsPart BThe teacher models putting a small collection of counters in a row, making sure that they make arepeating pattern eg

Possible questions include:

- can you describe your row of counters?- can you describe my row of counters?- can you make a row of counters like mine?- can you make another row of counters that has a pattern?In pairs, students make new rows of counters, describe them to each other, and record theirpatterns. At this early stage, it i s preferable to use materials that have only one attribute (egcolour) before using materials with multiple attributes

For students struggling withconcept, use pattern cardsand encourage one to onematching

More capable studentsshould be encourage to

extend pattern beyond anABAB pattern

counters, variety ofsorting objects thatcan be used to createpatterns

6-7Describing Repeating Patterns using NumbersThe teacher makes a repeating pattern using multilink cubes eg

This pattern is called a th ree pattern because the pattern repeats after every third cube. Possiblequestions include:- how many cubes are in each group that repeats? (three)- how many groups are in your pattern? (three)- what is the total number of cubes in the pattern? (nine)With teacher guidance, students record the pattern using drawings. They are encouraged to usenumbers in their recording.

For students struggling withconcept, use pattern cardsand encourage one to onematching

More capable studentsshould be encourage to drawpatterns independently

multilink cubes

8-9Making Repeating PatternsIn pairs, students are given collections of materials such as coloured counters, unifix cubes orshells, and are asked to make a pattern that repeats. Students then use drawings to show what

For students struggling withconcept, use pattern cardsand encourage one to one

counters, unifix cubes,shells, sorting objects


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they have done. Possible questions include:- can you describe your pattern?- which parts repeat?- how many pattern blocks are in each of the parts that repeat?Students should be encouraged to record this information in their own way on their drawings.

matching

More capable studentsshould be encourage to drawpatterns independently

Revision

ASSESSMENT OVERVIEW


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Sharon Tooney


Use direct andindirectcomparisons todecide which islonger, and

explain theirreasoning usingeverydaylanguage

3Who is tall, who is short?Students choose a classmate to stand beside. Students compare their heights by looking in amirror or by asking another pair of students to assist. Who is tall? Who is short? Students drawpictures of themselves with their partner and label the two figures as tall and shortAm I taller or shorter?

Students move independently around the classroom and identify three objects that are taller th anor shorter than themselves. Record by drawing and labelling.Alternatively, students choose a referent such as thei r desk and find three things that are shorterthan, longer than, higher than their desk.

Students with fine motorissues should be providedwith ready-maderepresentations of twostudents to label

One to one comparisonswhen comparing lengths

paper and pencil forrecording, mirror(optional), classroomfurniture

4Short and long paths and towersStudents use wooden blocks to make paths around the classroom and discuss whether they havemade short paths or long paths.Variations: make towers of different heights, snakes of different lengths, paint or draw long andshort lines.Longer than, shorter than our stringStudents in pairs cut a piece of string and then move around the classroom to find as many objectsas they can that are the same length as, longer than or shorter than the string. Students record

their findings by drawing and labelling


Pre-cut strings for thosestudents requiring support

Support to draw pictures

enough woodenblocks for each pair ofstudents to makeseveral paths ortowers, chalk, paint,play dough, streamersor balls of string,scissors, paper and

pencil for recording

5Sort Me!Given a collection of lengths of braid, streamers, cardboard strips or ribbon, students sort theminto a long pile and a short pile.Students record their lengths and label as long and short .Stand in orderSmall groups of students are ordered from tallest to shortest, e.g. students waiting to tell news.Students who are wearing shorts, students who have an apple for lunch.Use terminology shorter than, taller than, shortest and tallest .


Scribe to label

braid, cardboardstrips, ribbons orstreamers cut toobvious lengths, paperand pencil forrecording

6Straws in orderGiven a number of straws of different lengths, students put them in order from longest to shortest.Straws are used because they will not stand up so students have to decide which end will be the

baseline. These ends of the straws should be together.Cutting equal lengthsStudents cut a length of string or streamer and use this to cut a second piece the same length.Compare the lengths with others in the group and order from the shortest to the longest.Note: if the streamers or string tend to curl or kink, it may be necessary to sticky tape these to thedesk to compare length.


Pre-cut strings for thosestudents requiring support

straws of differentlengths, string orstreamers, scissors,

sticky tape

7Order the groupOrder from longest to shortest, three or more lengths which students have to straighten out andlay side by side, e.g. a skipping rope, a length of string and a rolled up streamer. Record and label


a collection of lengths,recording paper,pencil, students


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the lengths as longest and shortest . Report the results using comparative language.Gorilla armsStudents in pairs or a small g roup order the group members by length of outstretched arms.Compare arms in pairs by matching fi ngertips on one side as a baseline. Ensure that all members ofthe group have been matched, to find the order. Record and label.

9Revision

10

Assessment

ASSESSMENT OVERVIEW


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Sharon Tooney


STAGE:ES1 S1 S2 S3

STRAND:MEASUREMENT AND GEOMETRY

TERM:1 2 3 3

WEEK:1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Time KEY CONSIDERATIONS OVERVIEWOUTCOMESA student: describes mathematical situations using everyday language,actions, materials and informal recordings MAe-1WM sequences events, uses everyday language to describe thedurations of events, and reads hour time on clocks MAe-13MG

Background InformationDurationIn Early Stage 1, students begin to develop an understandingof the duration of time and learn to identify moments intime. An understanding of duration is introduced throughideas such as 'before', 'after', 'how long' and 'how soon'. Itshould be noted that time spans in Early Stage 1 are personal judgements. Moments in time include ideas such as daytime,today, days of the week and seasons. Sunday is commonlythe first day of the calendar week. A week, however, mayalso mean a period of seven days beginning on any day, eg'One week starting from Thursday'.Teachers should be aware of the multicultural nature of oursociety and of significant times in the year for differentcultural groups. These could include religious festival days,

national days and anniversaries.

LanguageStudents should be able to communicate using the followinglanguage: daytime , night-time , yesterday , today , tomorrow ,before , after , next , a long time , a short time , week , days ,weekdays , weekend days , time , morning , afternoon , clock ,analog , digital , hands (of a clock) , o'clock . The words 'long' and 'short' can be confusing to studentswho have only experienced these words in terms of lengthmeasurement. Students will need experience with thesewords in both length and time contexts.

References to time are often used inaccurately in everydaylanguage, eg 'I'll be a second', 'back in a minute'.

Compare and order the duration of events using theeveryday language of time use terms such as 'daytime', 'night -time', 'yesterday','today', 'tomorrow', 'before', 'after', 'next', 'morning' and'afternoon' sequence events in time compare the durati on of two events using everydaylanguage, eg 'It takes me longer to eat my lunch than it doesto clean my teeth'- describe events that take 'a long time' and events that take'a short time' (Communicating)










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7Using and understanding terms such as daytime, night-time, yesterday, today, tomorrowStudents identify, compare and label representations (photographs, pictures in stories and frommagazines, posters) of time as daytime and night-time . Describe events that take place of a day and a night . Draw and label daytime and night-time pictures.Create a class table depicting what the class did yesterday , what they will do today and what they

expect to do tomorrow . Students draw and label pictures of what they did yesterday , what theywill do today and what they expect to do tomorrow .

Pre-made representations ofday and night for student toattach labels to

pictures, storybooks,magazines, paper andpencil for recording

8Using and understanding terms such as before, after, next, morning and afternoonStudents identify, compare and label representations (photographs, pictures in stories and frommagazines, posters) of time as morning and afternoon . Describe events that take place of amorning and an afternoon . Draw and label morning and afternoon pictures.Discuss the difference between the terms before, after and next . Read stories, such as, Brown BearBrown Bear What Do You See? by or I Went Walking by Sue Machin. Discuss the animals in thetext using the terms before, after and next . Have students choose three characters that appear inorder and label them before, after and next .

Pre-made representations ofmorning and afternoon forstudent to attach labels to

pictures, storybooks,magazines, BrownBear Brown Bear WhatDo You See? by or IWent Walking by SueMachin, pencil andpaper for recording

9Revision

10Assessment

ASSESSMENT OVERVIEW


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STAGE:ES1 S1 S2 S3


TERM:1 2 3 3

WEEK:1 2 3 4 5 6 7 8 9 10

SUBSTRAND: 2D KEY CONSIDERATIONS OVERVIEWOUTCOMESA student: describes mathematical situations using everyday language,actions, materials and informal recordings MAe-1WM uses objects, actions, technology and/or trial and error toexplore mathematical problems MAe-2WM manipulates, sorts and describes representations of two-dimensional shapes, including circles, triangles, squares andrectangles, using everyday language MAe-15MG

Background InformationExperiences with shapes, even in Early Stage 1, should not belimited. It is important that students experience shapes thatare represented in a variety of ways, eg 'tall skinny' triangles,'short fat' triangles, right-angled triangles presented indifferent orientations and of different sizes, and shapes thatare represented using a variety of materials, eg paint, imageson the computer, string. Manipulation of a variety of realobjects and shapes is crucial to the development ofappropriate levels of language and representation.In Early Stage 1, it is important that teachers presentstudents with both regular and irregular shapes (regularshapes have all sides and all angles equal). However,students are not expected to use the terms 'regular' and'irregular' themselves.

Students should be given time to explore materials in orderto represent shapes by tearing, painting, drawing, writing, orcutting and pasting.

LanguageStudents should be able to communicate using the followinglanguage: shape , circle , triangle , square , rectangle , features ,side , straight line , curved line , open line , closed shape .The term 'shape' refers to a two-dimensional figure. Theterm 'object' refers to a three-dimensional figure.

Sort, describe and name familiar two-dimensional shapes inthe environment identify, represent and name circles, triangles, squa res andrectangles presented in different orientations, eg

- identify circles, triangles, squares and rectangles in picturesand the environment, including in Aboriginal art (ProblemSolving)- ask and respond to questions that help identify a particularshape (Communicating, Problem Solving) sort two -dimensional shapes according to features such assize and shape- recognise and explain how a group of two-dimensional

shapes has been sorted (Communicating, Reasoning) manipulate circles, triangles, squares and rectangles, an ddescribe their features using everyday language, eg 'A squarehas four sides'- turn two-dimensional shapes to fit into or match a givenspace (Problem Solving) make representations of two -dimensional shapes using avariety of materials, including paint, paper, body movementsand computer drawing tools- make pictures and designs using a selection of shapes, egmake a house from a square and a triangle (Communicating) draw a two -dimensional shape by tracing around one face

of a three-dimensional object identify and draw straight and curved lin es compare and describe closed shapes and open lines draw closed two -dimensional shapes without tracing- recognise and explain the importance of closing the shapewhen drawing a shape (Communicating, Reasoning)










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Sort, describe andname familiartwo-dimensionalshapes in theenvironment

2Free PlayIn groups, students participate in free play using a wide variety of materials on a regular basis egpattern blocks, wooden shapes, everyday two-dimensional objects. Free play sessions may also beused to practise teacher-directed activities.Possible questions include:

- can you sort the two-dimensional objects?- can you describe your sorting?- can you describe the features of each two-d imensional object?

Support person for playsessions

pattern block, woodenshapes, everyday tw0-dimensional objects

3Shape WalkStudents walk around the school and describe the various shapes they see eg These leaves lookround.Students are asked to use drawings to show what they found. These are collated and placed in aclass book for others to share.

Support person for shapewalk

4Tracing ObjectsIn pairs, students make a design or picture by tracing around the faces of various objects eg make apicture of a robot by tracing a variety of objects.Students share and describe their pictures and are asked to:

- explain the position of particular shapes- discuss the ways different students used a particular shape, and- identify any shape used in different orientations.

Pre-cut shapes to createpicture with and/or supportwith tracing

wooden shapes,pencils, paper

5Print ItStudents select an object from a collection of environmental and commercial materials such asfruit, stones, boxes and pattern blocks.They are asked to investigate the different parts of the object that can be painted and printed ontopaper. Students share and discuss the printed shapes and the ways they were able tocreate particular shapes.Variation: The teacher could cut some of the objects and ask the students to predict the shape/sthat could be made if the cut surface was printed. Students test their predictions by painting andprinting.

Support with printing fruit, stones, boxesand pattern blocks,paper, paint

6 LinesStudents are given a piece of string and are asked to make a straight line, a curved line o r a closedshape. They are asked to describe their line or shape, and draw what th ey create.Variation: Students could use computer software to draw a variety of closed shapes and openlines.

Support with recording string, paper andpencil for recording

7Making Shape PicturesStudents make a picture using different-sized paper shapes, including circles, squares, trianglesand rectangles. As students are working, the teacher asks the students to name the shapesthey are using.

Support to create picture pre-cut paper shapes,paper and glue


18/21

Sharon Tooney

Students glue their picture onto paper, add additional features, and describe their picture insentences to be scribed.Variation: Students could use a computer drawing p rogram to create a shape picture.

9Revision

10Assessment

ASSESSMENT OVERVIEW


19/21

Sharon Tooney


STAGE:ES1 S1 S2 S3


TERM:1 2 3 3

WEEK:1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Position KEY CONSIDERATIONS OVERVIEWOUTCOMESA student: describes mathematical situations using everyday language,actions, materials and informal recordings MAe-1WM describes position and gives and follows simple directionsusing everyday language MAe-16MG

Background InformationThere are two main ideas for students i n Early Stage 1:following an instruction to position an object or themselves,and describing the relative position of an object orthemselves. Some students may be able to describe theposition of an object in relation to themselves, but not inrelation to another object.In Early Stage 1, students use the terms 'left' and 'right' todescribe position in relation to themselves. They are notexpected to use the terms 'left' and 'right' to describe theposition of an object from the perspective of a person facingin the opposite direction until Stage 1.

LanguageStudents should be able to communicate using the following

language: position , between , next to , behind , inside ,outside, left , right , directions .

Describe position and movement give and follow simple directions to position an object orthemselves, eg 'Put the blue teddy in the circle'- follow directions to a point or place, including in mazes andgames (Reasoning)- direct simple computer-controlled toys and equipment tofollow a path (Communicating) describe the position of an object in relation to themselve susing everyday language, such as 'between', 'next to','behind' or 'inside', eg 'The table is behind me' describe the position of an object in relation to anotherobject using everyday language, such as 'between', 'next to','behind' or 'inside', eg 'The book is inside the box' describe the positions of objects in relation to themselvesusing the terms 'left' and 'right', eg 'The tree is on my right'

- use the terms 'left' and 'right' when referring to familiartasks, eg 'I hold my pencil in my right hand' (Communicating)- participate in movement games involving turning anddirection (Reasoning)










20/21

Sharon Tooney


Describe positionand movement 7

Simple DirectionsPlay simple games that involve following directions, e.g.- Simon Says- Red Light, Green Light (red= stop, green= go; add more colours and actions eg purple= hop,yellow= crawl, blue= turn around etc)

- I Spy, using the attributes of the object, students must listen to find object in the classroom andstand next to it- Treasure Hunts- I Am A Robot; in pairs students take turns at being the robot and the other must give directionsto move their robot around the classroom/playground

Use colour paddles as well aswords when playing RedLight, Green LightLimit the number ofinstructions that are given at

a time

8Describing PositionUsing a PowerPoint that has scrapbook layouts in it. Look at the pictures and have the studentstell everything they can about it. Look specifically for descriptions that contain position words --i.e."The apples are in the basket." If somebody gives me a description that is not position-related,guide them with questions, "Where is it?"

Record all of their position-related responses on a chart paper. Look for wo rds thatdescribe position--or where things are, underline them. Transfer them to a chart and keep up inthe room for future reference. Add new position words , to the chart as the class di scovers them.

Extended questioning

Laminated A3 copies of eachpicture to refer directly to

powerpoint, chartpaper and textas forrecording

9Revision

10Assessment

ASSESSMENT OVERVIEW


21/21

Sharon Tooney

mathematics program proforma

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