Mathematics Program Proforma Yr1 t1

Sharon Tooney

MATHEMATICS PROGRAM PROFORMA

STAGE: Yr 1 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 1 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › uses objects, diagrams and technology to explore mathematical problems MA1-2WM › supports conclusions by explaining or demonstrating how answers were obtained MA1-3WM › applies place value, informally, to count, order, read and represent two- and three-digit numbers MA1-4NA

Background Information By developing a variety of counting strategies and ways to combine quantities, students recognise that there are more efficient ways to count collections than counting by ones. Language Students should be able to communicate using the following language: count forwards, count backwards, number before, number after, more than, less than, number line, number chart, digit, zero, ones, groups of ten, tens, round to, coins, notes, cents, dollars. Students should be made aware that bus, postcode and telephone numbers are said differently from cardinal numbers, ie they are not said using place value language. Ordinal names may be confused with fraction names, eg 'the third' relates to order but 'a third' is a fraction. The word 'round' has different meanings in different contexts and some students may confuse it with the word 'around'.

Develop confidence with number sequences to 100 by ones from any starting point • count forwards and backwards by ones from a given two-digit number • identify the number before and after a given two-digit number - describe the number before as 'one less than' and the number after as 'one more than' a given number • read and use the ordinal names to at least 'thirty-first' Count collections to 100 by partitioning numbers using place value • count and represent large sets of objects by systematically grouping in tens • use and explain mental grouping to count and to assist with estimating the number of items in large groups • use place value to partition two-digit numbers • state the place value of digits in two-digit numbers • partition two-digit numbers in non-standard forms Recognise, model, read, write and order numbers to at least 100; locate these numbers on a number line • represent two-digit numbers using objects, pictures, words and numerals • locate and place two-digit numbers on a number line • apply an understanding of place value and the role of zero to read, write and order two-digit numbers • use number lines and number charts to assist with counting and ordering - give reasons for placing a set of numbers in a particular order • round numbers to the nearest ten • estimate, to the nearest ten, the number of objects in a collection and check by counting • solve simple everyday problems with two-digit numbers - choose an appropriate strategy to solve problems, including trial-and-error and drawing a diagram - ask questions involving two-digit numbers Recognise, describe and order Australian coins according to their value • identify, sort, order and count money using the appropriate language in everyday contexts • recognise that total amounts can be made using different denominations • recognise the symbols for dollars ($) and cents (c)

Learning Across The Curriculum

Cross-curriculum priorities Aboriginal &Torres Strait Islander histories & cultures Asia & Australia’s 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

Sharon Tooney

CONTENT WEEK TEACHING, LEARNING and ASSESSMENT

ADJUSTMENTS RESOURCES

2

Collections Present students with a large collection of items, such as counters, pebbles, or buttons, a supply of containers, such as patty papers or cups, and a large sheet of cardboard. They will also need two sets of numeral cards ranging from zero to nine. Divide the chart into a “tens” and a “ones” column. Present the collection of items to the students and allow them to count the items. Each time ten items are collected, the students place the items into a container and move the container to the left-hand side of the chart, that is, onto the “tens” column. Students then place a numeral card above the “tens” column, indicating how many groups of ten have been collected. As succeeding tens are collected, students continue to add them to the left-hand side of the chart and replace the numeral card accordingly. Remaining items are placed on the right-hand side of the chart, in the “ones” column. Students then place a corresponding numeral card above the “ones” column to form a two-digit number.

All activities should be adjusted according to where students fall on the Numeracy Continuum

counters, pebbles, or buttons, patty papers or cups, a large sheet of cardboard, two sets of numeral cards ranging from zero to nine

3

Bundling Present the students with large collections of popsticks. Have the students bundle the popsticks into groups of ten and place any remaining popsticks to the side of the bundles. Encourage students to count by tens to find the total and add on any remaining popsticks. Students should then label the collection using numeral cards. Interlocking blocks, such as Multilink, Unifix or Centicubes, could also be used. Trading game Supply students with a collection of base ten material. The students take turns to throw a die and take a corresponding number of base ten “shorts” from a central pile. On succeeding throws of the die, students add appropriate numbers of “shorts” to their collection. As the students collect ten “shorts” they swap or trade them for one base ten “long”. Continue the activity until one, or all students, can trade ten “longs” for a base ten “flat”.


popsticks, Multilink, Unifix or Centicubes, base ten material, dice

4

Counting on Prepare numeral cards in the range eleven to nineteen and place them face down on the floor. Provide the students with two collections of counters. One collection should consist of bundles of ten counters, all of the same colour. The second collection should consist of single counters of assorted colours. Students take turns to select a card. They then collect a corresponding number of counters, using the bundles of ten and single counters. Encourage students to count on from the bundle of ten. This activity may be varied by extending the range of numbers or by using ten strips (made of ten dots on strips of card) instead of counters.


numeral cards in the range eleven to nineteen, counters

5

Popsticks Make a base board by folding a piece of paper or cardboard in half to form two columns. Label the columns as “units” and “tens”. Construct a set of numeral cards for the range one to nine on white cards. These cards will be used to represent numerals in the “tens” column on the chart. Construct a second set of numeral cards in the range zero to nine on coloured card. These will be used to represent numerals in the “ones” column . Provide bundles of ten white popsticks and a pile of coloured popsticks. Shuffle the two decks of cards separately. Place the cards face down between


cardboard, numeral cards for the range zero to nine, popsticks

Sharon Tooney

the students. The students take turns to turn over a white card and a blue card to form a two-digit numeral and place the cards onto the chart. The students then read the numeral they have formed and collect a corresponding number of sticks, using the bundles of white popsticks and the coloured popsticks. Students then place the popsticks next to the numeral cards and allow others to verify that the number of popsticks used is correct.

6

Flip and see Provide each student with a large collection of popsticks and a base board divided into a “tens” and a “ones” column. Place numeral cards in the range zero to nine face down on the floor. The students take turns to flip over two numeral cards and place one card in the tens column and one card in the ones column on their base board. Students then bundle popsticks into tens and place the correct number of bundles and units onto their base board to match the numeral cards. Discuss how many tens and ones were made. Variations • Students complete the above activity and then swap the numeral cards from the tens column to the units column and vice-versa. They then repeat the activity. • Construct two sets of numeral cards in the range zero to nine. Flip over two numeral cards and ask the students to select identical numeral cards from the second set of cards. Ask students to place their cards in the tens and ones column so that they form the largest and the smallest number possible. • Organise students into pairs and provide each pair of students with a set of numeral cards in the range zero to nine. The students shuffle the cards and place them face down on the floor. They then take turns to select two numeral cards. Using the two cards selected, each student forms the largest two-digit number possible. The two students then compare their numbers and the player with the larger number scores ten points. Continue playing until one player gains a score of one hundred.


popsticks, base board divided into a “tens” and a “ones” column, numeral cards in the range zero to nine

7

Bucket count on Drop a small collection of blocks one by one, into a bucket. Ask students to count aloud as each block is added to the container. After dropping the blocks, show the students the contents of the bucket. Then hold the bucket above the eye level of the students. Ask the students to state how many blocks would be in the bucket if one more block was added. Repeat the question, changing the number of blocks to be added to two and three blocks. Encourage the students to count on from the number of blocks already in the bucket to find the total. Variation Ask the students to pretend there are a nominated number of blocks in the bucket. Drop additional blocks into the bucket. Students count on to find the total sum of the blocks in the bucket.


blocks, bucket

8

Money Matters Part A Students are given a collection of coins. They demonstrate different ways to make 10c, 20c and 50c (and then $1 and $2) using the coins. Students record their findings. Possible questions include: - how many different ways can you represent 50c?

More capable students could use notes as well as coins

collection of coins

Sharon Tooney

- what counting strategy did you use to determine the amount of money you had?

9 Money Matters Part B The teacher creates shopping situations where one student is given an amount of money to spend. They purchase a list of items. The shopkeeper totals the items and calculates the change. Students discuss strategies used to determine the cost of the list of items and the change to be given.

More capable students could buy items requiring them to work out change. Students having difficulty adding money may need visual supports to demonstrate what total amounts look like

collection of coins, shop items

10

Revision

ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

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

SUBSTRAND: Addition and Subtraction 1 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › uses objects, diagrams and technology to explore mathematical problems MA1-2WM › supports conclusions by explaining or demonstrating how answers were obtained MA1-3WM › uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers MA1-5NA

Language Students should be able to communicate using the following language: counting on, counting back, combine, plus, add, take away, minus, the difference between, total, more than, less than, double, equals, is equal to, is the same as, number sentence, strategy. The word 'difference' has a specific meaning in this context, referring to the numeric value of the group. In everyday language, it can refer to any attribute. Students need to understand that the requirement to carry out subtraction can be indicated by a variety of language structures. The language used in the 'comparison' type of subtraction is quite different from that used in the 'take away' type. Students need to understand the different uses for the = sign, eg 4 + 1 = 5, where the = sign indicates that the right side of the number sentence contains 'the answer' and should be read to mean 'equals', compared to a statement of equality such as 4 + 1 = 3 + 2, where the = sign should be read to mean 'is the same as'.

Represent & solve simple addition & subtraction problems using a range of strategies, including counting on, partitioning & rearranging parts • use terms add, plus, equals, is equal to, take away, minus & the difference between • use concrete materials to model add & sub problems involving 1 & 2 digit numbers • use concrete materials & a number line to model & determine difference between 2 numbers • recognise & use the symbols (+),(–) (=) • record number sentences in a variety of ways using drawings, words, numerals & mathematical symbols • recognise, recall & record combinations of 2 no.s that add to 10 • create, record & recognise combinations of 2 no.s that add to no.s up to & including 9 - model & record patterns for individual no.s by making all possible whole-number combinations - describe combinations for no.s using more, less & double • create, record & recognise combinations of 2 no.s that add to no.s from 11 up to & including 20 - use combinations for no.s up to 10 to assist with combinations for no.s beyond 10 • investigate & generalise the effect of adding zero to a number • use concrete materials to model commutative property for add & apply it to aid the recall of add facts • relate add & sub facts for numbers to at least 20 • use & record a range of mental strategies to solve add & sub problems involving 1 & 2 digit numbers, including: − counting on from the larger number to find the total of 2 numbers − counting back from a number to find the number remaining − counting on or back to find the difference between 2 numbers − using doubles & near doubles − combining numbers that add to 10 − bridging to 10 − using place value to partition - choose & apply efficient strategies for add & sub • use = sign to record equivalent no. sentences involving add, & to mean is the same as, rather than as an indication to perform an operation - check given no. sentences to determine if true/false & explain why




Sharon Tooney



2

Adding Counters Students are given five counters and a work mat marked with two large circles. Students are asked to place some of the counters in one circle and some in the other. Possible questions include: - how many counters did you put into each circle? - how many counters are there altogether? As students give their answers, the teacher models recording this as a number sentence. Students are asked to make as many different combinations to 5 as they can. The activity is repeated using a different number of counters eg 10, 20. Students practise recording number sentences

Allow students experiencing difficulty finding totals to physically count counters. Increase number of counters for those requiring extension.

counters , work mat marked with two large circles

3

Toss and Add Students toss three standard dice and race to see who can state the total number of dots first. Students are asked to share and explain their strategies. eg For this example, student strategies could include: - counting all of the dots - starting with the highest number and counting on the other dice one-by-one ie 4, 5, 6, 7 - starting with the known sum of two dice and counting on the third eg ‘4+1=5 and 2 more.’ - using visual imagery eg ‘I took the one dot and pretended it jumped onto the ‘four’ dice to make 5 dots, and then I added 2 more.’ Possible questions include: - can you find a quicker way to add? - can you add five more? - how many do you have altogether? - how did you get your answer? Variation: Students could repeat the activity using numbered dice or dice with larger numbers.

Reduce or increase number of dice depending on need. Allow for dots to be physically counted to check results.

dice

4

Take-away Box Part A Students count aloud while the teacher drops a number of cubes into a box. Students are asked to state the total number of cubes in the box. The teacher then removes and displays some of the cubes. Possible questions include: - how many cubes are left in the box? - how do you know? Students are encouraged to explain or demonstrate how the answer was obtained. The teacher empties the remaining cubes from the box and students check their answer. Students record the process as a number sentence. The activity is repeated using a different number of counters.

Allow physical counting of blocks to check results if needed. Students requiring extension, could write algorithm

cubes, box

Take-away Box Part B

Sharon Tooney

5 In pairs, students repeat Part A and are asked to record their actions and solutions using drawings, words and/or numerals.

6

Blocks on the Bowl In pairs, students are given a collection of cubes (up to 10) and a bowl. The bowl is turned upside down on the desk. Student A places the blocks on top of the bowl and Student B counts the blocks. While Student B looks away, Student A removes some of the blocks and places them under the bowl. Student A asks Student B ‘How many blocks are under the bowl?’ Student B records their answer. They check the actual number of blocks altogether. Students swap roles and repeat the activity using a different number of blocks.

Allow physical counting of blocks to check results if needed. Students requiring extension, could write algorithm

cubes, bowls

Make Your Calculator Count Students are shown how to use the process of repeatedly adding the same number on a calculator to count eg 1 + + = In pairs, students use the calculator to count from one by repeatedly pressing the ‘=’ button and record the counting numbers on a paper strip. This process can be repeated by constantly adding other numbers.

calculators

8

Selection of above activities revisited

9

Revision

10

Assessment

ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

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

SUBSTRAND: Patterns and Algebra 1 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › uses objects, diagrams and technology to explore mathematical problems MA1-2WM › creates, represents and continues a variety of patterns with numbers and objects MA1-8NA

Background Information Repeating patterns of objects or symbols are described using numbers that indicate the number of elements that repeat, eg A, B, C, A, B, C, … has three elements that repeat and is referred to as a 'three' pattern. In Stage 1, students further explore additive number patterns that increase or decrease. Patterns could now include any patterns observed on a number chart and these might go beyond patterns created by counting in ones, twos, fives or tens. This links closely with the development of Whole Numbers and Multiplication and Division. Language Students should be able to communicate using the following language: pattern, number line, number chart, odd, even.

Investigate and describe number patterns formed by skip counting and patterns with objects • identify and describe patterns when skip counting forwards or backwards by ones, twos, fives and tens from any starting point - use objects to represent counting patterns - investigate and solve problems based on number patterns • represent number patterns on number lines and number charts • recognise, copy and continue given number patterns that increase or decrease, eg 1, 2, 3, 4, … 20, 18, 16, 14, … - describe how number patterns are made and how they can be continued • create, record and describe number patterns that increase or decrease • recognise, copy and continue patterns with objects or symbols - recognise when an error occurs in a pattern and explain what is wrong • create, record and describe patterns with objects or symbols • describe a repeating pattern of objects or symbols in terms of a 'number' pattern, eg

- make connections between repeating patterns and counting, eg a 'three' pattern and skip counting by threes • model and describe 'odd' and 'even' numbers using counters paired in two rows - describe the pattern created by modelling odd and even numbers (Communicating)




Sharon Tooney



Investigate and describe number patterns formed by skip counting and patterns with objects

2

Counting Patterns The students are divided into two groups. A hundreds chart is displayed. The class counts by fives (to 100), referring to the hundreds chart. As they count, the groups take turns to name the next number in the sequence eg 5, 10, 15, 20, 25, 30 (where Group B says the bold numbers and Group A says the numbers in between). Possible questions include: - what do you notice about the numbers we are saying? - what do you notice about the numbers your group is saying? - look at all of the numbers we are saying on the hundreds chart. What pattern do you notice? - did we count number 35, …51, …85? How do you know? Variation: Students count by other multiples eg tens, twos.

Individual chart with multiples highlighted for students requiring support. Counting without hundreds chart.

hundreds chart

3

Frog Jumps A set of number cards are placed face down in order from 1 to 30. The teacher turns over cards 3, 6 and 9, and places the frog counter on number 9.

The teacher explains that Freddie the frog has jumped on some of the cards to make a number pattern. Students are asked: - what numbers can you see? - how many numbers is Freddie jumping over each time? - what numbers has Freddie jumped over? How do you know? - what number will Freddie jump on next? How do you know? - will Freddie jump on number 14? How do you know? Variation: The activity could be varied by: - repeating for other number patterns - placing the cards in descending order - removing the first few number cards to create a pattern that begins from a number other than 1.

Allow students to physically move frog to see count

number cards in order from 1 to 30, frog

4

Relating Repeating Patterns to Number Patterns Part A Students are asked to choose three different-coloured counters and create a ‘repeating pattern’. They are asked to assign a counting number to the last counter in each group and discuss. eg 3 6 9 12

● ● ● ● ● ● ● ● ● ● ● ● Students create a repeated pattern with two, four or five different-coloured counters. They assign counting numbers, record their patterns and discuss their results.

Fewer or more counters depending on ability. Extending pattern using 100s chart to support writing numbers

counters

5

Relating Repeating Patterns to Number Patterns Part B Students are asked to record their ‘repeating pattern’ (from Part A) on a 10 × 10 grid. They

Completed with support as needed

counters, hundreds chart

3 6 9

Sharon Tooney

continue their pattern to complete the grid. Students assign a number to the last counter in each group. 3 6 9 etc

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Possible questions include: - look at the colours, what pattern do you see? - can you tell me about the numbers you have recorded? - who can see a pattern in the numbers? What is the pattern? - what is the fourth number you have recorded? - when you count by threes, do you say the number 25?…36?….30?.…100? - can you show me the number that is the answer to 3 + 3 + 3?… and 3 + 3 + 3 + 3 + 3?

6

Make a Number Pattern Students are asked to make a number pattern that increases, or a number pattern that decreases. They are asked to: - describe their number pattern in words and record these words - continue their number pattern - explain why a particular number is/is not used in their number pattern - create another number pattern that has a particular number in it eg ‘create a number pattern with the number 10 in it’.


Making the Calculator Count Part A In pairs, students are given a calculator and are shown how to make it count by repeatedly adding the same number. For example, on some calculators students enter + 2 = = or + + 2 = = Students read the numbers displayed on the screen and record on an empty number line.


calculators, number lines

Sharon Tooney

_________________________________________ 0 2 4 6 8 10 12 14 16 18 20 22 24 26 Possible questions include: - what pattern do you see on the number line? - how many numbers did you land on? How many numbers did you jump over? - what would happen if you made your calculator count by fours?

8

Making the Calculator Count Part B In pairs, students are asked to start from a number other than zero. For example students enter 3 + 2 = = Students predict the next number in the sequence, press the appropriate keys and record the numbers pressed. Possible questions include: - what do you notice about these numbers? - why are the numbers different from those in Part A? - what would happen if you started from the number 10? Variation: The activity could be repeated for counting backwards by repeatedly subtracting the same number.


calculators

9

Revision

10

Assessment

ASSESSMENT OVERVIEW

Sharon Tooney



STRAND: MEASUREMENT AND GEOMETRY

TERM: 1 2 3 3

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

SUBSTRAND: Length 1 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › supports conclusions by explaining or demonstrating how answers were obtained MA1-3WM › measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres MA1-9MG

Background Information In Stage 1, measuring the lengths of objects using uniform informal units enables students to develop some key understandings of measurement. These include that: › units should be repeatedly placed end-to-end without gaps or overlaps › units must be equal in size › identical units should be used to compare lengths › some units are more appropriate for measuring particular objects › there is a relationship between the size of the chosen unit and the number of units needed. Using the terms 'make', 'mark' and 'move' assists students in understanding the concept of repeated units. By placing a unit on a flat surface, marking where it ends, moving it along and continuing the process, students see that the unit of measurement is the space between the marks on a measuring device and not the marks themselves. Recognising that a length may be divided and recombined to form the same length is an important component of conserving length. It is important that students have had some measurement experiences before being asked to estimate lengths and distances, and that a variety of estimation strategies is taught. Students will have an informal understanding of measurement prior to school, although this may not align to Western concepts of measurement. In particular, Aboriginal students often have developed a sense of measurement based on their self and their environment. Language Students should be able to communicate using the following language: length, distance, end, end-to-end, side-by-side, gap, overlap, measure, estimate, hand span.

Measure and compare the lengths of pairs of objects using uniform informal units • use uniform informal units to measure lengths and distances by placing the units end-to-end without gaps or overlaps - select appropriate uniform informal units to measure lengths and distances, eg paper clips instead of pop sticks to measure a pencil, paces instead of pop sticks to measure the length of the playground (Problem Solving) - measure the lengths of a variety of everyday objects, eg use hand spans to measure the length of a table (Problem Solving) - explain the relationship between the size of a unit and the number of units needed, eg more paper clips than pop sticks will be needed to measure the length of the desk (Communicating, Reasoning) • record lengths and distances by referring to the number and type of uniform informal unit used - investigate different informal units of length used in various cultures, including those used in Aboriginal communities (Communicating) • compare the lengths of two or more objects using appropriate uniform informal units and check by placing the objects side-by-side and aligning the ends - explain why the length of an object remains constant when units are rearranged, eg 'The book was seven paper clips long. When I moved the paper clips around and measured again, the book was still seven paper clips long' (Communicating, Reasoning) • estimate linear dimensions and the lengths of curves by referring to the number and type of uniform informal unit used and check by measuring - discuss strategies used to estimate lengths, eg visualising the repeated unit, using the process 'make, mark and move' (Communicating, Problem Solving)




Sharon Tooney



Measure and compare the lengths of pairs of objects using uniform informal units

3

Choose my unit Students choose from a collection of different units the ones they will use to measure a line (drawn on the floor with chalk or narrow tape). Use the units to make a line the same length as the one they are measuring on the floor. It is essential that students choose and use a set of identical units. Record which units were used and how the line was measured.

Line may need to be up off the floor for some students Use pictures and/or words for recording

selection of units: rods, straws, pop sticks, connecting blocks

4

Making Lengths Make a length the same as the one made by the teacher using units (eg pop sticks, paperclips) and glued onto cardboard. Students place their units: 1. in a straight line 2. not in a straight line (eg curved or zigzag line) Students comment on which line may be longer or shorter.


selection of units: rods, straws, pop sticks, matchsticks etc

5

Alternatives Use different units to measure the same length, for example, “I needed six straws or nine pop sticks”. Record the units used and how the length was measured.


units: rods, straws, pop sticks, skewers, matchsticks etc

6

Which one? Students are given a box of pieces of string or strips of paper. Students have to find the piece which is exactly five units long.


container of strips of paper/string, 1 piece to be exact length

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Who has the biggest head? Students measure around their heads with paper strips and mark correctly without overlap. Measure the length of string in units, (rods, paperclips, etc) to find who has the biggest head in their group. Record group measurements and the units used.

Completed with support as needed Activity should be altered if deemed inappropriate to measure heads

string, scissors units: rods, straws, connecting blocks, paper and pencils for recording

9 Revision

10 Assessment

ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

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

SUBSTRAND: Time 1 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › uses objects, diagrams and technology to explore mathematical problems MA1-2WM › describes, compares and orders durations of events, and reads half- and quarter-hour time MA1-13MG

Background Information 'Timing' and 'telling time' are two different notions. The first relates to the duration of time and the second is 'dial reading'. Both, however, assist students in understanding the passage of time and its measurement. Duration It is important in Stage 1 that students develop a sense of one hour, one minute and one second through practical experiences, rather than simply recalling that there are 60 minutes in an hour. Telling Time In Stage 1, 'telling time' focuses on reading the half-hour on both analog and digital clocks. An important understanding is that when the minute hand shows the half-hour, the hour hand is always halfway between two hour-markers. Students need to be aware that there is always more than one way of expressing a particular time, eg

Note: When writing digital time, two dots should separate hours and minutes, eg 9:30. In Aboriginal communities, calendars may vary in accordance with local seasonal and environmental changes, such as the flowering of plants and the migration patterns of animals, or according to significant events in the local community. Consult with local communities regarding specific local perspectives. Language Students should be able to communicate using the following language: calendar, days, date, month, year, seasons, time, clock, analog, digital, hour hand, minute hand, o'clock, half past. The terms 'hour hand' and 'minute hand', rather than 'big hand' and 'little hand', should be used to promote understanding of their respective functions.

Name and order months and seasons • name and order the months of the year • recall the number of days that there are in each month • name and order the seasons, and name the months for each season - describe the environmental characteristics of each season, eg 'Winter is cool and some trees lose their leaves' (Communicating) - recognise that in some cultures seasonal changes mark the passing of time, eg the flowering of plants and the migration patterns of animals are used by many peoples, including Aboriginal people (Reasoning) - recognise that in countries in the northern hemisphere, the season is the opposite to that being experienced in Australia at that time (Reasoning) Use a calendar to identify the date and determine the number of days in each month • identify a day and date using a conventional calendar - identify personally or culturally significant days (Communicating) - identify the different uses of calendars in various communities (Communicating) Tell time to the half-hour • read analog and digital clocks to the half-hour using the terms 'o'clock' and 'half past' • describe the position of the hands on a clock for the half-hour - explain why the hour hand on a clock is halfway between the two hour-markers when the minute hand shows the half-hour (Communicating, Reasoning) - describe everyday events with particular hour and half-hour times, eg 'We start school at 9 o'clock' (Communicating) • record hour and half-hour time on analog and digital clocks




Sharon Tooney



Name and order months and seasons Use a calendar to identify the date and determine the number of days in each month

Tell time to the half-hour

7

Months and seasons Months in Order • Say simple rhymes or sing songs that list the months of the year in order. • Students work in groups to order cards on which are written the months of the year. Compare students’ results and revise as necessary. Match that Month! • Students are given two sets of cards: − set A – 12 cards with the names of the 12 months of the year − set B – 12 cards with the number of days in each month of the year. They place all cards facedown. • Working in pairs, students take turns selecting one card from each set to turn over. If the cards selected are a ‘match’ between the name of the month and the number of days in the month, the student keeps the cards. If not, the cards are turned facedown again. After all the cards have been accounted for, the student with the most pairs of cards wins. Seasons Book or Poster For this activity, students can work in groups or individually with one or more seasons per group or individual. • Students construct a ‘seasons’ book or poster (either paper or electronic) using drawings, digital photos and/or images sourced online or from magazines. • Students compile lists of words or sentences to go with each season, including descriptions of some or all of the following: – weather, eg sunny, rainy, windy – temperature, eg hot, cold – observable changes in the environment, eg ‘Some trees lose their leaves in autumn’, ‘Flowers bloom in spring and summer’ – how people respond to the season in terms of clothing, household adjustments and activities, eg ‘We wear coats and scarves in winter’, ‘We go to the beach in summer’, ‘We need to turn the heater on in winter because it is cold’ – how animals respond to the season, eg ‘My pet loses more fur in summer than winter’, ‘Some birds fly to other places in winter’. • Each group or student presents their book or poster to the class and explains the relevance of the particular images and words or sentences chosen for each season.


two sets of cards, magazines, pictures, cardboard, paper, scissors, glue, computers

8

Calendars Days in a Month • Use a calendar to identify and record how many days are in each month of the year. • Say simple rhymes or sing songs that assist students in remembering how many days are in each month, such as: Thirty days hath September, April, June and November.


calendar

Sharon Tooney

All the rest have 31, Except for February alone, Which hath 28 days clear And 29 in each leap year. Discussion Discuss how a calendar can help you remember important dates. As you page through a calendar saying the name of each month, children stand if their birthday is in that month. For each month ask each child who is standing the date of his or her birthday and circle that date on the calendar. ask questions about your findings. - Discuss today's date and find it on the calendar. - When is your birthday? Does anyone in class have a birthday this month? - How many birthdays in January? - How many birthdays on Friday in April? - How many kids have birthday on same date in May? - How many have birthday in same week in June. - What is the first month, last month what comes after March and so on. - What is your favourite holiday? In what month does it occur?

9

Telling time Discuss the differences between the two clocks: digital and a clock with hands. Discuss the differences between the hour hand and minute hand. Discuss the fraction 1/2. Show 4 o'clock on a demonstration clock. Move the minute hand halfway around the clock to 6 while children count by fives. Possible questions - How many minutes have passed? - Where does the minute hand point? - Where does the hour hand point? - What time is it? Write four-thirty , 4:30 and half past 4 on the board. Continue moving the minute hand around the clock to 12 while children count by fives. Ask: - How much time has passed? - What time is it now? Discuss the two ways to read time at the half hour. (4:30 and half past 4) Where is the minute hand at half past the hour? Activities: 1. Play "Time Concentration." Prepare cards showing several times on the hour and half hour. Also prepare matching cards with clock faces illustrating these times. Turn all cards face down individually. Students may play one to one or form partners to play the game. One student turns over two cards, trying to match a clock face with the corresponding time card. If the cards match, the student removes the cards and keeps them. If the cards do not match, the student replaces the cards face down, and the next player takes a turn. The game continues until all the cards are matched. The player with the most matches wins. 2. Prepare cards showing clock faces on the half hour. The students will match the clock faces to cards which record the time in standard notation form or with the words 'half past' the hour.


demonstration clock, concentration cards

Sharon Tooney

3. Have students make their own TV guides. For each program the student must record the day, channel and time, and draw a clock face indicating when the show begins

10

Revision Assessment

ASSESSMENT OVERVIEW

Sharon Tooney

Time Concentration Cards

4:30

12:30

8:30

10:30

2:30

Sharon Tooney

1:30

3:30

11:30

7:30

5:30

Sharon Tooney




TERM: 1 2 3 3

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

SUBSTRAND: Length 1 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › supports conclusions by explaining or demonstrating how answers were obtained MA1-3WM › manipulates, sorts, represents, describes and explores two-dimensional shapes, including quadrilaterals, pentagons, hexagons and octagons MA1-15MG

Background Information Manipulation of a variety of real objects and shapes is crucial to the development of appropriate levels of visualisation, language and representation. The skills of discussing, representing and visualising three-dimensional objects and two-dimensional shapes are developing in Stage 1 and must be fostered through practical activities and communication. It is important that students have experience involving a broad range and variety of objects and shapes in order to develop flexible mental images and language. Students need to be able to recognise shapes presented in different orientations. They need to develop an understanding that changing the orientation of a shape does not change its features or its name. In addition, students should have experiences identifying both regular and irregular shapes, although it is not expected that students understand or distinguish between regular and irregular shapes in Stage 1. Regular shapes have all sides and all angles equal. Many shapes used in Aboriginal art are used with specific meanings. Local Aboriginal communities and many education consultants can provide examples. Further exploration of such meanings could be incorporated in students' studies within the Creative Arts Key Learning Area. Language Students should be able to communicate using the following language: shape, circle, triangle, quadrilateral, square, rectangle, pentagon, hexagon, octagon, orientation, features, side, vertex (vertices), vertical, horizontal, portrait (orientation), landscape (orientation), parallel. The term 'vertex' (plural: vertices) refers to the point where two straight sides of a two-dimensional shape meet (or where three or more faces of a three-dimensional object meet). The term 'shape' refers to a two-dimensional figure. The term 'object' refers to a three-dimensional figure.

Recognise and classify familiar two-dimensional shapes using obvious features • identify vertical and horizontal lines in pictures and the environment and use the terms 'vertical' and 'horizontal' to describe such lines - relate the terms 'vertical' and 'horizontal' to 'portrait' and 'landscape' page orientation, respectively, when using digital technologies (Communicating) • identify parallel lines in pictures and the environment and use the term 'parallel' to describe such lines - recognise that parallel lines can occur in orientations other than vertical and horizontal (Reasoning) - give everyday examples of parallel lines, eg railway tracks • manipulate, compare and describe features of two-dimensional shapes, including triangles, quadrilaterals, pentagons, hexagons and octagons - describe features of two-dimensional shapes using the terms 'side' and 'vertex' (Communicating) • sort two-dimensional shapes by a given attribute, eg by the number of sides or vertices - explain the attribute used when sorting two-dimensional shapes (Communicating, Reasoning) • identify and name two-dimensional shapes presented in different orientations according to their number of sides, including using the terms 'triangle', 'quadrilateral', 'pentagon', 'hexagon' and 'octagon',

eg - recognise that the name of a shape does not change when the shape changes its orientation in space, eg a square turned on its vertex is still a square - select a shape from a description of its features (Reasoning) - recognise that shapes with the same name may have sides of equal or different lengths (Reasoning) • recognise that rectangles and squares are quadrilaterals • identify and name shapes embedded in pictures, designs and the environment, eg in Aboriginal art - use computer drawing tools to outline shapes embedded in a digital picture or design (Communicating)




Sharon Tooney



Recognise and classify familiar two-dimensional shapes using obvious features

2

Sorting Shapes Students are given a collection of regular and irregular shapes with three sides, four sides, five sides and six sides. Students are asked to sort the shapes into groups according to the number of sides. Students select one of the groups and arrange the shapes to form a picture. Students write a description of their picture, commenting on the shapes they have used. Possible questions include: - can you show me how to draw and name each shape? - what can you tell me about each shape? - how are these shapes different/the same?

Provide a scribe where necessary

regular and irregular shapes with three sides, four sides, five sides and six sides

3

Making Shapes In small groups, students are given a die and straws of two different lengths. In turn, students roll the die and make a shape with the corresponding number of sides. Students are encouraged to make regular and irregular shapes. Students name each shape, and record their shapes in appropriate groups. Students discuss the difficulties encountered in making a shape when they roll a 1 or a 2, and develop a new rule for the game. For example, students may decide that a turn is missed if a 1 or a 2 is rolled.

Provide a scribe where necessary. Completed with support as needed

dice, straws

4

New Shapes from Old Shapes Students are given a variety of regular and irregular shapes. Students are asked to: - arrange two or more shapes to create a new shape eg combine 6 triangles to form a hexagon - cut a square into four triangles and put the triangles together to make other shapes eg a rectangle - cut a rectangle into two triangles and create new shapes. Students describe and record what they have done.

Some students might use fraction language in their description. Provide a scribe where necessary. Completed with support as needed

regular and irregular shapes, scissors, glue, paper, pencils

5

Shape Symmetry Students find shapes that have a line of symmetry by folding the shapes in half. In pairs, they are given a collection of regular and irregular shapes that could include squares, rectangles, triangles, trapeziums, rhombuses, hexagons and circles. Possible questions include: - which shapes can be folded in half? - which shapes can be folded in half in a different way? - which shapes do not have a line of symmetry? Students glue their shapes onto paper and record their findings.


regular and irregular shapes, paper, glue, pencils

6

Lines and Shapes in the Environment Students identify lines and shapes in the classroom and playground eg the flag pole, a telegraph pole, the edge of the roof, the edge of the floorboards. Students discuss and record their observations. They are encouraged to identify the most commonly occurring shapes, and horizontal and vertical lines.


7

Make a new shape In pairs, students are provided with geoboards and elastic bands. The teacher draws a triangle on the board and asks Student A to ‘make this shape on your geoboard’. The student names the shape and states the number of sides. Both students draw and label the shape on dot paper.


geoboards, elastic bands, dot paper, pencils

Sharon Tooney

Student B is then asked to add another side to the triangle on the geoboard. They name the new shape and state the number of sides. Again, both students draw and label the shape on dot paper.

10

Revision Assessment

ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

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

SUBSTRAND: Position 1 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › represents and describes the positions of objects in everyday situations and on maps MA1-16MG

Background Information Being able to describe the relative positions of objects in a picture or diagram requires interpretation of a two-dimensional representation. Locations that are familiar to Aboriginal students may not be limited to their home environments and may also include other locations within the community, eg local landmarks and organisations. Language Students should be able to communicate using the following language: position, left, right, directions, turn. In Early Stage 1, students used the terms 'left' and 'right' to describe position in relation to themselves. In Stage 1, students use the terms 'left' and 'right' to describe position from the perspective of a person facing in the opposite direction.

Give and follow directions to familiar locations • use the terms 'left' and 'right' to describe the positions of objects in relation to themselves and from the perspective of a person facing in the opposite direction, eg 'The ball is on her left' • give and follow directions, including directions involving turns to the left and right, to move between familiar locations, eg within the classroom or school - use amounts of turn (full and half) to describe direction (Communicating) • give and follow instructions to position objects in models and drawings, eg 'Draw the bird between the two trees' - give and follow simple directions using a diagram or description (Communicating) • describe the path from one location to another on drawings - use a diagram to give simple directions (Communicating) - create a path from one location to another using computer software (Communicating)


Cross-curriculum priorities Aboriginal &Torres Strait Islander histories & cultures Asia & Australia’s 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

Sharon Tooney



Give and follow directions to familiar locations

7

Model of a Farm In small groups, students make a model of a farm using small toys, pictures and junk materials. Students are asked to describe the position of objects in relation to other objects eg ‘The horses are next to the cows’, ‘The stable is behind the farmhouse.’ Students make a sketch of their model and plan a path the farmer could take each morning to ensure he feeds all of the animals. Students could act out the path on the model and record the path on the sketch. Variation: In pairs, students work on a computer and use simple shapes from a draw program to draw one of their sketched models. A line tool could be used to trace a route or path. Possible questions include: - can you sketch a model a friend has constructed? - can you describe the position of objects in your model? - what objects are on the left of the house? right of the house?

Provide a scribe where necessary. Completed with support as needed Recreate model in 3D using playdough

small toys, pictures and junk materials, paper, pencil, computers

8

Memory Model Students walk around the school observing the main buildings, landmarks and pathways. In small groups, students use blocks, small boxes and junk materials to reconstruct a model of the school from memory. Students are asked to identify the main features of their model eg ‘This is the play equipment.’ Possible questions include: - can you describe the position of features in relation to other features? eg ‘The toilets are next to the play equipment.’ - can you demonstrate and describe the route taken to get to particular parts of the school? - can you sketch your model and mark special routes onto your sketch in different colours?

Photographs of school to support students with special needs. Provide a scribe where necessary. Write how they get from one location to another

blocks, small boxes and junk materials

9

Partner Left and Right In pairs, facing each other, students follow a pattern for clapping eg ‘Clap right hands together, left hands together, then both hands together.’ Possible questions include: - what do you notice when you both clap left hands together? Students learn some dances involving a clapping sequence with students facing each other in pairs eg ‘Heel and Toe Polka’. Students could also learn other dances involving linking arms and moving right or left.

Strategic pairing of students or student with aide as necessary

dance music

10

Revision Assessment

Sharon Tooney

ASSESSMENT OVERVIEW

Sharon Tooney



STRAND: STATISTICS AND PROBABILITY

TERM: 1 2 3 3

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

SUBSTRAND: Data 1 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › supports conclusions by explaining or demonstrating how answers were obtained MA1-3WM › gathers and organises data, displays data in lists, tables and picture graphs, and interprets the results MA1-17SP

Background Information In Stage 1, students are introduced to the abstract notion of representing an object with a different object, picture or drawing. It is important that each object in a three-dimensional graph represents one object, except in the case where items are used in pairs, eg shoes. One object can also represent an idea, such as a person's preference. When collecting information to investigate a question, students can develop simple ways of recording. Some methods include placing blocks or counters in a line, colouring squares on grid paper, and using tally marks. A single mark in a tally represents one observation. Tally marks are usually drawn in groups of five. The first four marks are vertical, with the fifth mark drawn diagonally through the first four to make counting more efficient, eg

represents 3, represents 5, represents 9. Language Students should be able to communicate using the following language: information, data, collect, gather, display, objects, symbol, tally mark, picture, row.

Choose simple questions and gather responses • investigate a matter of interest by choosing suitable questions to obtain appropriate data • gather data and track what has been counted by using concrete materials, tally marks, words or symbols Represent data with objects and drawings where one object or drawing represents one data value and describe the displays • use concrete materials or pictures of objects as symbols to create data displays where one object or picture represents one data value (one-to-one correspondence), eg use different coloured blocks to represent different-coloured cars - record a data display created from concrete materials or pictures of objects (Communicating) • interpret information presented in data displays where one object, picture or drawing represents one data value, eg weather charts - describe information presented in simple data displays using comparative language such as 'more than' and 'less than', eg 'There were more black cars than red cars' (Communicating, Reasoning) - explain interpretations of information presented in data displays, eg 'More children like dogs because there are more dog pictures than cat pictures' (Communicating, Reasoning) - write a simple sentence to describe data in a display, eg 'The most popular fruit snack is an apple' (Communicating)




Sharon Tooney



Choose simple questions and gather responses

Represent data with objects and drawings where one object or drawing represents one data value and describe the displays

2

Tally Marks Explain and demonstrate the use of tally marks. Provide students sets of 10 paddle pop sticks each to create given numbers, as tally marks. This activity should be done as a whole class on the floor in a circle so that instant feedback can be given to students’ attempts. Play ‘Tally Mark’ match using cards that represent tally marks to 20 and number cards. The following games can be played: - Tally mark to tally mark match - Tally mark to numeral match - Tally mark to tally mark concentration - Tally mark to numeral concentration

More capable students can use numbers beyond twenty. Students having difficulty can start in the range of 1-5 or 1-10, depending on need.

tally mark cards

3

Sticky Data Everyone in the class will need a sticky note. Have students write their name on it and draw a picture of themself. You'll also need some large sheets of flipchart paper or you could work on the board or the floor. Draw two long lines on the paper/board/floor:

Students will use sticky notes and the lines to help find out the answers to some questions: - How many boys and how many girls are there in your group? - Which month has the most birthdays for your group? - How old are the children in your group? - Could you give a name to the lines in each case? - How can we use our sticky notes to answer that question? - Tell me about what you're doing.

You could follow up this activity with an interactive display. Draw some axes on an accessible area of and stick sticky notes up too. Slips of paper could offer suggestions for the axes' titles and blank slips could encourage children to create their own. If you would prefer to focus on sorting rather than block graphs, children could use any objects rather than identical sticky notes.

posted notes, chart paper

4

Ladybird Count Some children were playing a game. They collected cards with ladybirds on them. Here are the cards they had at the end of the game:

Aisha

Ben

Carmel

Danny

Some children could be challenged to show the info in more than 1 way. They may even be able to articulate which representation they think is best and why. Some children may prefer to represent their ideas using media other than paper, for example cubes, counters etc.

ladybird chart

Sharon Tooney

Elaine

Key questions - How many ladybirds does each child have? - How could you show that on a picture or chart?

5

Car Count In groups students use tally marks to record the types of transport that pass the school (ie. Cars, motorcycles, buses, trucks) within a set period of time. Back in class each group is to make a picture graph, using representations of vehicles and decide how they will name each axis of their graph. Possible questions include: - How will you label each axis of your graph? - Which vehicle was most common? - Which vehicle was least common? - Did you encounter a vehicle type that wasn’t in your original vehicle types? If yes what did you do?

Activity could be extended by having more capable students use lots of 5/10 to represent vehicle numbers on graph. To simplify activity use colour only as the criteria, using a table with colour codes to tally under.

paper and pencil, pictorial representations of vehicles

10

Revision Assessment

ASSESSMENT OVERVIEW

Sharon Tooney

Sharon Tooney

Sharon Tooney

1 4 3 2

Sharon Tooney

5 8 7 6

Sharon Tooney

9 10

14 13 15

11 12

17

16

20 19 18

Documents

Mathematics Program Proforma Yr1 t1