mathematics program proforma yr 2 t1

Sharon Tooney

MATHS PROGRAM : STAGE 0NE

Year Two

WEEKLY ROUTINE

Monday Tuesday Wednesday Thursday Friday

Whole Number 1 Terms 1-4 Number & Algebra Terms 1 & 3: Addition and Subtraction 1 / Patterns and Algebra 1 Terms 2 & 4 : Multiplication & Division 1 / Fractions and Decimals 1

Statistics & Probability Terms 1 & 3: Data 1 Terms 2 & 4 : Chance 1

Measurement & Geometry Term 1: Length 1 / Time 1 / 2D 1 Term 2: Mass 1 / 3D 1 / Position 1 Term 3: Volume and Capacity 1 / Time 1 / 2D 1 Term 4: Area 1 / 3D1 / Position 1

Sharon Tooney

K-6 MATHEMATICS SCOPE AND SEQUENCE

NUMBER AND ALGEBRA MEASUREMENT AND GEOMETRY STATISTICS & PROBABILITY

TERM

Whole Number

Addition & Subtraction

Multiplication & Division

Fractions & Decimals

Patterns & Algebra

Length Area Volume & Capacity

Mass Time 3D 2D Angles Position Data Chance

K 1 2 3 4

Yr 1 1 2 3 4

Yr 2 1 2 3 4

Yr 3 1 2 3 4

Yr 4 1 2 3 4

Yr 5 1 2 3 4

Yr 6 1 2 3 4

NB: Where a content strand has a level 1 & 2, the 1 refers to the lower grade within the stage, eg. Whole Number 1 in S1 is for Yr 1, Whole Number 2 is for Yr 2.

Sharon Tooney

MATHEMATICS PROGRAM PROFORMA

STAGE: Yr 2 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 Numbers 2 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 The learning needs of students are to be considered when determining the appropriate range of two- and three-digit numbers. Students should be encouraged to develop different counting strategies, eg if they are counting a large number of items, they can count out groups of ten and then count the groups. They need to learn correct rounding of numbers based on the convention of rounding up if the last digit is 5 or more and rounding down if the last digit is 4 or less. 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, groups of one hundred, hundreds, round to. The word 'and' is used when reading a number or writing it in words, eg five hundred and sixty three.

Develop confidence with number sequences from 100 by ones from any starting point • count forwards or backwards by 1s, from a given 3-digit number • identify the numbers before & after a given 3-digit number - describe the number before as 1 less than & the number after as 1 more than a given number Recognise, model, represent and order numbers to at least 1000 • represent 3-digit numbers using objects, pictures, words & numerals • use the terms more than & less than to compare numbers • arrange numbers of up to 3 digits in ascending order - use number lines & number charts beyond 100 to assist with counting & ordering - give reasons for placing a set of numbers in a particular order Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences • count forwards & backwards by 2s, 3s & 5s from any starting point • count forwards & backwards by 10s, on & off the decade, with 2 & 3 digit numbers • identify number sequences on number charts Group, partition and rearrange collections of up to 1000 in hundreds, tens and ones to facilitate more efficient counting • apply an understanding of place value & the role of zero to read, write & order 3 digit numbers - form the largest & smallest number from 3 given digits • count & represent large sets of objects by systematically grouping in 10s & 100s - use models such as base 10 material, interlocking cubes & bundles of sticks to explain grouping • use & explain mental grouping to count & assist with estimating the number of items in large groups • use place value to partition 3 digit • state the place value of digits in numbers of up to 3 digits • partition three-digit numbers in non-standard forms • round numbers to the nearest 100 • estimate, to the nearest 100, the number of objects in a collection & check by counting Count and order small collections of Australian coins and notes according to their value • use the face value of coins and notes to sort, order and count money - compare Australian coins and notes with those from other countries - determine whether there is enough money to buy a particular item • recognise that there are 100 cents in $1, 200 cents in $2, … • identify equivalent values in collections of coins and in collections of notes

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

Develop confidence with number sequences from 100 by ones from any starting point Recognise, model, represent and order numbers to at least 1000 Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences Group, partition and rearrange collections of up to 1000 in hundreds, tens and ones to facilitate more efficient counting Count and order small collections of Australian coins and notes according to their

2

Celebrity head Display a number line showing numbers from 1 to 100 so that all the students in the class can see it. Place movable marker tabs at either end of the strip. One student wears a headpiece to which a numeral card is attached. Ensure that the student does not see the number on the numeral card. Ask the student to have the class help to identify the “secret number”. The class, however, can respond only with a yes or no reply to each question. In response to the answers, the selected student then moves the tabs along the number line to indicate the range within which the “secret number” lies. Continue the process until the student is able to identify the number. Variations The price is right Display a vertical numeral strip to the students. Ask one student to think of a number on the numeral strip. The remainder of the class take turns to guess the number. After each guess, allow the student to point to the nominated number on the number line. The student then states if the guess is higher or lower than the number being thought of. Encourage the students to use the responses from previous guesses when making the next guess. Guess my number Provide a calculator for each pair of students. Ask one student to enter a number into the calculator and hide the screen. Instruct the partner to ask questions which will enable him or her to guess the hidden number on the calculator.

This activity could be modified by decreasing or increasing the range of numbers. Number lines on tables to refer to could also be necessary for some students.

number line in the range 1 to 100, headband, numeral cards, calculators

3

Grocery grab Display a collection of grocery packages of varying weight up to 1 kilogram. Allow the students to compare the weight of each item according to the number of grams indicated on each package. Have the students record the weight of each item in grams. Instruct the students to then sequence the items from lightest to heaviest. Variation Collect from catalogues pictures of items costing less than $1000 . Ensure the price of each item is clearly indicated. Present the catalogue items to the students and ask them to sequence the items in terms of cost. Wipe out Provide each student with a calculator. Ask the students to enter a specific three-digit number into their calculators. Choose one of the digits from the number entered and ask the students to use an arithmetical method to change the nominated digit to zero. For example, have the students enter the numeral 268 in their calculator. Follow this by asking, “How can you change the 6 to 0?”

It may be necessary to highlight and/or enlarge weights on packages. Number charts in the range 1 to 1000 maybe needed by some students as a reference. Large button calculators may be needed

grocery packages, shop catalogues, calculators, paper and pencil

4

Skip counting Lead the students in oral counting in unison by tens, up to 100, and then backwards from 100. Support the oral counting by pointing to the location of these numbers on the one hundred chart. Cover the multiples of ten on the hundred chart and have a student point to the position of each number as the class counts forwards or backwards by ten. Vary the activity by using other counting

Individual charts as a reference maybe needed. Extend activity by counting beyond 100

hundreds chart

Sharon Tooney

value

patterns, such as counting by twos or counting by fives.

5 Straw javelin Place masking tape on the floor to indicate a starting point. Organise the students into a line behind the starting point. Have the students take turns to throw a straw as far as they can. Provide the students with Unifix blocks which have been assembled into towers of ten, as well as single blocks. The students then measure the distance the straw travelled by placing the Unifix blocks along the floor from the starting point to the straw. Variations • Change the activity from throwing a straw to other actions, such as taking a giant step from the starting point and then measuring the distance of the steps using the Unifix blocks. • Organise the students into pairs. Provide each pair of students with lengths of string and ask them to use the string to measure their arm span and their height. After the students have completed measuring with the string, they place the string on the floor. Have the students use the towers of ten Unifix blocks to record the length of the string.

Some students may require one-on-one support to complete this activity. Measure using standard units as an extension activity.

masking tape, straws, unifix blocks, string, paper and pencil

6

Three-dice game Prepare a set of numeral cards for the numbers three to eighteen. Lay the cards face up in a line on the desk or floor. Have the students take turns to roll three dice and add together the numbers rolled, then take a corresponding numeral card. The game continues until all cards have been taken. If the numeral card has already been taken, the player’s turn is forfeited. Variations • Use a variety of dice, such as dot and numeral dice. • Provide each student with a set of numeral cards for the numbers three to eighteen. Have the students take turns to roll three dice and find the total. Each time a student states the total of the three dice, all students place a counter on the corresponding numeral card in their set. The game continues until all numerals have been covered.

Adjust activity according to student placement on the numeracy continuum

dice, numeral cards

7

The beanstalk This activity is best completed with a maximum of five students. Prepare Beanstalk base board using the BLM and a pack of instruction cards. The instruction cards should state the direction in which the student moves along the beanstalk, either up or down, and the number of spaces to move, for example, “go up three spaces.” Commence the activity by instructing each student to place a marker at position 10 on the beanstalk. In turns students take an instruction card, follow the directions and move their marker accordingly along the beanstalk. The winner is the first person to reach the castle at the top of the beanstalk. An option is to have the students record the number sentences.

Adjust activity according to student placement on the numeracy continuum

beanstalk baseboard, instruction cards, counters

8

Coin Values Students identify the face value of Australian coins and the combinations of smaller coins needed to add up to larger coin values. Eg. How much is this coin worth?

How many ways can I represent this amount using smaller coin denominations?

Adjust according to ability to recognise and count money

coins

Sharon Tooney

9

Count Money Up to $1 Students investigate adding coins to find a total, to purchase an item, etc Eg. How much money is there?

Adjust according to ability to recognise and count money

coins

10

Revision Assessment

ASSESSMENT OVERVIEW

Sharon Tooney

Sharon Tooney




TERM: 1 2 3 3

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

SUBSTRAND: Addition and Subtraction 2 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

Background Information It is appropriate for students in Stage 1 to use concrete materials to model and solve problems, for exploration and for concept building. Concrete materials may also help in explanations of how solutions were obtained. Addition and subtraction should move from counting and combining perceptual objects, to using numbers as replacements 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: 'taking away' from a group, and 'comparison' (ie determining how many more or less when comparing two groups). In performing a subtraction, students could use 'counting on or back' from one number to find the difference. The 'counting on or back' type of subtraction is more difficult for students to grasp than the 'taking away' type. Nevertheless, it is important to encourage students to use 'counting on or back' as a method of solving comparison problems once they are confident with the 'taking away' type. In Stage 1, students develop a range of strategies to aid quick recall of number facts and to solve addition and subtraction problems. They should be encouraged to explain their strategies and to invent ways of recording their actions. It is also important to discuss the merits of various strategies in terms of practicality and efficiency. Jump strategy on a number line – an addition or subtraction strategy in which the student places the first number on an empty number line and then counts forward or backwards, first by tens and then by ones, to perform a calculation. (The number of jumps will reduce with increased understanding.) Jump strategy method: eg 46 + 33

Jump strategy method: eg 79 – 33

Explore the connection between addition and subtraction • use concrete materials to model how addition and subtraction are inverse operations • use related addition and subtraction number facts to at least 20, eg 15 + 3 = 18, so 18 – 3 = 15 and 18 – 15 = 3 Solve simple addition and subtraction problems using a range of efficient mental and written strategies • use and record a range of mental strategies to solve addition and subtraction problems involving two-digit numbers, including: − the jump strategy on an empty number line − the split strategy, eg record how the answer to 37 + 45 was obtained using the split strategy − an inverse strategy to change a subtraction into an addition, eg 54 – 38: start at 38, adding 2 makes 40, then adding 10 makes 50, then adding 4 makes 54, and so the answer is 2 + 10 + 4 = 16 • select and use a variety of strategies to solve addition and subtraction problems involving one- and two-digit numbers - perform simple calculations with money, eg buying items from a class shop and giving change (Problem Solving) - check solutions using a different strategy (Problem Solving) - recognise which strategies are more efficient and explain why (Communicating, Reasoning) - explain or demonstrate how an answer was obtained for addition and subtraction problems, eg show how the answer to 15 + 8 was obtained using a jump strategy on an empty number line




Sharon Tooney

Split strategy – an addition or subtraction strategy in which the student separates the tens from the units and adds or subtracts each separately before combining to obtain the final answer. Split strategy method: eg 46 + 33

Inverse strategy – a subtraction strategy in which the student adds forward from the smaller number to obtain the larger number, and so obtains the answer to the subtraction calculation. Inverse strategy method: eg 65 – 37 start at 37 add 3 to make 40 then add 20 to make 60 then add 5 to make 65 and so the answer is 3 + 20 + 5 = 28 An inverse operation is an operation that reverses the effect of the original operation. Addition and subtraction are inverse operations; multiplication and division are inverse operations. Language Students should be able to communicate using the following language: plus, add, take away, minus, the difference between, equals, is equal to, empty number line, strategy. Some students may need assistance when two tenses are used within the one problem, eg 'I had six beans and took away four. So, how many do I have now?' The word 'left' can be confusing for students, eg 'There were five children in the room. Three went to lunch. How many are left?' Is the question asking how many children are remaining in the room, or how many children went to lunch?

Sharon Tooney



Explore the connection between addition and subtraction

Solve simple addition and subtraction problems using a range of efficient mental and written strategies

2

Related Addition Facts Students identify and write related addition facts for given algorithms. Eg. 13 + 1 = 14, students need to recognise that 1 + 13 = 14 is the related addition fact

Adjust according to student placement on the numeracy continuum

3

Related Subtraction Facts Students identify and write related subtraction facts for given algorithms. Eg. 20 - 5 = 15, students need to recognise that 20 - 15 = 5 is the related subtraction fact


4

Fact Families Students are encouraged to see the relationship between addition and subtraction by identifying the fact families that apply to given set of algorithms, by identifying the missing fact, for example: What fact is missing from this fact family?


5

Review - Add One-Digit Numbers - Sums to 10 Revise addition facts to ten, using friends of 10 where appropriate. Provide algorithms with and without pictorial representations (concrete materials) Eg.


6

Review - Ways to Make a Number - Sums to 10 Students use their knowledge of numbers to 10, to identify what they know about friends of ten and how to identify correct and incorrect addition problems. Eg.


7

Adding Doubles Students investigate doubles and near doubles to complete addition problems. Eg. 5 + 5 = , 2+ 2 = , 9 + 9 = etc


8

Add One Digit Numbers Students investigate addition problems using one digit numbers. Problems include both one and two digit answers. Algorithms should be presented by vertically and horizontally to demonstrate that the orientation doesn’t affect the outcome. Eg. Add:


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http://au.ixl.com/math/year-2/review-ways-to-make-a-number-sums-to-10�

Sharon Tooney

4 + 8 = , 5 + 7

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 2 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 › creates, represents and continues a variety of patterns with numbers and objects MA1-8NA

Background Information In Stage 1, describing number relationships and making generalisations should be encouraged when appropriate. Language Students should be able to communicate using the following language: pattern, missing number, number sentence.

Describe patterns with numbers and identify missing elements • describe a number pattern in words, eg 'It goes up by threes' • determine a missing number in a number pattern, eg 3, 7, 11, __, 19, 23, 27 - describe how the missing number in a number pattern was determined (Communicating, Reasoning) - check solutions when determining missing numbers in number patterns by repeating the process (Reasoning) Solve problems by using number sentences for addition or subtraction • complete number sentences involving one operation of addition or subtraction by calculating the missing number, eg find so that or - make connections between addition and related subtraction facts to at least 20 (Reasoning) - describe how a missing number in a number sentence was calculated (Communicating, Reasoning) • solve problems involving addition or subtraction by using number sentences - represent a word problem as a number sentence (Communicating, Problem Solving) - pose a word problem to represent a number sentence (Communicating, Problem Solving)




Sharon Tooney



Describe patterns with numbers and identify missing elements

Solve problems by using number sentences for addition or subtraction

2

Skip Counting Show different groups of items and ask students how many; telling them to count by 2s, 5s, 10s etc. Eg. How many combs are there? Count by tens.

Adjust the number of items according to ability

groups of items or pictorial representations of groups

3

Skip Counting Sequences Provide students with a variety of number sequences with missing elements. Have them determine and record the missing number by skip counting. Eg. Write the missing number in this sequence: 45, 50, 55, 60, , 70

Provide 100s chart as a reference.

number sequences

4

Counting Patterns Up to 100 Provide students with skip counting sequences to 100. Given the first number in a counting sequence, students are to complete the number sequence, using the skip counting strategy suggested. Eg. Count forward by tens from 20. 20, , , , , Count forward by twos from 36 36, , , , ,


counting sequences

5

Counting Patterns Up to 1000 Provide students with skip counting sequences to 1000. Given the first number in a counting sequence, students are to complete the number sequence, using the skip counting strategy suggested. Eg. Count forward by twos from 62. 62, , , , Count forward by twos from 8. 8, , , ,


counting sequences

6

Number Lines Up to 100 Identify where numbers come in the number sequence by locating given numbers on a number line. Eg. Which number comes just after 81?


number lines

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Sharon Tooney

Identifying the missing number in a number sequence to 100, using a number line. Eg. What is the missing number?

7 Hundreds Chart Students use skip counting strategies to locate and identify a number from the information presented by the teacher using a 100s chart. Eg. What number is 10 less than 96?

100s charts

8

Number Lines Up to 1000 Identify where numbers come in the number sequence by locating given numbers on a number line. Eg. Which number comes between 979 and 981?

Order given numbers to 1000, using a number line to assist


number lines

9

Revision

10

Assessment

ASSESSMENT OVERVIEW

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Sharon Tooney



STRAND: MEASUREMENT AND GEOMETRY

TERM: 1 2 3 3

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

SUBSTRAND: Length 2 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 Students should be given opportunities to apply their understanding of measurement, gained through experiences with the use of uniform informal units, to experiences with the use of the centimetre and metre. They could make a measuring device using uniform informal units before using a ruler, eg using a length of 10 connecting cubes. This would assist students in understanding that the distances between marks on a ruler represent unit lengths and that the marks indicate the endpoints of each unit. When recording measurements, a space should be left between the number and the abbreviated unit, eg 3 cm, not 3cm. Refer also to background information in Length 1. Language Students should be able to communicate using the following language: length, distance, straight line, curved line, metre, centimetre, measure, estimate.

Compare and order several shapes and objects based on length, using appropriate uniform informal units • relate the term 'length' to the longest dimension when referring to an object • make and use a tape measure calibrated in uniform informal units, eg calibrate a paper strip using footprints as a repeated unit - use computer software to draw a line and use a simple graphic as a uniform informal unit to measure its length • compare and order two or more shapes or objects according to their lengths using an appropriate uniform informal unit - compare the lengths of two or more objects that cannot be moved or aligned • record length comparisons informally using drawings, numerals and words, 7 by referring to the uniform informal unit used Recognise and use formal units to measure the lengths of objects • recognise the need for formal units to measure lengths and distances • use the metre as a unit to measure lengths and distances to the nearest metre or half-metre - explain and model, using concrete materials, that a metre-length can be a straight line or a curved line • record lengths and distances using the abbreviation for metres (m) • estimate lengths and distances to the nearest metre and check by measuring • recognise the need for a formal unit smaller than the metre • recognise that there are 100 centimetres in one metre, ie 100 centimetres = 1 metre • use the centimetre as a unit to measure lengths to the nearest centimetre, using a device with 1 cm markings, eg use a paper strip of length 10 cm • record lengths and distances using the abbreviation for centimetres (cm) • estimate lengths and distances to the nearest centimetre and check by measuring




Sharon Tooney



Compare and order several shapes and objects based on length, using appropriate uniform informal units Recognise and use formal units to measure the lengths of objects

2 Measure With One Unit Students are given one specific unit (eg. One popstick, streamer or 1m ruler). Measure and compare objects in the classroom or playground, such as the circumference of the tree.

Student support where necessary

units: rods, straws, posticks, streamers, etc

3

Who Wins? One beetle walks around two sides of a desk or book, and her friend walks diagonally across the book. Which beetle will walk the furthest? Vary this activity by choosing different routes.


units: paper clips, match sticks, etc, paper and pencil

4

Make a Ruler Students make their own rulers based on an informal unit (teddy bear, paperclip) or a body part (foot, hand span). Students should align units, especially teddy bears or paperclips, end to end. Mark the scale on the ruler and use it to measure objects. (This may need 2 lessons; one to make the ruler and another to measure)


units: paperclips, teddy bears, match sticks, cardboard, strips, pencil and paper

5

Make a Decimetre Students work in pairs and make a ruler using 1cm grid on light card. Cut out a 10cm strip and colour one long edge as the measuring edge. Label the centimetre end points from 1 to 10. Find and record objects which measure longer than 10cm, less than 10cm or longer than 100cm


1cm grid on light card, scissors, coloured pencils, pencils, paper

6

Straw Toss Who can throw a straw the furthest; how much further is it than the next best throw? Measure and record the distance thrown, using a 10cm strip. Find the difference between the longest and shortest throw.


straws, 10cm strips, pencils, paper

7

What’s the Difference Students use different units to measure the same object and are asked to explain why the measurements are different (eg. Athena measured the book as 5 rods but Alex measured it as 15 paperclips). Alternatively a 1m ruler or a 10cm strip could be used.


paper, pencils, items for use as units of measure (10cm strips, 20cm strips, blocks, Cuisenaire rods, paperclips, popsticks, etc)

8

Body Parts Students work in groups of three or four use a body length (or hand span or the length of an arm or leg) as the unit of measure to find the width of the classroom. Students record their results and then explain why the measurements from several groups may be different. During a class discussion, students predict how many more or fewer units will be needed when the measurement is expressed in a different unit.


paper strips or streamers for a measuring unit, pencils and paper for recording

9 Towering Metres Build a tower that is one metre high. Check height with a metre ruler. Record how the estimate was made, and measure the result. Ready, Set, Go! Students work in small groups to estimate, then measure and record the process. - How long does it take to write and measure a legible sentence 1 metre long?


building objects for tower, metre ruler, paper and pencils, watch sticks, modelling dough

Sharon Tooney

- How long does it take to make and measure a line of pens (posticks, matchsticks) one metre long? - How long does it take to make and measure a modelling dough snake one metre long?

10

Assessment

ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

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

SUBSTRAND: Time 2 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 › describes, compares and orders durations of events, and reads half- and quarter-hour time MA1-13MG

Background Information Refer to background information in Time 1. Language Students should be able to communicate using the following language: calendar, week, days, date, month, time, clock, analog, digital, hour hand, minute hand, clockwise, numeral, hour, minute, second, o'clock, half past, quarter past, quarter to. Refer also to language in Time 1.

Describe duration using months, weeks, days and hours • use a calendar to calculate the number of months, weeks or days until an upcoming event • estimate & measure the duration of an event using a repeated informal unit, eg the number of times you can clap your hands while the teacher writes your name - solve simple everyday problems about time & duration - recognise that some cultures use informal units of time, eg the use of tidal change in Aboriginal communities • compare & order the duration of events measured using a repeated informal unit, eg It takes me 10 claps to write my name but only 2 claps to say my name • use the terms hour, minute & second • experience & recognise activities that have a duration of 1 hour, half an hour or a quarter of an hour, 1 minute, & a few seconds - indicate when it is thought that an activity has continued for 1 hour, 1 minute or 1 second - compare & discuss the relationship between time units, eg an hour is a longer time than a minute - make predictions about the duration of time remaining until a particular school activity starts or finishes Tell time to the quarter-hour using the language of past & to • read analog & digital clocks to the quarter-hour using the terms past & to, eg It is a quarter past 3, It is a quarter to 4 • describe the position of the hands on a clock for quarter past & quarter to - describe the hands on a clock as turning in a 'clockwise' direction - associate the numerals 3, 6 & 9 with 15, 30 & 45 minutes & with terms quarter past, half past & quarter to, respectively • identify which hour has just passed when the hour hand is not pointing to a numeral • record quarter-past & quarter-to time on analog & digital clocks




Sharon Tooney



Describe duration using months, weeks, days and hours Tell time to the quarter-hour using the language of past & to

7

Reading Clocks Students revise telling time on an analog clock, writing time as numbers separated by a colon eg.


clocks, paper and pencil

8

Seasons Students examine and revise seasons. Identifying the months that each season covers and the order in which the seasons occur (months should be accurately ordered). Eg.

Students describe seasons using appropriate words and images to accurately depict the differences between seasons. Eg. Seasons posters, books, pamphlets


season charts, calendars, magazines, scissors, glue, paper and pencil

9

Read a Calendar Students use a calendar to identify and mark familiar dates, eg. - Their birthday - Special days (ie. Christmas, Easter, etc) - Significant school dates (ie. School photo day, sports carnival, Anzac day assembly, etc) - Beginning and end of the school term Students use calendars to identify given dates and to determine dates before and after a given date on a calendar. Eg.


calendar templates, paper and pencils

10

Revision Assessment

Sharon Tooney

ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

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

SUBSTRAND: 2D 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › manipulates, sorts, represents, describes and explores two-dimensional shapes, including quadrilaterals, pentagons, hexagons and octagons MA1-15MG

Background Information In Stage 1, students need to have experiences involving directions and turning. Discussions about what represents a 'full-turn', a 'half-turn' and a 'quarter-turn' will be necessary. Relating this information to students physically may be helpful, eg by playing games such as 'Simon Says' with Simon saying to make turns. Digital technologies such as computer drawing tools may use the terms 'move', 'rotate' and 'flip horizontal', or various other terms, to describe transformations. The icons for these functions may assist students in locating the required transformations. Language Students should be able to communicate using the following language: shape, twodimensional shape (2D shape), circle, triangle, quadrilateral, square, rectangle, pentagon, hexagon, octagon, orientation, features, symmetry, slide, flip, turn, full-turn, half-turn, quarter-turn, clockwise, anti-clockwise. In Stage 1, students refer to the transformations of shapes using the terms 'slide', 'flip' and 'turn'. While in Stage 2, students are expected to use the terms 'translate', 'reflect' and 'rotate', respectively. Linking the vocabulary of half-turns and quarter-turns to students' experiences with clocks may be of benefit. A shape is said to have line symmetry if matching parts are produced when it is folded along a line of symmetry. Each part represents the 'mirror image' of the other.

Describe and draw two-dimensional shapes, with and without the use of digital technologies • use term 'two-dimensional' to describe plane (flat) shapes • make representations of 2D shapes in different orientations using concrete materials - combine & split single shapes & arrangements of shapes to form new shapes, eg create a hexagon from six triangles • draw & name 2D shapes in different orientations, with & without the use of digital technologies - recognise that the name of a shape does not change if its size or orientation in space is changed Investigate the effect of one-step slides and flips, with and without the use of digital technologies • identify a 1-step slide or flip of a single shape & use the terms slide & flip to describe the movement of the shape • perform a 1-step slide or flip with a single shape - recognise that sliding or flipping a shape does not change its size or features - describe the result of a 1-step slide or flip of a shape • record the result of performing 1-step slides & flips, with & without the use of digital technologies - copy & manipulate a shape using the computer functions for slide & flip • make designs with line symmetry using paper-folding, pattern blocks, drawings & paintings - recognise connection between line symmetry & performing a flip Identify and describe half-turns and quarter-turns • identify full, ½ & ¼ -turns of a single shape & use the terms turn, full-turn, ½ turn & ¼ turn to describe the movement of the shape • identify & describe amounts of turn using terms anti/clockwise • perform full, ½ & ¼ -turns with a single shape - recognise that turning a shape does not change its size or features - describe the result of a turn of a shape • record the result of performing full, ½ & ¼ -turns of a shape, with & without the use of digital technologies - copy & manipulate a shape using the computer function for turn • determine the number of ½ -turns required for a full-turn & the number of ¼ -turns required for a full-turn - connect the use of ¼ & ½ -turns to the turn of the minute hand on a clock for the passing of ¼ & ½ -hours




Sharon Tooney



Describe and draw two-dimensional shapes, with and without the use of digital technologies Investigate the effect of one-step slides and flips, with and without the use of digital technologies Identify and describe half-turns and quarter-turns

2

Naming Shapes Identify and name 2D shapes, including quadrilaterals, pentagons, hexagons and octagons. Ensure that students understand that these shapes are grouped under the term ‘two-dimensional’ Students should be encouraged to draw shapes on dot paper; identifying the number of sides and corners of each shape. Create a shape house; draw a large square and triangle, so you have the basis for a house shape. Students then, trace pattern blocks, filling in the square section with smaller squares, the triangle roof with triangles (facing upwards and downwards in order that the roof is filled) rectangle for the door, hexagons/pentagons/circles/squares etc for the windows, a circle for a sunshine and a rectangle chimney. Students then name the shapes that they used to complete their house.

Shape charts as a reference for naming and spelling

2D shapes, dot paper, pencils, paper

3

Classifying Shapes Students work in small groups. Provide each group with a range of 2D shapes. Each group must name each of the shapes that they have and decide upon a way of classifying them into groups. Each group needs to report back to the class; explaining how they classified their shapes and which shapes they placed in each group.

Shape charts as a reference for naming and spelling

2D shapes, paper and pencil

4

Sliding and Flipping Define the term ‘slide’:

Define the term ‘flip’:

Collect a variety of transparent coloured plastic 2D shapes, such as rectangles, squares, rhombuses, parallelograms, hexagons and trapeziums. The teacher demonstrates and describes what happens to a shape when it is flipped across a line (flip needs to be demonstrated with a solid shape or a picture on an overhead). The teacher repeats to demonstrate what happens to a shape it is slid.

In pairs, students choose a shape and practise flipping and sliding the shape. Students identify

Slide and flip reference charts on desks as needed

paper and pencil, shapes

Sharon Tooney

how the shape was moved and draw what happens after the shapes crossed the dotted line.

Students hypothesise about what given shapes would look like if they were flipped across a line,

then draw what they believe the shape will look like.

5

Sliding and Flipping Again Teacher provides students with a series of 2D pictures; each one in it’s original orientation and then either flipped or slid. Students must identify the way in which the shape has been moved from it’s original orientation. Play concentration with shape and word cards demonstrating flips and slides. Students must match a picture and word card correctly to keep the cards. The player with the most correct matches wins.

Slide and flip reference charts on desks as needed

concentration cards

6

Turning Define the term ‘turn’:

Teacher demonstrates what happens to a shape when it is turned (half turn, quarter turn, full turn):

Students use pattern blocks to trace and demonstrate a half turn, quarter turn, full turn; labelling each appropriately.

Turn reference charts on desks as needed.

pattern blocks, paper and pencil

7

Turning Again Teacher defines and demonstrates the terms ‘clockwise’ and ‘anticlockwise’, in relation to turning a shape. Have students stand in a circle and walk ‘clockwise’ and ‘anticlockwise’ on command. Have students trace, turn and trace shapes again, in both a clockwise and anticlockwise direction. Have students label their drawings using arrows to indicate the direction in which the turn was made.

A clock as a reference point may be helpful for this activity

Turn reference charts on desks as needed.

clock, pattern blocks, paper and pencil

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 2 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 › gathers and organises data, displays data in lists, tables and picture graphs, and interprets the results MA1-17SP

Background Information Categorical variables can be separated into distinct groups or categories, eg the different colours of smarties in a box, the types of favourite fruit of class members. A key indicating one-to-one correspondence in a picture graph uses one symbol to represent one response/item, eg = 1 flower. Language Students should be able to communicate using the following language: information, data, collect, gather, category, display, symbol, tally mark, picture graph, list, table, equal spacing, key, baseline

Identify a question of interest based on one categorical variable and gather data relevant to the question • pose suitable questions that will elicit categorical answers & gather the data, eg 'Which school sport is the most popular with our class members?', 'How did each student in our class get to school today?' - predict the likely responses within data to be collected - determine what data to gather in order to investigate a question of interest, eg colour, gender, type of animal, sport Collect, check and classify data • collect data on familiar topics through questioning, eg 'How many students are in our class each day this week?' - use tally marks to assist with data collection • identify categories of data & use them to sort data, eg sort data collected on attendance by day of the week & into boys & girls present Create displays of data using lists, tables and picture graphs and interpret them • represent data in a picture graph using a baseline, equal spacing, same-sized symbols & a key indicating 1-to-1 correspondence - identify misleading representations of data in a picture graph, eg where the symbol used to represent 1 item is shown in different sizes or where symbols are not equally spaced - use digital technologies to create picture graphs • display data using lists & tables -use displays to communicate information gathered in other learning areas, eg data gathered in a unit on families or local places • interpret information presented in lists, tables & picture graphs - describe data displayed in simple tables & picture graphs found in books & created by other students • record observations based on tables & picture graphs developed from collected data




Sharon Tooney



Identify a question of interest based on one categorical variable and gather data relevant to the question Collect, check and classify data Create displays of data using lists, tables and picture graphs and interpret them

2

Posing the Question Discuss with the students possible topics that would be suitable and interesting to collecting data for to graph, for example, student names. Ask the students what sort of data could be collected about the names of students in the class and have them pose suitable questions, for example, How many letters does each person’s name have? Brainstorm as many interest topics as possible that the students would like to collect information about. Discuss the appropriateness of topics with regard to ability to collect data and create a shortlist of the most popular topics. In groups have students pose a question for each chosen topic area. Groups share these with the class, the teacher recording each suggested question. After all groups have shared, as a class decide on which question is the best/most suitable for each topic.


paper and pencil

3

Collecting Data Using the topics and questions decided upon in the previous lesson, divide students into groups, giving each an equal number of questions to collect data on. Revise the use of tally marks.

Have students collect the data for the questions that their group has been given, using tally marks.


paper and pencil, questions from previous lesson

4

Picture Graphs Define picture graphs:

Using the above example, provide representations of the same graph where the pictures are not

the same size or equally spaced. Discuss with the students the implications of misleading data

presentation. Devise a set of rules for creating a picture graph.

Using the results from the previous lesson, have the students create their own picture graph for

one of the topic areas that they collected data for. Symbols used by students should represent

one-to-one correspondence of data collected.


paper and pencil, picture graphs, data from previous lesson

5

Picture Graphs Online Use online picture graph maker sites to collect data and create a picture graph online. The teacher should demonstrate how to use the online format first. Suitable online sites include: http://mathsclass.net/comments/online-picture-graphs


computers

http://mathsclass.net/comments/online-picture-graphs�

Sharon Tooney

http://www.softschools.com/math/data_analysis/pictograph/make_your_own_pictograph/ http://primaryschoolict.com/pictograph/

10

Revision Assessment

ASSESSMENT OVERVIEW

http://www.softschools.com/math/data_analysis/pictograph/make_your_own_pictograph/�

http://primaryschoolict.com/pictograph/�

mathematics program proforma yr 2 t1

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