Gayle Pinn
Yerong Creek PS 2013
Term 3
1 / Whole NumberAngles
ES1/St 1 data
St 4- Right-angled triangles
2 / Whole Number
Position
S 4- Volume
3 / Addition and Subtraction
Data
ST 4- Data Collection and Representation
4 / Addition and Subtraction
Chance
ES1 revision
St 4- Probability
5 / Multiplication and Division
Length
St 4- Length
6 / Multiplication and Division
Area
St4- area
7 / Fractions and Decimals
V&C
length
St4- V&C
8 / Fractions and Decimals
Mass
V&C
St 4- Ratio and rates
9 / Patterns and Algebra
Time
10 / Patterns and Algebra
Time
Term 3 Week 1
Whole Number / Computation with integers
Early Stage 1 / Stage 1 / Stage 2 / Stage 3 / Stage 4
General Capabilities / Year A: Intercultural understanding
Year B: Asia and Australia’s engagement with Asia
Outcome / describes mathematical situations using everyday language, actions, materials and informal recordings MAe 1WM
› uses objects, actions, technology and/or trial and error to explore mathematical problems MAe 2WM
› uses concrete materials and/or pictorial representations to support conclusions MAe 3WM
› counts to 30, and orders, reads and represents numbers in the range 0 to 20 MAe 4NA / › 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 / · uses appropriate terminology to describe, and symbols to represent, mathematical ideas MA21WM
· selects and uses appropriate mental or written strategies, or technology, to solve problems MA22WM
· checks the accuracy of a statement and explains the reasoning used MA23WM
· applies place value to order, read and represent numbers of up to five digits MA24NA / · describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA31WM
· selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations MA32WM
· gives a valid reason for supporting one possible solution over another MA33WM (Unit 2)
· orders, reads and represents integers of any size and describes properties of whole numbers MA34NA / communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols MA4-1WM
• applies appropriate mathematical techniques to solve problems MA4-2WM
• recognises and explains mathematical relationships using reasoning MA4-3WM
• compares, orders and calculates with integers, applying a range of strategies to aid computation MA4-4NA
Content Area / Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point / Recognise, model, read, write and order numbers to at least 100; locate these numbers on a number line / Recognise, model, represent and order numbers to at least 10 000 / Recognise, represent and order numbers to at least tens of millions. / Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies
Recognise, model, represent and order numbers to at least 1000 / Recognise, represent and order numbers to at least tens of thousands / Investigate everyday situations that use integers; locate and represent these numbers on a number line
Background Information / In Early Stage 1, students are expected to be able to count to 30. Many classes have between 20 and 30 students, and countingthe number of students is a common activity. Students will also encounter numbers up to 31 in calendars.
Counting is an important component of number and the early learning of operations. There is a distinction between counting by rote and counting with understanding. Regularly counting forwards and backwards from a given number will familiarise students with the sequence. Counting with understanding involves counting with one-to-one correspondence, recognising that the last number name represents the total number in the collection, and developing a sense of the size of numbers, their order and their relationships. Representing numbers in a variety of ways is essential for developing number sense.
Subitising involves immediately recognising the number of objects in a small collection without having to count the objects. The word 'subitise' is derived from Latin and means 'to arrive suddenly'.
In Early Stage 1, forming groups of objects that have the same number of elements helps to develop the concept of equality. / 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. / The place value of digits in various numerals should be investigated. Students should understand, for example, that the '5' in 35 represents 5 ones, but the '5' in 53 represents 50 or 5 tens. / Students need to develop an understanding of place value relationships, such as 10thousand=100hundreds=1000tens=10000ones. / To divide two- and three- digit numbers by a two- digit number, students may be taught the long division algorithm or, alternatively, to transform the division into a multiplication.
So, becomes . Knowing
that there are two fifties in each 100, students may try 7, obtaining 52 × 7 = 364, which is too large. They may then try 6, obtaining 52 × 6 = 312. The answer is .
Students also need to be able to express a division in the following form in order to relate multiplication and
Students also need to be able to express a division in the following form in order to relate multiplication and division: 356 = 6 × 52 + 44, and then division by 52 gives
.Students should have some understanding of integers, as the concept is introduced in Stage 3 Whole Numbers 2. However, operations with integers are introduced in Stage 4.
Complex recording formats for integers, such as raised signs, can be confusing. On printed materials, the en-dash ( – ) should be used to indicate a negative number and the operation of subtraction. The hyphen ( - ) should not be used in either context. The following formats are recommended:
Brahmagupta (c598– c665), an Indian mathematician and astronomer, is noted for the introduction of zero and negative numbers in arithmetic.
Purpose/Relevance of Substrand
The positive integers (1, 2, 3, ...) and 0 allow us to answer many questions involving 'How many?', 'How much?', 'How far?', etc, and so carry out a wide range of daily activities. The negative integers (..., –3, –2, –1) are used to represent 'downwards', 'below', 'to the left', etc, and appear in relation to everyday situations such as the weather (eg a temperature of –5° is 5° below zero), altitude (eg a location given as –20 m is 20 m below sea level), and sport (eg a golfer at –6 in a tournament is 6 under par). The Computation with Integers substrand includes the use of mental strategies, written strategies, etc to obtain answers – which are very often integers themselves – to questions or problems through addition, subtraction, multiplication and division
Language / Students should be able to communicate using the following language:count forwards, count backwards, number before, number after, more than, less than, zero, ones, groups of ten, tens, is the same as, coins, notes, cents, dollars.
The teen numbers are often the most difficult for students. The oral language pattern of teen numbers is the reverse of the usual pattern of 'tens first and then ones'.
Students may use incorrect terms since these are frequently heard in everyday language, eg'How much did you get?' rather than 'How many did you get?' when referring to a score in a game.
To represent the equality of groups, the terms 'is the same as' and 'is equal to' should be used. In Early Stage1, the term 'is the same as' is emphasised as it is more appropriate for students' level of conceptual understanding. / 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'. / Students should be able to communicate using the following language:number before, number after, more than, greater than, less than,largest number, smallest number, ascending order, descending order, digit, zero, ones, groups of ten, tens, groups of one hundred, hundreds, groups of one thousand, thousands, place value, round to.
The word 'and' is used between the hundreds and the tens when reading and writing a number in words, but not in other places, eg3568 is read as 'three thousand, five hundred and sixty-eight'.
The word 'round' has different meanings in different contexts, eg'The plate is round', 'Round 23to the nearest ten'. / Students should be able to communicate using the following language:ascending order, descending order, zero, ones, tens, hundreds, thousands, tens of thousands, hundreds of thousands, millions, digit, place value, expanded notation, round to, whole number, factor, highest common factor (HCF), multiple, lowest common multiple (LCM).
In some Asian languages, such as Chinese, Japanese and Korean, the natural language structures used when expressing numbers larger than 10000 are 'tens of thousands' rather than 'thousands', and 'tens of millions' rather than 'millions'. For example, in Chinese (Mandarin), 612000 is expressed as '61 wàn, 2 qiān', which translates as '61 tens of thousands and 2 thousands'.
The abbreviation 'K' is derived from the Greek word khilios,meaning 'thousand'. It is used in many job advertisements to represent salaries (ega salary of $70 K or $70000). It is also used as an abbreviation for the size of computer files (ega size of 20 K, meaning twenty thousand bytes).
Students should be able to communicate using the following language:number line, whole number, zero, positive number, negative number, integer, prime number, composite number, factor, square number, triangular number.
Words such as 'square' have more than one grammatical use in mathematics, egdraw a square (noun), square three (verb), square numbers (adjective) and square metres (adjective). / Teachers should model and use a variety of expressions for mathematical operations and should draw students' attention to the fact that the words used for subtraction and division questions may require the order of the numbers to be reversed when performing the operation. For example, '9 take away 3' and 'reduce 9 by 3' require the operation to be performed with the numbers in the same order as they are presented in the question (ie 9 – 3), but 'take 9 from 3', 'subtract 9 from 3' and '9 less than 3' require the operation to be performed with the numbers in the reverse order to that in which they are stated in the question (ie 3 – 9).
Similarly, 'divide 6 by 2' and '6 divided by 2' require the operation to be performed with the numbers in the same order as they are presented in the question (ie 6 ÷ 2), but 'how many 2s in 6?' requires the operation to be performed with the numbers in the reverse order to that in which they appear in the question
(ie 6 ÷ 2).
Resources / Orange GDB pg. 1,2,3,4, 5, 8, 10, 11, 12, 13, 16, 17, 18, 19, 20, 24, 25, 26, 30, 32, 33, 34, 36, 37, 40, 41, 42, 43 / Lime GDB pg. 1, 2, 3, 13, 28, 29, 34, 35, 46 / Blue GDB pg. 2, 3, 24 / Emerald GDB Pg. 2, 19
Learning Activities
Term 3 Week 1
Data / Angles / Right-angled Triangle
Early Stage 1 / Stage 1 / Stage 2 / Stage 3 / Stage 4
General Capabilities / Year A: Intercultural understanding
Year B: Asia and Australia’s engagement with Asia
Outcome / › describes mathematical situations using everyday language, actions, materials and informal recordings MAe1WM
› uses concrete materials and/or pictorial representations to support conclusions MAe3WM
› represents data and interprets data displays made from objects MAe17SP / › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA11WM
› uses objects, diagrams and technology to explore mathematical problems MA12WM (Unit 2)
› supports conclusions by explaining or demonstrating how answers were obtained MA13WM
› gathers and organises data, displays data in lists, tables and picture graphs, and interprets the results MA117SP / › uses appropriate terminology to describe, and symbols to represent, mathematical ideas MA21WM
› checks the accuracy of a statement and explains the reasoning used MA23WM (Unit 2)
› identifies, describes, compares and classifies angles MA216MG / › describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA31WM
› measures and constructs angles, and applies angle relationships to find unknown angles MA316MG / › communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols MA41WM
› applies appropriate mathematical techniques to solve problems MA42WM
› applies Pythagoras’ theorem to calculate side lengths in right-angled triangles, and solves related problems MA416MG
Content Area / Simpledata displays and interpret the displays / Choose simple questions and gather responses / Identifyangles as measures of turn and compareangle sizes in everyday situations / Estimate, measure and compareangles using degrees
Construct angles using a protractor / InvestigatePythagoras' theorem and its application to solving simple problems involvingright-angled triangles
Create displays of data using lists, tables andpicture graphs and interpret them / Compareangles and classify them as equal to, greater than or less than a right angle / Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles