dubbowestoc.weebly.comdubbowestoc.weebly.com/uploads/1/0/0/8/...2_2016.docx · Web viewDubbo West Public School Stage 3 Mathematics Scope and Sequence. Collaborated by Mitchell

Dubbo West Public School Stage 3 Mathematics Scope and Sequence

Dubbo West Public School

Mathematics Scope and Sequence

Stage 3Term 2

Collaborated by Mitchell Welham 2016

Dubbo West Public School Stage 3 Mathematics Scope and SequenceSyllabus Outcomes

Whole Number Addition and Subtraction Multiplication and Division Fractions and Decimals Patterns and AlgebraMA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers

MA3-5NA selects and applies appropriate strategies for addition and subtraction with counting numbers of any size

MA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

MA3-7NA compares, orders and calculates with fractions, decimals and percentages

MA3-8NA analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane

Length Area Volume and Capacity Mass Time 3D Objects 2D SpaceMA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length

MA3-10MG selects and uses the appropriate unit to calculate areas, including areas of squares, rectangles and triangles

MA3-11MG selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacity

MA3-12MG selects and uses the appropriate unit and device to measure the masses of objects, and converts between units of mass

MA3-13MG uses 24-hour time and am and pm notation in real-life situations, and constructs timelines

MA3-14MG identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views

MA3-15MG manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

Angles Position Data ChanceMA3-16MG measures and constructs angles, and applies angle relationships to find unknown angles

MA3-17MG locates and describes position on maps using a grid-reference system

MA3-18SP uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables

MA3-19SP conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes

Working Mathematically

MA3-1WM Uses appropriate terminology to describe, and symbols to represent, mathematical ideas.MA3-2WM Selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations.MA3-3WM Checks the accuracy of a statement and explains the reasoning used.



Term 2 Week 1

Syllabus OutcomesMA3-4NA orders, reads and represents integers of any size and describes properties of whole numbersMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-19SP conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes

Mon

day

Year 5 Year 6Strand: Number and AlgebraFactors (page 65)Use division to identify missing factors.

Record factors of various composite numbers, noting that the number itself and one are also factors.Work backwards to find three numbers that multiply together to produce a certain number, e.g.

60 = __ x __ x __

Strand: Number and AlgebraExpanding numbers (page 65)Expand numbers, e.g.227 386 = 200 000 + 20 000 + 7000 + 300 + 80 + 6Write numbers in words, e.g. 356 257Identify numbers from clues, e.g.

I have a 6 in the tens of thousands, 7 in the hundreds of...

Tues

day

Strand: Measurement and GeometryStreet directories (page 118)Read and interpret a street directory to: identify streets found at particular coordinates give the coordinates of certain streets write directions on how to travel from one location to another draw a path from one location to anotherApply a scale to give the approximate length of streets.

Strand: Number and AlgebraPrime factors (page 118)Understand and use the terms:

prime number composite number prime factor factor tree

Complete factor trees in order to identify prime factors.

Wed

nesd

ay

Strand: Number and AlgebraMultiplication (page 60)Complete examples, e.g.

326× 4

Use multiplication as a problem-solving strategy.Write a problem to suit an algorithm. 125

× 5

Strand: Number and Algebra4-digit multiplication (page 60)Complete examples.Find the missing numbers in worked examples.

22 33 35 × 6 1 4 1 3 0

Use data about an office block to solve problems, e.g.If a building has 8 floors, 298 lights per floor, how many lights altogether?

Thur

sday

Strand: Statistics and ProbabilityChance experiments (page 20)Investigate probability: Predict the most likely score when two dice are rolled Tally results Identify most frequent score Explain why 7 has a greater chance of occurring than 12Given a bag of coloured marbles: Identify the most likely colour to be drawn out first Describe the likelihood of one colour being drawn out first, e.g.

50/50 or even Identify the least likely colour to be drawn out firstDecide whether one colour is more or less likely than another to be drawn first

Strand: Statistics and ProbabilityChance predictions (page 20)Predict the likelihood of each of 5 shape cards being selected first (one card has been repeated and therefore has twice as much chance as the other cards).Conduct an experiment by selecting cards from a set. Repeat 20 times.Explain how results compared with predictions.Use a sample of 10 coloured marbles to predict the colours of 100 marbles in a bag.Expand the prediction to 500 marbles.



Term 2 Week 1

Syllabus OutcomesMA3-4NA orders, reads and represents integers of any size and describes properties of whole numbersMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-19SP conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes

Frid

ay

Strand: Statistics and ProbabilityDot plots (page 24)Recognise a dot plot as a number line that uses dots to record the frequency of events.

Interpret dot plots to identify:frequencyrangeclusters.

Strand: Statistics and ProbabilitySide-by-side column graphs (page 24)Read and interpret a graph to identify features such as: the city with the highest maximum temperature the city with the lowest minimum temperature the city with the greatest difference between minimum and

maximum temperaturesthe average maximum temperatures of Darwin, Sydney and Melbourne



Term 2 Week 2Syllabus OutcomesMA3-5NA selects and applies appropriate strategies for addition and subtraction with counting numbers of any sizeMA3-18SP uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables

Mon

day

Year 5 Year 6Strand: Number and AlgebraAddition and estimation (page 82)Complete additions with a variety of addends.Examine a series of estimated sums to see if they are reasonable or unreasonable, e.g. 149 + 52 ≈ 250 is unreasonable 331 + 71 ≈ 400 is reasonable

Given the prices of airline tickets to London offered by different companies, calculate the best option for a family.

Strand: Number and AlgebraSubtraction of 5- and 6- digit numbers (page 82)Complete subtractions by: rounding to the nearest 1000 to estimate the difference calculating the exact answerWrite a word problem to match a solution.Refer to a chart to compare navy ships, e.g. number of crew length mass speed

Tues

day

Strand: Number and Algebra5-digit subtraction (page 90)Complete examples with random trading.Given a population table, calculate differences between cities such as Wagga Wagga (42 848) and Dubbo (30 102).

Strand: Number and AlgebraSubtraction of 5- and 6-digit numbers (page 90)Complete examples using measurement units, e.g. tonnes

7 9 5 2 8 6– 3 4 7 2 7 5

Refer to a table to calculate differences in price between Australia’s most expensive cars, e.g. Mercedes ($366 999) and BMW ($263 999).Complete details on a ‘log book’ to calculate the distance travelled per trip.

Wed

nesd

ay

Strand: Number and Algebra6-digit addition (page 102)Complete examples with 2 addends.Choose between addition and subtraction as strategies to find missing numbers in algorithms.

5 2 3 4

2 7 2 4+ 1 4 0 2 5

8 7 8 8 Solve problems based on prices of motor vehicles.

Strand: Number and AlgebraAddition of 4-, 5- and 6-digit numbers (page 102)Complete examples with up to four addends.Use data presented in a table to calculate the area of each state and territory, e.g.Queensland is 362 000 km2 larger than the Northern Territory(1 346 000 km2).

Thur

sday

Strand: Statistics and ProbabilityColumn graphs (page 37)Investigate the most common vowel in a paragraph: Read a paragraph from any source Make a table to tally the number of times each vowel appears Present the tallied data as a column graph

Read, interpret and present tabled data as a column graph.

Strand: Statistics and ProbabilityChance and column graphs (page 37)Test the conjecture: six will be the most frequent score when 3 dice are rolled. Make own prediction Roll 3 dice 60 times Record and tally results Display data on a column graph Identify score with highest frequencyExplain why a score such as 11 is more likely than 3.Use knowledge of the probability scale of 0 to 1 to decide whether statements are true or false, e.g. The chance of rolling an even number is about 0.5 True.



Term 2 Week 2Syllabus OutcomesMA3-5NA selects and applies appropriate strategies for addition and subtraction with counting numbers of any sizeMA3-18SP uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables

Frid

ay

Strand: Statistics and ProbabilityProbability (0 – 1) (page 46)Chance can be recorded on a scale from 0 to 1.0 describes an event that is impossible.1 describes an event that is certain to happen.0.5 describes two events with an equal chance of happening.All other points on the scale are given a numerical value between 0 and 1.

Match ‘chance’ words to a chance number line, e.g.

A ImpossibleB UnlikelyC Even chanceD UnlikelyE Certain

Use the scale 0 to 1 to rate the likelihood of events happening, e.g.It will rain today. 0.1I’ll watch TV today. 0.8List events that could happen tomorrow and rate their probability.

Strand: Statistics and ProbabilityChance from zero to one (page 46) Events that are certain to happen are given the probability of 1. Events that will never happen are given the probability of 0. Events that could happen are rated between 0 and 1.

Rate the likelihood of events happening on a scale of 0 to 1, e.g.A person has blue eyes.Describe events to match probability ratings, e.g. 0.3Rate the likelihood of one colour being the winning colour on various spinning wheels.



Term 2 Week 3

Syllabus OutcomesMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-14MG identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different viewsMA3-15MG manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

Mon

day

Year 5 Year 6Strand: Number and AlgebraThree digits multiplied by one digit (page 52)

H T O12 14 5

× 3

7 3 5

Model and discuss the process.Complete examples.

Use multiplication as a problem-solving strategy.

Strand: Number and Algebra4-digit multiplication (page 52)Model the multiplication process.

Th H T O12 16 14 5

× 37 9 3 5

Step 13 × 5 = 15. Trade the ten ones for one 10. Write the 5 in the ones column.Step 23 × 4 tens = 12 tens plus 1 ten = 13 tens. Trade the 10 tens for one hundred. Write the 3 in the tens column.Step 33 × 6 hundreds = 18 hundreds plus 1 hundred = 19 hundreds. Trade the 10 hundreds for one thousand. Write the 9 in the hundreds column.Step 43 × 2 thousands = 6 thousands plus 1 thousand equals7 thousands. Write the 7 in the thousands column.

Complete examples.Solve problems.

Create and solve 4-digit x 1-digit multiplications.

Tues

day

Strand: Number and Algebra3-digit division (page 64)Model the division process.Share 426 sheep among three paddocks.

Share out the hundreds. Each paddock gets 1.

Trade the 1 hundred left over for 10 tens. Now share the 12 tens. Each paddock gets 4.

Share out the 6 ones. Each paddock gets 2.

Complete examples without trading but with remainders.

Complete examples with trading.

Use mental strategies to complete divisions,e.g. 2464 ÷ 4 = ____2400 ÷ 4 = 600 60 ÷ 4 = 15 4 ÷ 4 = 1Therefore 2464 ÷ 4 = 616

Strand: Number and algebraExtended multiplication (page 64)Model and discuss extended multiplication.

Complete examples.Use multiplication as a problem-solving strategy.

Wed

nesd

ay

Strand: Number and AlgebraOrder of operations (page 68)Read, discuss and model the rules for the order of operations: brackets first, e.g. (3 × 6) × 7 = 126 left to right, e.g. 3 × 8 ÷ 2 = 12 multiplication and division before addition and subtraction, e.g. 6 +

8 × 3 = 30Complete a variety of examples employing all the order of operations rules, e.g. 6 + (3 × 7) = 8 × 7 ÷ 2 = 7 + 64 ÷ 8 = 3 + 99 ÷ 3 =

Strand: Number and AlgebraOrder of operations (page 68)Read, discuss and model the rules for the order of operations: brackets first, e.g. (3 + 6) × 7 = 63 multiplication and division before addition and subtraction, e.g. 6

+ 8 × 3 = 30 left to right, e.g. 3 × 8 ÷ 2 = 12Complete a variety of examples employing all the order of operations rules, e.g. (9 – 4) × 5 = 72 + 88 ÷ 4 = 4.2 × 4 + 3 =



Term 2 Week 3

Syllabus OutcomesMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-14MG identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different viewsMA3-15MG manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

Thur

sday

Strand: Measurement and GeometryDescribing objects (page 58)Match models of prisms to their descriptions and names, e.g.For the descriptions, include the number of vertices, edges and faces, as well as other clues. A hexagonal prism might be identified from the description ‘I have 12 vertices and 18 edges. 2 of my 8 faces are hexagonal whilst the others are rectangular.’Use knowledge of properties of prisms and pyramids to identify facts such as the: shapes needed to make an hexagonal prism number of parallel faces on a hexagonal prismidentical faces on a pentagonal pyramid

Strand: Measurement and GeometryDrawing objects from views (page 58)Sketch a shape given its top, front and side views.Describe the similarities and differences between two 3D objects, e.g. a rectangular pyramid and a pentagonal prism.

Frid

ay

Strand: Measurement and GeometryNaming prisms and pyramids (page 21)Review properties of prisms and pyramids.Prisms have two bases that are the same shape and size. All other faces on a prism are rectangular. Prisms are named from their bases.Pyramids have only one base with all other faces being triangles. The triangular faces meet at a common vertex. Pyramids are named from their bases.Match illustrations to names, e.g. rectangular prism rectangular pyramid square pyramid triangular pyramidcube

Strand: Measurement and GeometryReviewing 3D objects (page 21)Review properties of prisms and pyramids.Prisms have two bases that are the same shape and size. All other faces on a prism are rectangular. Prisms are named from their bases.Pyramids have only one base with all other faces being triangles. The triangular faces meet at a common vertex. Pyramids are named from their bases.Match illustrations to names, e.g. rectangular prism rectangular pyramid square pyramid triangular pyramid cubeConstruct skeletal models of a cube, a rectangular prism and a square pyramid.



Term 2 Week 4

Syllabus OutcomesMA3-4NA orders, reads and represents integers of any size and describes properties of whole numbersMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-16MG measures and constructs angles, and applies angle relationships to find unknown angles

Mon

day

Year 5 Year 6Strand: Number and AlgebraRoman numerals (page 73)Investigate how Roman numerals are structured.Consult a table to convert numbers into Roman numeral, e.g. 365 = CCCLXVComplete Roman numeral magic squares, e.g.

VIII IV V

VI

Strand: Number and AlgebraRoman numerals (page 73)Investigate how Roman numerals are structured.Consult a table to convert numbers into Roman numeral, e.g. 724 = DCCXXIVName the next term in a sequence, e.g. V VI VII ____ XXIV XXIII XXII ____ LXXV LXXX LXXXV ____Using a signpost featuring Roman numerals, calculate distances between towns, e.g.

Oberon 200 kmBlackheath 130 km

70 km

Write any 5 numbers between 100 and 300 in Roman numerals.

Tues

day

Strand: Number and AlgebraMultiplication methods (page 132) Mental strategies, e.g. for 23 × 4 think 4 × 20 (80) plus

4 × 3 (12) = 92 Written 2 4 2

× 4 Front end, e.g. multiply the hundreds, then the tens and then the

ones: 235 × 6 = 200 × 6 = 1200 30 × 6 = 180

5 × 6 = 30 1410

Strand: Number and AlgebraRoman numerals (page 132)Investigate how Roman numerals are structured.Consult a table to convert numbers into Roman numerals, e.g. 33 = XXXIII and 365 = CCCLXVConvert measurements and dates into Roman numerals.

Eiffel Tower 300 metresCCC metres

1889MDCCLXXXIX

Wed

nesd

ay

Strand: Number and AlgebraAverages (page 83)Model and demonstrate the strategy used to calculate the ‘average’ (mean).Calculate the average for sets of scores, e.g.40, 36, 32 = 108 3 = 36Solve problems based on averages.

Strand: Number and AlgebraDividing by tens and finding averages (page 83)Develop a strategy to divide by multiples of 10

480 80 = Think 480 10 = 48 48 8 = 6

Complete examples.Recall that averages are found by adding all scores in a group and dividing by the number of scores.Find the average of sets of numbers.Solve ‘average’ problems.

Thur

sday

Strand: Measurement and GeometryProtractors (page 28)Observe that a 180° protractor can be read from both ends.Label a protractor to show its supplementary angles.Name angle types and size of angles depicted in illustrations, e.g.

obtuse 120°Use a protractor to measure the size of various angles.

Strand: Measurement and GeometryMeasure and construct angles (page 28)Use a protractor to construct: acute angles right anglesobtuse angles



Term 2 Week 4

Syllabus OutcomesMA3-4NA orders, reads and represents integers of any size and describes properties of whole numbersMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-16MG measures and constructs angles, and applies angle relationships to find unknown angles

Frid

ay

Strand: Measurement and GeometryTriangles (page 42)Recognise that triangles: have 3 sides have 3 angles have 3 angles that total 180°

Triangles can be classified as:

Investigate the properties of each type of triangle, e.g. which triangle has all sides of equal length?Identify right-angled triangles.Sketch examples of each type of triangle.

Strand: Measurement and GeometryTriangles/angles (page 42)Identify properties of these triangles: equilateral scalene isosceles right-angleUse a protractor to measure angles in triangles and then classify each triangle.Calculate the missing angle in triangles.



Term 2 Week 5

Syllabus OutcomesMA3-7NA compares, orders and calculates with fractions, decimals and percentagesMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-15MG manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

Mon

day

Year 5 Year 6Strand: Number and Algebra4-digit multiplication (page 94)Observe and understand the trading process for the shortened form of multiplication.

Complete examples, e.g. 4962 × 5 = Round multiplicand to the nearest 1000 in order to estimate the product.

Solve problems.

Strand: Number and AlgebraMultiplying decimals/money (page 94) model the process of multiplying decimals emphasise the role of the decimal pointComplete examples, e.g.

$256.48× 8

Solve problems, e.g.7 boxes each with a mass of 2.75 kg. What is the total mass?Use knowledge of multiplication of decimals and a calculator’s memory function to solve shopping problems.

Investigate combinations of shopping items that total between $26 and $29.

Tues

day

Strand: Number and AlgebraImproper fractions (page 95)Recognise that improper fractions have a numerator larger than the

denominator, e.g.Write improper fractions to describe diagrams.

=

Use number lines to identify improper fractions.

Strand: Number and AlgebraAdd and subtract fractions/mixed numerals (page 95)Add fractions with related denominators, e.g.

Complete examples using an equivalence chart if necessary.Subtract fractions with related denominators, e.g.

Solve problems, e.g.

If she ate and her friend ate , how much was left?

Wed

nesd

ay

Strand: Number and Algebra5-digit addition (page 72)Complete examples, e.g.

3 5 9 7 42 0 6 0 7

+ 3 0 7 0 8

Refer to a map of Australia with distances marked and calculate the length of journeys, e.g. Hobart to Sydney via Melbourne = 610 km + 706 km = 1316 km

Strand: Number and AlgebraSubtracting decimals/money (page 72)Read and interpret a bank statement to: determine the balance at given times find the total amount deposited add extra entries including the cheque number, amount in debit

column and progressive balanceDiscuss alternative methods of payment other than by cash or cheque.

Thur

sday

Strand: Measurement and GeometryConstructing shapes (page 54)Use a protractor and ruler to construct: a 6 cm × 4 cm rectangle a 6 cm × 6 cm square Use a protractor to find the size of various reflex angles using the

strategy of ‘Measure the smaller angle, then deduct it from 360°’.

Strand: Measurement and GeometryDrawing rectangles and squares (page 54)Use geometric tools to construct: a 10 cm × 6 cm rectangle a 6 cm × 6 cm squareIdentify lines of symmetry on both shapes.Identify sets of parallel lines on both shapes.Observe that each shape’s diagonals are equal.



Term 2 Week 5

Syllabus OutcomesMA3-7NA compares, orders and calculates with fractions, decimals and percentagesMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-15MG manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

Frid

ay

Strand: Measurement and GeometryRotational symmetry (page 67)Draw lines of symmetry on 2D shapes.Draw the other half of a shape using a line of symmetry.Define rotational symmetry.Make tracings of shapes to test for rotational symmetry, e.g.

Strand: Measurement and GeometrySymmetry review (page 67)Recognise that a shape has: line symmetry if both parts match when folded along a line rotational symmetry if it matches the original shape more than

once through a full rotationIdentify how many lines of symmetry shapes have.Given a shape butted against a line of symmetry, draw the other half.Make tracings of shapes to test for rotational symmetry, e.g.



Term 2 Week 6

Syllabus OutcomesMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-7NA compares, orders and calculates with fractions, decimals and percentagesMA3-18SP uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables

Mon

day

Year 5 Year 6Strand: Number and Algebra3-digit division (page 78)Demonstrate the division process.Share 573 books among four schools.

Share out the hundreds. Each school gets 1. One hundred is left over.

Trade the 1 hundred left over for 10 tens. Now share the 17 tens. Each school gets 4.

Trade the 1 ten left over for 10 ones. Share out the 13 ones. Each school gets 3. There is a remainder of 1.

Complete examples, e.g.

Write a problem to suit an algorithm, e.g.

Strand: Number and AlgebraDividing 5-digit numbers (page 78)Complete operations and record remainders as fractions.

Use division to: solve problems

crack a code

Tues

day

Strand: Number and AlgebraOrdering decimals (page 79)Place decimals on a hundreds chart from 0.01 to 1Order groups of decimals from smallest to largest, e.g.

0.57 0.31 0.13 1.00

Draw lines to match decimals to positions on a number line.

Strand: Number and AlgebraPercentages (page 79)Recognise that a simple way to find a percentage of an amount is to think of it as a fraction, e.g.

10% of $20 = of $20 = $2

Match percentages to fractions, e.g. 25% = Calculate discounts, e.g. 20% of $60Complete a chart to calculate the number of goals scored e.g.

Name Attempts % GoalsSam 20 25% 5

Open-ended investigation.

Wed

nesd

ay

Strand: Number and AlgebraReading numbers (page 87)Recognise that numbers are read in groups of hundreds, tens and ones.Convert numbers expressed in words into numerals, e.g.Two hundred and sixteen thousand, four hundred and twenty-six becomes 216 426.Refer to a table showing area of Australian states: place them in order of sizemake comparisons between the states, e.g. Western Australia is more than double the size of New South Wales

Strand: Number and AlgebraAdding and subtracting mixed numbers (page 87)Subtract unit fractions from one whole, e.g.

Subtract fractions from whole numbers greater than one.Use a number line to assist with adding and subtracting mixed

numerals, e.g.



Term 2 Week 6

Syllabus OutcomesMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-7NA compares, orders and calculates with fractions, decimals and percentagesMA3-18SP uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables

Thur

sday

Strand: Statistics and ProbabilityLine graphs (page 50)Understand that meaning can be attached to any point along the line of a line graph.Express data presented in a table as a line graph, e.g.

L 6 12 18 24 30 36 42Km 50 100 150 200 250 300 350

Interpret the line graph, e.g.How many litres would the car use on a 400 kilometre trip?Represent data about time and distance on a line graph.Make meaningful judgements about: data lying on the linedata beyond the line, that is, if the line graph was to be extended to a point not included in the table of presented data

Strand: Statistics and ProbabilityLine graphs (page 50)Read and interpret a line graph, e.g.

How long was their stop?Given three line graphs, select the one that accurately represents the data in a table.

Frid

ay

Strand: Statistics and ProbabilityDatabases (page 62)Examine how data can be organised into a database.Add data to an existing database.Create subsets of data from a database, e.g. Friends who live in Kensington.

Strand: Statistics and ProbabilityPotentially misleading data (page 62)Recognise that data can be misleading depending on the source.Decide whether data statements are credible or not given the source of the information and/or any bias.Study a pair of graphs representing similar data and explain why one could be considered to be misleading.

The graph only shows an overall increase of 30 cents but as the y axis is calibrated in increments of 10 cents the rises and falls appear to be more significant.



Term 2 Week 7Syllabus OutcomesMA3-7NA compares, orders and calculates with fractions, decimals and percentagesMA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length

Mon

day

Year 5 Year 6Strand: Number and AlgebraAdding and subtracting fractions (page 91)Use shapes to model addition of fractions, e.g.

Complete addition sentences, e.g.

Complete subtractions, e.g. Identify pairs of fractions that can be either added or subtracted to

produce

Strand: Number and AlgebraEquivalent fractions (page 91)

Refer to a fractions chart to select fractions of equivalent value, e.g.

Use symbols <, = and > to compare fractions, e.g.

Create equivalent fractions by multiplying a fraction’s numerator and denominator by the same number,

e.g.

Tues

day

Strand: Number and AlgebraNumber patterns with fractions (page 92)Complete patterns with fractions on number lines, e.g.

Complete addition and subtraction patterns without number lines.

Strand: Number and AlgebraGeometric patterns (page 92)Construct tables to show the number of sides in a series of: hexagons, octagons, decagons and dodecagons.Write rules to describe the patterns.Calculate the number of sides on 9 hexagons and 11 octagons.Create a table to show the number of sides on either a heptagon, a pentagon or a nonagon.

Wed

nesd

ay

Strand: Number and AlgebraFractions of a collection (page 99)Recognise that fractions can name part of a group, e.g.

Find unit fractions of numbers, e.g.

Use an array to find fractions of a group of 48, e.g.

Use knowledge of unit fractions to solve problems, e.g.

of the 96 seats in the restaurant…Use knowledge of unit fractions to solve fractions with numerators greater than 1, e.g.

If of a group is worth 5 what would of the group be worth?

Strand: Number and AlgebraEquivalent fractions (page 99)Create equivalent fractions by multiplying a fraction’s numerator and denominator by the same number, e.g.

Identify relationship between fractions with related denominators in order to make equivalent fractions, e.g.

Multiply numerator and denominator by 6.Investigate to find as many fractions as possible that are equivalent

to Continue equivalent fraction patterns, e.g.



Term 2 Week 7Syllabus OutcomesMA3-7NA compares, orders and calculates with fractions, decimals and percentagesMA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length

Thur

sday

Strand: Measurement and GeometryPerimeter (page 59)Calculate the perimeter of various shapes after measuring and recording the shapes’ dimensions.Create staircase shapes on 5-mm dot paper that have perimeters of 12 cm and 16 cm.Calculate the perimeter of three gardens given their dimensions.

Strand: Measurement and GeometryMetres, centimetres and millimetres (page 59)Measure a distance of 10 m in the playground and count the number of steps equal to 10 m.Use above knowledge to estimate familiar distances, e.g. length of netball court.Use knowledge of metric units to convert measurements into other units, e.g.6 cm = mm9250 m = kmOrder units from shortest to longest, e.g. 19 cm, 9 m, 250 mmSolve problems, e.g.How wide is the room if 8 strips of wallpaper each 500 mm wide were needed . . .?

Frid

ay

Strand: Measurement and GeometrySquare metres (page 63)Apply the area formula to calculate the area of rectangles.Apply a simple scale, e.g. 1 cm = 1 m, in order to calculate the area of rectangles.Solve area problems e.g.What would it cost to carpet a room 4 m long and 3 m wide if the carpet is $20 per m2?

Strand: Measurement and GeometryUsing a scale (page 63)Read and interpret the plan view of a house drawn to scale in order to calculate costs associated with: carpeting some areas tiling some areas fencing the perimeterAdd other costs such as the initial purchase price, a pool and a garage to find the total cost of building the house.



Term 2 Week 8

Syllabus OutcomesMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-7NA compares, orders and calculates with fractions, decimals and percentagesMA3-8NA analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian planeMA3-17MG locates and describes position on maps using a grid-reference system

Mon

day

Year 5 Year 6Strand: Number and AlgebraDivision by ten (page 98)Model and discuss the process.575 nails were shared among 10 carpenters.

Divide 57 tens by 10. Each carpenter gets 5.

Trade the 7 tens left for 70 ones. Now share the 75. Each gets 7 with a remainder of 5.

Answer: 57 remainder 5

Examine a series of estimates to divisions to see if they are reasonable or unreasonable, e.g.388 ÷ 4 100 is reasonable.

Solve ‘average’ problems.

Strand: Number and AlgebraDividing large numbers (page 98)Model the division process.

Complete examples.Use a calculator to divide large numbers.Solve problems that involve finding the time taken to complete journeys, i.e. Time = distance ÷ average speed

Tues

day

Strand: Number and AlgebraDecimal place value (page 107)Record the place value of digits, e.g.256.73 7 represents 7 tenthsWrite the number before and after each decimal. _______________ 36.273 __________________

_______________ 357.24 __________________

Convert fractions into decimals.Use a calculator to divide numerator by denominator.Read and interpret a measurement chart to identify:

the tallest person the shortest person

the person 1mm shorter than…

Strand: Number and AlgebraDividing decimals/money (page 107)Model the process of dividing decimals.Emphasise the role of the decimal point.Complete examples, e.g.

Solve shopping problems, e.g.If 3 tomato sauce bottles cost $1.86, how much would 1 bottle cost?Calculate the amount saved when buying multiple packs compared to an equivalent number of unit packs.

E.g. a six-pack of soap for $3 compared to 6 soaps at 80c each.

Wed

nesd

ay

Strand: Number and AlgebraInverse operations (page 144)Use multiplication to check that the quotient in a number sentence is correct, e.g.12 ÷ 4 = 3 check 3 × 4=12Use multiplication to check that division algorithms are correct.

1 4

× 4

5 6

Use rounding to estimate the quotient when dividing.

Strand: Number and AlgebraEquivalent number sentences (page 144)Solve equations by calculating the value of missing numbers, e.g.If ■ = 5, solve 3 × ■ = ▲Work backwards to supply the missing decimal in number sentences, e.g. 5 × = 3.5Create number sentences to solve problems, e.g.If you multiply me by 3 and add 4 the answer is 19 × 3 + 4 = 19



Term 2 Week 8

Syllabus OutcomesMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-7NA compares, orders and calculates with fractions, decimals and percentagesMA3-8NA analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian planeMA3-17MG locates and describes position on maps using a grid-reference system

Thur

sday

Strand: Measurement and GeometryUsing scale (page 47)Study a conventional scale as seen in maps and atlases.

Apply a scale to work out the distance being represented by various lines.Read and interpret a map and its scale to determine distance, e.g. 1 cm = 20 km_____________ = 80 km

Strand: Number and AlgebraSquare numbers (page 47)Recognise that square numbers can be arranged in the shape of a square array and that they are equal to the number multiplied by itself.Create labels to describe 1², 2², 3² and 4²e.g.

4 x 4 = 16Model and label 5², 6², and 7²Recognise that square numbers follow a pattern, i.e.

1 +3 4 +5 9 +7 16 +9 25

Use pattern to identify the first ten square numbers.Solve number sentences, e.g.10² + 5² 7² + 9² 200 – 11² 400 – 13²

Frid

ay

Strand: Measurement and GeometryPlan views (page 80)Interpret the plan view of a flat in order to calculate the length and breadth of the rooms.

On 1-cm dot paper, draw the plan view of a room given: a scale of 2 cm = 1 m the position of objects in the roomthe dimensions of objects in the room

Strand: Number and AlgebraTriangular numbers (page 80)Construct a pattern on dot paper for the first 17 triangular numbers.Observe and record the ‘growth pattern’.Use this pattern to predict the next four triangular numbers.

Observe, discuss and identify triangular numbers within Pascal’s triangleIdentify counting numbers 1, 2, 3, 4 etc. on the diagonals within Pascal’s triangle.

Examine Fibonacci’s Sequence.Identify the next three Fibonacci numbers in a sequence beyond 13.



Term 2 Week 9

Syllabus OutcomesMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-19SP conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes

Mon

day

Year 5 Year 6Strand: Number and Algebra4-digit multiplication (page 116)Complete examples, such as:

Recognise that the symbol K is used to represent multiples of a thousand, e.g.$36 000 can be written as $36K.Write amounts expressed using the K symbol in full, e.g.$356K = $356 000

Round prices to the nearest $1000 in order to estimate the total cost of multiple units. Record answers using the K symbol.

Strand: Number and AlgebraMultiplying fractions (page 116)Explore strategies: repeated addition e.g.

multiply numerator by whole number and divide that product by denominator, e.g.

multiply numerators and multiply denominators, e.g.

Tues

day

Strand: Number and AlgebraThree digits multiplied by two digits (page 120)Complete examples, e.g.

152× 12

Use multiplication to solve problems.

Strand: Number and AlgebraMultiplication by 2 digits (page 120)Complete examples, e.g. 3446

× 35Calculate costs involved in buying lots of office equipment, e.g. 18 copiers @ $5460 each.Use rounding as a strategy for checking multiplications.

Wed

nesd

ay

Strand: Number and AlgebraCalculator memory (page 117)Recognise the purpose and function of the M+ and MR keys on a calculator.Complete an example.Using the memory function

Socks Stapler Magazine Ball Felt-tip pen$4.55 $5.50 $4.75 $8.50 $7.35

Sue bought 3 pairs of socks, 2 staplers and 3 balls. How much did she spend?

Step 1Enter $4.55 × 3 on your calculator and press M+Step 2Enter $5.50 × 2 on your calculator and press M+Step 3Enter $8.50 × 3 on your calculator and press M+Step 4Press MR on your calculator to find the total of $50.15

Use the memory function to calculate the total costs for a series of purchases.

Strand: Number and AlgebraCalculator: multiplication and division (page 117)Demonstrate how the M+ and MR keys on a calculator can be used to solve a problem.Solve shopping problems based on data provided.Write and solve a problem using a calculator’s memory function.Solve equations using the M+, M-and MR functions, e.g. (100 – 57) – (80 ÷ 16) =

Thur

sday

Strand: Statistics and ProbabilityChance (page 70)Examine a series of spinners to determine the likelihood of a particular colour being the winning colour.

Use terms such as ‘50% chance’ and ‘1 in 4 chance’ to compare the likelihood of a particular colour being the winning colour.Use a scale of 0 to 1 to rate the likelihood of colours on a spinner being the winning colour.

Strand: Statistics and ProbabilityChance from zero to one (page 70)Use the range of 0 to 1 to rate the likelihood of events happening, e.g. it will rain todaya red counter will be selected first from a group



Term 2 Week 9

Syllabus OutcomesMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-19SP conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes

Frid

ay

Strand: Statistics and ProbabilityLine graphs (page 74)Read and interpret a line graph showing temperature over a period of time.Recognise an emerging pattern in a table and use this data to create a line graph, e.g.Plot the data in the table below onto a graph, with seconds on the horizontal axis and litres on the vertical axis.

Sec. 10 20 30 40 50 60 70L 2 4 6 8 10 12 14

Strand: Measurement and GeometryMeasuring angles with a 360° protractors (page 74)Record angles formed on shaded section of a 360° protractor.

Realise that the total of the shaded and unshaded sections of the protractors add to 360°Examine intersecting lines and understand their properties, i.e. vertically opposite angles are equal.Measure angles at the vertex of intersecting lines, e.g.

Draw intersecting lines and measure their angles.



Term 2 Week 10

Syllabus OutcomesMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-11MG selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacityMA3-14MG identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views

Mon

day

Year 5 Year 6Strand: Number and AlgebraDistributive law (page 86)Demonstrate a mental strategy, e.g. 543 × 6Think: 6 x (500 + 40 + 3)Therefore 6 x 500 = 3000

6 x 40 = 240 6 x 3 = 18

3258Use a grid to show distribution, e.g. 5 x 367

Strand: Number and AlgebraExtended multiplication (page 86)Complete examples and explain why the second line always has a zero in the ones column.Use multiplication to solve a problem.

Use multiplication to solve a number cross.

Tues

day

Strand: Number and AlgebraMultiplication by tens (page 103)Complete grids for × 10, × 100 and × 1000.Round the multiplicand to the nearest 10 or 100 to approximate answers, e.g. 813 × 8 ≈ 6400.Model the written algorithm.

Th H T O24 5

× 4 0

1 8 0 0

Step 1Put the 0 down because you are multiplying by 10.Step 2Multiply by 4 using the shortened method.

Complete examples.

Strand: Number and AlgebraMultiplication by tens (page 103)Complete a multiplication chart for ×10, ×100 and ×1000.Model the process for multiplication by tens.

Complete examples, e.g.126

× 30

Complete multiplications by: rounding the larger number to the nearest 100 or 1000 to

estimate the productcalculating the exact answer

Wed

nesd

ay

Strand: Number and AlgebraTwo digits multiplied by two digits (Page 106)Model and discuss long multiplication.Long multiplication by 2 digits:

2 7

× 2 5

1 3 5 27 × 5 = 135

5 4 0 27 × 20 = 540

6 7 5 (27 × 5) + (27 × 20) = 675 (135 + 540)

Complete examples.Solve a volume problem given the number of soup tins contained in a carton and the number of cartons per pallet.

Strand: Number and AlgebraMultiplication by 2 digits (page 106)Review the multiplication process.Explain why there is always a zero in the units column of the second row of working.Complete examples, e.g. 4 5 2

× 4 5

Use ‘guess and check’ strategies to match multipliers to worked examples, e.g.

9 6×

4 8 03 8 4 04 3 2 0

Refer to a map with distances marked to calculate distance flown on various flights, e.g.34 trips from Sydney to Brisbane (752 km × 34).



Term 2 Week 10

Syllabus OutcomesMA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operationMA3-11MG selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacityMA3-14MG identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views

Thur

sday

Strand: Measurement and GeometryTop, front and side views (page 71)Understand that 3D objects can be represented by drawings of their views from the top, front and side.Locate prisms, pyramids and cones and draw their views from the top, front and side.Observe 3D models and draw their three views, e.g.

Strand: Measurement and GeometryConstruct and draw 3D objects (page 71)Make models of 3D shapes then draw their top, front and side views on grid paper.

Build 3D shapes given their top, front and side views.

Create two rectangular prisms using 36 cubes. Record each shape’s length, width and height.

Frid

ay

Strand: Measurement and GeometryConstructing objects (page 93)Match 3D objects to their top, front and side views, e.g.

Given an object’s views, make and sketch that shape

Strand: Statistics and ProbabilityMisleading data (page 93)Understand that data presented in graphs may be misleading.

The same data can be presented differently e.g.Graph A indicates that membership is full and has increased rapidly over 10 years.Graph B shows a more gradual increase.Examine a graph and associated newspaper article to determine whether the text matches the graphed data.Find own examples of misleading data in the media.


Documents

dubbowestoc.weebly.comdubbowestoc.weebly.com/uploads/1/0/0/8/...2_2016.docx · Web viewDubbo West Public School Stage 3 Mathematics Scope and Sequence. Collaborated by Mitchell