Maths Objectives/Learning Outcomes Bridging Document5th, 6th (Primary) and Junior Cycle (Post-Primary)

STRAND: NUMBERStrand Unit: Place Value

5th Class 6th Class Junior Cycle, Post-Primary

Planet Maths 5th Class Planet Maths 6th Class Active Maths 1 Complete Course for 2014 Exam

The child should be enabled to The learner should be able to

Read, write and order whole numbers and decimalspp. 9–11, 67

Read, write and order whole numbers and decimalspp. 11–14, 64

Round whole numbers and round decimals p. 12

Round decimalsp. 67

Justify approximations and estimates of calculationsChapter 6 (Rounding)

Identify place value in whole numbers and decimalspp. 9–11, 67

Identify place value in whole numbers and decimalsp. 65

271Planet Maths Teacher Resources • 6th Class

272Planet Maths Teacher Resources • 6th Class

Strand Unit: Operations

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Estimate sums, differences, products and quotients of whole numbersp. 15

Estimate sums, differences, products and quotients of decimals

Revisit models such as decomposition, skip counting, arranging items in arrays and accumulating groups of equal size (pp. 20–24) to make sense of operations of addition, subtraction, (pp. 16–19) multiplication, and division (pp. 24–29) in N where the answer is NChapter 2 Natural Numbers

Add and subtract whole numbers and decimals (to 3 decimal places), without and with a calculatorpp. 14–17

Add and subtract whole numbers and decimals (to 3 decimal places), without and with a calculatorpp. 16–19, 66

Multiply a decimal (up to 3 places) by a whole number, without and with a calculatorpp. 28–31, 84–87, 88

(5th Class)Multiply a three-digit number by a two-digit number p. 30Multiply a decimal by a whole number, without and with a calculator p. 31Multiply a whole number by 10, 100, 1,000 p. 33Multiply a decimal by a decimal, without and with a calculatorpp. 32, 78–81

Generalise observations of arithmetic operations

Divide a 3-digit number by a 2-digit number, without and with a calculatorpp. 39–42, 95–98

Divide a 4-digit number by a 2-digit number, without and with a calculatorpp. 40–43

Divide a decimal number by a whole number, without and with a calculatorpp. 95–98

(5th) Divide a decimal by a whole numberp. 88Divide a decimal number by a decimal, without and with a calculator pp. 89–91

Strand Unit: Fractions

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Compare and order fractions and identify equivalent forms of fractions with denominators 2–12pp. 45–48, 54

Compare and order fractions and identify equivalent forms of fractionsp. 45

Investigate models to help think about the operations of addition, subtraction, (pp. 68–71) multiplication, (pp. 72–73) and division of rational numbers in Z (pp. 73–75) Chapter 5 Rational NumbersExpress improper fractions as mixed numbers

and vice versa and position them on the number line

Express improper fractions as mixed numbers and vice versa and position them on the number line p. 46

Add and subtract simple fractions and simple mixed numbers pp. 55–59

Add and subtract simple fractions and simple mixed numbers. p. 48

Multiply a fraction by a whole numberp. 60

Multiply a fraction by a fractionpp. 59–62

Express tenths, hundredths and thousandths in both fraction and decimal formp. 69

Express tenths, hundredths and thousandths in both fractional and decimal formp. 47

Use the equivalence of fractions, (pp. 66 -67) decimals and percentages to compare proportions(pp. 82–91)Consolidate their understanding of the relationship between ratio and proportion(pp. 75–77)Chapter 5 Rational NumbersChapter 6 Decimals and Percentages

Divide a whole number by a unit fraction p. 61

Understand and use simple ratiospp. 118–120

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274Planet Maths Teacher Resources • 6th Class

Strand Unit: Decimals and Percentages

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Develop an understanding of simple percentages and relate them to fractions and decimalspp. 109–110, 119

Use percentages and relate them to fractions and decimalspp. 65, 93–96pp. 107–110

Calculate percentages (pp. 90–94)Use the equivalence of fractions, decimals (pp. 83–86) and percentages to compare proportionsChapter 6 Decimals and PercentagesCompare and order fractions and decimals

pp. 111Compare and order percentages of numberspp. 93–94, 107, 110

Solve problems involving operations with whole numbers, fractions, decimals and simple percentagespp. 68, 70, 72–75, 112, 114, 120–122

Solve problems relating to profit and loss, discount, VAT, interest, increases, decreasespp. 108–109, 133, 150–153

Solve problems that involve finding profit or loss, % profit or loss (on the cost price), (pp. 291–293) discount, % discount, (p. 294) selling price, (VAT pp. 282–290) compound interest for not more than 3 years, (pp. 299–300) income tax (standard rate only) net pay (including other deductions of specified amounts) (pp. 279–282) Chapter 16

Strand Unit: Number Theory

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Identify simple prime and composite numbersp. 82

Identify simple prime and composite numbersp. 69

Consolidate their understanding of prime numbers in N (p. 21)

Identify square and rectangular numbersp. 83

Identify and explore square numbersp. 70

Use the notation for an for a, n ∈ NUse the notation for a1/2 , a ∈ NChapter 15Indices and Reciprocals p. 265

Identify factors and multiplespp. 80–81

Identify and explore simple square rootsp. 70

Identify common factors and multiplespp. 71–72

Consolidate their understanding of factors, multiples, in N (p. 20)

Write whole numbers in exponential formp. 71

Apply the rules for indices (where a ∈ *Z, p,q, ∈ *N)ap aq = a p+q ap =a p-q p>qaq (ap)q= apq

Chapter 15Indices and Reciprocals pp. 268–272

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276Planet Maths Teacher Resources • 6th Class

STRAND: ALGEBRA Strand Unit: Directed Numbers

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Identify positive and negative numbers in contextpp. 133–136

Identify positive and negative numbers on the number linepp. 136–138

Investigate models such as the number line (pp. 51–52) to illustrate the operations of addition, subtraction, (pp. 53–55) multiplication and division in Z (pp. 56–60)Chapter 4 IntegersAdd simple positive and negative numbers on

the number linepp. 137–139

Strand Unit: Rules and Properties

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Explore and discuss simple properties and rules about brackets and priority of operationpp. 145–146

Know simple properties and rules about brackets and priority of operationpp. 165–166

Perform the operations in their order including brackets (pp. 60–61)Generalise observations of arithmetic operations:• use tables to represent a repeating-pattern

situation (pp. 128–131)• generalise and explain patterns and

relationships in words and numbers (pp. 133–134)

• write arithmetic expressions for particular terms in a sequence (pp. 134–135)

• use simple graphs as a tool for analysing relations

Chapter 8 Number Patterns

Identify relationships and record verbal and simple symbolic rules for number patternspp. 143–144

Identify relationships and record symbolic rules for number patternspp. 167–168

Strand Unit: Equations

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Translate number sentences with a frame into word problems and vice versapp. 158–60

Translate word problems with a variable number sentencesp. 182

Interpret equations of the form f(x) = g(x) as a comparison of functions of the formax where a ∈ Z, x ∈ Rax + b where a,b ∈ Z, x ∈ Rax2 + bx +c where a,b,c ∈ Z, x ∈ Ra2x where a ∈ N, x ∈ Ra3x where a ∈ N, x ∈ RUse graphical methods to find approximate solutions to f (x) = g(x)Chapter 29 Solving Problems Using Algebra p. 477

Solve one-step number sentences and equationspp. 157–159

Solve one-step number sentences and equationspp. 181–182

Strand Unit: Variables

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Explore the concept of a variable in the context of simple patterns, tables and simple formulae and substitute values for variablespp. 179–180

Use tables, diagrams and graphs as tools for representing and analysing linear, quadratic and exponential patterns and relations (exponential relations limited to doubling and tripling) (pp. 134–139) Chapter 8 Number Patterns

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Strand Unit: Operations

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

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STRAND: SHAPE AND SPACE Strand Unit: 2D Shapes

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Make informal deductions about 2D shapes and their propertiesp. 33

Make informal deductions about 2D shapes and their propertiesp. 54

Prove in a parallelogram opposite sides and opposite angles are equal and the diagonals bisect each other (pp. 217–219)Chapter 13 : Geometry II: Theorems

Use angle and line properties to classify and describe triangles and quadrilateralspp. 34–35

Use angle and line properties to classify and describe triangles and quadrilateralsp. 55

Construct triangles given length of 3 sides, SAS and ASA dataChapter 25SSS (pp. 408–410)SAS (pp. 410–412)ASA (pp. 412–414)Chapter 25 Constructions II

Construct triangles from given sides or anglesp. 55

Identify the properties of a circlepp. 138–140

Identify the properties of a circlepp. 141–144

Develop an understanding of the relationship between diameter, circumference and pi(pp. 323–327)Chapter 18 Area and Volume

Construct a circle of given radius or diameterp. 139

Construct a circle of given radius or diameterp. 141

Tessellate combinations of 2D shapes p. 141 Tessellate combinations of 2D shapes p. 57

Classify 2D shapes according to their lines of symmetry

Classify 2D shapes according to their lines of symmetry p. 56

Use drawings to show central symmetry (p. 450) and axial symmetry (p. 452)Locate axes of symmetry in simple shapes pp. 446–448)Chapter 27 Transformation Geometry

Plot simple co-ordinates and apply where appropriate pp. 189–192

Use 2D shapes and properties to solve problems p. 36

Use 2D shapes and properties to solve problems p. 56

Strand Unit: Operations

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Strand Unit: 3D Shapes

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Identify and examine 3D shapes and explore relationships, including tetrahedron (faces, edges and vertices)pp. 162–165

Identify and examine 3D shapes and explore relationships, including octahedron (faces, edges and vertices)pp. 155–158

Investigate the nets of rectangular solids(pp. 331–335)Find the volume of rectangular solids(pp. 335–337)Chapter 18 Area and Volume

Draw the nets of simple 3D shapes and construct shapesp. 165

Draw the nets of simple 3D shapes and construct shapesp. 158

Strand Unit: Lines and Angles

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Recognise, classify and describe angles and relate angles to shape and the environmentp. 62, 65

Recognise, classify and describe angles and relate angles to shapep. 35

Recognise angles in terms of a rotation Recognise angles in terms of a rotation. p. 38 Angles and Rotation (pp. 169–172)

Estimate, measure and construct angles in degreesp. 63

Estimate, measure and construct angles in degreesp. 36

Bisect an angle with a compass and straight edge (pp. 182–184)Chapter 12 Constructions I

Explore the sum of the angles of a trianglep. 64

Explore the sum of the angles in a quadrilateralp. 37

Prove the angles in a triangle add to 180 degrees (p. 212, 383) Chapter 13 Geometry II: Theorems

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Strand Unit: Operations

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

280Planet Maths Teacher Resources • 6th Class

STRAND: MEASURES Strand Unit: Length

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Select and use appropriate instruments of measurement

Select and use appropriate instruments of measurementp. 83

Estimate and measure length using appropriate metric unitspp. 90–91

Rename measures of lengthp. 85

Estimate and measure the perimeter of regular and irregular shapes (mm, cm, m and km)pp. 92–93

Estimate and measure the perimeter of regular and irregular shapes (mm, cm, m and km)p. 84

Use and interpret scales on maps and plansp. 86

Draw and interpret scaled diagrams (pp. 338–339)

Strand Unit: Operations

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Strand Unit: Area

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Discover that the area of a rectangle is length by breadthpp. 130–131

Recognise that the length of the perimeter of a rectangular shape does not determine the area of its shapep. 112

Investigate nets of rectangular solids(pp. 331–335)

Estimate and measure the area of regular and irregular 2D shapespp. 128–129, 131

Calculate the area of regular and irregular 2D shapesp. 113, 144

Find (OL) Perform calculations involving (HL)

Surface area of rectangular solids (pp. 331–335)Chapter 18 Area and Volume

Measure the surface area of specified 3D shapes pp. 115

Calculate area using square cm and square metrespp. 128

Calculate area using ares and hectarespp. 114

Compare visually square metres and square centimetres

Identify the relationship between square metres and square centimetrespp. 114

Find the area of a room from a scale planpp. 115

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Strand Unit: Operations

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

282Planet Maths Teacher Resources • 6th Class

Strand Unit: Weight

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Select and use appropriate instruments of measurement pp. 154

Select and use appropriate instruments of measurement p. 160

Estimate and measure weight using appropriate metric units pp. 153–155

Rename measures of weight (as decimals or fractions) pp. 161–163

Calculate interpret and apply units of measure and time

Strand Unit: Capacity

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Select and use appropriate instruments of measurement pp. 176–179

Select and use appropriate instruments of measurement p. 184

Estimate and measure capacity using appropriate metric units p. 179

Rename measures of capacity (as decimals or fractions) pp. 184–186

Find (OL) Perform calculations involving (HL)

Find the volume of a cuboid experimentallyp. 187

Volume of rectangular solids and cylinders (p. 331)

Strand Unit: Operations

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Strand Unit: Time

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Read and interpret timetables and the 24-hour clock (digital and analogue)p. 107

Explore international time zonesp. 105

Make value for money calculations and judgements (pp. 284–290) Chapter 16 Applied Arithmetic

Interpret and convert between times in 12-hour and 24-hour formatpp. 105–106

Explore the relationship between time, distance and average speedpp. 102–104

Solve problems that involve calculating average speed, distance and time (pp. 311–314)Chapter 17 Distance, Speed and Time

Strand Unit: Money

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Compare ‘value for money’ using unitary methodpp. 115–117

Explore value for moneypp. 131–132

Make value for money calculations and judgements (pp. 284–290) Chapter 16 Applied Arithmetic

Convert other currencies to euro and vice versap. 134

Use the equivalence of fractions, decimals (pp. 83–86) and percentages to compare proportions (pp. 90–92)Consolidate their understanding of the relationship between ratio and proportion(pp. 75–77)Chapter 5 Rational Numbers

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Strand Unit: Operations

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

284Planet Maths Teacher Resources • 6th Class

STRAND: DATA Strand Unit: Representing and Interpreting Data

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Collect, organise and represent data using pictograms, single and multiple bar charts and simple pie chartspp. 21–22, 169–170

Collect, organise and represent data using pie charts and trend graphspp. 23–24, 177

Select appropriate graphical or numerical* methods to describe the sample (univariate data only) (pp. 234–235)Use pie charts, (pp. 239–241)bar charts (pp. 235–239)line plots (pp. 234–235)histograms (equal intervals) (pp. 244–246)and stem and leaf plots to display data(pp. 242–244)

Read and interpret pictograms, single and multiple bar charts and pie chartspp. 19–22, 168–170

Read and interpret pie charts and trend graphsp. 22, 177

Interpret graphical summaries of data

Compile and use simple data sets Compile and use simple data setsp. 24, 176

Explore and calculate averages of simple data setsp. 20, 167

Explore and calculate averages of simple data setsp. 21, 174–175

Use a variety of summary statistics to analyse the data: central tendency – mean, mode and median, (pp. 246–252)variability – range (p. 252)

Use data sets to solve problems Use data sets to solve problemsp. 176

Plan an experiment Select a sample and appreciate the importance of representativeness so as to avoid biased samples (p. 247–250)Design a plan to collect data on the basis of above knowledge Employ the plan to collect the dataChapter 14 Statistics

Strand Unit: Operations

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Strand Unit: Chance

5th Class 6th Class Junior Cycle, Post-PrimaryThe child should be enabled to The learner should be able to

Identify and list all possible outcomes of simple random processespp. 182–185

Identify and list all possible outcomes of simple random processesp. 126

Apply the principle that in the case of equally likely outcomes the probability is given by the number of outcomes of interest divided by the total number of outcomes (p. 103)Chapter 3

Estimate the likelihood of occurrence of eventsp. 181–182

Estimate the likelihood of occurrence of events; order on a scale from 0 to 100%, 0 to 1p. 127–128

Decide whether an everyday event is likely or unlikely to occur (pp. 99–101)Appreciate that probability is a quantity that gives a measure on a scale of 1 – 10 of how likely an event is to occur (pp. 102–115)Apply the principle of counting (pp. 43–45, 115–119)Chapter 3 Fundamental Principle of CountingChapter 7 Probability

Construct and use frequency charts and tablespp. 182–185

Construct and use frequency charts and tables p. 129

285Planet Maths Teacher Resources • 6th Class

1. Twitter

Ranking Name Followers Months since joined1 Lady Gaga 11,090,482 39

2 Justin Bieber 27

3 Barack Obama 52

4 Britney Spears 33

5 Kim Kardashian 28

6 Katy Perry 28

7 Ashton Kutcher 7,001,133 30

Source: Twitaholic.com. Accessed 23/07/2011

1. The table above is of famous people with the highest number of followers on Twitter. Can you match these figures with each celebrity?

7,962,560 8,299,326 10,518,053 8,789,249 7,982,565

(Ask your teacher if you may use a calculator for some questions) 2. Which person has seven million nine hundred and sixty two thousand five hundred and

sixty followers? 3. Write in words the number of people following Barack Obama. 4. Round Britney Spears’ number of followers to the nearest million. 5. Round Lady Gaga’s number of followers to the nearest hundred thousand. 6. Round Kim Kardashian’s number of followers to the nearest ten thousand. 7. Round Justin Bieber’s number of followers to the nearest thousand. 8. Based on the information above, what is the average number of followers they gained

each month? (rounded to 2 decimal points) 9. How do these figures compare with the overall ratings? 10. Ask your teacher for permission to visit Twitaholic.com and find out what the latest

statistics are and whether the rankings have changed. How many more followers has each person gained?

Suggestions for Integration:

English:Discuss celebrity cultureOrDebate the advantages and disadvantages of Twitter

History:Imagine you a historical figure (e.g. Michael Collins/Thomas Francis Meagher/Queen Elizabeth I). Write some of the tweets they might have written during their significant historical times.

286 Planet Maths Teacher Resources • 6th Class

Answers:

Ranking Name Followers Months since joined

Average joined per month

1 Lady Gaga 11,090,482 39 284,371.33

2 Justin Bieber 10,518,053 27 389,557.52

3 Barack Obama 8,789,249 52 169,024.02

4 Britney Spears 8,299,326 33 251,494.73

5 Kim Kardashian 7,982,565 28 285,091.61

6 Katy Perry 7,962,560 28 284,377.14

7 Ashton Kutcher 7,001,133 30 233,371.10

2. Katy Perry 3. Eight million, seven hundred and

eighty nine thousand, two hundred and forty nine

4. 8,000,000 5. 11,100,000 6. 7,980,000 7. 10,518,000 8. See table above 9. Justin Bieber has the most new

followers per month and Barack Obama has the least

287Planet Maths Teacher Resources • 6th Class

2. The ConcertStephen and his sister Emily would like to go to a concert in Croke Park, but getting their parents to agree might be a problem as business is quiet in Dad’s shop. They think it might be a good idea to offer to buy a ticket between them for one of their parents as they must be accompanied by an adult. They decide to draw up a type of ‘business plan’ outlining how much it will cost and how they will earn the money they need.

Stephen needs to save:Tickets €55.0012 share of ticket for adult €27.50Bus transport €15.00Food and drinks €25.00Hoodie €35.00 How much does he need in total? (€157.50)

Emily needs to save:Tickets €55.0012 share of ticket for adult €27.50Bus transport €15.00Food and drinks €25.00DVD €20.00How much does she need in total? (€142.50)

The children usually get €10 pocket money each week.If the concert is 4 weeks away, how much money is each child short? (Stephen €117.50. Emily €102.50)

Stephen and Emily usually help in Dad’s shop by tidying and helping to pack shelves. They earn an extra €5 per hour.How many hours does each child need to work to make up the shortfall? (Stephen 23hr 30min Emily 20h 30min)

Their parents are impressed with the children’s planning and agree to bring them to the concert. Four weeks later, the whole family set off at 3:40pm. The satnav shows their arrival time as 5:08pm. How long will their journey take? (1 hr 28min)

Road works delay them 15 minutes. What is their adjusted arrival time on the 24-hour clock? (17:23)

How many minutes have they to spare before the concert starts? (37min)

The journey is 128km. Dad’s car does 15km per litre. (km/pl) How many litres are needed for the round journey? (to 1 decimal point) (256

15 = 17.1litres)

Petrol costs €1.45 per litre. How much will the journey both ways cost? (€24.80)

The toll on the motorway is €2.85. How much for both journeys? (€5.70)

How much will the journey both ways cost in petrol and tolls? (€30.50)

If the 4 of them had gone on the bus, how much would it have cost? (4 x €15 = €60)

288 Planet Maths Teacher Resources • 6th Class

By how much cheaper or dearer was the car? (Car cheaper by €29.50 not taking wear and tear into account)

They decide to split the cost of the petrol and tolls between the 4 of them.How much does each have to contribute? (€7.63)

Dad dropped Mum and the children off at the concert. ‘We’ll meet you here 45 minutes after the concert finishes, don’t be late!’ he said.If the concert finishes at 9:30, at what time will the family meet up? (Digital time) (10:15pm)

Stephen decided to go buy a hoodie. They were priced at €36 with 1212% discount. How much

did he have to pay? (€36 – €4.50 = €31.50) Emily looked at the DVD’s. They were €16.95 each or 3 for €45. How much would be saved by buying 3? (€50.85 - €45 = €5.85)

The concert finished 20 minutes later than advertised. What time did it end in analogue time? (10 to 10)

How many minutes have they to get to their meeting place? (25 mins)

The children arrived just as Dad was pulling in. ‘Great,’ he said, ‘now, if our journey home takes us the same amount of time as our journey here, what time will it be when we get home?’ but all he could hear from the back seats was gentle snoring!

289Planet Maths Teacher Resources • 6th Class