## Educators' Guide for Pedagogy and Assessment

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### Learning Area: Mathematics

# Mathematics > LEVEL 5

### Learning Area Outcome: I understand the structure of the number system and the relationship between numbers.

## Subject Focus: Number - The number system

1] I can read, write and order whole numbers to ten thousand in figures and words.

WRITING

2] I can recognise, read and position whole numbers on a number line.

COGNITIVE LEARNING

3] I can understand the place value of any digit in a whole number up to ten thousand.

4] I can compare and order whole numbers up to ten thousand and include symbols such as <, > or =.

5] I can read, say, order and write ordinal numbers to one hundred.

WRITING

6] I can identify odd and even numbers to ten thousand.

7] I can count forward and backwards in 1s, 2s, 10s and 100s starting from any whole number less than or equal to 1000.

WRITING

8] I can count forward and backwards in steps of 3, 4, or 5 to and from any whole number less than or equal to 50.

WRITING

9] I can count forward/backwards in steps of 25 and 50 to/from 500.

WRITING

10] I can recall the first ten multiples of the following numbers: 2, 3, 4, 5, 8 & 10.

11] I can understand what a half and a quarter are and can recognise them in shapes and in small numbers of objects.

12] I can understand that 0.1 represents a tenth.

13] I can understand that 0.5 represents a half.

COGNITIVE LEARNING

14] I can recognise simple fractions that are parts of a whole.

COGNITIVE LEARNING

15] I can recognise mixed numbers which include a whole number and a fraction.

COGNITIVE LEARNING

16] I can recognise and use simple equivalent fractions.

COGNITIVE LEARNING

17] I can compare and order simple fractions and position them on a number line.

18] I can state one number lying between two whole numbers.

WRITING

2] I can recognise, read and position whole numbers on a number line.

COGNITIVE LEARNING

3] I can understand the place value of any digit in a whole number up to ten thousand.

4] I can compare and order whole numbers up to ten thousand and include symbols such as <, > or =.

5] I can read, say, order and write ordinal numbers to one hundred.

WRITING

6] I can identify odd and even numbers to ten thousand.

7] I can count forward and backwards in 1s, 2s, 10s and 100s starting from any whole number less than or equal to 1000.

WRITING

8] I can count forward and backwards in steps of 3, 4, or 5 to and from any whole number less than or equal to 50.

WRITING

9] I can count forward/backwards in steps of 25 and 50 to/from 500.

WRITING

10] I can recall the first ten multiples of the following numbers: 2, 3, 4, 5, 8 & 10.

11] I can understand what a half and a quarter are and can recognise them in shapes and in small numbers of objects.

12] I can understand that 0.1 represents a tenth.

13] I can understand that 0.5 represents a half.

COGNITIVE LEARNING

14] I can recognise simple fractions that are parts of a whole.

COGNITIVE LEARNING

15] I can recognise mixed numbers which include a whole number and a fraction.

COGNITIVE LEARNING

16] I can recognise and use simple equivalent fractions.

COGNITIVE LEARNING

17] I can compare and order simple fractions and position them on a number line.

18] I can state one number lying between two whole numbers.

### Learning Area Outcome: I understand the structure of the number system and the relationship between numbers.

## Subject Focus: Number - The number system (Assistive Technology & Other Resources)

1] I can use assistive technology

*e.g. tablets and computers*and other learning resources*e.g. Cuisenaire rods, Unifix cubes*to learn about numbers and their properties.### Learning Area Outcome: I can calculate mentally and using pencil and paper and assistive technology. I can calculate to the most appropriate level of accuracy. I can check the reasonableness of the answers obtained in calculations by rounding numbers and making rough approximations.

## Subject Focus: Number - Numerical calculations (Whole Numbers, Decimal Numbers & Fraction Numbers - The Four Operations)

1] I can add 100 or 1,000 to any whole number.

COGNITIVE LEARNING

2] I can understand that I can add numbers in any order and get the same result.

COGNITIVE LEARNING

3] I can work out a small difference by counting up from the smaller to the larger number.

4] I can understand that subtraction is the inverse of addition and vice versa. I can also state and write a substraction statement corresponding to a given addition statement and vice versa

COGNITIVE LEARNING

5] I can add/subtract 9 or 11 by adding/subtracting 10 and then adjusting by 1.

COGNITIVE LEARNING

6] I can use column addition and subtraction with up to three-digit numbers.

COGNITIVE LEARNING

7] I can work through situations involving addition and subtraction with two-digit numbers.

COGNITIVE LEARNING

8] I can derive all pairs of 100 in multiples of 5 and 10.

COGNITIVE LEARNING

9] I can derive all number pairs that total 100.

COGNITIVE LEARNING

10] I can derive all pairs of multiples of 50 with a total of 1000.

COGNITIVE LEARNING

11] I can derive all pairs of multiples of 100 with a total of 1000.

12] I can understand that multiplication is multiple groups or repeated addition.

COGNITIVE LEARNING

13] I can understand that I can multiply numbers in any order and get the same result.

COGNITIVE LEARNING

14] I can understand division as equal sharing.

COGNITIVE LEARNING

15] I can understand division as equal grouping or repeated subtraction.

COGNITIVE LEARNING

16] I can understand that division is the inverse of multiplication. I can also state and write a division statement corresponding to a given multiplication statement i.e 2, 3, 4, 5 and 10 multiplication facts, and vice versa

COGNITIVE LEARNING

17] I can mentally multiply an integer by multiples of 10 and 100.

COGNITIVE LEARNING

18] I can recognise unit fractions such as

COGNITIVE LEARNING

19] I can double whole numbers up to 500.

COGNITIVE LEARNING

20] I can halve even numbers up to 500.

21] I can understand halving as the inverse of doubling.

COGNITIVE LEARNING

22] I can find remainders after division, restricted to dividends up to 100 and divisors up to 10.

COGNITIVE LEARNING

23] I can work through simple one-step situations using addition, subtraction, multiplication and/or division.

I can also give a rough estimate of the answer of such situations and I can check the reasonableness of the answer.

24] I can round any whole two-digit number to the nearest ten and any three-digit number to the nearest hundred.

25] I can find fractions of shapes and simple whole numbers.

COGNITIVE LEARNING

26] I can read and interpret scales involving whole numbers.

READING AND UNDERSTANDING

COGNITIVE LEARNING

2] I can understand that I can add numbers in any order and get the same result.

COGNITIVE LEARNING

3] I can work out a small difference by counting up from the smaller to the larger number.

4] I can understand that subtraction is the inverse of addition and vice versa. I can also state and write a substraction statement corresponding to a given addition statement and vice versa

*e.g. if 4 + 3 = 7 then 7 - 3 = 4 and vice versa.*COGNITIVE LEARNING

5] I can add/subtract 9 or 11 by adding/subtracting 10 and then adjusting by 1.

COGNITIVE LEARNING

6] I can use column addition and subtraction with up to three-digit numbers.

COGNITIVE LEARNING

7] I can work through situations involving addition and subtraction with two-digit numbers.

COGNITIVE LEARNING

8] I can derive all pairs of 100 in multiples of 5 and 10.

COGNITIVE LEARNING

9] I can derive all number pairs that total 100.

COGNITIVE LEARNING

10] I can derive all pairs of multiples of 50 with a total of 1000.

COGNITIVE LEARNING

11] I can derive all pairs of multiples of 100 with a total of 1000.

12] I can understand that multiplication is multiple groups or repeated addition.

COGNITIVE LEARNING

13] I can understand that I can multiply numbers in any order and get the same result.

COGNITIVE LEARNING

14] I can understand division as equal sharing.

COGNITIVE LEARNING

15] I can understand division as equal grouping or repeated subtraction.

COGNITIVE LEARNING

16] I can understand that division is the inverse of multiplication. I can also state and write a division statement corresponding to a given multiplication statement i.e 2, 3, 4, 5 and 10 multiplication facts, and vice versa

*e.g. if 4*×*3 = 12 then 12*÷ 3 = 4 and vice versa.COGNITIVE LEARNING

17] I can mentally multiply an integer by multiples of 10 and 100.

COGNITIVE LEARNING

18] I can recognise unit fractions such as

*½*and ¼ and use them to find fractions of shapes and numbers. I can also understand the relationship between fractions such as*½*and ¼ and division*e.g. ½ means 1*÷*2 and vice versa.*COGNITIVE LEARNING

19] I can double whole numbers up to 500.

COGNITIVE LEARNING

20] I can halve even numbers up to 500.

21] I can understand halving as the inverse of doubling.

COGNITIVE LEARNING

22] I can find remainders after division, restricted to dividends up to 100 and divisors up to 10.

COGNITIVE LEARNING

23] I can work through simple one-step situations using addition, subtraction, multiplication and/or division.

I can also give a rough estimate of the answer of such situations and I can check the reasonableness of the answer.

24] I can round any whole two-digit number to the nearest ten and any three-digit number to the nearest hundred.

25] I can find fractions of shapes and simple whole numbers.

COGNITIVE LEARNING

26] I can read and interpret scales involving whole numbers.

READING AND UNDERSTANDING

### Learning Area Outcome: I can calculate mentally and using pencil and paper and assistive technology. I can calculate to the most appropriate level of accuracy. I can check the reasonableness of the answers obtained in calculations by rounding numbers and making rough approximations.

## Subject Focus: Number - Numerical calculations (Money & Consumer Mathematics)

1] I can understand that 1 euro is equal to 100 cent.

2] I can work out totals up to a hundred euro and give the correct change.

3] I can handle small amounts of money in classroom situations

4] I can plan an activity within a given budget

5] I can use receipts, simple menus, entrance tickets to work out totals and change.

6] I can understand that prices marked as €0.99 are a marketing strategy to make prices more attractive.

2] I can work out totals up to a hundred euro and give the correct change.

3] I can handle small amounts of money in classroom situations

*e.g. keeping track of money collected from small change for charity money collections*.4] I can plan an activity within a given budget

*e.g. using tickets, travel brochures, price lists, menus ...*5] I can use receipts, simple menus, entrance tickets to work out totals and change.

6] I can understand that prices marked as €0.99 are a marketing strategy to make prices more attractive.

### Learning Area Outcome: I can calculate mentally and using pencil and paper and assistive technology. I can calculate to the most appropriate level of accuracy. I can check the reasonableness of the answers obtained in calculations by rounding numbers and making rough approximations.

## Subject Focus: Number - Numerical calculations (Assistive Technology & Other Resources)

1] I can use assistive technology

*e.g. tablets and computers*and other resources*e.g. Cuisenaire rods, Unifix cubes, base 10 blocks*appropriate to this level to calculate and to learn about numerical calculations.### Learning Area Outcome: I can recognise and describe patterns and relationships in various mathematical ways and can use algebraic manipulations.

## Subject Focus: Algebra – Fundamentals of Algebra

1] I can recognise and extend simple pictorial patterns and number sequences formed by counting any positive integer in constant steps.

2] I can recognise the use of an empty box symbol to stand in for an unknown number and can find the unknown number.

COGNITIVE LEARNING

2] I can recognise the use of an empty box symbol to stand in for an unknown number and can find the unknown number.

COGNITIVE LEARNING

### Learning Area Outcome: I can recognise and describe patterns and relationships in various mathematical ways and can use algebraic manipulations.

## Subject Focus: Algebra – Fundamentals of Algebra (Assistive Technology & Other Resources)

1] I can use assisitive technology

*e.g. tablets and computers*and other resources appropiate to this level to learn about the fundamentals of algebra.### Learning Area Outcome: I understand and can use forms of measurement and can make reasonable estimations.

## Subject Focus: Shape, space and measures – Measures (Angles)

1] I can show and label the four compass points.

COGNITIVE LEARNING

2] I can understand that a right angle is a quarter of a whole turn and can recognise such angles in 2D shapes and in the environment.

COGNITIVE LEARNING

3] I can make and describe right angle turns including turns between the four compass points.

COGNITIVE LEARNING

4] I can recognise, measure and draw angles of 90° and 180° without the use of a protractor.

COGNITIVE

5] I can compare an angle with a right angle.

COGNITIVE LEARNING

2] I can understand that a right angle is a quarter of a whole turn and can recognise such angles in 2D shapes and in the environment.

COGNITIVE LEARNING

3] I can make and describe right angle turns including turns between the four compass points.

COGNITIVE LEARNING

4] I can recognise, measure and draw angles of 90° and 180° without the use of a protractor.

COGNITIVE

5] I can compare an angle with a right angle.

### Learning Area Outcome: I understand and can use forms of measurement and can make reasonable estimations.

## Subject Focus: Shape, space and measures – Measures (Length, Area, Volume, Mass & Capacity)

1] I can understand that the length of an object is a measure of distance between the endpoints of an object.

2] I can understand that the mass of an object is a measure of the amount of material in an object.

3] I can understand that the capacity of a container is the total amount of fluid that can be poured into the container.

4] I can read and write the vocabulary related to length, mass and capacity.

WRITING

5] I know the standard metric units of length i.e kilometres, metres, centimetres and millimetre; mass i.e kilograms and grams; and, capacity i.e litres and millilitres. I also know the abbreviations of these standard units and I can understand the relationships between different units of the same measure.

COGNITIVE LEARNING

6] I can estimate, measure and compare lengths, masses, and, capacities.

COGNITIVE LEARNING

7] I can use the decimal notation to express measures of length, mass and capacity.

8] I can convert and use larger to smaller standard metric units of mass i.e. kg, g; length i.e. km, m, cm, mm; and capacity i.e. l, ml, and vice versa.

9] I can suggest and use measuring eauipement to estimate and/or measure length mass and capacity.

10] I can draw a line to the nearest centimetre.

2] I can understand that the mass of an object is a measure of the amount of material in an object.

3] I can understand that the capacity of a container is the total amount of fluid that can be poured into the container.

4] I can read and write the vocabulary related to length, mass and capacity.

WRITING

5] I know the standard metric units of length i.e kilometres, metres, centimetres and millimetre; mass i.e kilograms and grams; and, capacity i.e litres and millilitres. I also know the abbreviations of these standard units and I can understand the relationships between different units of the same measure.

COGNITIVE LEARNING

6] I can estimate, measure and compare lengths, masses, and, capacities.

COGNITIVE LEARNING

7] I can use the decimal notation to express measures of length, mass and capacity.

8] I can convert and use larger to smaller standard metric units of mass i.e. kg, g; length i.e. km, m, cm, mm; and capacity i.e. l, ml, and vice versa.

9] I can suggest and use measuring eauipement to estimate and/or measure length mass and capacity.

10] I can draw a line to the nearest centimetre.

### Learning Area Outcome: I understand and can use forms of measurement and can make reasonable estimations.

## Subject Focus: Shape, space and measures – Measures (Time)

1] I can read and write the vocabulary related to time.

WRITING

2] I can use standard units of time and know the relationships between them.

3] I can convert and use larger to smaller standard units of time i.e hours, minutes and seconds, and vice versa.

4] I can read and use the 12 hour clock in both analogue and digital.

5] I can read and use a calendar.

READING AND UNDERSTANDING

6] I can estimate and measure time using seconds, minutes and hours.

COGNITIVE LEARNING

WRITING

2] I can use standard units of time and know the relationships between them.

3] I can convert and use larger to smaller standard units of time i.e hours, minutes and seconds, and vice versa.

4] I can read and use the 12 hour clock in both analogue and digital.

5] I can read and use a calendar.

READING AND UNDERSTANDING

6] I can estimate and measure time using seconds, minutes and hours.

COGNITIVE LEARNING

## Subject Focus: Shape, space and measures – Measures (Assistive Technology & Other Resources)

1] I can use assisitive technology

*e.g. tablets and computers*and other resources*e.g. plactic money, cardboard clocks, 2D and 3D plastic shapes, measuring instruments*appropriate to this level to learn about measures.### Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

## Subject Focus: Shape, space and measures – Euclidean geometry (Lines & Lines Segments)

1] I can describe and draw pictures and patterns.

COGNITIVE LEARNING

COGNITIVE LEARNING

### Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

## Subject Focus: Shape, space and measures – Euclidean geometry (Triangles)

1] I can recognise, name, draw and describe the simple 2D shape: the triangle.

COGNITIVE LEARNING

COGNITIVE LEARNING

### Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

## Subject Focus: Shape, space and measures – Euclidean geometry (Quadrilaterals)

1] I can recognise, name, sketch and describe the simple 2D shapes: the square and the rectangle.

COGNITIVE LEARNING

COGNITIVE LEARNING

## Subject Focus: Shape, space and measures – Euclidean geometry (Polygons)

1] I can sort, and classify simple 2D shapes using their various properties.

COGNITIVE LEARNING

COGNITIVE LEARNING

## Subject Focus: Shape, space and measures – Euclidean geometry (3D Shapes)

1] I can recognise and name the simple 3D shapes: the cube and the cuboid.

COGNITIVE LEARNING

COGNITIVE LEARNING

## Subject Focus: Shape, space and measures – Euclidean geometry (Assistive Technology & Other Resources)

1] I can use assistive technology

*e.g. tablets and computers*and other resources*e.g. 2D and 3D plastic shapes*appropriate to this level to learn about measures.### Learning Area Outcome: I can describe position and movement of shapes in a plane.

## Subject Focus: Shape, space and measures – Transformation geometry (Movement)

1] I can understand what right, left, up and down mean and can move an object in each of these directions. I can also describe the movement of the object in each of these directions.

COGNITIVE LEARNING

2] I can read and write the vocabulary related to position, direction and movement.

WRITING

3] I can describe and find the position of a square on a grid of squares with rows and columns labelled.

COGNITIVE LEARNING

2] I can read and write the vocabulary related to position, direction and movement.

WRITING

3] I can describe and find the position of a square on a grid of squares with rows and columns labelled.

### Learning Area Outcome: I can describe position and movement of shapes in a plane.

## Subject Focus: Shape, space and measures – Transformation geometry (Reflections)

1] I can recognise reflective symmetry in a square.

COGNITIVE LEARNING

2] I can identify and draw lines of symmetry in simple 2D shapes.

COGNITIVE LEARNING

3] I can recognise shapes with no, one and two lines of symmetry.

COGNITIVE LEARNING

4] I can draw the other half of a simple symmetrical object inspired by examples of symmetry in nature.

COGNITIVE LEARNING

COGNITIVE LEARNING

2] I can identify and draw lines of symmetry in simple 2D shapes.

COGNITIVE LEARNING

3] I can recognise shapes with no, one and two lines of symmetry.

COGNITIVE LEARNING

4] I can draw the other half of a simple symmetrical object inspired by examples of symmetry in nature.

COGNITIVE LEARNING

### Learning Area Outcome: I can describe position and movement of shapes in a plane.

## Subject Focus: Shape, space and measures – Transformation geometry (Rotations)

1] I can describe right angle rotations.

### Learning Area Outcome: I can describe position and movement of shapes in a plane.

## Subject Focus: Shape, space and measures – Transformation geometry (Assistive Technology & Other Resources)

1] I can use assistive technology

*e.g. tablets and computers*and other resources*e.g. 2D and 3D plastic shapes*appropriate to this level to learn about transformation geometry.### Learning Area Outcome: I can collect, analyse, interpret and communicate statistical information.

## Subject Focus: Data handling and chance – Statistics

1] I can collect, sort, organise and classify data in a table.

2] I can read and interpret a frequency table.

3] I can complete a frequency table.

4] I can read and interpret a block graph.

COGNITIVE LEARNING

5] I can construct a block graph.

PRACTICAL

6] I can work through a situation by representing and interpreting data in tables, graphs and charts.

COGNITIVE LEARNING

7] I can read and interpret a pictograph where the symbol represents one or two units.

8] I can draw a pictograph where the symbol represents one or two units.

9] I can read and interpret a Carroll diagram.

COGNITIVE

2] I can read and interpret a frequency table.

3] I can complete a frequency table.

4] I can read and interpret a block graph.

COGNITIVE LEARNING

5] I can construct a block graph.

PRACTICAL

6] I can work through a situation by representing and interpreting data in tables, graphs and charts.

COGNITIVE LEARNING

7] I can read and interpret a pictograph where the symbol represents one or two units.

8] I can draw a pictograph where the symbol represents one or two units.

9] I can read and interpret a Carroll diagram.

COGNITIVE

### Learning Area Outcome: I can collect, analyse, interpret and communicate statistical information.

## Subject Focus: Data handling and chance – Statistics (Assistive Technology & Other Resources)

1] I can use assistive technology

*e.g. tablets and computers*and other learning resources to learn about statistics.### Learning Area Outcome: I understand ideas of chance and uncertainty.

## Subject Focus: Data handling & chance – Probability (Assistive Technology & Other Resources)

1] I can use assistive technology

*e.g. tablets and computers*and other learning resources to learn about probability.