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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.



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 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 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



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.



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.



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



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

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



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



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



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 (Polygons)

1] I can sort, and classify simple 2D shapes using their various properties.
 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 (3D Shapes)

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



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



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



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.




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