Primary 5 Mathematics
Lessons in primary 5 mathematics. This course is still being developed; independent practice and assessment coverage is incomplete.
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Numbers and relationships
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Topics
Primary 5 Mathematics
- Numbers and relationshipsSuggested next · 2 core lessonsBuild and connect the representations and methods in numbers and relationships.
- Fractions and bar modelsSuggested next · 7 core lessonsBuild and connect the representations and methods in fractions.
- DecimalsSuggested next · 1 core lessonBuild and connect the representations and methods in decimals.
- PercentagesSuggested next · 2 core lessonsBuild and connect the representations and methods in percentages.
- Rate and speedSuggested next · 1 core lessonBuild and connect the representations and methods in rate and speed.
- Measurement and shapesSuggested next · 6 core lessonsBuild and connect the representations and methods in measurement and shapes.
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Lessons in primary 5 mathematics. This course is still being developed; independent practice and assessment coverage is incomplete.
Learning goals
- Read and write numerical representations
- Multiply whole numbers
- Divide whole numbers
- Evaluate expressions with operation order and brackets
- Express a whole-number quotient as a fraction
- Express a general fraction as a decimal
- Add and subtract mixed-number amounts
- Multiply a proper fraction by a whole number
- Multiply an improper fraction by a whole number
- Multiply two proper fractions
- Multiply a proper and an improper fraction
- Multiply two improper fractions
- Multiply a mixed number by a whole number
- Multiply a decimal by 10, 100 or 1000
- Divide a decimal by 10, 100 or 1000
- Multiply a decimal by another multiple of ten
- Divide a decimal by another multiple of ten
- Express a decimal measurement in the smaller unit
- Express a measurement as a decimal in the larger unit
- Express a part as a percentage of its whole
- Write a percentage as a simplest fraction
- Write a fraction as a percentage
- Write a percentage as a decimal
- Write a decimal as a percentage
- Calculate a percentage part of a whole
- Calculate a discount and the sale price
- Calculate a stated percentage tax and the total price
- Calculate one year's simple interest and balance
- Use rate, speed, distance and time relationships
- Identify a triangle's base and perpendicular height
- Calculate the area of a triangle
- Calculate the area of a composite plane figure
- Distinguish area, perimeter and volume and their units
- Construct geometric figures from stated conditions
- Calculate the volume of a cube or cuboid
- Calculate the volume of liquid in a rectangular tank
- Relate cubic centimetres to millilitres and litres
- Apply the sum of angles on a straight line
- Apply the sum of angles around a point
- Deduce all unknown angles at two intersecting lines
- Apply the sum of parts of a right angle
- Use the guaranteed side and angle properties of an isosceles triangle
- Use the guaranteed side and angle properties of an equilateral triangle
- Use perpendicular sides and complementary angles of a right-angled triangle
- Deduce every missing angle from the equal sides of an isosceles triangle
- Deduce all three angles from an equilateral triangle
- Deduce missing angles in a right-angled triangle
- Apply the sum of the three interior triangle angles
- Connect triangle, rectangle and square facts to deduce angles in a drawn composite figure
- Use all guaranteed side and angle relations of a parallelogram
- Use all guaranteed side and angle relations of a rhombus
- Identify a trapezium's parallel pair and corresponding angle sums
- Deduce every missing angle in a parallelogram
- Deduce every missing angle in a rhombus
- Deduce missing angles on both nonparallel sides of a trapezium
- Connect parallelogram and connected shape facts to deduce angles using existing lines
- Connect rhombus and connected shape facts to deduce angles using existing lines
- Connect trapezium and connected shape facts to deduce angles using existing lines
Syllabus statements covered
- reading and writing numbers in numerals and in words
- multiplying and dividing by 10, 100, 1000 and their multiples without calculator
- order of operations without calculator
- use of brackets without calculator
- dividing a whole number by a whole number with quotient as a fraction
- expressing fractions as decimals
- adding and subtracting mixed numbers
- multiplying a proper/improper fraction and a whole number without calculator
- multiplying a proper fraction and a proper/ improper fractions without calculator
- multiplying two improper fractions
- multiplying a mixed number and a whole number
- multiplying and dividing decimals (up to 3 decimal places) by 10, 100, 1000 and their multiples without calculator
- converting a measurement from a smaller unit to a larger unit in decimal form, and vice versa • kilometres and metres • metres and centimetres • kilograms and grams • litres and millilitres
- expressing a part of a whole as a percentage
- use of %
- finding a percentage part of a whole
- finding discount, GST and annual interest
- rate as the amount of a quantity per unit of another quantity
- finding rate, total amount or number of units given the other two quantities
- concepts of base and height of a triangle
- area of triangle
- finding the area of composite figures made up of rectangles, squares and triangles
- building solids with unit cubes
- measuring volume in cubic units, cm³/m³, excluding conversion between cm³ and m³
- drawing cubes and cuboids on isometric grid
- volume of a cube/cuboid
- finding the volume of liquid in a rectangular tank
- relationship between ℓ (or ml) with cm³
- angles on a straight line
- angles at a point
- vertically opposite angles
- finding unknown angles
- properties of • isosceles triangle • equilateral triangle • right-angled triangle
- angle sum of a triangle
- finding unknown angles without additional construction of lines
- properties of • parallelogram • rhombus • trapezium
- finding unknown angles without additional construction of lines