Singapore

6.1 Fractions

• 6.1.1 Four operations

  • 6.1.1.1 Include division of a whole number/proper fraction by a proper fraction without using calculators.

    • Divide whole numbers by unit fractions using models (P6-J.1)
    • Reciprocals (P6-J.2)
    • Divide whole numbers and unit fractions (P6-J.3)
    • Divide whole numbers by fractions (P6-J.4)
    • Divide fractions (P6-J.5)

6.2 Percentage

• 6.2.1 Percentage

  • 6.2.1.1 Include:

    • 6.2.1.1.a finding the whole given a part and the percentage,

      • Sale prices: find the original price (S1-M.7)

    • 6.2.1.1.b finding percentage increase/decrease,

      • Find the percent: discount and mark-up (S1-M.6)

6.3 Ratio

• 6.3.1 Ratio

  • 6.3.1.1 Include:

    • 6.3.1.1.a expressing one quantity as a fraction of another, given their ratio, and vice versa,

    • 6.3.1.1.b finding how many times one quantity is as large as another, given their ratio, and vice versa,

    • 6.3.1.1.c expressing one quantity as a fraction of another given the two quantities,

    • 6.3.1.1.d finding the whole/ one part when a whole is divided into parts in a given ratio,

    • 6.3.1.1.e solving word problems involving 2 pairs of ratios.

      • Compare ratios: word problems (P6-M.7)

6.4 Speed

• 6.4.1 Distance, time and speed

  • 6.4.1.1 Include:

    • 6.4.1.1.a concepts of speed and average speed,

    • 6.4.1.1.b relationship between distance, time and speed

      • 6.4.1.1.b.1 Distance = Speed × Time,

      • 6.4.1.1.b.2 Speed = Distance ÷ Time,

      • 6.4.1.1.b.3 Time = Distance ÷ Speed,

    • 6.4.1.1.c calculation of speed, distance or time given the other two quantities,

    • 6.4.1.1.d writing speed in different units such as km/h, m/min, m/s and cm/s,

    • 6.4.1.1.e solving up to 3-step word problems involving speed and average speed.

6.5 Measurement

• 6.5.1 Area and circumference of circle

  • 6.5.1.1 Include:

    • 6.5.1.1.a use of formulae to calculate the area and circumference of a circle,

      • Circles: calculate area, circumference, radius and diameter (P6-V.13)

    • 6.5.1.1.b finding the area and perimeter of

      • 6.5.1.1.b.1 semicircle (half circle)

        • Semicircles: calculate area, perimeter, radius and diameter (P6-V.15)

      • 6.5.1.1.b.2 quarter circle

        • Quarter circles: calculate area, perimeter and radius (P6-V.16)

    • 6.5.1.1.c solving word problems involving area and perimeter.

      • Circles: word problems (P6-V.14)

• 6.5.2 Area and perimeter of composite figure

  • 6.5.2.1 Include finding the area and perimeter of a figure made up of some of the following shapes: square, rectangle, triangle, semicircle and quarter circle.

    • Area of composite figures (P6-V.5)
    • Area between two rectangles (P6-V.6)
    • Area between two triangles (P6-V.7)
    • Area between two circles (P6-V.8)
    • Area of composite figures with triangles, semicircles and quarter circles (P6-V.17)

• 6.5.3 Volume of cube and cuboid

  • 6.5.3.1 Include:

    • 6.5.3.1.a finding one dimension of a cuboid given its volume and the other dimensions,

      • Volume and surface area of cubes and rectangular prisms (P6-V.19)

    • 6.5.3.1.b finding the length of one edge of a cube given its volume,

      • Volume and surface area of cubes and rectangular prisms (P6-V.19)

    • 6.5.3.1.c finding the height of a cuboid given its volume and base area,

    • 6.5.3.1.d finding the area of a face of a cuboid given its volume and one dimension,

    • 6.5.3.1.e use of the symbols "square root" and "cube root",

    • 6.5.3.1.f solving word problems involving volume of a cube/ cuboid.

6.6 Geometry

• 6.6.1 Geometrical figures

  • 6.6.1.1 Include finding unknown angles in geometrical figures involving square, rectangle, parallelogram, rhombus, trapezium and triangle.

    • Find missing angles in triangles and quadrilaterals (P6-T.8)

• 6.6.2 Nets

  • 6.6.2.1 Include:

    • 6.6.2.1.a 2-D representation of cube, cuboid, cone, cylinder, prism and pyramid,

      • Nets of three-dimensional figures (P6-U.3)
      • Front, side and top view (P6-U.4)

    • 6.6.2.1.b identifying nets of the following solids

      • 6.6.2.1.b.1 cube,

        • Nets of three-dimensional figures (P6-U.3)

      • 6.6.2.1.b.2 cuboid,

        • Nets of three-dimensional figures (P6-U.3)

      • 6.6.2.1.b.3 prism,

        • Nets of three-dimensional figures (P6-U.3)

      • 6.6.2.1.b.4 pyramid,

        • Nets of three-dimensional figures (P6-U.3)

    • 6.6.2.1.c identifying the solid which can be formed by a given net,

      • Nets of three-dimensional figures (P6-U.3)

    • 6.6.2.1.d making 3-D solids from given nets.

6.7 Data analysis

• 6.7.1 Pie charts

  • 6.7.1.1 Include:

    • 6.7.1.1.a reading and interpreting pie charts,

      • Pie charts (P5-R.17)
      • Pie charts with fractions (P6-W.14)

    • 6.7.1.1.b solving 1-step problems using information presented in pie charts.

      • Pie charts (P5-R.17)
      • Pie charts with fractions (P6-W.14)

6.8 Algebra

• 6.8.1 Algebraic expressions in one variable

  • 6.8.1.1 Include:

    • 6.8.1.1.a representation of an unknown number using a letter,

      • Write variable expressions (P6-S.1)
      • Write variable expressions: word problems (P6-S.2)

    • 6.8.1.1.b simple algebraic expressions such as

      • 6.8.1.1.b.1 y ± 2, 6 ± y

        • Write variable expressions: word problems (P6-S.2)

      • 6.8.1.1.b.2 y + y

        • Write variable expressions: word problems (P6-S.2)

      • 6.8.1.1.b.3 3y

        • Write variable expressions: word problems (P6-S.2)

      • 6.8.1.1.b.4 y/2

        • Write variable expressions: word problems (P6-S.2)

      • 6.8.1.1.b.5 3±y/5

    • 6.8.1.1.c interpreting

      • 6.8.1.1.c.1 3y as y + y + y or 3 × y

      • 6.8.1.1.c.2 y/2 as y ÷ 2 or 1/2 × y

      • 6.8.1.1.c.3 3±y/5 as (3 ± y) ÷ 5 or 1/5 × (3 ± y)

    • 6.8.1.1.d simplification of algebraic expressions,

      • Identify equivalent expressions (P6-S.6)

    • 6.8.1.1.e evaluation of simple algebraic expressions by substitution,

      • Evaluate variable expressions with whole numbers (P6-S.3)
      • Evaluate variable expressions with decimals (P6-S.4)

    • 6.8.1.1.f solving word problems involving algebraic expressions.