Teachers are free to plan their own lessons, but there are some well-established practices to build on. The following proposals are based on these practices.
In GRADE 5 MATHS, the NUMBERS area deals with "big numbers" and consolidates fractions and decimal numbers. Negative numbers and powers are introduced. Divisibility rules and prime numbers can be discussed. Work on mental calculation, estimation and looking for number patterns is strengthened. Ancient ways of writing numbers can be explored, to build a historical awareness of how mathematical ideas have developed over time and across cultures. Work on algebraic symbols resumes, to represent relations and generalise patterns.
In the SPACE AND FIGURES area, pupils work on the key elements of plane figures (vertices, angles, sides, heights, diagonals, lines of symmetry) and of solids (vertices, faces, edges), also with dynamic geometry software. They calculate the perimeter and area of polygons and explore the circle and its circumference. They work on the Cartesian plane and with geometric drawing tools.
In the LOGIC area, pupils work on strategies in two-player games and on explaining them, learning to justify their choices explicitly. Work on quantifiers, connectives and argumentation is strengthened. Pupils write programs that contain loops or make the program take decisions based on a condition ("if... then..."). They assess whether the program fits the task, fixing any errors. Work on programs and on game strategies can go hand in hand.
In the RELATIONS, DATA AND PREDICTIONS area, work on probability continues, up to quantifying the probability of simple events in experiments with bags of coloured balls, coins or dice. The main units of measurement are used and converted, also introducing measures of volume and discussing how they relate to measures of capacity. Charts are interpreted and constructed. Data are analysed, finding the median, mode and arithmetic mean when they suit the type of data and help to understand and communicate a phenomenon. Percentages and fractions are used to describe everyday situations and to represent statistical data.
PROBLEMS are tackled, with attention to their meaning and to explaining and comparing solution strategies. As well as problem solving, pupils work on problem posing.