• N: the set of natural numbers, N = {1,2,3,4…} • Z: the set of integers, including 0 • Q: the set of rational numbers
Number: they develop a unified understanding of number, recognising fractions, decimals (that have a finite or a repeating decimal representation), and percentages as different representations of rational numbers.
Addition, subtraction, multiplication, and division and extend their whole number understanding to rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division.
Explaining and interpreting the rules for addition, subtraction, multiplication and division with negative numbers by applying the properties of arithmetic, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero)
Representing problems set in context, using diagrams to solve the problems so they can appreciate how the mathematical concepts are related to real life.
Solve problems involving fractional amounts set in context.
I should be able to:
Foundation Level
– revisit the operations of addition, multiplication, subtraction and division in the following domains: • N of natural numbers • Z of integers • Q of rational numbers and use the number line to represent the order of these numbers
– investigate models such as decomposition, skip counting, arranging items in arrays and accumulating groups of equal size to make sense of the operations of addition, subtraction, multiplication and division, in N where the answer is in N including their inverse operations
– investigate the properties of arithmetic: commutative, associative and distributive laws and the relationships between them
– appreciate the order of operations, including the use of brackets
– investigate models, such as the number line, to illustrate the operations of addition, subtraction, multiplication and division in Z
– generalise and articulate observations of arithmetic operations
– investigate models to help think about the operations of addition, subtraction, multiplication and division of rational numbers
– consolidate the idea that equality is a relationship in which two mathematical expressions hold the same value
– analyse solution strategies to problems
– calculate percentages
– use the equivalence of fractions, decimals and percentages to compare proportions
– consolidate their understanding and their learning of factors, multiples and prime numbers in N and the relationship between ratio and proportion
– check a result by considering whether it is of the right order of magnitude and by working the problem backwards; round off a result
– make and justify estimates and approximations of calculations
– present numerical answers to the degree of accuracy specified
– express non-zero positive rational numbers in the form a x10n, where n ∈ Z and 1 ≤ a < 10