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Curriculum Planning Guidelines – Progression Points – Familiarisation tools
Mathematics – Structure (Level 4)
Students find examples of the three possible relationships between two sets explaining verbally or illustrating
with Venn diagrams including disjoint such as odd and even numbers, intersecting (overlapping) such as
multiples of 4 and 6, or subset such as the set of squares is a subset of the set of rectangles. They give
examples to illustrate a given condition such as draw triangles with at least two equal sides.
Students identify variables in everyday life, such as temperature, and describe how it changes during the day.
Students explain that addition and subtraction are inverse operations. They create and solve number sentences
using trial and error or known facts using more than one operation, such as ∆ x 4 + 6 = 22. They recognise the
distributive property of multiplication, and use it for calculation short cuts, such as 4 x 99 = 4 x 100 – 4 x 1 =
400 – 4 = 396.
Students correctly use the words none, some or all to describe relationships, illustrating these with Venn
diagrams and two-way tables, such as explaining why all squares are rectangles, and some rectangles are
squares. They give examples to illustrate given conditions, including drawing a variety of quadrilaterals with
at least one right angle and line symmetry.
Students describe situations in which one variable depends on another, such as height of a child depends on
age. They construct number patterns by following a recursion rule, such as odd numbers start at 1 and add 2
each time and describe the result.
Students create and solve number sentences using trial and error or known facts, using more than one
operation and brackets and describe their meaning, such as (∆ – 4) x 6 = 30. They use the distributive
property of division for performing division mentally or in writing, such as 68 ÷ 4 = 40 ÷ 4 + 28 ÷ 4 = 10 + 7
= 17.
Students illustrate a given overlapping set relationship with Venn diagrams and correctly use the words none,
some or all to describe relationships such as they draw the set of rhombuses and the set of rectangles showing
the set of squares as the intersection or the overlap.
Students construct number patterns by using a formula for the value based on the number’s position in the
pattern such as finding the fifth term, multiply 5 by 100 and add 1 and describe the result.
Students explain that division undoes the operation of multiplication, and vice versa, so multiplication and
division are inverse operations. They recognise the logical impossibility of dividing by zero. They create and
solve number sentences using trial and error or known facts using more than one operation, including
division, such as (10 – ∆ ) ÷ 4 + 6 = 8) and relate this to a real world situation such.
They use the distributive property of multiplication, such as 24 x 19 = 24 x (10 + 9) = 24 x 10 + 24 x 9 = 240
+ 216 = 456.
At Level 4 students form and specify sets of numbers, shapes and objects according to given criteria
and conditions (for example, 6, 12, 18, 24 are the even numbers less than 30 that are also multiples of
three). They use venn diagrams and karnaugh maps to test the validity of statements using the words
none, some or all (for example, test the statement ‘all the multiples of 3, less than 30, are even
numbers’).
Students construct and use rules for sequences based on the previous term, recursion (for example, the
next term is three times the last term plus two), and by formula (for example, a term is three times its
position in the sequence plus two).
Students establish equivalence relationships between mathematical expressions using properties such
as the distributive property for multiplication over addition (for example, 3 × 26 = 3 × (20 + 6)).
Students identify relationships between variables and describe them with language and words (for
example, how hunger varies with time of the day).
Students recognise that addition and subtraction, and multiplication and division are inverse
operations. They use words and symbols to form simple equations. They solve equations by trial and
error.
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