Understanding Cognitive Levels in ICAS :

Cognitive Level Description Example in ICAS Context
Recall / Remembering Recall facts, terms, units, definitions without manipulation Know that 1 kilometre = 1000 metres
Understanding Explain or interpret facts; classify, describe, or summarize Explain the meaning of a pie chart
Applying Use information in new or practical situations Calculate the area of a rectangle given its dimensions
(Pattern Recognition) Identify regularities, trends, or rules among data or sequences Predict the next number in a sequence: 2, 4, 8, ?
Reasoning / Analyzing Break down problems, infer relationships, or make logical deductions Determine the rule of a pattern: 3, 5, 8, 12, 17, ?
Creating / Modeling Combine knowledge to generate new ideas or models Create an equation to model a real-world relationship
Evaluating Make judgments based on criteria, often comparing alternatives Compare which measurement estimate is most reasonable

ICAS Mathematics – Cognitive Abilities Focus by Module :

Cognitive Ability Number & Arithmetic Algebra & Patterns Measures & Units Space & Geometry Chance & Data
Recall ●● ● ●●● ● ●
Understanding ●● ●● ●●● ●● ●●
Applying ●●● ● ●●● ●●● ●●
Pattern Recognition ●● ●●● ● ● ●●
Reasoning ●●● ●●● ● ●●● ●●
Creating / Modeling ● ●●● ● ●● ●
Evaluating ● ●● ● ● ●●

1 Number & Arithmetic – ICAS Year 6 Mathematics

Knowledge Structure Map :

[2] Place Value ─────┐
                     ├─► [1] Compare & Order
                     └─► Core Operations ( [3] + [4] )
                             │
        ┌────────────────────┼──────────────────────────┐
        ▼                    ▼                          ▼
     [5] Fractions       [7] Decimals              [8] Percentages
        │                    │                          │
        └──────────► Interconversion ◄──────────────────┘
                         │
         ┌───────────────┼──────────────┐
         ▼               ▼              ▼
     [9] Estimation   [10] Patterns   [11] Word Problems (Application)
No. Content Description Difficulty (Typical High-Frequency Items) Sample (w/ Difficulty Level)
1 Compare and order whole numbers Compare multi-digit numbers and place them in ascending/descending order Easy Which number is greatest: 4,320; 4,203; 4,230? (Easy)
2 Place value reasoning Reason about digits in large numbers (e.g. value of a digit, digit swap) Medium In 82,409, which digit is in the thousands place? (Medium)
3 Addition and subtraction (multi-step) Perform multi-digit operations, often in word problems Medium Jake had $245 and spent $89. How much is left? (Medium)
4 Multiplication and division Use times tables, long multiplication or division in real-world contexts Medium–Hard What is 48 × 36? (Hard)
5 Fraction operations Perform addition, subtraction or equivalence of fractions Medium What is 3/4 − 1/2? (Medium)
6 Fraction of a quantity Apply fractions to real numbers Easy What is 2/5 of 35? (Easy)
7 Decimal operations Compare or compute with decimals, including tenths/hundredths Medium What is 3.6 + 1.45? (Medium)
8 Percentages Calculate percentages of quantities Medium–Hard What is 15% of 80? (Medium)
9 Estimation and rounding Round to nearest 10, 100 or estimate results Easy Estimate the sum: 498 + 312 (Easy)
10 Number patterns Identify rules in arithmetic sequences Medium What comes next: 3, 6, 12, 24, ? (Medium)
11 Complex multi-step word problems Solve real-life problems using several steps and operations Hard Mia buys 3 packs of pens at $4.50 each and 2 notebooks at $6.25 each. How much does she spend? (Hard)

2 Algebra & Patterns – ICAS Year 6 Mathematics

Knowledge Structure Map :

[1] Number Patterns ───────┐
                           ├─► [2] Visual Patterns
                           └─► [3] Identify the Rule
                                   │
         ┌─────────────────────────┴────────────────────────┐
         ▼                                                  ▼
   [6] Input-Output Tables                            [7] Function Rules
         │                                                  │
         └────► [4] Symbols for Unknowns ◄─────┬────────────┘
                                               │
                               ┌───────────────┴───────────────┐
                               ▼                               ▼
                         [5] Solve Equations             [8] Substitution
No. Content Description Difficulty (Typical High-Frequency Items) Sample (w/ Difficulty Level)
1 Identify and continue number patterns Recognise and extend number sequences involving arithmetic/geometric rules Easy–Medium What comes next: 5, 10, 20, 40, ? (Easy)
2 Identify and continue visual patterns Extend repeating or growing patterns in shapes or grids Medium What is the next shape in the pattern? △◯△◯△◯? (Medium)
3 Determine the rule of a pattern Describe or infer the rule governing a number or shape pattern Medium–Hard What is the rule: 2, 5, 10, 17, 26, ? (Hard)
4 Use a symbol to represent unknowns Use letters or symbols to represent unknown numbers in expressions Medium What number does x represent if x + 3 = 9? (Medium)
5 Solve simple equations Find the value of a variable that satisfies a given equation Medium–Hard Solve: 3x = 18 (Medium)
6 Input-output tables and relationships Understand number machines or input-output rules Medium Input: 2 → Output: 7, Input: 3 → Output: 9. What’s the rule? (Medium)
7 Create or complete function rules Identify or construct the rule behind a pattern or function table Hard The rule is: output = 2x + 3. What is the output when x = 5? (Hard)
8 Substitute into expressions Substitute known values into simple algebraic expressions Medium If y = 4, what is the value of 2y + 3? (Medium)

Logical Relationships Between Algebra & Patterns Knowledge Points :

  1. Entry level : Start by recognizing number and visual patterns ([1], [2]), to build foundational “pattern thinking.”
  2. Rule Generalization : Transition from observing to deducing the rule ([3]), learning to describe it using words or expressions.
  3. Function Modeling : Use tables or functions to represent input-output relationships ([6], [7]), which leads to using variables.
  4. Algebraic Expression and Solving : Introduce variables and letters ([4]), then gradually move to solving equations ([5]), and substitution ([8]).

3 Measures & Units – ICAS Year 6 Mathematics

Knowledge Structure Map :

[1] Time ───────┐
                │
[6] Temperature │
                └─► [2] Units of Measure (length, mass, capacity)
                              │
         ┌────────────────────┼────────────────────┐
         ▼                    ▼                    ▼
   [3] Unit Conversion   [4] Estimation      [5] Money Calculations
                              │                    │
                              └──────────► [7] Real-World Problems
No. Content Description Difficulty (Typical High-Frequency Items) Sample (w/ Difficulty Level)
1 Read and interpret time Read analog and digital clocks; calculate time intervals Easy–Medium How many minutes are there between 2:15 pm and 3:40 pm? (Medium)
2 Work with units of length, mass, capacity Measure or compare using standard metric units Medium Which is heavier: 3.2 kg or 3,200 g? (Medium)
3 Convert between units Convert between mm–cm–m, g–kg, mL–L, minutes–hours, etc. Medium–Hard How many millilitres are there in 3.5 litres? (Medium)
4 Estimate and compare quantities Make reasonable estimates and compare magnitudes Medium Which is the best estimate for the weight of a schoolbag: 2 kg, 20 kg or 200 kg? (Medium)
5 Solve problems involving money Perform calculations using dollars and cents Medium If a book costs $12.45 and you pay with $20, how much change do you get? (Medium)
6 Understand temperature Interpret or compare temperature readings Easy Which temperature is colder: –5°C or 3°C? (Easy)
7 Solve real-world measurement problems Apply measurement in practical contexts Hard A pool is 25 m long. How far does Jack swim in 6 laps? (Hard)

4 Space & Geometry – ICAS Year 6 Mathematics

Knowledge Structure Map :

[1] 2D Shapes ───────────┐
                         ├─► [3] Symmetry
                         └─► [7] Perimeter & Area
                                     ▲
                                     │
[2] 3D Objects ─────┐        [8] Visualise & Transform Shapes
                    └─► [6] Transformations (rotate/reflect/translate)
                          │
                          └─► [4] Angles & [5] Position & Direction
No. Content Description Difficulty (Typical High-Frequency Items) Sample (w/ Difficulty Level)
1 Recognise and classify 2D shapes Identify triangles, quadrilaterals, and polygons based on their properties Easy–Medium Which of these is a quadrilateral with only one pair of parallel sides? (Medium)
2 Recognise and describe 3D objects Identify cubes, prisms, pyramids, and their faces/edges/vertices Medium How many edges does a rectangular prism have? (Medium)
3 Symmetry (line and rotational) Identify lines of symmetry or rotational symmetry in shapes or patterns Medium How many lines of symmetry does a regular hexagon have? (Medium)
4 Angle types and comparisons Identify right, acute, obtuse, and straight angles; compare angle sizes Medium Which angle is obtuse: 30°, 45°, 90°, or 120°? (Medium)
5 Position and direction Interpret turns, compass directions, coordinates, and maps Medium Facing North, turn 270° clockwise. Which direction now? (Medium)
6 Geometric transformations Recognise translation, reflection, rotation Medium–Hard Which figure is the result of rotating shape A 90° clockwise? (Hard)
7 Perimeter and area of 2D shapes Calculate perimeter and area of rectangles, triangles, compound shapes Medium–Hard What is the area of a rectangle 8 cm by 6 cm? (Medium)
8 Visualise and manipulate shapes Mentally flip, rotate, or decompose shapes Hard Which net will form a cube? (Hard)

5 Chance & Data – ICAS Year 6 Mathematics

Knowledge Structure Map :

[1] Read Data Displays ─────┐
                            └─► [2] Compare Data
                                      │
                                      ├─► [3] Calculate Totals & Averages
                                      │
                                      └─► [5] Compare Probabilities
                                                ▲
                                       [4] Chance Vocabulary
                                                │
                                          [6] Probability Reasoning
No. Content Description Difficulty (Typical High-Frequency Items) Sample (w/ Difficulty Level)
1 Read and interpret data displays Read data from tables, column graphs, picture graphs, pie charts, etc. Easy–Medium How many students chose blue as their favourite colour? (Easy)
2 Compare and interpret data Compare values across different categories in a graph or table Medium Which sport was most popular among Year 6 students? (Medium)
3 Calculate totals, averages, and differences Add, subtract or average values from datasets Medium–Hard What is the average score of 5 students with scores: 6, 8, 7, 9, 10? (Medium)
4 Understand chance vocabulary Interpret likelihood using terms like certain, likely, unlikely, impossible Easy Which event is “impossible”: Getting heads on a coin, rolling a 7 on a 6-sided die, etc.? (Easy)
5 Compare probability of events Rank or compare events based on their chance of occurring Medium Which is more likely: Drawing a red ball from Bag A or Bag B? (Medium)
6 Simple probability reasoning Use fractions or ratios to express chance in simple experiments Medium–Hard A bag has 2 red and 3 green marbles. What is the chance of picking a red one? (Hard)

Reference