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Reasoning · Patterns
State the rule. Then test it.
Logic and coding lessons
Patterns, logic puzzles and step-by-step coding thinking from the Ontario math curriculum, with worked examples and complete answers.
Else If Chains: Many Choices, First Match Wins
Write and trace If, Else If and Else chains: check conditions from the top, stop at the first match, and put the conditions in the right order.
Repeating Patterns: Find the 20th or 100th Item
Find the core of a repeating pattern, use its length and the remainder to name the 20th or 100th item, count items and trace a short program.
Nested Loops: A Repeat Inside a Repeat
Trace loops inside loops, multiply to count how many times the inside steps run, print rows of stars and walk a robot around a grid with a nested repeat.
Order of Steps: Why Sequence Matters in a Program
Trace short programs step by step, see why changing the order of steps changes the answer, and fix a program by reordering or replacing one step.
Find the Bug: Trace, Spot the Error and Fix the Program
Practise debugging: trace a program step by step, compare it with what it should do, find off-by-one, wrong-start and wrong-test bugs, and choose the right fix.
Find the Rule: Number Patterns and Loops
Find the rule in a number pattern, predict later terms, tell add from multiply, trace a loop that builds a pattern and debug a program that goes wrong.
And, Or, Not: Combine Conditions in Programs
Combine conditions with and, or and not, trace which part decides the answer, count items in a loop with two tests and fix a program whose or should be and.
Sort a List: Pick the Smallest, Swap It Forward, Repeat
Put a list in order with a plan: find the smallest item, swap it into place, repeat. Learn the swap with temp, trace each round and debug sorting programs.
Search a List: Is It There, and Where?
Search a list one item at a time. Use a found flag, remember the position of a match, stop early when you find it, and fix search bugs.
Biggest So Far: Find the Largest Value in a List
Loop through a list and keep the biggest value seen so far. Trace a max variable, flip it to find the smallest, and fix four common bugs.
Counters and Totals: Put an If Inside a Loop
Loop through a list, test each item with an If, then count the matches or add them up. Trace counters and totals, and fix four common tally bugs.
Lists: Store Many Values and Loop Through Each One
Keep many values in one list, read an item by its position, then use For each to say, add up or count every item and fix common list bugs.
Functions with Inputs: One Function, Different Numbers
Trace functions that take inputs: swap in each call's number, predict what the robot does or says, keep two inputs in order and fix a wrong call.
Functions: Name a Group of Steps and Use It Again
Define a function, call it by name and give it an input. Count the commands it saves, trace robot paths and fix a bug once so it is fixed everywhere.
Repeat Until: Loops That Stop When a Condition Is True
Trace repeat-until loops step by step, count how many passes run, spot loops that never stop, and fix off-by-one bugs in counting programs.
If–Else: Programs That Make Decisions
Check comparisons such as >, < and ==, trace which branch of an if–else runs for each input, use an if inside a loop and fix a > versus >= boundary bug.
Track a Variable: Follow a Program Step by Step
Follow short programs one command at a time, record each new value of a variable in a trace table, predict what the program says, and fix a reset bug.
Logic Puzzles: Use Clues to Rule Things Out
Solve who-has-what puzzles with a grid of checks and crosses, put people in order from clues, and decide when a statement must be true and when you simply cannot tell.
Code a Robot Path: Turns, Loops and Finding the Bug
Give a grid robot exact instructions: move forward, turn left or right, repeat steps with a loop, and find the one wrong step in a broken program.
Shortest Path: Find the Fewest Moves on a Grid
Count moves on a grid, work out why a wall forces a detour, compare routes and use a number wave to find the shortest path from S to G.
Use a consistent rule rather than choosing the picture or number that feels different.
A rule you can check
For this exercise, the rule is “multiples of 6”. In 12, 18, 24, 31, 36, the outlier is 31 because the other four numbers divide exactly by 6.
A sequence is not a proof of a unique rule
Short sequences can fit more than one invented rule. Our practice names the intended rule or asks you to explain a simple consistent relationship. A plausible alternative should be discussed, not silently marked wrong.
Try a letter transformation
Move each letter one position forward in the alphabet: C becomes D, A becomes B, and T becomes U. The same rule changes CAT to DBU.
CCAT & Gifted Screening Guide
Read the DDSB process, nine reasoning skills, score language, nonverbal strategies and an eight-week practice framework.
Open the CCAT guide →Try it, then check
Public practice is not saved. Answers and explanations remain available without an account.