Number Algorithms
Following an algorithm
An algorithm is a precise sequence of steps followed exactly to produce a result. In number work it is a rule like "start at 3, add 2 each step", which generates 3, 5, 7, 9, 11. Following an algorithm means carrying out each step in order, without skipping or guessing, and seeing what set of numbers it produces. This idea — a fixed procedure that always gives the same result — is the foundation of the unit and a first taste of computational thinking, where exact, repeatable steps turn a starting number into a whole sequence.
An adding rule
The simplest number algorithms use addition: start somewhere and add a fixed amount each step. "Start 2, add 3" gives 2, 5, 8, 11, 14; "start 5, add 5" gives 5, 10, 15, 20, 25. Each step does the same thing, so the sequence climbs by equal jumps. Additive algorithms, named in this descriptor, produce the steady counting patterns a child already knows from skip counting, now seen as the output of a rule. Creating an adding rule and running it is the most direct way to generate a set of numbers with an algorithm.
A multiplying rule
Algorithms can use multiplication instead: start somewhere and multiply by a fixed number each step. "Start 1, multiply by 2" gives 1, 2, 4, 8, 16; "start 1, multiply by 3" gives 1, 3, 9, 27, 81. Because each step multiplies, the numbers grow far faster than an adding rule, by equal-sized factors rather than equal jumps. Multiplicative algorithms are the other kind named in this descriptor, and contrasting them with adding rules shows how the choice of operation shapes the whole sequence: addition builds steadily, multiplication accelerates.
A decision in the steps
Algorithms become more powerful when a step includes a decision: a choice that depends on the number. A rule like "if the number is even, halve it; if it is odd, add 1" branches differently for 6 (even, halve to 3) than for 5 (odd, add 1 to 6). The algorithm checks a condition and picks the matching step. Decisions, named directly in this descriptor, let a single algorithm respond to what it meets, and they are the heart of how real computer programs work — following steps but choosing among them based on the data.
Spotting the pattern
The numbers an algorithm generates form a pattern, and the final skill is to identify and describe it. Given 2, 4, 6, 8 a child should see "add 2 each time"; given 1, 2, 4, 8, "double each time". Describing the emerging pattern, named in this descriptor, means putting the rule into words by comparing each number to the one before. This closes the loop: an algorithm generates numbers from a rule, and reading the pattern recovers the rule from the numbers. Recognising and describing these patterns is what makes the sequences meaningful rather than just lists.
Algorithms and their patterns
Pulling the unit together, an algorithm is a sequence of steps — sometimes with a decision — that uses addition or multiplication to generate a set of numbers, and every such set has a pattern that can be described. A table makes the link plain: "start 3, add 2" gives 3, 5, 7, 9; "start 1, double" gives 1, 2, 4, 8. Adding rules step up evenly, multiplying rules grow by factors, and decisions let steps branch. With following steps, adding and multiplying rules, decisions, and pattern-spotting, a child can follow and create number algorithms and describe the patterns they produce — the final strand of Year 4 number and a foundation for the computational thinking ahead.