Trace a Conditional Algorithm

Trace an if/else rule and a repeated action using small supplied inputs.

Mr. S Teaches · Original starter mini-lesson · MS7-TECH-01 · Elective / rotation; availability varies

Learning objective

Predict the outputs of a conditional algorithm for four inputs and explain the boundary case using precise terms.

Before you begin

Follow numbered instructions and identify an input and output.

Gather your materials

Paper
Pencil
Four input cards labeled 0, 1, 2 and 3

Language to know

Condition: A statement a program tests as true or false.
Branch: A path chosen when a condition is tested.
Loop: Instructions repeated according to a rule.
Output: A result produced by an algorithm.

Understand the concept

An algorithm can choose a branch. This fictional badge algorithm takes a whole-number input n from 0 to 3. If n is at least 2, set color to blue; otherwise set color to green. Then repeat n times: draw one dot. Output the color and the row of dots. The color decision and repetition answer different questions. “At least 2” includes 2. When n = 0, repeating zero times draws no dots; it does not mean repeat forever. Trace each instruction in order rather than guessing from a pattern.

Teach it step by step

Copy the input limit and algorithm. Underline “at least 2” and say which values make it true.
Trace n = 2: choose the branch first, then count two repetitions and record the output.
Trace n = 0, 1 and 3 with input, condition result, color and dot count as column headings.
Write a technical explanation using condition, branch, loop and output accurately. Explain why n = 2 is a useful boundary test.

Make the thinking visible

Worked example or model response

For n = 2, the condition 2 ≥ 2 is true, so the blue branch is chosen; the loop draws two dots. For n = 1, it is false, so the output is green with one dot. Choosing green for n = 2 would reveal a boundary error.

Guided practice

Together test a draft description that says “if n is greater than 2.” Compare its output at n = 2 with the original algorithm and name the changed condition.

Independent practice

Complete the four-row trace table for inputs 0–3 and write four sentences explaining the decisions and repeated action. Add a test for n = 4 and explain why the input specification matters before predicting a supported output.

Quick assessment

Is “repeat n times” the same instruction as “repeat until n changes”? Explain with n = 0.

Answer key & assessment criteria

Answers and teaching guidance

Guided: With greater than 2, n = 2 takes the green branch rather than blue. The inequality changed from ≥ to >.
Independent: n=0 → green, no dots; n=1 → green, one dot; n=2 → blue, two dots; n=3 → blue, three dots. Input 4 is outside the stated supported range, so the specification must be extended before treating its result as a required behavior.
Quick check: No. A count-controlled loop with n=0 runs zero times. “Until n changes” depends on a stopping condition and could fail to stop if no instruction changes n.

Look for: Look for accurate tracing and explanation of boundary conditions. No programming syntax or online account is required.

Make it work for your learner

More support

Use colored branch cards with text labels as well as color, and move one counter for each loop repetition.

Extension challenge

Change the color rule to “n is even.” Specify what happens at zero, trace all four inputs again and compare branch decisions.

Selected contributions · Official sources

Standards connections

Subject-content alignment not yet verified

Supporting Common Core connection

W.7.2.d

Common Core · Grade 7

Use computing vocabulary precisely to explain algorithm behavior.

Read the official standard ↗

The explanation practices domain language; it does not establish verified computer-science content standards or full programming competence.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.

A curriculum map. A place to start.

These 96 original mini-lessons sample selected skills across grades 6–8. This is a starter curriculum map and lesson collection, not a complete year of daily instruction, every standard, or an accredited course.

Contributes to Common Core standard identifies a selected math or English skill. Grade-specific codes retain their actual grade. Science and social studies use a Supporting Common Core literacy connection only for the reading or writing activity described; this does not establish subject-content alignment.

Contributes to NGSS performance expectation describes a partial science connection to a grades 6–8 band expectation. A paper model or short data task does not fulfill the entire performance expectation. Each mapping explains its limits. Science and social studies grade placements are suggested; course sequences vary.

Visual arts, music and computing may be electives or rotations. Course availability and health/PE requirements vary. Where no verified subject-content mapping is recorded, the lesson states Subject-content alignment not yet verified. Any supporting Common Core activity is identified separately.

Use North Carolina’s Standard Course of Study ↗ for local planning. No NC alignment is claimed without a verified crosswalk. Standards are briefly paraphrased here; use each official source for its full wording.