Algorithms with Selection and Repetition

Overview

One class period. Students meet the three building blocks of algorithms: sequencing, selection, and repetition (2.1.A.1 to 2.1.A.3). They trace algorithms with a decision and with a loop, show them as numbered steps and as flowcharts with a decision diamond (2.1.A.4), and see that changing the order of the blocks changes the result (2.1.A.5).

Stay inside the topic boundary. Selection and repetition are taught as ideas in plain-language steps and flowcharts; the Java if statement is Topic 2.3 and loops are Topics 2.7 and 2.8. The only Java is two short sequencing examples, plus the Math.abs and indexOf methods that students already know from Topics 1.11 and 1.15.

Show slide 2, the morning routine. Students talk with a partner: which steps happen every day exactly once, and which can change? Take two or three answers. Look for “the umbrella step” (depends on rain) and “brushing” (depends on how long it takes). Do not name the building blocks yet.

1. Goals (slide 3).
2. Three building blocks (2.1.A.1, slide 5). Sequencing is steps done in order, each once. Selection is a decision that chooses the next step; another name is decision making. Repetition is repeating steps until a goal is reached; another name is looping, and the repeated steps are a loop.
3. Find them in the routine (slide 6). Go down the table: steps 1 and 4 are sequencing, step 2 is selection, step 3 is repetition. Stress that the whole list is still a sequence. Selection and repetition live inside the order.
4. A recipe that stirs three times (slide 7). Three separate “Stir” steps are still sequencing, and three is a guess. “Stir until there are no lumps” is repetition because the goal decides when to stop.

1. A decision chooses the next step (2.1.A.2, slide 9). Selection depends on a true or false decision; the question is the condition. Walk the flowchart with a rainy day and a sunny day: each takes one arrow out of the diamond.
2. Pause and try (slide 10). Students trace “if the score is at least 70, say pass; otherwise say try again” for 85, 70, and 64: pass, pass, try again. 70 is the case to discuss, because “at least” includes the boundary.

1. A loop repeats until its goal is reached (2.1.A.3, slide 12). Trace the jug table row by row: check the goal first, pour 3 if it is not met. Each time through is a pass. It takes 4 passes and the jug ends at 12 cups, not 10, because the check happens before each pass.
2. A goal that is never reached (slide 13). Starting at 0 and adding 2 until x is 7 jumps from 6 to 8 and never equals 7. This is an infinite loop. Give students 30 seconds to change one thing so the loop stops (change 7 to 8, or start x at 1, or add 1). Collect more than one fix.

1. Flowchart pieces (2.1.A.4, slide 15). Start and Stop, a step box, a decision diamond with a true arrow and a false arrow, and an arrow back for repetition.
2. The jug loop as a flowchart (slide 16). A loop is a decision plus an arrow back. The diamond asks about the goal before each pass, and the true arrow leaves the loop. Have students match each line of the written version to a shape.

1. Add, then halve (2.1.A.5, slide 18). Show BonusThenDouble and DoubleThenBonus. Students predict the two outputs (Points: 30 and Points: 25), then run or reveal them. Same two steps, different order, different result. The same is true when a step moves inside or outside a loop or before or after a decision.

int points = 10;
points += 5;
points *= 2;
System.out.println("Points: " + points);

int points = 10;
points *= 2;
points += 5;
System.out.println("Points: " + points);

2. Where does the decision go? (slide 19). Version A checks the water once, after the loop. Version B checks it inside the loop on every dish, so only version B can drain the sink more than once. Students answer with a partner, then share.

Hand out the Decide and Repeat puzzle worksheet. If time allows, students start question 1 (sort the steps) in class. Questions 3 to 10 are homework. Question 3 settles the Think First guess from question 2’s page (add the bonus, then double: 90). Question 6 fixes a loop that never stops.

Show slide 21. Partners finish the sentence starter: “Selection _ once and picks a path, but repetition _ until ___.” Then give the exit ticket (about five minutes). Question 1 checks the three building blocks (2.1.A.1 to 2.1.A.3), question 2 checks tracing a loop (2.1.A.3), and question 3 checks that order changes the result (2.1.A.5). Slide 20 (vocabulary) is for students to keep as a reference. Re-teach the weakest question at the start of Topic 2.2.