Decomposing a problem into sub-problems

Name:

Date:

Class:

Quick Questions

Shade in the A or B circle for each question.

1. Which best describes decomposition?

A Splitting a big problem into smaller sub-problems

B Making a problem bigger so it is harder to solve

2. A class wants an app to track canteen orders. Which is a sensible first step?

A Break it into sub-problems like taking orders, working out the total and showing the receipt

B Try to solve the whole app in one go without any plan

3. In a quiz app, which sub-problem is the INPUT?

A The student types in their answer

B The app shows 'Correct!' on the screen

4. In a quiz app, which sub-problem is the PROCESS?

A The student taps the answer button

B Checking if the answer matches the right one

5. In a step counter app, which sub-problem is the OUTPUT?

A Counting each step from the sensor

B Displaying the total steps on the screen

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1decomposition		AShowing the score is an output sub-problem, not an input. Input is getting the player's answer.
2input, process, output		BThree kinds of sub-problems: getting data in, working with it, and showing the result
3Sub-problems that are independent can be solved separately by different people		CThis does not split the problem into smaller parts. It should be split into sub-problems like input (answers), process (check score) and output (show result).
4After solving each sub-problem, combine the solutions to solve the whole problem		DSub-problem A: design the quiz questions Sub-problem B: design the score screen
5Decompose a quiz app: 1. Make the whole app at once		ESplitting a big problem into smaller sub-problems that can each be solved on their own
6Sub-problems: Input = the score is shown on screen		FCombine: menu + order form + receipt = canteen ordering app

Definitions

decomposition

Fill in the Blanks

Complete each line of code by filling in the missing parts.

Problem: Make a quiz score app Sub-problem 1: _____ the answers Sub-problem 2: Process the score

Sub-problem 1: Input the answers Sub-problem 2: _______ the score Sub-problem 3: Output the result

Input: type in the quiz answers Process: add up the correct answers ______: show the final score

Problem: Plan a class party _________ into: food, music, invites Solve each part on its own

Sub-problem A: solved on its own Sub-problem B: solved on its own solution = _______(A, B)

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A COMBINE Quiz App

B INPUT: read the answer

C PROCESS: check the answer

D OUTPUT: show the score

Question 2

A DECOMPOSE Weather App

B INPUT: get the city name

C PROCESS: find the forecast

D OUTPUT: get the city name

E END

Question 3

A DECOMPOSE Canteen Orders

B PROCESS: read the order

C PROCESS: add up the cost

D OUTPUT: print the receipt

Question 4

A SUB A: design the board

B SUB B: write the rules

C A must wait for B to finish

D Combine A and B at the end

Question 5

A SUB A: count the votes

B SUB B: make the chart

C COMBINE A and B before solving

D Result: one working program

Answer Key

Decomposing a problem into sub-problems

Section A: Quick Questions

A — Splitting a big problem into smaller sub-problems

A — Break it into sub-problems like taking orders, working out the total and showing the receipt

A — The student types in their answer

B — Checking if the answer matches the right one

B — Displaying the total steps on the screen

Section B: Match the Pairs

decomposition → Splitting a big problem into smaller sub-problems that can each be solved on their own

input, process, output → Three kinds of sub-problems: getting data in, working with it, and showing the result

Sub-problems that are independent can be solved separately by different people → Sub-problem A: design the quiz questions Sub-problem B: design the score screen

After solving each sub-problem, combine the solutions to solve the whole problem → Combine: menu + order form + receipt = canteen ordering app

Decompose a quiz app: 1. Make the whole app at once → This does not split the problem into smaller parts. It should be split into sub-problems like input (answers), process (check score) and output (show result).

Sub-problems: Input = the score is shown on screen → Showing the score is an output sub-problem, not an input. Input is getting the player's answer.

Section C: Definitions

decomposition — Splitting a big problem into smaller sub-problems, such as input, process and output. Each part can be solved on its own, then the solutions are combined.

Section D: Fill in the Blanks

Problem: Make a quiz score app
Sub-problem 1: Input the answers
Sub-problem 2: Process the score

Sub-problem 1: Input the answers
Sub-problem 2: Process the score
Sub-problem 3: Output the result

Input: type in the quiz answers
Process: add up the correct answers
Output: show the final score

Problem: Plan a class party
Decompose into: food, music, invites
Solve each part on its own

Sub-problem A: solved on its own
Sub-problem B: solved on its own
solution = combine(A, B)

Section E: Spot the Error

A — The first step is to split the big problem into smaller parts, so the line should start with DECOMPOSE. COMBINE is what you do later, once the parts are solved.

D — Getting the city name is an input sub-problem, not an output. The output sub-problem should show the weather to the user.

B — Reading the order is an input sub-problem. The process sub-problem should do the work on the data, such as adding up the cost.

C — Independent sub-problems can each be solved on their own. A should not need to wait for B, so the line should say A can be solved without B.

C — You combine the solutions after each sub-problem has been solved. The line should say COMBINE A and B at the end.