5-1 Intro to Logical Thinking

Objectives:
  • Students will use logical reasoning to solve number sequence problems.
  • Students will explain the rule for a number sequence and predict which number(s) comes next


Engage

Watch: What is an Algorithm?

YouTube Video


Designing a Traffic Sign

Logical reasoning is the process of applying rules to problem solving. 
Algorithms are designed as a set of steps to follow to solve a problem. 
At the same time, a set of rules is determined. For example, 
  • if a condition is met, do this
  • if not, do that
These rules govern the path that is followed through the algorithm.
Rules are built using logical reasoning to ensure that the algorithm performs correctly.

This sign gives drivers a simple way to follow an algorithm designed to make traffic more safe and effective.
  • If in left lane, left turn only
  • If in center lane, left turn only
  • If in right lane, then left turn or move forward
Why use logical reasoning?
When trying to solve a problem, it may be that more than one solution is found. A different algorithm can be built from each solution. 
Logical reasoning determines if algorithms will work by predicting what happens when the algorithm’s steps - and the rules they consist of - are followed. Predictions from each algorithm can be used to compare solutions and decide on the best one.

First, understand the problem

Before an algorithm can be designed, it is important to check that the problem is completely understood. 
There are a number of basic things to know in order to really understand the problem:
  • What are the inputs into the problem?
    - using the example of the traffic sign, what could have been the problem before they made the sign at that intersection?
  • What will be the outputs of the problem?
    - what will happen when we consider all the ways that the sign can be designed to help modify the current traffic problem?
  • In what order do instructions need to be carried out?
    - how do we design a sign at a dangerous intersection that can be easily understood that makes traffic flow effectively?
  • What decisions need to be made in the problem?
    - where do we need traffic to go to make the intersection safer?
  • Are any areas of the problem repeated?
    - do we need more than one lane to do the same thing to help traffic flow safely? 
Once these basic things are understood, it is time to design the algorithm. 
  • In the traffic sign example, how would we use logical reasoning to design the algorithm to route traffic so the flow is safe and effective?

Logic: Think-Pair-Share


As stated above, an algorithm is a sequence of instructions, or a set of rules for performing a specific task, similar to following the steps in a recipe for baking cookies. Here is a simple number sequence that uses multiplication:  8, 16, 32, 64, __
  1. With your elbow partner, work out and explain the rule for this number sequence:  8, 16, 32, 64, __
  2. What number comes next in the sequence?
  3. Write the rule on a sheet of paper (for example: “double the last number” and add in the next number in the sequence, or128).
    This is the rule for solving the problem, and therefore a simple rule based algorithm.

    Questions:
    • How did you work out the rule?
    • How did you use logical reasoning?
      Hint: logical reasoning is concerned with how a problem is solved rather than simply ‘knowing’ the right answer. It is the journey, rather than the destination that is important.


    Section 3

    Worksheet
    • With your partner, using this worksheet, solve the number sequence problems in the first column.
    • In the second column explain the rule
    • In the third column, explain how you worked it out.
    • If you finish early, create your own number sequence problem with the rule and explanation included in the columns.


    Solving a Number Sequence Problem
    • With your partner, using this worksheet, solve the number sequence problems in the first column.
    • In the second column explain the rule
    • In the third column, explain how you worked it out.
    • If you finish early, create your own number sequence problem with the rule and explanation included in the columns.


    Check Your Understanding

    • What is logical reasoning?
    • What is logical reasoning used for?




    If you finish early: Add text.