Year 7AC9M7SP01

Two-Dimensional Views and Sorting Algorithms

Represent objects in 2 dimensions; discuss and reason about the advantages and disadvantages of different representations. Design and create algorithms involving a sequence of steps and decisions that will sort and classify sets of shapes according to their attributes, and describe how the algorithms work.

A solid object has to be shown on flat paper, and every way of doing that loses something. Sorting shapes reliably needs a set of yes-or-no questions asked in a fixed order.

Method

Front, side and top views

Three flat drawings that together describe one solid.

Every representation trades something away

A net shows all faces but hides the shape. A drawing shows the shape but hides the back.

An algorithm is yes-or-no questions in a fixed order

Same questions, same order, same answer every time.

Worked example

e.g.

\text{Write an algorithm that sorts any quadrilateral.}

Start with the question that splits the group most evenly. $\text{Are both pairs of opposite sides parallel?}$
If no, ask the next distinguishing question. $\text{One pair parallel? } \rightarrow \text{ trapezium}$
If yes, narrow further. $\text{Are all angles } 90^\circ?$
Keep splitting until only one name is left. $\text{All sides equal? } \rightarrow \text{ square, else rectangle}$
Test it on a shape you know to check it terminates. $\text{a rhombus reaches exactly one answer} \quad\checkmark$

Practice

Think about what each view or question tells you.

\text{Which view shows the height of a cylinder?}

Answer

\text{front or side}

\text{What does a top view of a cone look like?}

Answer

\text{a circle with a centre point}

\text{Why is one view not enough to identify a solid?}

Answer

\text{Different solids can share the same view.}

\text{First question to sort triangles by sides?}

Answer

\text{Are all three sides equal?}

\text{Why must the questions be in a fixed order?}

Answer

\text{So the same shape always reaches the same name.}