Find the next shape in a growing pattern

Learning Objectives Identify the repeating elements and changes within a sequence of growing shapes. Describe the 'growth rule' or transformation applied from one shape to the next in a pattern. Predict and draw the next shape in a given visual pattern sequence. Analyze patterns involving changes in quantity, orientation, size, or arrangement of geometric figures. Articulate their reasoning for predicting the next shape in a pattern. Differentiate between various types of growth patterns (e.g., additive, rotational, layered). Have you ever noticed how some things grow or change in a predictable way, like the rings of a tree or the petals of a flower? 🌸 What if shapes could do the same? In this lesson, we'll explore the fascinating world of growing shape patt...

TermDefinitionExample PatternA pattern is a regular, repeated arrangement or sequence, especially in a visual design or mathematical sequence.A sequence of shapes like square, square-square, square-square-square shows a pattern of adding one square each time. SequenceA sequence is an ordered list of items, numbers, or shapes that follow a specific rule or pattern.Triangle, Square, Pentagon, Hexagon is a sequence of polygons where the number of sides increases by one. Growth RuleA growth rule describes the specific operation or change that occurs from one element to the next in a pattern or sequence, allowing it to 'grow' or transform.If a pattern adds two circles to the previous shape, the growth rule is 'add two circles'. AttributeAn attribute is a characteristic or p...

Component Analysis Rule $$S_n = \{C_{n,1}, C_{n,2}, ..., C_{n,k}\}$$ Identify the individual components ($C$) of each shape ($S$) at step $n$. Break down each shape in the pattern into its constituent parts or attributes (e.g., number of elements, type of elements, arrangement, color, orientation). This helps to see what is changing and what is staying the same. Growth Rule Identification $$C_{n+1,i} = R_i(C_{n,i})$$ Determine the specific rule ($R_i$) that transforms each changing component ($C_i$) from step $n$ to step $n+1$. Once components are identified, look for the relationship between corresponding components in consecutive shapes. Is it adding, subtracting, rotating, reflecting, scaling, or changing type? Quantify this change. Prediction Rule $$S_{next} = \tex...