Math Problem Statement

What is the next figure in each row based on the observed pattern?

Solution

This image seems to be a pattern recognition problem asking to identify and draw the next figure in each row. Let's analyze each row and figure out the correct pattern:

  1. Row 1: The shapes alternate between a triangle with a small circle and just a triangle. The triangles are rotating clockwise by 45 degrees in each step. The next shape should be just a triangle rotated 45 degrees from the previous one, with no small circle.

  2. Row 2: The shapes alternate between a star and an increasing number of points on the star (from 4 to 5 to 6). The next figure should be a 7-pointed star.

  3. Row 3: The rectangles are consistently placed but have changing widths. The width increases with each figure. The next rectangle should have a wider base than the previous one.

  4. Row 4: The diamond shapes are increasing in width (elongation horizontally). The next figure should be a wider diamond, with a more stretched horizontal axis.

  5. Row 5: The circles are concentric, with an increasing number of rings. The first has none, the second has one ring, and the third has two rings. The next shape should be a circle with three concentric rings.

Here are five related questions:

  1. What pattern are you noticing in terms of rotational symmetry in the first row?
  2. How does the number of star points increase systematically in the second row?
  3. Can you identify a geometric sequence in the dimensions of the rectangles in the third row?
  4. How is the symmetry changing in the diamond shapes from row four?
  5. What is the rule for adding rings to the circles in the fifth row?

Tip: Always observe both shape transformation and positional changes when working with patterns.

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Math Problem Analysis

Mathematical Concepts

Pattern Recognition
Geometric Transformation
Rotational Symmetry

Formulas

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Theorems

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Suitable Grade Level

Grades 5-7