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Squares in a Geometric Pattern

7.2.1 Squares in a Geometric Pattern

7.2.1 • Squares in a Geometric Pattern

Warm Up

How does each expression represent the number of small squares in the figure?

An image of a block of squares. Begin with row 1 at the bottom of the figure. There are eight squares on rows 1, 2, 3 and 4 and five squares on rows 5 – 6. There are six squares missing from the upper right corner of the block.
1.

Expression A: 6·8−2·36·8−2·3

Compare your answer:

There are 6 rows with 8 small squares, but from this, 2 rows of 3 small squares have been removed.

2.

Expression B: 4·8+2·54·8+2·5

Compare your answer:

There are 4 rows of 8 small squares, and to this, 2 rows of 5 small squares are added.

3.

Expression C: 8+8+8+8+5+58+8+8+8+5+5

Compare your answer:

This counts each row, starting from the bottom.

4.

Expression D: 5·6+3·45·6+3·4

Compare your answer:

There are 5 columns of 6 small squares and 3 columns of 4 small squares.

Building Character: Proactivity

A student with long dark hair raises their hand while sitting at a desk with papers. Behind them is a clock, a bulletin board, a shelf with boxes, and a globe.

Proactivity is the ability to take initiative. There’s evidence that proactivity is one of the qualities that distinguished the greatest American presidents from their peers.

Think about your current sense of proactivity. Are the following statements true for you??

  • I am always looking for better ways of doing things.
  • I love to challenge the status quo.

Don’t worry if none of these statements are true for you. Developing this trait takes time. Your first step starts today!