How plenty of Squares space there on a Checkerboard?

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We might see this difficulty as rather easy, counting just the 64 little (1x1) squares.

However, the board additionally has 2 x 2 squares, 3 x 3 squares, and so on. Clock this video clip to check out one way to think around the other sized squares:




You are watching: Number of squares on a checkerboard

A systematic method of count the squares can be helpful:

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What did you realize?How countless 3 x3 Squares room there ~ above a Checkerboard?What is the total number of squares are there on a Checkerboard?

Extension

How countless cubes are there in an 8x8x8 cube such as this?

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AuthorEda Aydemir

Target Grades3 – 12

TagsStudent Exploration, Algebra, Geometry, Number Theory

Common core Standards6.EE.A.2Write, read, and evaluate expressions in which letters stand because that numbers. (a) compose expressions that record operations v numbers and with letters standing for numbers. (b) determine parts of an expression utilizing mathematical state (sum, term, product, factor, quotient, coefficient). Watch one or more parts of one expression as a single entity. (c) advice expressions at particular values of their variables. Encompass expressions that arise native formulas supplied in real-world problems. Execute arithmetic operations, consisting of those entailing whole- number exponents, in the conventional order once there are no parentheses come specify a details order (Order the Operations). • 7.EE.B.4Use variables come represent amounts in a real-world or math problem, and also construct straightforward equations and also inequalities come solve problems by reasoning about the quantities. (a) settle word problems leading come equations that the form px + q = r and also p(x + q) = r, wherein p, q, and also r are specific rational numbers. Resolve equations of these creates fluently. Compare an algebraic systems to an arithmetic solution, identifying the succession of the operations supplied in each approach. (b) fix word troubles leading come inequalities the the kind px + q > r or px + q • 8.EE.A.2Use square root and also cube root icons to stand for solutions come equations of the kind x² = p and also x³ = p, wherein p is a positive rational number.

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Advice square roots of tiny perfect squares and also cube roots of tiny perfect cubes. Know that √2 is irrational.