How countless Squares space there ~ above a Checkerboard?

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We might see this problem as somewhat easy, counting simply the 64 tiny (1x1) squares.

However, the board also has 2 x 2 squares, 3 x 3 squares, and so on. Clock this video clip to see one means to think around the various other sized squares:




You are watching: How many squares are on a checkerboard

A systematic method of counting the squares deserve to 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 top top a Checkerboard?

Extension

How many cubes room 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 also evaluate expression in which letter stand because that numbers. (a) compose expressions that document operations v numbers and also with letters standing because that numbers. (b) identify parts of one expression using mathematical state (sum, term, product, factor, quotient, coefficient). View one or an ext parts of an expression together a solitary entity. (c) advice expressions at details values of their variables. Include expressions the arise native formulas offered in real-world problems. Execute arithmetic operations, consisting of those including whole- number exponents, in the conventional order once there space no parentheses to specify a specific order (Order that Operations). • 7.EE.B.4Use variables come represent quantities in a real-world or math problem, and also construct simple equations and also inequalities come solve troubles by reasoning about the quantities. (a) fix word problems leading to equations that the type px + q = r and p(x + q) = r, whereby p, q, and also r are particular rational numbers. Fix equations of these creates fluently. Compare an algebraic systems to one arithmetic solution, identify the succession of the operations provided in each approach. (b) resolve word difficulties leading to inequalities that the type px + q > r or px + q • 8.EE.A.2Use square root and also cube root signs to stand for solutions come equations that the kind x² = p and also x³ = p, whereby p is a hopeful rational number.

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