How countless Squares space there top top a Checkerboard?

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We might see this trouble as rather easy, counting simply the 64 small (1x1) squares.

However, the board additionally has 2 x 2 squares, 3 x 3 squares, and so on. Watch this video clip to see one way to think about the various other sized squares:




You are watching: How many squares on a checkerboard

A systematic method of count the squares can be helpful:

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What did friend realize?How numerous 3 x3 Squares room there on a Checkerboard?What is the total variety of squares are there ~ above a Checkerboard?

Extension

How plenty of cubes space there in one 8x8x8 cube such together this?

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AuthorEda Aydemir

Target Grades3 – 12

TagsStudent Exploration, Algebra, Geometry, Number Theory

Common main point Standards6.EE.A.2Write, read, and evaluate expression in which letter stand because that numbers. (a) compose expressions that record operations v numbers and also with letter standing because that numbers. (b) identify parts of one expression utilizing mathematical state (sum, term, product, factor, quotient, coefficient). Watch one or more parts of one expression together a single entity. (c) advice expressions at specific values of their variables. Incorporate expressions that arise from formulas used in real-world problems. Execute arithmetic operations, consisting of those involving whole- number exponents, in the standard order as soon as there room no parentheses to specify a details order (Order the Operations). • 7.EE.B.4Use variables come represent quantities in a real-world or mathematical problem, and construct simple equations and also inequalities to solve difficulties by reasoning about the quantities. (a) solve word difficulties leading to equations of the kind px + q = r and also p(x + q) = r, wherein p, q, and also r are particular rational numbers. Solve equations that these develops fluently. To compare an algebraic solution to one arithmetic solution, identify the sequence of the operations used in every approach. (b) deal with word difficulties leading come inequalities that 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 that the type x² = p and also x³ = p, wherein p is a optimistic rational number.

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