How countless Squares are there top top a Checkerboard?

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

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




You are watching: How many squares in a checker board

A systematic means of count the squares have the right to be helpful:

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What did you realize?How countless 3 x3 Squares room there on a Checkerboard?What is the total variety of squares room there top top a Checkerboard?

Extension

How countless cubes room there in an 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 expressions in which letters stand because that numbers. (a) compose expressions that record operations v numbers and also with letters standing because that numbers. (b) determine parts of an expression making use of mathematical state (sum, term, product, factor, quotient, coefficient). View one or much more parts of an expression together a single entity. (c) advice expressions at specific values of your variables. Encompass expressions the arise from formulas provided in real-world problems. Do arithmetic operations, including those entailing whole- number exponents, in the typical order when there room no parentheses come specify a certain order (Order that Operations). • 7.EE.B.4Use variables come represent quantities in a real-world or math problem, and also construct basic equations and inequalities to solve problems by reasoning about the quantities. (a) fix word difficulties leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Deal with equations that these creates fluently. To compare an algebraic equipment to one arithmetic solution, identifying the succession of the operations provided in each approach. (b) solve word troubles leading to inequalities the the kind px + q > r or px + q • 8.EE.A.2Use square root and cube root symbols to represent solutions come equations that the type x² = p and x³ = p, where p is a confident rational number.

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Advice square root of small perfect squares and cube root of small perfect cubes. Know that √2 is irrational.