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6 .21

6 .21. Investigate, describe, and extend numerical and geometric patterns, including triangular numbers, patterns formed by powers of 10, and arithmetic sequences. 6.21 Vocabulary pg-52

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6 .21

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  1. 6.21 Investigate, describe, and extend numerical and geometric patterns, including triangular numbers, patterns formed by powers of 10, and arithmetic sequences

  2. 6.21 Vocabulary pg-52 Geometric pattern- A sequence that is composed of shapes, figures, and diagrams can be called a geometric pattern. Geometric patterns may involve shape, size, angles, transformations of shapes, and growth. Triangular number- A triangular number can be represented geometrically as a certain number of dots arranged in a triangle, with one dot in the first (top) row and each succeeding lower row having one more dot that the row above it. To find the next triangular number, a new row is added to an existing triangle, and total number of dots counted. Square Number- A square number can be represented geometrically as the number of dots in a square array. Square numbers are perfect squares and are the numbers that result from multiplying any whole number by itself (e.g., 36 = 6  6). Consecutive- Following one after the other in order. Slide- Also called translation. A slide is the result of moving a figure in any direction within a given area. Dilation-The result of enlarging or shrinking a figure by a scale amount Arithmetic sequence- A set of numbers that expresses a specific pattern. Common difference- students must determine the difference, called the common difference, between each succeeding number in order to determine what is added to each previous number to obtain the next number. (Hint: what is happening between the first number and the second number? The second number and the third number?) Flip- Also called reflection. It is the result of flipping a figure over a line, so as to see a mirror image of the figure. Turn- Also called rotation. It is the result of turning a figure around a point or a vertex. Pg 51 6.21 practice POWERS OF TEN 10110 x 1= 10 10210 x 10= 100 10310 x 10 x 10= 1,000 10410 x 10 x 10 x 10= 10,000 10510 x 10 x 10 x 10 x 10= 100,000 10 x 10 x 10 x 10 x 10 x 10= 1,000,000 Triangular Numbers, just add a row to the bottom. What is the number in the 7th position? (3, 3+3=6, 6+4=10, 10+5=15….. Perfect squares! What is the number in the 6th position? 2x2 3x3, 4x4….. Transformations- Dilate (change size) Turn (rotation) Flip (reflection) Slide (translation) Fibonacci Sequence! (sequence of numbers) each number is the sum of the previous two numbers, starting with 0 and 1. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 … 1+0=1 1+1=2 2+1=3 3+2=5 5+3=8 and so on……… The higher up in the sequence, the closer two consecutive "Fibonacci numbers" of the sequence divided by each other will approach the golden ratio (approximately 1 : 1.618 or 0.618 : 1)

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