Unwrapped Standard 4
... 3. The angles in all triangles have a sum of 180 degrees. 4. Polygons are classified by the number of sides. 5. Similar triangles are proportional. 6. Ordered pairs are graphed on a coordinate plane. 7. A transversal line forms different types and pairs of angles. Essential Questions from Big Ideas ...
... 3. The angles in all triangles have a sum of 180 degrees. 4. Polygons are classified by the number of sides. 5. Similar triangles are proportional. 6. Ordered pairs are graphed on a coordinate plane. 7. A transversal line forms different types and pairs of angles. Essential Questions from Big Ideas ...
Integer Work With Tiles
... Division is the inverse of multiplication and can also be seen as repeated addition or subtraction in a problem with two factors. The first number is the dividend and tells us what number is our goal. The second number is the divisor and tells us the size of the groups we are adding or removing to m ...
... Division is the inverse of multiplication and can also be seen as repeated addition or subtraction in a problem with two factors. The first number is the dividend and tells us what number is our goal. The second number is the divisor and tells us the size of the groups we are adding or removing to m ...
Adding and subtracting integers
... tiles than positive tiles (the absolute value of the negative integer is greater than the absolute value of the positive integer.) The result will be positive if both integers are positive, or if there are more positive tiles than negative tiles (the absolute value of the positive integer is greater ...
... tiles than positive tiles (the absolute value of the negative integer is greater than the absolute value of the positive integer.) The result will be positive if both integers are positive, or if there are more positive tiles than negative tiles (the absolute value of the positive integer is greater ...
Proving Triangles Similar
... Side-Side-Side Similarity (SSS~) Theorem If all of the corresponding sides of 2 triangles are proportional, then the triangles are similar. ...
... Side-Side-Side Similarity (SSS~) Theorem If all of the corresponding sides of 2 triangles are proportional, then the triangles are similar. ...
Second round Dutch Mathematical Olympiad
... The top row of these tiles always starts with a 1. In a matching combination, the bottom row must therefore start with a 1 as well. This rules out the first tile being of type D. Type C is ruled out as well, since otherwise the second tile must have a top row starting with 0. The first tile of a mat ...
... The top row of these tiles always starts with a 1. In a matching combination, the bottom row must therefore start with a 1 as well. This rules out the first tile being of type D. Type C is ruled out as well, since otherwise the second tile must have a top row starting with 0. The first tile of a mat ...
Classify each triangle by its side lengths and angle measurements
... Line of symmetry: A line through a figure that creates two halves that match exactly. Obtuse angle: An angle with a measure greater than 90 degrees but less than 180 degrees. Parallelogram: A quadrilateral with two pairs of parallel sides. For example, squares, rectangles, and rhombuses are parallel ...
... Line of symmetry: A line through a figure that creates two halves that match exactly. Obtuse angle: An angle with a measure greater than 90 degrees but less than 180 degrees. Parallelogram: A quadrilateral with two pairs of parallel sides. For example, squares, rectangles, and rhombuses are parallel ...
Penrose tiling
A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated these sets in the 1970s. The aperiodicity of the Penrose prototiles implies that a shifted copy of a Penrose tiling will never match the original. A Penrose tiling may be constructed so as to exhibit both reflection symmetry and fivefold rotational symmetry, as in the diagram at the right. A Penrose tiling has many remarkable properties, most notably:It is non-periodic, which means that it lacks any translational symmetry. It is self-similar, so the same patterns occur at larger and larger scales. Thus, the tiling can be obtained through ""inflation"" (or ""deflation"") and any finite patch from the tiling occurs infinitely many times.It is a quasicrystal: implemented as a physical structure a Penrose tiling will produce Bragg diffraction and its diffractogram reveals both the fivefold symmetry and the underlying long range order.Various methods to construct Penrose tilings have been discovered, including matching rules, substitutions or subdivision rules, cut and project schemes and coverings.