Test New Form
1 Using Math Playground
2 Activity Testing
Key Standards Supported
Reading Foundational Skills
Read with sufficient accuracy and fluency to support comprehension.
Read on-level text with purpose and understanding.
Read on-level text orally with accuracy, appropriate rate, and expression on successive readings.
Use context to confirm or self-correct word recognition and understanding, rereading as necessary.
Know and apply grade-level phonics and word analysis skills in decoding words.
Know the spelling-sound correspondences for common consonant digraphs.
Decode regularly spelled one-syllable words.
Know final -e and common vowel team conventions for representing long vowel sounds.
Use knowledge that every syllable must have a vowel sound to determine the number of syllables in a printed word.
Decode two-syllable words following basic patterns by breaking the words into syllables.
Read words with inflectional endings.
Recognize and read grade-appropriate irregularly spelled words.
Similarity, Right Triangles, And Trigonometry
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Explain and use the relationship between the sine and cosine of complementary angles.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Verify experimentally the properties of dilations given by a center and a scale factor:
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.