Students can use this app –- with teacher guidance –- to review explanations and diagrams, look up formulas, and enter data into calculators to check their work. Some calculators show and explain processes as well as answers.Continue reading Show less
Mathinary is a no-frills math reference good for formulas and formula calculations, particularly for geometry. The formula calculators in this app are where the bang is, particularly for geometry but also finance (and a few conversions). Trigonometry does not have its own menu, but the Unit Circle section explains graphic representations of the trigonometric functions sine, cosine, and tangent, etc. So if that's what your students need, this one is for you.
Users choose among seven menu items, most with submenus. Geometry and algebra are best represented, with 23 (plane and solid) and 10 pages, respectively. If a student chooses to review a rhombus, the About section has a labeled diagram, a definition, and some extra details. The formulas tab repeats the diagram and lists three formulas for area and one for perimeter. Students enter data in the calculator tab input boxes –- for instance, three side lengths (diagonal, diagonal, and side) –- and hit Calculate: 5, 7, and 8 give an area of 17.5.Continue reading Show less
It's okay, but could definitely be better. Downsides include too-small text, occasional incomplete explanations, and poorly developed content. While some content is acceptable for younger middle schoolers, like algebra and numbers, the explanations for these easier topics are not always thorough or clear. Since the app originates from the University of Edinburgh, some of the language and math processes are a bit different than what the average U.S. kid is used to (sinus for sine, etc.) and may just confuse them more.Continue reading Show less
Key Standards Supported
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Expressing Geometric Properties With Equations
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Derive the equation of a parabola given a focus and directrix.
(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
Expressions And Equations
Write and evaluate numerical expressions involving whole-number exponents.
Write, read, and evaluate expressions in which letters stand for numbers.
Apply the properties of operations to generate equivalent expressions.
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
Geometric Measurement And Dimension
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
(+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Identify the shapes of two-dimensional cross-sections of three- dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Explain a proof of the Pythagorean Theorem and its converse.
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Similarity, Right Triangles, And Trigonometry
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.
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.
The Number System
Fluently divide multi-digit numbers using the standard algorithm.
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.