NRICH's Upper Secondary offering is an interesting collection of games and puzzlers that address a range of skills. While the site states that the content here is for 11th- and 12th-graders, there are a few activities that would be fine for students in sixth grade or above. It's important to know that the site was developed in the U.K., so some of the concepts and language may be unfamiliar. If you teach in the United States, give yourself some extra time to align NRICH's resources to your curriculum.
For your students, the games and puzzlers here are a rich resource for taking math concepts a step further than what they may be used to. Many of the activities are particularly useful for gifted students, or for anyone who thrives on unique opportunities to explore and expand their learning. Before starting a typical unit with your class, spend some time looking for activities that could challenge and inspire, based on what you know about your students. Work the activities in as follow-up exercises, or as an occasional extra challenge for students who've mastered the standard curriculum in your class.Continue reading Show less
Key Standards Supported
Arithmetic With Polynomials And Rational Expressions
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Conditional Probability And The Rules Of Probability
Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.
(+) Use permutations and combinations to compute probabilities of compound events and solve problems.
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
Geometric Measurement And Dimension
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
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.
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.
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Verify experimentally the properties of rotations, reflections, and translations:
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Seeing Structure In Expressions
Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
Similarity, Right Triangles, And Trigonometry
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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.
The Complex Number System
Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.
Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
The Number System
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
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.
Vector And Matrix Quantities
(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
(+) Add and subtract vectors.
Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
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