The purpose of this curriculum guide is to provide OER lesson material and support activities for Pythagorean Theorem instruction. It is geared towards GED® requirements. Both printable and online options are provided.

This problem was designed to explore equivalence of change (ie. if a 10% decrease isn't the opposite of a 10% increase, what is? ) and to move students towards the concept: exponential growth and decay.

In this activity, students will learn to define variables that can be used to reference values and expressions. Once defined, their variables can be used repeatedly throughout a program as substitutes for the original values or expressions.

The primary purpose of this task is to illustrate certain aspects of the mathematics described in the A.SSE.1. The task has students look for structure in algebraic expressions related to a context, and asks them to relate that structure to the context. In particular, it is worth emphasizing that the task requires no algebraic manipulation from the students.

'Tricks' tap into children's natural curiosity and can provide the motivation for exploring the underlying mathematics in order to unpick how they are done. This Nrich problem explores a "trick" to provide an engaging context in which to explore place value and in particular 'adding nine' as 'adding ten and subtracting one'.

This task does not actually require that the student solve the system but that they recognize the pairs of linear equations in two variables that would be used to solve the system. This is an important step in the process of solving systems.

The Nrich problem offers opportunities to think about area, proportion and fractions, while offering an informal introduction to the mathematics of infinity and convergence which would not normally be met by younger students, to tempt their curiosity.

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.

This Nrich problem gives learners practice in fractions (tenths) as well as in addition and subtraction in a challenging form.

This Nrich problem uses the idea of sequences in a very tangible form. Children will need to recognize odd and even numbers as well as be able to count fluently both backwards and forwards. They will also have opportunities to justify their answers.

The Nrich game as introduced is intended for children who are just beginning to become confident with small numbers. However there are many variations, some suggested below, that make it suitable for older children. As with many of the NRICH games, consolidation of basic number facts is combined with an element of strategic thinking.

" Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems."

This Nrich activity provides a context for doubling multiples of 5. The children will also be noticing and describing patterns.

This team-building task is designed to develop students' team-working skills. If you wish to learn more about these skills, and find other team-builder tasks, take a look at this article.

This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units.

Unit fractions are the first fractions children meet, and here we discover some very surprising and interesting characteristics of these familiar numbers. Some of these characteristics were known to the ancient Egyptians whilst other conjectures are yet to be proved. Whilst meeting both old and new mathematical ideas, students can improve their fluency in addition and subtraction of fractions and be challenged to generalize and explain their findings.

The topic of music can make a good connection between science and mathematics. The nature of sound and the working of the ear are rich areas of applied mathematics. The ratio emphasis follows from harmonics or overtones and rests on ideas like lowest common multiple.

This task asks students to use inverse operations to solve the equations for the unknown variable, or for the designated variable if there is more than one. Two of the equations are of physical significance and are examples of Ohm's Law and Newton's Law of Universal Gravitation.

The purpose of this task is to directly address a common misconception held by many students who are learning to solve equations. Because a frequent strategy for solving an equation with fractions is to multiply both sides by a common denominator (so all the coefficients are integers), students often forget why this is an "allowable" move in an equation and try to apply the same strategy when they see an expression.