This lesson unit is intended to help teachers assess how well students are able to solve problems involving area and volume, and in particular, to help you identify and assist students who have difficulties with the following: computing perimeters, areas and volumes using formulas; and finding the relationships between perimeters, areas, and volumes of shapes after scaling.

This lesson unit is intended to help teachers assess how well students can: Understand the concepts of length and area; use the concept of area in proving why two areas are or are not equal; and construct their own examples and counterexamples to help justify or refute conjectures.

This article is for elementary teachers putting together fraction units. There is a discussion of activities and misconceptions.

This Nrich problem starts with a simple situation which can be analyzed quickly using mental methods, but which provides a starting point for tackling a more challenging problem. The challenge can be tackled at many different levels, using trial and improvement (perhaps using spreadsheets), looking for number patterns, or with a more formal algebraic approach.

Ordering fractions can seem like quite a mundane and routine task. This Nrich problem encourages students to take a fresh look at the process of comparing fractions, and offers lots of opportunities to practice manipulating fractions in an engaging context where students can pose questions and make conjectures.

This tasks examines how to calculate the area of an equilateral triangle using high school geometry.

This Nrich can be very engaging. It has the ability to introduce pupils to some logical reasoning as well as being solvable by trial and improvement.

This lesson unit is intended to help you assess how well students working with square numbers are able to: choose an appropriate, systematic way to collect and organize data, examining the data for patterns; describe and explain findings clearly and effectively; generalize using numerical, geometrical, graphical and/or algebraic structure; and explain why certain results are possible/impossible, moving towards a proof.

In this unit, children learn about attributes of shapes, compose and decompose composite shapes.

This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties: solving problems by determining the lengths of the sides in right triangles; and finding the measurements of shapes by decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

EL Education has revised the workshop model to align with the Common Core instructional shifts, embed ongoing assessment to increase responsiveness to student needs, and help students develop self-reliance and perseverance. The first component in this revised workshop (Workshop 2.0) asks students to “grapple” independently with a problem or task. The second component is a collaborative opportunity for students to be metacognitive about their own approaches, justify their mathematical reasoning, and consider others’ mathematical reasoning and thinking.

This video lesson uses the technique of induction to show students how to analyze a seemingly random occurrence in order to understand it through the development of a mathematical model. Using the medium of a simple game, Dr. Lodhi demonstrates how students can first apply the 'rules' to small examples of the game and then, through careful observation, can begin to see the emergence of a possible pattern. Students will learn that they can move from observing a pattern to proving that their observation is correct by the development of a mathematical model. Dr. Lodhi provides a second game for students in the Teacher Guide downloadable on this page. There are no prerequisites for this lesson and needed materials include only a blackboard and objects of two different varieties - such as plain and striped balls, apples and oranges, etc. The lesson can be completed in a 50-minute class period.

This Nrich problem provides a fraction-based challenge for students who already possess a good understanding of fraction addition and subtraction, and it leads to algebraic manipulation of that same process.

This Nrich task gives opportunities for pupils to explore, to discover, to analyze and communicate. It's a real catalyst for pupils' curiosity. It allows pupils to approach it in whatever way they find most helpful. It also provides opportunities for using and extending visualizing skills. The activity also opens out the possibility of pupils asking “I wonder what would happen if . . .?” showing their resilience and perseverance.

This Nrich low threshold high ceiling task is accessible to everyone. It gives children the chance to share the way they picture (visualize) numbers and their methods of counting. One of the key features of this task is that it can be interpreted differently, depending on the image, so that children can decide for themselves whether they are counting individual fruit, cartons of fruit... Therefore there may also be an opportunity for children to develop their estimation skills as well as appreciating different ways of counting.

The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.

This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context.

This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.

This lesson is about the estimation of the value of Pi. Based on previous knowledge, the students try to estimate Pi value using different methods, such as: direct physical measurements; a geometric probability model; and computer technology. This lesson is designed to stimulate the learning interests of students, to enrich their experience of solving practical problems, and to develop their critical thinking ability. To understand this lesson, students should have some mathematic knowledge about circles, coordinate systems, and geometric probability. They may also need to know something about Excel. To estimate Pi value by direct physical measurements, the students can use any round or cylindrical shaped objects around them, such as round cups or water bottles. When estimating Pi value by a geometric probability model, a dartboard and darts should be prepared before the class. You can also use other games to substitute the dart throwing game. For example, you can throw marbles to the target drawn on the floor. This lesson is about 45-50 minutes. If the students know little about Excel, the teacher may need one more lesson to explain and demonstrate how to use the computer to estimate Pi value. Downloadable from the website is a video demonstration about how to use Excel for estimating Pi.