In this Nrich problem, the familiar context of sharing provides an opportunity in which to explore fractions in a variety of ways. The task involves finding fractional quantities of whole numbers as well as dividing a unit into equal pieces.

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.

Working individually or in groups, students explore the concept of stress (compression) through physical experience and math. They discover why it hurts more to poke themselves with mechanical pencil lead than with an eraser. Then they prove why this is so by using the basic equation for stress and applying the concepts to real engineering problems.

Reasoning to Find Area: Lesson 2

FInding Area by Decomposing and Rearranging
This lesson begins by revisiting the definitions for area that students learned in earlier grades. The goal here is to refine their definitions (MP6) and come up with one that can be used by the class for the rest of the unit. They also learn to reason flexibly about two-dimensional figures to find their areas, and to communicate their reasoning clearly (MP3).

The area of two-dimensional figures can be determined in multiple ways. We can compose a figure using smaller pieces with known areas. We can decompose a figure into shapes whose areas we can determine and add the areas of those shapes. We can also decompose it and rearrange the pieces into a different but familiar shape so that its area can be found. The two key principles in this lesson are:

Figures that match up exactly have equal areas. If two figures can be placed one on top of the other such that they match up exactly, then they have the same area.
A figure can be decomposed and its pieces rearranged without changing its area. The sum of the areas of the pieces is equal to the area of the original figure. Likewise, if a figure is composed of non-overlapping pieces, its area is equal to the sum of the areas of the pieces. In other words, area is additive.
Students have used these principles since grade 3, but mainly to decompose squares, rectangles, and their composites (e.g., an L-shape) and rearrange them to form other such figures. In this lesson, they decompose triangles and rearrange them to form figures whose areas they know how to calculate.

The purpose of this task is to have students work on a sequence of area problems that shows the advantage of increasingly abstract strategies in preparation for developing general area formulas for parallelograms and triangles.

The purpose of this task is to give 4th grade students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90_ and that angle measure is additive.

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

In this Cyberchase video, Inez and Digit identify the location of the transformation using their knowledge of parallel and intersecting lines.

This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade.

This Nrich activity provides a context for practicing counting on in 1s and 10s (and later 100s). Children will also be invited to find out how far from 50 they end up so they will be practicing finding the difference between two numbers. It encourages children to find more than one way of getting to a solution.

The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing.

The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers.

Unit: Area and Surface Area
Lesson 9: Formula for the Area of a Triangle

In this lesson students begin to reason about area of triangles more methodically: by generalizing their observations up to this point and expressing the area of a triangle in terms of its base and height.

Students first learn about bases and heights in a triangle by studying examples and counterexamples. They then identify base-height measurements of triangles, use them to determine area, and look for a pattern in their reasoning to help them write a general formula for finding area (MP8). Students also have a chance to build an informal argument about why the formula works for any triangle (MP3).

A structured geometry program teacher edition of daily lesson plans and teacher supports to accompany the College Access Reader: Geometry student edition.

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 short video and interactive assessment activity is designed to give fifth graders an overview of quadrilaterals.

This lesson was created by School Library Media Specialist, Pam Harland, and Math teachers Rebecca Hanna and Carissa Maskwa to model text-based inquiry in STEM. Over the course of the unit, students will explore a variety of texts and grow in their knowledge of fractals, city design, and ability to use informational text to support their inquiry and research.The unit was created in year two of the School Librarians Advancing STEM Learning (SLASL) project, led by the Institute for the Study of Knowledge Management (ISKME) in partnership with Granite State University, New Hampshire, and funded by the Institute for Museum and Library Services (IMLS).

This Nrich problem is useful for those pupils who are coming to terms with spatial representation of fractions where area is concerned rather than just length. Pupils' visualizations vary a great deal and this may prove very difficult for some and yet readily accessible to others.