Students practice their multiplication skills using robots with wheels built from LEGO® MINDSTORMS® NXT kits. They brainstorm distance travelled by the robots without physically measuring distance and then apply their math skills to correctly calculate the distance and compare their guesses with physical measurements. Through this activity, students estimate parameters other than by physically measuring them, practice multiplication, develop measuring skills, and use their creativity to come up with successful solutions.

In this lesson, students use historical nonstandard units (digits, hand, cubit, yard, foot, pace, fathom) to estimate the lengths of common objects and then measure using modern standard units. They will discover the usefulness of standardized measurement units and tools. An activity sheet (pdf), assessment options and other commentary are provided.

The activities in this four-lesson unit enable students to use their knowledge of number, measurement, and geometry to solve interesting problems. Planning and visualizing, estimating and measuring, and testing and revising are components of the ladybug activities. Students design "virtual paths" that enable a ladybug to either hide under a leaf or go through a maze. They develop navigational skills by testing their path and revising it. Two interactive Java applets (Ladybug Mazes and Hiding Ladybug, cataloged separately) support student solutions.

This lesson introduces students to the measurable attribute of length and provides practice in measuring length using non-standard units. The lesson is launched using the story Ladybug on the Move by Richard Fowler. Lesson objectives, teaching ideas, and handouts are included.

In this 5-lesson unit, students engage in measurement activities involving length, area, volume, time, and weight, using objects, pictures and symbols. Students practice measuring using standard and nonstandard units. Some lessons are introduced using children's literature.

In this three-lesson unit, students participate in activities in which they focus on connections between mathematics and children’s literature. Three pieces of literature are used to teach geometry and measurement topics in the mathematics curriculum, i.e. using and describing geometric figures, estimating the volume of an irregular solid, and exploring the need for a standard unit of length. Activity worksheets and ideas for extension are included.

This collection of five lessons explores 3rd grade mathematical concepts in the context of the outdoor classroom. These lessons span various math and science curricular units and include:Arrays in Nature (modeling multiplication)Measurement in Nature (length/mass and traits of organisms)Fraction Snow Cakes (fractions)Engineering and Design - Flight (measurement/data and forces)BioBlitzes (measurement/data, diversity and traits)

Students learn the metric units engineers use to measure mass, distance (or length) and volume. They make estimations using these units and compare their guesses with actual values. To introduce the concepts, the teacher needs access to a meter stick, a one-liter bottle, a glass container that measures milliliters and a gram scale.

In this math lesson, learners measure distances using an outline cutout of their own feet. This enables learners to practice using nonstandard units. This activity is recommended as a follow up to the "Measuring with Teacher's Feet" lesson (see related resources). This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

Este módulo reúne las ideas de similitud y congruencia y las propiedades de la longitud, el área y las construcciones geométricas estudiadas durante todo el año. También incluye las propiedades específicas de los triángulos, cuadriláteros especiales, líneas paralelas y transversales, y movimientos rígidos establecidos y construidos sobre esta historia matemática. El enfoque de este módulo está en las posibles relaciones geométricas entre un par de líneas de intersección y un círculo dibujado en la página.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
This module brings together the ideas of similarity and congruence and the properties of length, area, and geometric constructions studied throughout the year.  It also includes the specific properties of triangles, special quadrilaterals, parallel lines and transversals, and rigid motions established and built upon throughout this mathematical story.  This module's focus is on the possible geometric relationships between a pair of intersecting lines and a circle drawn on the page.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

El módulo 3 comienza extendiendo las experiencias de jardín de infantes de los estudiantes con una comparación de longitud directa con la comparación indirecta por la cual la longitud de un objeto se usa para comparar las longitudes de otros dos objetos. Más largo que y más corto que se llevan a un nuevo nivel de precisión al introducir la idea de una unidad de longitud. Luego, los estudiantes exploran la utilidad de medir con unidades similares. El módulo se cierra con estudiantes que representan e interpretan datos.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
Module 3 begins by extending students’ kindergarten experiences with direct length comparison to indirect comparison whereby the length of one object is used to compare the lengths of two other objects.  Longer than and shorter than are taken to a new level of precision by introducing the idea of a length unit.  Students then explore the usefulness of measuring with similar units. The module closes with students representing and interpreting data.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Students are given a general overview of nanotechnology principles and applications, as well as nanomaterials engineering. Beginning with an introductory presentation, they learn about the nano-scale concept and a framework for the length scales involved in nanotechnology. Engineering applications are introduced and discussed. This prepares students to conduct the associated activity in which they relate the nano-length scale to everyday objects. At completion, students are able to identify nanotechnology applications and have a frame of reference for the second lesson of the unit.

Student groups work with manipulatives—pencils and trays—to maximize various quantities of a system. They work through three linear optimization problems, each with different constraints. After arriving at a solution, they construct mathematical arguments for why their solutions are the best ones before attempting to maximize a different quantity. To conclude, students think of real-world and engineering space optimization examples—a frequently encountered situation in which the limitation is the amount of space available. It is suggested that students conduct this activity before the associated lesson, Linear Programming, although either order is acceptable.

This interactive Flash animation allows students to explore size estimation in one, two and three dimensions. Multiple levels of difficulty allow for progressive skill improvement. In the simplest level, users estimate the number of small line segments that can fit into a larger line segment. Intermediate and advanced levels offer feature games that explore area of rectangles and circles, and volume of spheres and cubes. Related lesson plans and student guides are available for middle school and high school classroom instruction. Editor's Note: When the linear dimensions of an object change by some factor, its area and volume change disproportionately: area in proportion to the square of the factor and volume in proportion to its cube. This concept is the subject of entrenched misconception among many adults. This game-like simulation allows kids to use spatial reasoning, rather than formulas, to construct geometric sense of area and volume. This is part of a larger collection developed by the Physics Education Technology project (PhET).

In this lesson plan, students are asked to use measurement skills to perform an experiment. The data from the experiment is then recorded in a table and analyzed to determine the median and range. The lesson plan includes a PDF document for data collection and analysis, as well as extension suggestions for higher level thinkers.

Students build scale models of objects of their choice. In class they measure the original object and pick a scale, deciding either to scale it up or scale it down. Then they create the models at home. Students give two presentations along the way, one after their calculations are done, and another after the models are completed. They learn how engineers use scale models in their designs of structures, products and systems. Two student worksheets as well as rubrics for project and presentation expectations and grading are provided.

In this 5-lesson multi-media unit, students will explore various real-world applications of different forms of measurement, including time and distance. They will make estimations and calculations. Throughout the unit, students will be using online resources to familiarize themselves with coral reefs, the nation of Belize, and to plan a pretend scuba diving trip. Activity sheets (pdf), links to online resources, assessment options and other commentary are provided.

Students strengthen their communicate skills about measurements by learning the meaning of base units and derived units, including speed one of the most common derived units (distance/time). Working in groups, students measure the time for LEGO MINDSTORMS(TM) NXT robots to move a certain distance. The robots are started and stopped via touch sensors and programmed to display the distance traveled. Using their collected data, students complete a worksheet to calculate the robots' (mean/average) speeds at given motor powers.

Students work as engineers to design and test trebuchets (in this case LEGO® MINDSTORMS® robots) that can launch objects. During the testing stage, they change one variable at a time to study its effect on the outcome of their designs. Specifically, they determine how far objects travel depending on their weights. As students learn about the different components of robot design and the specific function controls, they determine what design features are important for launching objects.