Mathematically Productive Instructional Routines (MPIR) are short (10ish minutes), daily exercises aimed at building number sense. These six different MPIR are part of the Mathematically Productive Instructional Routines collection from the Washington Office of Public Instruction and the Washington Association of Educational Service Districts.

In this unit, students will read and interpret primary sources to address the question “How do we measure the attainment of human rights?” By exploring the Universal Declaration of Human Rights, the UN’s Guide to Indicators of Human Rights, and data about development indicators from multiple databases, students will unpack the complexities of using indicators to measure human rights.

Monitor the temperature of a melting ice cube and use temperature probes to electronically plot the data on graphs. Investigate what temperature the ice is as it melts in addition to monitoring the temperature of liquid the ice is submerged in.

This lesson unit is intended to help teachers assess how well students are able to: interpret a situation and represent the constraints and variables mathematically; select appropriate mathematical methods to use; make sensible estimates and assumptions; investigate an exponentially increasing sequence; and communicate their reasoning clearly.

Study the motion of a toy car on a ramp and use motion sensors to digitally graph the position data and then analyze it. Make predictions about what the graphs will look like, and consider what the corresponding velocity graphs would look like.

(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.)

En el módulo 3, la comprensión de los estudiantes de la adición y la resta de las fracciones se extiende desde el trabajo anterior con equivalencia de fracción y decimales. Este módulo marca un cambio significativo lejos de la centralidad de los grados elementales de las diez unidades de base al estudio y el uso del conjunto completo de unidades fraccionarias desde el avance de grado 5, especialmente como se aplica al álgebra.

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

English Description:
In Module 3, students' understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades' centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra.

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

Take a breath — where does the oxygen you inhaled come from? In our changing world, will we always have enough oxygen? What is in water that supports life? What is known? How do we know what we know about our vast oceans? These are just a few of the driving questions explored in this interactive STEAM high school curriculum module.

Students in marine science, environmental science, physics, chemistry, biology, integrated science, biotechnology and/or STEAM courses can use this curriculum module in order to use real-world, big data to investigate how our “invisible forest” influences ocean and Earth systems. Students build an art project to represent their new understanding and share this with the broader community.

This 4-week set of lessons is based on the oceanographic research of Dr. Anne Thompson of Portland State University in Oregon, which focuses on the abundant ocean phytoplankton Prochlorococcus. These interdisciplinary STEAM lessons were inspired by Dr. Thompson’s lab and fieldwork as well as many beautiful visualizations of Prochlorococcus, the ocean, and Earth. Students learn about the impact and importance of Prochlorococcus as the smallest and most abundant photosynthetic organism on our planet. Through the lessons, students act as both scientists and artists as they explore where breathable oxygen comes from and consider how to communicate the importance of tiny cells to human survival.

This module is written as a phenomenon-based, Next Generation Science Standards (NGSS) three-dimensional learning unit. Each of the lessons below also has an integrated, optional Project-Based Learning component that guides students as they complete the PBL process. Students learn to model a system and also design and evaluate questions to investigate phenomena. Students ultimately learn what is in a drop of ocean water and showcase how their drop contributes to our health and the stability and dynamics of global systems.

This lesson unit is intended to help teachers assess how well students are able to: recognize and visualize transformations of 2D shapes; and translate, reflect and rotate shapes, and combine these transformations. It also aims to encourage discussion on some common misconceptions about transformations.

Explore your own straight-line motion using a motion sensor to generate distance versus time graphs of your own motion. Learn how changes in speed and direction affect the graph, and gain an understanding of how motion can be represented on a graph.

This lesson unit is intended to help teachers assess how well students are able to identify and use geometrical knowledge to solve a problem. In particular, this unit aims to identify and help students who have difficulty in: making a mathematical model of a geometrical situation; drawing diagrams to help with solving a problem; identifying similar triangles and using their properties to solve problems; and tracking and reviewing strategic decisions when problem-solving.

This unit consists of five lessons encouraging younger learners to engineer increasingly better towers using blocks and recycled materials. Each 30 minute lesson ("phase") includes goals, discussion, activity instructions, extensions, and student worksheets.

Phase 1: Paper Cut-Outs Activity
Phase 2: Building Blocks Activity
Phase 3: Number of Blocks Activity
Phase 4: Building within a Space Activity
Phase 5: Recycled Tower Activity

NGSS: K-2-ETS1-1, K-2-ETS1-2, K-2-ETS1-3

Common Core ELA: RI.2.1, W.2.6, W.2.8, SL.2.5

Common Core Math: MP.2, MP.4, MP.5, 2.MD.D.10