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.

This is three examples of "Type III" documents that I have prepared for students to write about math. Our school uses the Collins system of writing, but these could be adapted to a variety of classroom settings. The topics could be middle school or early high school topics, and they are set up to allow students to indepedently express their knowledge of the given topics in short essay form.

In addition to the writing prompts, I have included a rubric that students use to peer-edit each others' rough drafts. Students then use this feedback form to make the necessary corrections and submit a subsequent final draft.

This lesson unit is intended to help you assess how well students are able to: Interpret a situation and represent the variables mathematically; select appropriate mathematical methods to use; explore the effects on the area of a rectangle of systematically varying the dimensions whilst keeping the perimeter constant; interpret and evaluate the data generated and identify the optimum case; and communicate their reasoning clearly.

This lesson unit is intended to help you assess how well students are able to: Calculate the mean, median, mode, and range from a frequency chart; and to use a frequency chart to describe a possible data set, given information on the mean, median, mode, and range.

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.

This lesson unit is intended to help teachers assess how well students are able to: make sense of a real life situation and decide what math to apply to the problem; understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model; represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams; and interpret the results and communicate their reasoning clearly.

This resource is an integrated unit spanning math, economics and English. This unit is focused on the the subject of the minimum wage and the themes of equity, financial stability and quality of life.

This lesson unit is intended to help teachers assess how well students are able to: Understand conditional probability; represent events as a subset of a sample space using tables and tree diagrams; and communicate their reasoning clearly.

This lesson unit is intended to help teachers assess how well students understand conditional probability, and, in particular, to help teachers identify and assist students who have the following difficulties: representing events as a subset of a sample space using tables and tree diagrams; and understanding when conditional probabilities are equal for particular and general situations.

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.

This lesson unit is intended to help you assess how well students are able to: interpret a situation and represent the variables mathematically; select appropriate mathematical methods; interpret and evaluate the data generated; and communicate their reasoning clearly.

This lesson unit is intended to help teachers assess how well students are able to: choose appropriate mathematics to solve a non-routine problem; generate useful data by systematically controlling variables; and develop experimental and analytical models of a physical situation.

This lesson unit is intended to help you assess how well students use algebra in context, and in particular, how well students: explore relationships between variables in everyday situations; find unknown values from known values; find relationships between pairs of unknowns, and express these as tables and graphs; and find general relationships between several variables, and express these in different ways by rearranging formulae.

Review of 2 x 1 Digit Multiplication and Instruction for 3 by 1 Multiplication with practice activities. 

(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.

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; explore the effects of systematically varying the constraints; interpret and evaluate the data generated and identify the optimum case, checking it for confirmation; and communicate their reasoning clearly.

This lesson unit is intended to help sixth grade teachers assess how well students are able to: Analyze a realistic situation mathematically; construct sight lines to decide which areas of a room are visible or hidden from a camera; find and compare areas of triangles and quadrilaterals; and calculate and compare percentages and/or fractions of areas.

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.

In this activity, students explore phase change at a molecular level. They trace the path of an atom to view intermolecular interactions and investigate how temperature relates to phase change. Upon activity completion, students will be able to give examples of phase change, explain how the input of energy into a system affects the state of matter, and describe how both latent heat and evaporative cooling play a role in changes of phase.