Zooming In On Figures Unit Overview Type of Unit: Concept; Project Length …
Zooming In On Figures
Unit Overview
Type of Unit: Concept; Project
Length of Unit: 18 days and 5 days for project
Prior Knowledge
Students should be able to:
Find the area of triangles and special quadrilaterals. Use nets composed of triangles and rectangles in order to find the surface area of solids. Find the volume of right rectangular prisms. Solve proportions.
Lesson Flow
After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures. The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts. The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views. The unit ends with a unit examination and project presentations.
Mathematically Productive Instructional Routines (MPIR) are short (10ish minutes), daily exercises aimed at …
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 paper makes recommendations for developing mathematics instruction for English Language Learners …
This paper makes recommendations for developing mathematics instruction for English Language Learners (ELLs) aligned with the Common Core State Standards. The recommendations can guide teachers, curriculum developers, and teacher educators as they develop their own ways of supporting mathematical reasoning and sense-making for ELLs.Some instructional recommendations discussed in the paper include: Focus on ELL students' mathematical reasoning, not the correctness of their mathematical language use. Shift to a focus on mathematical discourse practices; move away from simplified views of language. Support ELL students as they engage in complex mathematical language. Use ELL students' language and experiences as resources. Provide professional development to enhance teachers' awareness of ways to support ELs as they develop both language and mathematical knowledge.
This lesson unit is intended to help you assess how well students …
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 …
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 …
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 …
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 lesson unit is intended to help teachers assess how well students …
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 …
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 …
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 …
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 …
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 teachers assess how well students …
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 …
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? …
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.
Personal Finance by Rachel Siegel and Carol Yacht is a comprehensive Personal …
Personal Finance by Rachel Siegel and Carol Yacht is a comprehensive Personal Finance text which includes a wide range of pedagogical aids to keep students engaged and instructors on track.
This book is arranged by learning objectives. The headings, summaries, reviews, and problems all link together via the learning objectives. This helps instructors to teach what they want, and to assign the problems that correspond to the learning objectives covered in class.
Personal Finance includes personal finance planning problems with links to solutions, and personal application exercises, with links to their associated worksheet(s) or spreadsheet(s). In addition, the text boasts a large number of links to videos, podcasts, experts' tips or blogs, and magazine articles to illustrate the practical applications for concepts covered in the text.
This lesson unit is intended to help teachers assess whether students are …
This lesson unit is intended to help teachers assess whether students are able to: identify when two quantities vary in direct proportion to each other; distinguish between direct proportion and other functional relationships; and solve proportionality problems using efficient methods.
Adult education classrooms are commonly comprised of learners who have widely disparate …
Adult education classrooms are commonly comprised of learners who have widely disparate levels of mathematical problem-solving skills. This is true regardless of what level a student may be assessed at when entering an adult education program or what level class they are placed in. Providing students with differentiated instruction in the form of Push and Support cards is one way to level this imbalance, keeping all students engaged in one high-cognitive task that supports and encourages learners who are stuck, while at the same time, providing extensions for students who move through the initial phase of the task quickly. Thus, all students are continually moving forward during the activity, and when the task ends, all students have made progress in their journey towards developing conceptual understanding of mathematical ideas along with a productive disposition, belief in one’s own ability to successfully engage with mathematics.
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