Math lesson plans using Understanding by Design from Trinity University

## Collection Contents

### Understanding Geometry as an Axiomatic System

by Lani deGuia

By Danielle KendrickAfter completing the Algebra I review and introducing several computational aspects of geometry including distance formula, midpoint formula, etc., we will introduce the idea of geometry as an axiomatic system. In this unit, we will decide what role rules play in governing behavior. Students will define and identify the four components of an axiomatic system; defined terms, undefined terms, axioms/postulates, and theorems. They will explore various axiomatic systems and decide how these systems dictate how appropriate behavior looks. We will explore Euclidean Geometry abstractly considering it at its most basic form, a set of rules that determine how geometric objects behave.Students will be asked to create simple axiomatic systems. Since this task requires students to think very abstractly, it has been scaffolded to ensure that it is accessible to students at varying developmental levels. The unit has been designed to allow students the opportunity to explore both Euclidean and Non-Euclidean geometries, as well as, make connections between the mathematical world and the “real world”. The ultimate goal of this unit is to answer the questions: “When will I ever use this?” and “Outside of math class, why does this matter?”These works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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### Modeling the World

by Lani deGuia

By Jeremy MartinPre-Requisites for the Unit: Students should have studied exponential and polynomial functions and linear regression before starting this unit.Context: This unit is envisioned as an end of course unit for Pre-Calculus. The unit is designed specifically to incorporate elements of Calculus and Statistics for students interested in taking either AP course.Unit Goals: Students should come out of this unit with the ability to perform polynomial and exponential regression and interpret the residuals and coefficient of determination in context of the model’s goodness of fit. Students will gain proficiency in using computers and calculators to display data and create regression models.These works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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### How Do We Measure?

by Lani deGuia

By Kyla McGlynnStudents directly explore and compare the attributes of length, area, weight, and capacity using a variety of informal measurement instruments correctly and meaningfully. Students describe comparisons of each attribute using proper vocabulary.
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### Where everyone’s PLACE is VALUED: A Numeration Unit

by Lani deGuia

By Karen MorrisonThis is our first unit in 3rd grade math. It focuses specifically on Base Ten/Numeration, with a main emphasis on place value and money. Aligned with state standards, the students will be able to read, write in the three different forms (standard, expanded and written) and compare numbers up to the hundred-thousand place; additionally, students will be able to count collections of bills & coins and to solve real-world situations in which money is exchanged. The performance assessment is entitled: Ritzy Roadrunner Resort. Students will be invited to participate in an imaginative ritzy summer vacation, much like present day Atlantis Paradise Island. This culminating activity is differentiated, leveled based on students various points of entry and skill acquisition throughout the unit. As ?families on a summer trip? the students, in groups, will be assigned different package deals with varying ?terms and conditions.? Mathematical expectations include skills from needing to accurately rank activites & resturaunt items from most expensive to least expensive, using simple addition to determine money costs within a defined limit, up to giving higher students a budget and requiring them to provide you, the ?hotel manager,? a balance sheet of purchases. This performance assessment will be graded on a rubic provided. We hope you enjoy your stay at the Roadrunner Resort: Where every place is valued! *Unit activities provided from R.I.S.D. –double check for acceptable use policy*
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### Take a Chance on Probability-7th grade

by Lani deGuia

By Melanie R. WebbThe goal of this unit is for students to understand that probability is a measure that weuse to make predictions about future events. Whereas some outcomes areindependent of one another, others are dependent on the outcome of previous events,which affects the probability.Throughout the unit, students will explore probabilities through experimental andtheoretical situations and problems.The unit culminates with the students creating what they perceive to be a fair and fungame of chance. These works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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by Lani deGuia

By Ashley DavisAlgebra II Pre-AP/GT students will demonstrate proficiency of the four ways to solve systems of equations. Throughout the unit, students will complete practice problems on systems of equations and inequalities using algebraic techniques. As the culminating piece, students will create an original system of equations word problem and then write a persuasive essay on which method would be best to solve the system. Using the STAAR writing standards to write the persuasive essay, students will support their thesis by solving the system with each of the four methods. Students will also provide a counter-example as part of the STAAR standards. Finally, students will justify the correctness of the solution and evaluate the efficiency of the method.These works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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### Converting and Ordering Rational Numbers

by Lani deGuia

By Danielle Kunetz and Melanie WebbThe goal of this unit is for students to understand that numbers have equivalencies in many representations and in order to compare rational numbers, they must be expressed using the same representation.Throughout the unit, students compare and order rational numbers first within the same representation, and then learn to convert between representations to compare numbers between different forms.The unit culminates with the students using what they have learned to analyze statistics of a basketball team in order to form a starting line-up with what they perceive to be the best players on the team.Some supplementary materials were collected and adapted from many teachers in North East Independent School district.These works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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### This graph is speaking to me; how do I listen?

by Lani deGuia

By Matthew PattyThis unit is written to address the 8th Grade Mathematics TEKS focused around statistics. Students will begin with an exploratory lesson in which they develop the requirements of a valid survey. They will then research and design three separate surveys that could be used to make claims about a population in their area. Next, students will pair up and carry out a survey at a local location. After the surveys, the students will bring their data back to the classroom and create presentations using at least four different types of graphical representations. Accompanying each graphical representation must be at least one complex and valid conclusion. Students must then present their conjectures to the class and be able to defend them with numerical and graphical evidence.These works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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### Measurement: Surviving our Multi-Dimensional World

by Lani deGuia

By Courtney BryandMeasurement: Surviving our Multi-Dimensional World is a measurement unit with a “Survivor” theme. Many components are based on the project based learning activity Stranded! The unit begins and ends in a survivor scenario - students are stranded on a deserted island and must use a piece of scrap metal (an irregular figure) to design a device to catch fresh rain water so they can survive until they are rescued.Throughout the unit, students build understanding of measurement concepts through hands on learning activities and collaboration with peers. Students learn to use measurement concepts to describe the world around them. The unit culminates with teams of students designing, building, and testing three-dimensional water catchment devices from a two dimensional figure. Students use observations and calculations to maximize the volume of their device, and tests its effectiveness through modeling activities.The unit is designed for a 7th Grade Pre-AP class and incorporates both 7th and 8th grade measurement concepts including: area and perimeter of polygons, circles, and irregular figures; volume of prisms, cylinders, pyramids, cones and spheres; nets and surface area of prisms, cylinders, and pyramids; how perimeter, area, and volume are affected by dimensional change.These works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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### Shapes

by Lani deGuia

By Beth Morrow and Anne PeppersThis unit addresses the Texas Pre-Kindergarten Guidelines “Child recognizes/describes common shapes” (MVC1) and “Child slides, flips, turns shapes to demonstrate they remain the same” (MVC4), as well as the math standard “Child covers an area with shapes.” At the conclusion of this unit, students will know:- names and features (number of sides/angles) of common shapes: rectangle, square, triangle, circle, oval, and rhombus; and- shapes remain the same regardless of their position;and will be able to:- identify and describe common shapes: rectangle, square, triangle, circle, oval, and rhombus- cover an area with shapes and explain how they did so- combine shapes to create an imageThese works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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### Number, Numbers Everywhere! But Whatever Do I Think? 1st Grade Numerical Fluency

by Lani deGuia

By Audrey TanThis unit is designed as a beginning of the year math unit. Students will have had exposure to number recognition, counting, and patterns.The unit is designed to help students explore and gain confidence with numbers to 100. Students will understand the relationship between numbers and build a foundation for estimation. They will count, compare, and order numbers. Students will discuss the abundance of numbers that they encounter in their everyday lives and the importance of being able to count accurately.Throughout the unit students will develop their numerical fluency through games and hands on activities. The unit is centered around collaborative learning.Students will conclude the unit with a performance task where they will imagine themselves as zookeepers. Students will use a zookeeper log to complete their daily tasks. They will use their knowledge and skills acquired throughout the unit to complete their zookeeper duties. Students will be assessed using a rubric.These works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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### Where’s My Home? The Case of the Lost Digit – Place Value

by Lani deGuia

By Jennifer YuThis place value unit has been designed as a beginning of the year 3rd grade math unit. The purpose of the unit is to give students an understanding of numbers and how they are given a value. Students will understand that all numbers are made up of digits (0-9) and the position of the digits affect the value of the number. They will also understand that we order numbers to organize in everyday situations. Students will learn to read, write, and expand numbers. They will also learn to order numbers from least to greatest and greatest to least. They will then be asked to transfer their understanding of place value by imagining they have been hired as a librarian and completing their duties through organizing and ordering library books.These works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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### Proportional Relationships

by Lani deGuia

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### Bits and Pieces -- Working with Fractions

by Lani deGuia

By Kathleen KildayIn this unit, students will be introduced to fractions. Students will have practice identifying commonly used fractions using physical models, pictures, numbers, and word problems. Using these skills, students will recognize equivalent fractions and be able to sort fractions from largest to smallest and vice versa. Students will also be introduced to adding and subtracting these commonly used fractions. To demonstrate their knowledge of fractions, students will be asked to complete a performance assessment. The students will be given a recipe and 2 situations. The students will use the given information to amend the recipe for the appropriate number of guests for each situation. The students will record the new recipes as well as their mathematic reasoning. Due to the severity of disabilities presented by my students, this unit contains a great deal of repetition. These activities can be repeated as many times as necessary to accommodate the needs of your students. The pace of this unit can be sped up or slowed down as needed. Keep in mind that it will be important for your to monitor student understanding throughout and make instructional decisions accordingly.
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### Think Inside the Box: Using Tables to Understand Number Patterns

by Lani deGuia

By Kristen Lesher & Carrie Susong This two-week unit introduces students to more sophisticated number patterns and teaches students how to describe the relationship between two sets of data in a table. In the unit, students will identify patterns in everyday situations, record those patterns in the form of a table, and begin to use arithmetic expressions as well as other strategies to describe relationships between sets of data in a table. The performance task will ask students to create tables comparing age relationships. Students will describe the relationship between sets of data in each table using both written and verbal communication.These works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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### Math and Me

by Lani deGuia

By McKinley Rich The purpose of this unit is to have students question and analyze their opinions about mathematics. Students, particularly in math, have very strong perceptions of themselves as a learner. These self-perceptions have many different roots, and in this unit students will analyze the origin and perpetuation of such perceptions. Through a series of articles and some moments of self-reflection, students will look for answers to the questions: “What perceptions do I have about math?” and “What has shaped and will continue to shape my perceptions about math?”. While this is unlike 99% of math units, I believe that in order for students to be successful in math, they must understand that they are capable and competent enough to complete problem-solving tasks. And so, we must give students an opportunity to reflect upon their history in mathematics and let them address any negative pre-conceived ideas they have about math or their abilities as a mathematician.These works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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### Rules, What Rules? (Linear Equations, y =, x/y Tables, Graphing)

by Lani deGuia

By Catherine RisingerThe students will be introduced to linear equations. The main understandings that I want my students to develop is that even though there are multiple ways to solve problems, each way and representation can convey the same information. Students will demonstrate their knowledge of linear equations by solving them using a situation, algebraically, graphically, and using a table. Students will be able to generate a different representation of data given another representation of the same data. Students will explore real world examples of linear equations and discuss when different representations of linear equations are better models to use even though all the representations convey the same information. Students will apply what they have learned over the course of the 7 days and apply their knowledge of linear equations in the performance task. Each student will create a picture using only straight lines and then write the directions on how to get from each set of points on a coordinate plane as well as writing the equation of each line. Students will be assessed on the accuracy of their equations, using only straight lines to create their picture, a direction sheet of “code”, and a self-assessment of how they felt they did using the 3-2-1 strategy.These works are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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### Rational Numbers

by Lani deGuia

By Courtney SpickelmierThis 6-7 week unit is designed to provide students with a deep understanding of rational numbers and what they represent: a part of a whole. The unit encompasses many aspects of working with rational numbers including converting between different forms of rational numbers, comparing and ordering rational numbers, understanding the relationship between improper and mixed number fractions, performing operations with rational numbers, finding percentages, and applying such skills to real world situations. Throughout this unit, students are given the opportunity to discover relationships between numbers, make connections to the real world and other mathematical topics, and reinforce skills through large groups, small groups and independent activities.
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### Surface Area and Volume

by Lani deGuia

The students will be introduced to the surface area and volume of cylinders, prisms, pyramids, and cones. The main questions on which the unit is focused are: - What are different ways that three-dimensional objects are described or depicted? - What types of problems are solved using three-dimensional objects? They will participate in activities to help them create the formulas for both surface area and volume and become comfortable using these formulas to solve real-world problems and create their own applications. They will also analyze the relationship between surface area and volume. The culminating activity in this unit is a project in which the students will design a new container for M&M’s. They will compare and contrast different shapes and sizes in order to determine the best container. They will calculate the surface areas and volumes of their choices and pick one container to construct. They will draw a net of this figure with all the specifications needed to manufacture the container and draw different views of the container. Finally, they will present their finished product to the class and reflect on the process.Repository CitationGoetz, Maeve, "Surface Area and Volume" (2008). Understanding by Design: Complete Collection. Paper 67.http://digitalcommons.trinity.edu/educ_understandings/67Creative Commons LicenseThis work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
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### Ratios and Proportions

by Lani deGuia

In this unit students will be introduced to ratios and proportions. Students will have practice identifying ratios from pictures, graphs, models and word problems. Using these skills, students will then be able to identify proportional ratios and use ratios to describe proportional situations as well as to predict outcomes. To demonstrate their knowledge of ratios and proportional reasoning, students will complete a project assessment. The students will be given a recipe and then have to calculate the amounts of ingredients needed for various numbers of servings. The students will write down new versions of the recipes to be included in a class recipe book. To ensure that the recipes do have proportional amounts of ingredients, students may bring in a sample of their recipe to share with the class.Repository CitationMurphy, Lisa, "Ratios and Proportions" (2008). Understanding by Design: Complete Collection. Paper 66.http://digitalcommons.trinity.edu/educ_understandings/66Creative Commons LicenseThis work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
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### Probability and Statistics

by Lani deGuia

In this 7th grade unit, students will be required to put their mathematical minds to work as they develop an understanding of both theoretical and experimental probabilities and as they learn to analyze and communicate data effectively. Students will use real life data to explore measures of central tendency and how different measures may lead to different conclusions about the same information. Through the performance assessment, students will collect and analyze data, choosing the best way to communicate their findings. Finally, students will have the opportunity to apply their knowledge of theoretical probability to make predictions and will test those predictions using experimental probability. Concerning Statistics, the students will understand that there are many was to communicate information, but that some ways are better than others. They will also understand that the way information is presented influences our interpretation of it. Concerning probability, students will understand that for every even there are many possible outcomes, but some outcomes are more likely. They will also understand that the actual outcome of a situation is not always the same as the most likely outcome.Repository CitationSpickelmier, Courtney, "Probability and Statistics" (2008). Understanding by Design: Complete Collection. Paper 52.http://digitalcommons.trinity.edu/educ_understandings/52Creative Commons LicenseThis work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
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### Fractions

by Lani deGuia

Fractions are part of a whole or part of a group (set). Fractions are equal to each other in different forms (example: ½ = 2/4). Fractions can be simplified.Repository CitationVon Hoff, Carol, "Fractions" (2008). Understanding by Design: Complete Collection. Paper 68.http://digitalcommons.trinity.edu/educ_understandings/68Creative Commons LicenseThis work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
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### Linear Inequalities

by Lani deGuia

The students will be introduced to linear inequalities and systems of linear inequalities. The main understandings that I want to develop in my students are that there are many methods to solving math problems and that solving the problem is not always enough (mathematically correct solutions are not always the best solutions). They will need to analyze the solutions they develop to determine whether or not their answer is reasonable. Students will demonstrate their knowledge of linear equalities by solving them algebraically, graphically, and using a table. Students will compare and contrast linear equations to linear inequalities. They will explore real-world examples of linear inequalities and discuss when linear inequalities are necessary to solve certain problems. Students will apply what they have learned to a project. Each student will open a store of their choosing. They must decide how many of two products they would like to have at their store based upon the amount of space each takes up and the profit earned by each product. They will also compare this simplified problem to what the problem would be like in the real world.Repository CitationGoetz, Maeve, "Linear Inequalities" (2006). Understanding by Design: Complete Collection. Paper 13.http://digitalcommons.trinity.edu/educ_understandings/13Creative Commons LicenseThis work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
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### What is Measurement?

by Lani deGuia

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### What Are Rational Numbers?

by Lani deGuia

In this pre-algebra unit of rational numbers, students will further their understanding of rational numbers and its application to everyday experiences. Pre-algebra is the stepping stone to high school mathematics. Therefore, it is imperative for students to recognize and demonstrate that there are appropriate situations in which rational numbers should be used and their usefulness to us. In the culminating performance task, students are asked to develop and present a plan for the BBQ that they will be hosting for a specified number of people. The BBQ scenario allows students to apply their knowledge of rational numbers in order to do comparison shopping at 3 different grocery stores. The unit concludes with why students shopped the way that they did and a self-evaluation of what they have learned.Repository CitationRisinger, Catherine, "What Are Rational Numbers?" (2005). Understanding by Design: Complete Collection. Paper 5.http://digitalcommons.trinity.edu/educ_understandings/5Creative Commons LicenseThis work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
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