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Math, Grade 6, Getting Started

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Getting Started Type of Unit: Introduction Prior Knowledge Students should be able to: Solve and write numerical equations for whole number addition, subtraction, multiplication, and division problems. Use parentheses to evaluate numerical expressions. Identify and use the properties of operations. Lesson Flow In this unit, students are introduced to the rituals and routines that build a successful classroom math community and they are introduced to the basic features of the digital course that they will use throughout the year. An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the lesson routines: Opening, Work Time, Ways of Thinking, Apply the Learning, Summary of the Math, and Reflection. Students learn how to present their work to the class, the importance of taking responsibility for their own learning, and how to effectively participate in the classroom math community. Students then work on Gallery problems to further explore the program’s technology resources and tools and learn how to organize their work. The mathematical work of the unit focuses on numerical expressions, including card sort activities in which students identify equivalent expressions and match an expression card to a word card that describes its meaning. Students use the properties of operations to identify equivalent expressions and to find unknown values in equations.

Material Type: Unit of Study

Math, Grade 7, Samples and Probability

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Samples and ProbabilityType of Unit: ConceptualPrior KnowledgeStudents should be able to:Understand the concept of a ratio.Write ratios as percents.Describe data using measures of center.Display and interpret data in dot plots, histograms, and box plots.Lesson FlowStudents begin to think about probability by considering the relative likelihood of familiar events on the continuum between impossible and certain. Students begin to formalize this understanding of probability. They are introduced to the concept of probability as a measure of likelihood, and how to calculate probability of equally likely events using a ratio. The terms (impossible, certain, etc.) are given numerical values. Next, students compare expected results to actual results by calculating the probability of an event and conducting an experiment. Students explore the probability of outcomes that are not equally likely. They collect data to estimate the experimental probabilities. They use ratio and proportion to predict results for a large number of trials. Students learn about compound events. They use tree diagrams, tables, and systematic lists as tools to find the sample space. They determine the theoretical probability of first independent, and then dependent events. In Lesson 10 students identify a question to investigate for a unit project and submit a proposal. They then complete a Self Check. In Lesson 11, students review the results of the Self Check, solve a related problem, and take a Quiz.Students are introduced to the concept of sampling as a method of determining characteristics of a population. They consider how a sample can be random or biased, and think about methods for randomly sampling a population to ensure that it is representative. In Lesson 13, students collect and analyze data for their unit project. Students begin to apply their knowledge of statistics learned in sixth grade. They determine the typical class score from a sample of the population, and reason about the representativeness of the sample. Then, students begin to develop intuition about appropriate sample size by conducting an experiment. They compare different sample sizes, and decide whether increasing the sample size improves the results. In Lesson 16 and Lesson 17, students compare two data sets using any tools they wish. Students will be reminded of Mean Average Deviation (MAD), which will be a useful tool in this situation. Students complete another Self Check, review the results of their Self Check, and solve additional problems. The unit ends with three days for students to work on Gallery problems, possibly using one of the days to complete their project or get help on their project if needed, two days for students to present their unit projects to the class, and one day for the End of Unit Assessment.

Material Type: Unit of Study

Math, Grade 7, Zooming In On Figures

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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.

Material Type: Unit of Study

Math, Grade 7, Constructions and Angles

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Constructions and Angles Unit Overview Type of Unit: Concept Prior Knowledge Students should be able to: Use a protractor and ruler. Identify different types of triangles and quadrilaterals and their characteristics. Lesson Flow After an initial exploratory lesson involving a paper folding activity that gets students thinking in general about angles and figures in a context, the unit is divided into two concept development sections. The first section focuses on types of angles—adjacent, supplementary, complementary, and vertical—and how they are manifested in quadrilaterals. The second section looks at triangles and their properties, including the angle sum, and how this affects other figures. In the first set of conceptual lessons, students explore different types of angles and where the types of angles appear in quadrilaterals. Students fold paper and observe the angles formed, draw given angles, and explore interactive sketches that test many cases. Students use a protractor and ruler to draw parallelograms with given properties. They explore sketches of parallelograms with specific properties, such as perpendicular diagonals. After concluding the investigation of the angle types, students move on to the next set. In the second set of conceptual development lessons, students focus on triangles. Students again fold paper to create figures and certain angles, such as complementary angles. Students draw, using a protractor and ruler, other triangles with given properties. Students then explore triangles with certain known and unknown elements, such as the number of given sides and angles. This process starts with paper folding and drawing and continues with exploration of interactive sketches. Students draw conclusions about which cases allow 0, 1, 2, or an infinite number of triangles. In the course of the exploration, students discover that the sum of the measure of the interior angles of a triangle is 180°. They also learn that the sum of the measures of the interior angles of a quadrilateral is 360°. They explore other polygons to find their angle sum and determine if there is a relationship to angle sum of triangles. The exploration concludes with finding the measure of the interior angles of regular polygons and speculating about how this relates to a circle. Lastly, students solve equations to find unknown angle measures. Using their previous experience, students find the remaining angle measures in a parallelogram when only one angle measure is given. Students also play a game similar to 20 Questions to identify types of triangles and quadrilaterals. Having completed the remaining lessons, students have a four-day Gallery to explore a variety of problems. The unit ends with a unit assessment.

Material Type: Unit of Study

Math, Grade 7, Proportional Relationships

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Proportional Relationships Type of Unit: Concept Prior Knowledge Students should be able to: Understand what a rate and ratio are. Make a ratio table. Make a graph using values from a ratio table. Lesson Flow Students start the unit by predicting what will happen in certain situations. They intuitively discover they can predict the situations that are proportional and might have a hard time predicting the ones that are not. In Lessons 2–4, students use the same three situations to explore proportional relationships. Two of the relationships are proportional and one is not. They look at these situations in tables, equations, and graphs. After Lesson 4, students realize a proportional relationship is represented on a graph as a straight line that passes through the origin. In Lesson 5, they look at straight lines that do not represent a proportional relationship. Lesson 6 focuses on the idea of how a proportion that they solved in sixth grade relates to a proportional relationship. They follow that by looking at rates expressed as fractions, finding the unit rate (the constant of proportionality), and then using the constant of proportionality to solve a problem. In Lesson 8, students fine-tune their definition of proportional relationship by looking at situations and determining if they represent proportional relationships and justifying their reasoning. They then apply what they have learned to a situation about flags and stars and extend that thinking to comparing two prices—examining the equations and the graphs. The Putting It Together lesson has them solve two problems and then critique other student work. Gallery 1 provides students with additional proportional relationship problems. The second part of the unit works with percents. First, percents are tied to proportional relationships, and then students examine percent situations as formulas, graphs, and tables. They then move to a new context—salary increase—and see the similarities with sales taxes. Next, students explore percent decrease, and then they analyze inaccurate statements involving percents, explaining why the statements are incorrect. Students end this sequence of lessons with a formative assessment that focuses on percent increase and percent decrease and ties it to decimals. Students have ample opportunities to check, deepen, and apply their understanding of proportional relationships, including percents, with the selection of problems in Gallery 2.

Material Type: Unit of Study

7.3 Metabolic Reactions

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Unit Summary This unit on metabolic reactions in the human body starts out with students exploring a real case study of a middle-school girl named M’Kenna, who reported some alarming symptoms to her doctor. Her symptoms included an inability to concentrate, headaches, stomach issues when she eats, and a lack of energy for everyday activities and sports that she used to play regularly. She also reported noticeable weight loss over the past few months, in spite of consuming what appeared to be a healthy diet. Her case sparks questions and ideas for investigations around trying to figure out which pathways and processes in M’Kenna’s body might be functioning differently than a healthy system and why.  Students investigate data specific to M’Kenna’s case in the form of doctor’s notes, endoscopy images and reports, growth charts, and micrographs. They also draw from their results from laboratory experiments on the chemical changes involving the processing of food and from digital interactives to explore how food is transported, transformed, stored, and used across different body systems in all people. Through this work of figuring out what is causing M’Kenna’s symptoms, the class discovers what happens to the food we eat after it enters our bodies and how M’Kenna’s different symptoms are connected. This unit builds towards the following NGSS Performance Expectations (PEs) as described in the OpenSciEd Scope & Sequence: MS-LS1-3, MS-LS1-5, MS-LS1-7, MS-PS1-1, MS-PS1-2. The OpenSciEd units are designed for hands-on learning, and therefore materials are necessary to teach the unit. These materials can be purchased as science kits or assembled using the kit material list. Additional Unit InformationNext Generation Science Standards Addressed in this UnitPerformance ExpectationsThis unit builds toward the following NGSS Performance Expectations (PEs):

Material Type: Activity/Lab, Lesson, Module

8.2 Sound Waves

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Unit Summary In this unit, students develop ideas related to how sounds are produced, how they travel through media, and how they affect objects at a distance. Their investigations are motivated by trying to account for a perplexing anchoring phenomenon — a truck is playing loud music in a parking lot and the windows of a building across the parking lot visibly shake in response to the music. They make observations of sound sources to revisit the K–5 idea that objects vibrate when they make sounds. They figure out that patterns of differences in those vibrations are tied to differences in characteristics of the sounds being made. They gather data on how objects vibrate when making different sounds to characterize how a vibrating object’s motion is tied to the loudness and pitch of the sounds they make. Students also conduct experiments to support the idea that sound needs matter to travel through, and they will use models and simulations to explain how sound travels through matter at the particle level. This unit builds toward the following NGSS Performance Expectations (PEs) as described in the OpenSciEd Scope & Sequence: MS-PS4-1, MS-PS4-2. The OpenSciEd units are designed for hands-on learning and therefore materials are necessary to teach the unit. These materials can be purchased as science kits or assembled using the kit material list.

Material Type: Activity/Lab, Lesson, Module

6.2 Thermal Energy

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Unit Summary This unit on thermal energy transfer begins with students testing whether a new plastic cup sold by a store keeps a drink colder for longer compared to the regular plastic cup that comes free with the drink. Students find that the drink in the regular cup warms up more than the drink in the special cup. This prompts students to identify features of the cups that are different, such as the lid, walls, and hole for the straw, that might explain why one drink warms up more than the other.  Students investigate the different cup features they conjecture are important to explaining the phenomenon, starting with the lid. They model how matter can enter or exit the cup via evaporation However, they find that in a completely closed system, the liquid inside the cup still changes temperature. This motivates the need to trace the transfer of energy into the drink as it warms up. Through a series of lab investigations and simulations, students find that there are two ways to transfer energy into the drink: (1) the absorption of light and (2) thermal energy from the warmer air around the drink. They are then challenged to design their own drink container that can perform as well as the store-bought container, following a set of design criteria and constraints. This unit builds toward the following NGSS Performance Expectations (PEs) as described in the OpenSciEd Scope & Sequence: MS-PS1-4*, MS-PS3-3, MS-PS3-4, MS-PS3-5, MS-PS4-2*, MS-ETS1-4. The OpenSciEd units are designed for hands-on learning and therefore materials are necessary to teach the unit. These materials can be purchased as science kits or assembled using the kit material list.

Material Type: Activity/Lab, Lesson, Module

The Water Cycle Game

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The water cycle game helps you learn how water molecules move through various places including rivers, the ocean, the earth’s surface, the atmosphere and clouds. Actions such as evaporation, runoff, condensation, precipitation, soil absorption and ground water expansion move water from one zone to another.

Material Type: Activity/Lab, Game, Homework/Assignment, Simulation

Length Scales in the Solar System

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A dynamically simplified solar system is constructed from online data to explore the real solar system on many different scales. The realistically scaled solar system is surprising because nothing is visible due to the presence of many different scales. That is why it is usually rescaled in animations or illustrations. This is nice but gives us a wrong sense of distances and sizes. This Demonstration is intended to show the solar system's different scales in their full glory. Since it is hardly possible to see anything when the real scales are used, controls have been added to modify the sizes of the celestial bodies.

Material Type: Activity/Lab, Diagram/Illustration, Homework/Assignment, Interactive, Simulation, Teaching/Learning Strategy

Author: Cedric Voisin

English Language Arts, Grade 12, Project: Self-Portrait

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This project unit—a multimedia self-portrait published in digital form—is the capstone of your students' high school careers. It is a chance for them to pause and reflect on where they've been, where they're going, and who they are as a person. Students will reflect on what they want others to know about them: what they want their message to be and what types of media they might use to convey that message. Students will have the opportunity to express themselves in many different formats—through writing, of course, but also through other media of their choosing. Students will be able to convey your message through visual art, photography, a graphic novel, audio, poetry, or video—practically any type of media they want! ACCOMPLISHMENTS Students will complete a multimedia self-portrait, capturing important aspects of the essence of themselves. Students will contribute one chapter from their multimedia self-portrait to a class anthology. Students will present one chapter from their multimedia self-portrait to the class. GUIDING QUESTIONS These questions are a guide to stimulate thinking, discussion, and writing on the themes and ideas in the unit. For complete and thoughtful answers and for meaningful discussions, students must use evidence based on careful reading of the texts. How is late adolescence a moment of internal and external change? What are the most important qualities of your character—past, present, and future? How can you portray these key aspects of yourself using multimedia? BENCHMARK ASSESSMENT: Cold Read During this unit, on a day of your choosing, we recommend you administer a Cold Read to assess students’ reading comprehension. For this assessment, students read a text they have never seen before and then respond to multiple-choice and constructed-response questions. The assessment is not included in this course materials.

Material Type: Unit of Study

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