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  • Grade 7 Math Unit 5

    Geometry

    Unit description: Students will solve real-life and mathematical problems involving angle measures, area, circumference, surface area and volume.

    Essential Outcomes of the Unit

    Geometry- Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

    7.G.4 Apply the formulas for the area and circumference of a circle to solve problems

    7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step

    problem to write and solve simple equations for an unknown angle in a figure.

    Other Standards Addressed in the Unit

    Geometry- Draw, construct, and describe geometrical figures and describe the relationships between them.

    7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

    7.G.2 Draw triangles when given measures of angles and/or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

    7.G.6 Solve real-world and mathematical problems involving area of two-dimensional objects

    composed of triangles and trapezoids. Solve surface area problems involving right prisms and right pyramids composed of triangles and trapezoids. Find the volume of right triangular prisms, and solve volume problems involving three dimensional objects composed of right rectangular prisms.

    7.G.3 Describe the two-dimensional shapes that result from slicing three-dimensional solids parallel or perpendicular to the base.

    Essential Questions and Big Ideas

    How do I apply my knowledge of angles to find missing measurements?

    • Supplementary angles are angles that make a straight angle or 180 degrees. 
    • Complementary angles are angles that make a right angle or 90 degrees.  
    • Vertical angles are opposite each other when two lines intersect and they are equal.  
    • Adjacent angles share a vertex.  
    • Triangles have three angles that add up to 180 degrees.  

    What makes a circle a circle? What does it mean to talk about the size of a circle?

    • The set of points in a plane that are the same distance from another point define a circle. 
    • The radius, diameter, circumference, and area of a circle are related; you can use them to talk about the size of a circle.

    What are scale drawings and how are they useful? 

    • Scale drawings are drawn proportional to real world measurements.  
    • A scale drawing can be created to represent smaller versions of projects.  

    How do I draw, construct, and describe geometrical figures and describe the relationships between them?

    • The area of a shape can be found by decomposing it into known figures, such as triangles and rectangles. 
    • Areas and volumes of triangular shapes can be related to rectangular shapes. 

    Download the complete Grade 7 Math Unit 5 framework to customize for your own planning.

  • Grade 8 Math Unit 5

    Functions of Geometry

    Unit description: In this unit the students will  learn to define, evaluate, and compare functions. They will solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. 

    Download the complete Grade 8 Math Unit 5 framework to customize for your own planning.

    Essential Outcomes of the Unit

    Functions

    Define, evaluate, and compare functions.

    8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

    8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

    Other Standards Addressed in the Unit

    Functions

    Define, evaluate, and compare functions.

    8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. Recognize examples of functions that are linear and nonlinear.

    Geometry

    Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

    8.G.9 Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and real world problems.

    Essential Questions and Big Ideas

    • How do you use functions to model relationships between quantities? 
      • A function is a rule that assigns to each input exactly one output. 
      • The rule for a function determines the relationship.  

    • How can algebra, graphs, tables, and verbal descriptions be used to represent and compare functions?  
      • Functions can be compared based on their rates of change. 
      • Functions can be compared based on their slopes.  
      • Functions can be compared based on their y-intercepts.  

    • Are all linear equations functions? Are all functions linear? How do you know?
      • Functions written in the form y = mx+b are linear functions.  
      • Linear functions have a constant rate of change.  

    • What is the relationship between volume of cones, cylinders, and spheres?
      • The volume of a cylinder can be found by 𝛑r2 h
      • The volume of a cone can be found by 𝛑r2 (h3).
      • The volume of a sphere is 43𝛑r3

    • The volume of a cone is ⅓ of the volume of a cylinder.  
      • When h = 2r, the volume of a cone and a sphere together create a cylinder.  

  • Grade 4 Social Studies Unit 6

    Westward Movement and Industrialization

    Unit description: In this unit, students will study the important role New York State played in the growth of the United States. Students will study life during the 1800s and how people traveled west looking for opportunities. In addition, students will have the opportunity to explore how  economic activities in New York State are varied and have changed over time, including improvements in transportation and technology.

    Standards

    Standards: 1, 3, 4; Themes: MOV, TCC, GEO, ECO, TECH

    Essential Questions and Big Ideas

    Big idea of the Unit: New York State played an important role in the growth of the United States.

    How did people moving west affect economic changes over time in New York State? 

    • After the Revolution, New Yorkers began to move and settle farther west, using roads many of which had begun as Native American trails. To connect the Great Lakes with the Atlantic Ocean, the Erie Canal was built.
    • Existing towns expanded and new towns grew along the canal.

    How did developments in transportation and communication technology have an effect on communities, the State, and the world?

    • The invention of the steam engine and telegraph made transportation and communication faster and easier.

    How were the economic sections of farming, mining, lumbering, and finance affected during this post-revolutionary time?

    • Entrepreneurs and inventors associated with New York State have made important contributions to business and technology
    • Between 1865 and 1915, rapid industrialization occurred in New York State. Over time, industries and manufacturing continued to grow. 

    What role does Industrialization play in the growth of the United States?

    • As manufacturing moved out of New York State, service industries and high-technology industries have grown.

    Download the complete Grade 4 Social Studies Unit 6 framework to customize for your own planning.

  • Grade 7 Math Unit 4

    Unit description: In this unit the students will learn to gather and analyze data to make informed decisions, interpret variability  and predict future outcomes based on data analysis.

    Essential Outcomes of the Unit

    Statistics and Probability

    Investigate chance processes and develop, use, and evaluate probability models.

    7.SP.8 Find probabilities of compound events using organized lists, sample space tables, tree diagrams, and simulation.

    7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

    7.SP.8b Represent sample spaces for compound events using methods such as organized lists, sample space tables, and tree diagrams. For an event described in everyday language, identify the outcomes in the sample space which compose the event.

    7.SP.8c Design and use a simulation to generate frequencies for compound events. 

    Essential Questions and Big Ideas

    How do you measure the probability of an event?

    • You can use words such as unlikely and certain, or a number between 0 and 1 to represent the probability that an event will occur.

    How do you measure the probability of more than one event?

    • A compound event is an event associated with a multi-step action. You can find the number of outcomes of a multi-step process by finding the product of the number of possible outcomes of each step of the process.

    Can you use probability to predict future events?

    • You can perform trials and collect data to find experimental probability. You can reason about all of the possible outcomes of an event and find theoretical probability.

     

    Download the complete Grade 7 Math Unit 4 framework to customize for your own planning.

  • Grade 8 Social Studies Unit 5

    Great Depression

    Unit description:  In this unit, students will study how economic and environmental disasters in the 1930s created hardships for many Americans. In addition, students will investigate, despite much debate about the appropriate role of government, how President Franklin D. Roosevelt helped to create intensive government interventions in the United States economy and society. 

    Standards 

    Standards: 1, 3, 5; Themes: TCC, SOC, GOV, ECO

    Essential Questions and Big Ideas

    Big idea of the unit: Economic and environmental disasters in the 1930s created hardships for many Americans.

    What economic practices of the 1920s contributed to the coming of the Great Depression?

    • Risky investing, protectionism, and overproduction led to the collapse of the stock market, a wave of bank failures, and a long and severe downturn in the economy called the Great Depression.

    What were the lasting effects of the Great Depression on American families?

    • Lasting effects of the Great Depression on American families were loss of jobs, wealth, and homes, noting varying effects based on class, race, and gender. 
    • Deteriorating conditions in New York City and other communities within New York state during the Great Depression.

    What was the purpose of the New Deal and what were the long lasting effects on society and economic life?

    • President Roosevelt issued the New Deal in an attempt to revive the economy and help Americans deal with the hardships of the Great Depression. 
    • These New Deal reforms had a long-lasting effect on the role of government in American society and its economic life, but did not resolve all of the hardships Americans faced.

    Download the complete Grade 8 Social Studies Unit 5 framework to customize for your own planning.

  • Grade 8 Math Unit 4

    Linear Equations

    Unit description: Students will extend their understanding of equations to represent real world contexts to consider linear equations.  Students will leave this unit able to solve linear equations and recognize the number of solutions to a linear equation.  

    Download the complete Linear Equations framework to customize for your own planning.

    Essential Outcomes of the Unit

    Expressions and Equations

    Understand the connections between proportional relationships, lines, and linear equations.

    8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

    Analyze and solve linear equations and pairs of simultaneous linear equations.

    8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and combining like terms. Note: This includes equations that contain variables on both sides of the equation.

    Other Standards Addressed in the Unit

    Expressions and Equations

    Understand the connections between proportional relationships, lines, and linear equations.

    8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

    Analyze and solve linear equations and pairs of simultaneous linear equations.

    8.EE.7 Solve linear equations in one variable.

    8.EE.7a Recognize when linear equations in one variable have one solution, infinitely many solutions, or no solutions. Give examples and show which of these possibilities is the case by successively transforming the given equation into simpler forms

    8.EE.8 . Analyze and solve pairs of simultaneous linear equations.

    8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Recognize when the system has one solution, no solution, or infinitely many solutions

    8.EE.8b Solve systems of two linear equations in two variables with integer coefficients: graphically, numerically using a table, and algebraically. Solve simple cases by inspection.

    8.EE.8c Solve real-world and mathematical problems involving systems of two linear equations in two variables with integer coefficients

    Essential Questions and Big Ideas

    What is a linear equation in one variable? 

    • A linear equation in one variable, is one where there is only one variable and that variable does not have an exponent.  

    How do I simplify terms in an equation?   

    • Like terms can be combined or subtracted. 
    • Like terms are terms with the same variable.  
    • The distributive property can be used to expand an expression or equation.  

    How can I determine the number of solutions to a linear equation?  

    • If an equation ends with an untrue statement, there are no solutions. 
    • If an equation ends with a true statement, there are infinite solutions.  
    • If an equation ends with an x = statement, there is one solution.  

    Download the complete Linear Equations framework to customize for your own planning.

  • Grade 8 Math Unit 3

    Similarity

    Unit description: In this unit the students will  learn to identify properties of dilations and compositions of dilations, describe the effect of dilations on two-dimensional figures in general and using coordinates. They will apply the Pythagorean Theorem to two and three dimensions using real world examples.

    Download the complete Number Pairs Similarity framework to customize for your own planning.

    Essential Outcomes of the Unit

    Geometry

    Understand congruence and similarity using physical models, transparencies, or geometry software

    • 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
    • 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

    Understand and apply the Pythagorean Theorem

    8.G.7 . Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions.

    Other Standards Addressed in the Unit

    Geometry

    Understand congruence and similarity using physical models, transparencies, or geometry software

    • 8.G.4 Know that a two-dimensional figure is similar to another if the corresponding angles are congruent and the corresponding sides are in proportion. Equivalently, two two-dimensional figures are similar if one is the image of the other after a sequence of rotations, reflections, translations, and dilations. Given two similar two-dimensional figures, describe a sequence that maps the similarity between them on the coordinate plane.

    Understand and apply the Pythagorean Theorem

    • 8.G.6 Understand a proof of the Pythagorean Theorem and its converse.
    • 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

    Essential Questions and Big Ideas

    How can you change a figure’s position or size on a 2-D coordinate plane?

    • A figure can be moved using translation, rotation, reflection without changing its size or shape.
    • A figure can change its size through dilation without changing its shape.

    How do you recognize congruence and similarity in figures?

    • Figures that are congruent if the corresponding angles and sides are the same. 
    • Figures are similar if the corresponding angles are the same but the sides may be different.

    How can angle relationships be used to find missing angle measures?

    • Complementary angles have a sum of 90 degrees.
    • Supplementary angles have a sum of 180 degrees.
    • Vertical angles are equivalent.
    • The sum of the interior angles of a triangle is 180 degrees.
    • The sum of the exterior angles of a triangle is 360 degrees.
    • Alternate interior angles are equal.
    • Alternate exterior angles are equal.

    What is the Pythagorean Theorem?  

    • The Pythagorean Theorem is the way to solve for a missing side length in a right triangle. 
    • The Pythagorean Theorem can be proved geometrically or algebraically. 

    Download the complete Number Pairs Similarity framework to customize for your own planning.

  • Grade 4 Social Studies Unit 5

    In Search of Freedom and a Call for Change

    Unit description: In this unit, students will investigate how different groups of people did not have equal rights and freedoms and how as people worked to bring about change, the struggle for rights and freedoms was one factor in the division of the United States that resulted in the Civil War. Students will also begin exploring Women’s Rights and the role New York State played in the Civil War. 

    Essential Outcomes of the Unit

    1. Investigate factors in the division of the United States that resulted in the Civil War. 
    2. Explore Women’s Rights and the role New York State played in the Civil War. 

    Standards

    Standards: 1, 3, 4; Themes: MOV, TCC, GEO, ECO, TECH

    Essential Questions and Big Ideas

    Big idea of the unit: People in America worked to bring about change.

    How did people work to fight against slavery and for change?

    • People worked in a variety of ways to fight slavery.  
    • Samuel Cornish and William Lloyd Garrison worked to educate people about slavery through print. Fredrick Douglass worked to fight slavery by speaking about his experiences as a slave. Harriet Tubman established a system of support, called the Underground Railroad, to help escaped slaves make it to freedom.

    What rights that were given to men were denied to women during the 1800s? 

    • Women during the 1800s fought to gain equal rights to men, including the right to vote.

    Who were some of the most influential people who took action to bring about change?

    • Amelia Bloomer, Sojourner Truth, Elizabeth Cady Stanton, Lucretia Mott, Susan B. Anthony, Matilda Joslyn Gage, and Elizabeth Blackwell were some of the notable people who worked to make change in the Women’s Suffrage Movement.

    What issues resulted in the Civil War?

    • The United States became divided over several issues, including slavery, resulting in the Civil War. 

    What role did New York play in the Civil War? 

    • New York State supported the Union during the Civil War; providing soldiers, equipment, and food.

    Download the complete Grade 4 Social Studies Unit 5 framework to customize for your own planning.

  • Grade 3 ELA Unit 4

    Making Connections Between Genres to Support a Claim

    Unit description: In this culminating unit, students will ask and answer questions and make text connections across various genres. Students will use this genre study to both create various forms of verbal and written responses.

    Students will use their understanding of genres to produce an argumentative response to a cross-curricular prompt, requiring use of multiple genres to collect evidence to support their claims.

    Download the complete Grade 3 ELA Unit 4 framework to customize for your own planning.

    Essential Outcomes of the Unit

    Reading

    • 3R1. Develop and answer questions to locate relevant and specific details in a text to support an answer or inference.

    3R3. In literary texts, describe character traits, motivations, or feelings, drawing on specific details from the text. (RL) In informational texts, describe the relationship among a series of events, ideas, concepts, or steps in a text, using language that pertains to time, sequence, and cause/effect. (RI)

    Reading Foundations- Fluency

    3RF4. Read grade-level text with sufficient accuracy and fluency to support comprehension.

    Language

    3L1. Demonstrate command of the conventions of academic English grammar and usage when writing or speaking.

    3L2. Demonstrate command of the conventions of academic English capitalization, punctuation, and spelling when writing

    3L4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases, choosing flexibly from a range of strategies.

    3L5. Demonstrate understanding of word relationships and nuances in word meanings.

    3L6. Acquire and accurately use conversational, general academic, and content-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went out for dessert).

    Writing

    3W1. Write an argument to support claim(s), using clear reasons and relevant evidence.

    Speaking and Listening

    3SL1. Participate and engage effectively in a range of collaborative discussions with diverse peers and adults, expressing ideas clearly, and building on those of others.

    3SL2.  Determine the central ideas and supporting details or information presented in diverse texts and formats (e.g., including visual, quantitative, and oral). 

    3SL4. Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace.

    All Standards Addressed in this Unit

    • See Reading Foundations Units: 3RF3 a-d
    • 3R1, 3R3, 3R6, 3R7, 3R9
    • 3RF4
    • 3L1, 3L2, 3L3, 3L4 , 3L5, 3L6
    • 3W1
    • 3SL1, 3SL2, 3SL3, 3SL4, 3SL6

    Essential Questions and Big Ideas

    How are genres similar and different?

      • Good readers look for similarities and differences within and across genres
      • Readers use text connections and connections to other classes to look for similarities across different texts and genres 
      • Authors choose to write in a certain genre to create a particular effect with their readers 

    Why is it important to make and support a strong claim?

      • We make claims all the time in life; it’s important to provide valid support for your argument
      • Authors make claims in their writing; good readers identify them and determine if they are valid
      • Good writers create their own claims and choose multiple pieces of evidence to support them 

  • Grade 7 Math Unit 3

    Ratios and Proportional Relationships

    Unit description: In this unit, students will learn to extend knowledge of proportional relationships and ratios related to scale drawings and other real-world situations. They will represent a relationship between two quantities by identifying a constant of proportionality or unit rate. They will also apply proportional relationships and ratios to percent problems.

    Essential Outcomes of the Unit

    Ratios and Proportional Relationships

    Analyze proportional relationships and use them to solve real-world and mathematical problems.

    • 7.RP.1 Compute unit rates associated with ratios of fractions.
    • 7.RP.2 Recognize and represent proportional relationships between quantities.
    • 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Note: Examples of percent problems include: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.

    Other Standards Addressed in the Unit

    Ratios and Proportional Relationships

    Analyze proportional relationships and use them to solve real-world and mathematical problems.

    • 7.RP.2a Decide whether two quantities are in a proportional relationship.
    • 7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
    • 7.RP.2c Represent a proportional relationship using an equation.
    • 7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

    Download the complete Ratios and Proportional Relationships framework to customize for your own planning.