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Author: Capital Region BOCES

  • Grade 4 Math Unit 5

    Conversions, Area, and Perimeter

    Unit description: Students will learn how to complete metric conversions, as well as customary conversions for length and time.  Students will extend their knowledge of area and perimeter from third grade to complete multi-step real world and mathematical problems involving area, perimeter, and different types of rectangles. 

    Essential Outcomes of the Unit

    Measurement and Data- Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit

    • NY-4.MD.1 Know relative sizes of measurement units: ft., in.; km, m, cm. Know the conversion factor and use it to convert measurements in a larger unit in terms of a smaller unit: ft., in.; km, m, cm; hr., min., sec. Given the conversion factor, convert all other measurements within a single system of measurement from a larger unit to a smaller unit. Record measurement equivalents in a two-column table.
    • NY-4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. e.g., Find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

    Other Standards Addressed in the Unit

    Measurement and Data- Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit

    • NY-4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money. 
    • NY-4.MD.2a Solve problems involving fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. 
    • NY-4.MD.2b Represent measurement quantities using diagrams that feature a measurement scale, such as number lines. Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

    Measurement and Data- Represent and interpret data

    NY-4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit 1/2 , 1/4 , 1/8. Solve problems involving addition and subtraction of fractions by using information presented in line plots.

    Essential Questions and Big Ideas

    • How do I convert different sized units?
      • The metric system is based on powers of 10. 
      • There are 12 inches in 1 foot. 
      • There are 60 minutes in an hour.
      • There are 60 seconds in a minute. 
      • Conversions can be recorded in tables.  `
    • How do I solve area and perimeter word problems involving rectangles? 
      • Area represents the total amount of space a flat shape takes up. 
      • Perimeter represents the distance around a shape. 
    • How do I solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money?
      • Distances can be added or compared.
      • Times can be added or subtracted using understandings of minutes and hours. 
      • Volumes can be added or compared based on measurements in beakers or other tools. 
      • Masses can be added or compared based on measurements on scales or other tools. 
      • Money can be added or compared using understandings of cents and dollars. 
    • How do I represent data using a line plot?
      • Line plots represent numerical data. 
      • Xs represent data points of a numerical value. 
      • The scale on a line plot must have equal sized units.

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

  • Grade 7 Social Studies Unit 3

    American Independence

    Unit description: Growing tensions over political power and economic issues sparked a movement for independence from Great Britain. New York played a critical role in the course and outcome of the American Revolution. In this unit students will study how conflicts between France and Great Britain in the 17th and 18th centuries in North America altered the relationship between the colonies and Great Britain. Students will investigate how American colonial leaders outlined their grievances against British policies and actions in the Declaration of Independence. In addition, students will examine how the outcome of the American Revolution was influenced by military strategies, geographic considerations, the involvement of the Haudenosaunee (Iroquois) and other Native American groups in the war.

    Standards

    Standards: 1, 4, 5; Themes: TCC, GOV, ECO

    Essential Questions and Big Ideas

    • Big idea of the unit: Growing tensions over political power and economic issues sparked a movement for independence from Great Britain.
    • What altered the relationship between the colonies and Great Britain in the 17th and 18th centuries?
      • Conflicts between France and Great Britain in the 17th and 18th centuries in North America altered the relationship between the colonies and Great Britain.
    • What was the colonial response to the British government enacting and attempting to enforce new political and economic policies in the colonies?
      • Stemming from the French and Indian War, the British government enacted and attempted to enforce new political and economic policies in the colonies. These policies triggered varied colonial responses, including protests and dissent.
    • What ideas and influences lead to the writing of the Declaration of Independence?
      • Influenced by Enlightenment ideas and their rights as Englishmen, American colonial leaders outlined their grievances against British policies and actions in the Declaration of Independence.
    • What factors impacted the outcome of the American Revolution?
      • The outcome of the American Revolution was influenced by military strategies, geographic considerations, the involvement of the Haudenosaunee (Iroquois) and other Native American groups in the war, and aid from other nations.

    Download the complete Grade 7 Social Studies Unit 3 framework to customize for your own planning.

  • Kindergarten Math Unit 5

    Comparison of Length, Weight, Capacity, and Numbers to 10

    Unit description: In this unit the students will learn to compare numbers of objects in groups within ten. They will compare and describe two objects’ measurable attributes such as height, weight, length and capacity.

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

    Essential Outcomes of the Unit

    Counting and Cardinality- Compare numbers.

    NY-K.CC.6 Identify whether the number of objects in one group is greater than (more than), less than (fewer than), or equal to (the same as) the number of objects in another group. Note: Include groups with up to ten objects.

    Measurement and Data- Describe and compare measurable attributes.

    NY-K.MD.1 Describe measurable attributes of an object(s), such as length or weight, using appropriate vocabulary.

    Other Standard Addressed in the Unit

    Measurement and Data- Describe and compare measurable attributes.

    NY-K.MD.2  Directly compare two objects with a common measurable attribute and describe the difference.

    Essential Questions and Big Ideas

    • What does it mean to compare?  
      • Comparing represents identifying if an amount is greater, lesser, or equal to another.  

    • How do I compare length? 
      • Lengths can be compared by lining objects up end to end and identifying which is longer or shorter.  

    • How do I compare height?  
      • Heights can be compared by lining objects up end to end and identifying which is longer or shorter.  

    • How do I compare weight?  
      • Weight represents how heavy an object is and can be compared by thinking about objects.  

     

  • Grade 3 Math Unit 5

    Time, Liquid and Mass Measurement and Graphing

    Unit description:  Students will develop an understanding of how to understand and relate time, liquid, and mass in word problems. Students will also build on their ability to create bar and picture graphs with scales other than one. They will also represent data using line plots.

    Download the complete Grade 3  Unit 5 framework to customize for your own planning.

    Essential Outcomes of the Unit

    Measurement and Data- Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

    • NY-3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve one-step word problems involving addition and subtraction of time intervals in minutes.

    Measurement and Data- Represent and interpret data.

    • NY-3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in a scaled picture graph or a scaled bar graph.
    • NY-3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

    Other Standards Addressed in the Unit

    Measurement and Data- Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

    • NY-3.MD.2a Measure and estimate liquid volumes and masses of objects using grams (g), kilograms (kg), and liters (l).
      Note: Does not include compound units such as cm3 and finding the geometric volume of a container.
    • NY-3.MD.2b Add, subtract, multiply, or divide to solve one-step word problems involving masses or liquid volumes that are given in the same units.Note: Does not include multiplicative comparison problems involving notions of “times as much.”

    Essential Questions and Big Ideas

    How do I solve word problems involving time?

    • There are 60 minutes in an hour.
    • Number lines can be used to represent time.

    How do I solve word problems involving masses and volumes?

    • Mass represents how much matter is in an item (similar to weight).
    • Volume represents the amount of space a 3-D shape takes up.

    How do I represent data using graphs?

    • Graphs can model data using scales besides one.

    How do I represent data using a line plot?

    • Line plots represent numerical data using Xs.

    Download the complete Grade 3  Unit 5 framework to customize for your own planning.

  • Grade 2 Social Studies Unit 5

    Economic Systems

    Unit description: In this unit, students will investigate how communities face different challenges in meeting their needs and wants. Students will examine how the availability of resources to meet basic needs varies across urban, suburban, and rural communities and how people make decisions to buy, sell, and use money based on their needs, wants, and the availability of resources. Students will also continue their study of scarcity, goods, services, and be introduced to the idea of taxes. In addition, students will study how a community requires the interdependence of many people performing a variety of jobs and services to provide basic needs and wants.

    Download the complete Grade 2 Social Studies – Economic Systems framework to customize for your own planning.

    Standards

    • Standard 1-U.S. & N.Y. History
    • Standard 3-Geography
    • Standard 4-Economics
    • Standard 5-Civics, Citizenship and Gov’t

    Essential Questions and Big Ideas

    Big Idea of the Unit: The economic health of a community is dependent on the amount of goods and services compared to the wants and needs of the people.

    • How does sharing resources help build our communities?
      • When communities share resources they add to the success of the community overall.
    • How does money play a role in goods and services?
      • The monetary value of goods and services is determined based on their availability and the wants and needs of the community.
    • What types of services and products does my community offer?
      • Communities offer goods and services that provide for the wants and needs of the people in the community.
      • Communities have similar and unique wants and needs.

    Prerequisite Skills

    Grade 2 “My Community and Other Communities” is organized into five units of study—Individual Development and Cultural Identity; Civic Ideals and Practices; Geography, Humans, and the Environment; Time, Continuity, and Change; and Economic Systems. These units represent five of the unifying themes of social studies, and may be presented in any order.

  • 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.

  • Grade 6 Social Studies Unit 3

    Early River Valley Civilizations in the Eastern Hemisphere

    Unit description: Complex societies and civilizations developed in the Eastern Hemisphere.Although these complex societies and civilizations have certain defining characteristics in common, each is also known for unique cultural achievements and contributions. In this unit, students will study early human communities in the Eastern Hemisphere and how they adapted to and modified the physical environment.

    Standards

    Standards: 2, 3; Themes: ID, TCC, GEO, SOC

    Essential Questions and Big Ideas

    • Big idea of the unit: Complex societies and civilizations developed in the Eastern Hemisphere.
    • How did humans living together in settlements develop and give identity to their group?
      • Humans living together in settlements develop shared customs, beliefs, ideas, and languages that give identity to the group.
    • What are the common characteristics of complex societies and civilizations?
      • Complex societies and civilizations share the common characteristics of religion, job specialization, cities, government, language/record keeping system, technology, and social hierarchy. People in Mesopotamia, the Yellow River valley, the Indus River valley, and the Nile River valley developed complex societies and civilizations.
    • How do we see these common characteristics evidenced in specific identified societies and civilizations?
      • Mesopotamia, Yellow River valley, Indus River valley, and Nile River valley complex societies and civilizations adapted to and modified their environment to meet the needs of their population.
    • What influenced the access that groups and individuals had to power, wealth, and jobs?
      • Political and social hierarchies influenced the access that groups and individuals had to power, wealth, and jobs and influenced their roles within a society.

    Download the complete Grade 6 Social Studies Unit 3 framework to customize for your own planning.

  • Grade 5 Social Studies Unit 5

    Comparative Cultures

    Unit description: The countries of the Western Hemisphere are diverse and the cultures of these countries are rich and varied. Due to their proximity to each other, the countries of the Western Hemisphere share some of the same concerns and issues. In this unit, students will study how countries of the Western Hemisphere have varied characteristics and contributions that distinguish them from other countries. Students will also investigate how countries in the Western Hemisphere face a variety of concerns and issues specific to the region.

    Standards 

    Standards: 1, 2; Themes: ID, MOV, SOC

    Essential Questions and Big Ideas

    Big idea of the unit: The countries of the Western Hemisphere are diverse and the cultures of these countries are rich and varied.

    What are they key cultural characteristics of the United States, Canada, Mexico, and the Caribbean?

    • Key cultural characteristics include things such as the languages, religions and contributions,

    What is a current issue that two or more Western Hemisphere countries are facing together? 

    • Issues neighboring countries face together change over time. Some examples include environmental issues, immigration, and trade.

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

  • Kindergarten Social Studies Unit 5

    Economic Systems

    Unit description: In this unit, students will examine the idea that people have economic needs and wants. Students will identify basic human needs, and distinguish between a need and want. Students will learn about goods and services in an economy and how they impact the needs and wants of the people in a community. In addition, students will learn about scarcity and of goods and services and be given the opportunity to identify examples of this. 

    Standards 

    Standard 4- Economics

    Standard 5- Civics, Citizenship and Gov’t

    Essential Questions and Big Ideas

    Big Idea: Economic systems help satisfy people’s economic wants and needs.

    What is the difference between a want and a need?

    • A need is something that you must have to survive.
    • A want is something that you would like but that you do not need to survive.

    What are goods and services and how do they help satisfy people’s wants and needs? 

    • Goods are things that people buy.
    • Services are when people pay other people to do work.

    What is scarcity and how does it affect people’s wants and needs? 

    • When there is not a lot of something, it is called scarce.
    • When goods and services are scarce, there are less to fulfill people’s wants and needs.

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

  • Grade 6 Math Unit 3

    Rational Numbers

    Unit description:  In this unit the students will learn to develop the concept of opposite numbers and absolute values, and that zero is its own opposite. They will use positive and negative numbers to represent real-world quantities and compare and order integers and rational numbers with and without number lines. The students will describe the relationship between rational numbers in real-world contexts through comparison and using understanding of absolute value. The students will learn to plot points in all four quadrants, find the distance between points, identify reflections across both axes, and create polygons. 

    Download the complete Rational Numbers framework to customize for your own planning.

    Essential Outcomes of the Unit

    The Number System 

    Apply and extend previous understandings of numbers to the system of rational numbers.

    • 6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in real world contexts, explaining the meaning of 0 in each situation. 
    • 6.NS.6 Understand a rational number as a point on the number line. Use number lines and coordinate axes to represent points on a number line and in the coordinate plane with negative number coordinates.
    • 6.NS.6a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. Recognize that the opposite of the opposite of a number is the number itself, and that 0 is its own opposite.
    • 6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line. Find and position pairs of integers and other rational numbers on a coordinate plane.
    • 6.NS.7 Understand ordering and absolute value of rational numbers. 

    Other Standards Addressed in the Unit

    The Number System 

    Apply and extend previous understandings of numbers to the system of rational numbers

    • 6.NS.6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
    • 6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line.
    • 6.NS.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts
    • 6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
    • 6.NS.7d Distinguish comparisons of absolute value from statements about order. 
    • 6.NS.8 Solve real-world and mathematical problems by graphing points on a coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

    Geometry

    Solve real-world and mathematical problems involving area, surface area, and volume

    • 6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices. Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

    Essential Questions and Big Ideas

    How are positive and negative numbers used?

    • Quantities having more or less than zero are described using positive and negative numbers.

    How do rational numbers relate to integers?

    • Number lines are visual models used to represent the density principle: between any two whole numbers are many rational numbers, including decimals and fractions.
    • The rational numbers can extend to the left or to the right on the number line, with negative numbers going to the left of zero, and positive numbers going to the right of zero.

    What is modeled on the coordinate plane?

    • The coordinate plane is a tool for modeling real-world and mathematical situations and for solving problems.