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  • MCCRS.Math.Practice.MP.6
2D Representations of 3D Objects
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This lesson unit is intended to help teachers assess how well students are able to visualize two-dimensional cross-sections of representations of three-dimensional objects. In particular, the lesson will help you identify and help students who have difficulties recognizing and drawing two-dimensional cross-sections at different points along a plane of a representation of a three-dimensional object.

Subject:
Geometry
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
4.NF.C.5  Use Concrete Referents to Solve Problems
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This resource provides students with the opportunity to base arithmetic explanations/reasoning on concrete referents such as diagrams, connecting diagrams to a written method. Students will express a fraction with a denominator 10 as an equivalent fraction with a denominator of 100 and use that information to solve a problem.

Subject:
Mathematics
Material Type:
Activity/Lab
Assessment
Homework/Assignment
Author:
MSDE Admin
Linda Schoenbrodt
Amanda Ray
Date Added:
10/04/2018
8th Grade Core Math Review
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Students will create an interactive Powerpoint game where they will create real world problems that are used as clues to move on to the next level. Problems include all 8th grade math standards.

Subject:
Mathematics
Material Type:
Interactive
Author:
Linda Ridings
Date Added:
01/28/2016
CTE Architecture: Fences
Conditions of Use:
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This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Subject:
Architecture and Design
Geometry
Material Type:
Activity/Lab
Homework/Assignment
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
Career Technical Education
Date Added:
03/01/2012
CTE Architecture: Framing a House
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This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Subject:
Architecture and Design
Geometry
Ratios and Proportions
Material Type:
Activity/Lab
Assessment
Homework/Assignment
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
Career Technical Education
Date Added:
03/05/2012
Calculating Volumes of Compound Objects
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This lesson unit is intended to help teahcers assess how well students solve problems involving measurement, and in particular, to identify and help students who have the following difficulties; computing measurements using formulas; decomposing compound shapes into simpler ones; using right triangles and their properties to solve real-world problems.

Subject:
Geometry
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Concord Consortium: Solar Oven
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Elementary grade students investigate heat transfer in this activity to design and build a solar oven, then test its effectiveness using a temperature sensor. It blends the hands-on activity with digital graphing tools that allow kids to easily plot and share their data. Included in the package are illustrated procedures and extension activities. Note Requirements: This lesson requires a "VernierGo" temperature sensing device, available for ~ $40. This item is part of the Concord Consortium, a nonprofit research and development organization dedicated to transforming education through technology. The Consortium develops digital learning innovations for science, mathematics, and engineering.

Subject:
Engineering
Education
Life Science
Ecology
Forestry and Agriculture
Mathematics
Chemistry
Physics
Material Type:
Activity/Lab
Diagram/Illustration
Lecture Notes
Provider:
Concord Consortium
Provider Set:
Concord Consortium Collection
Author:
The Concord Consortium
Date Added:
04/02/2013
Crosscurricular Approach to the Child Labor Practices of the 1800s and 1900s Industrial Revolution
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This a a cross curricular unit encompassing English, History, and Math Common Core Standards to teach the Child Labor practices of 1800s U.S. with the tragedy of Triangle Shirtwaist Factory Fire of 1911 which lead to child labor reform throughout the world and into the modern era.

Subject:
Arts and Humanities
Mathematics
Social Science
Material Type:
Activity/Lab
Assessment
Data Set
Diagram/Illustration
Homework/Assignment
Lecture
Lecture Notes
Lesson Plan
Primary Source
Reading
Simulation
Teaching/Learning Strategy
Author:
Shelley Arca, Victoria Birbeck, Navpre
Navpreet Bedi
Victoria Birbeck
Date Added:
06/25/2017
Estimations and Approximations: The Money Munchers
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This lesson unit is intended to help you assess how well students are able to: Model a situation; make sensible, realistic assumptions and estimates; and use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem.

Subject:
Geometry
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Forces and Interaction: Buoyancy
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Students will conduct a number of investigations involving density and buoyancy to understand the forces applied to objects and the resulting interactions among them.

Subject:
Physical Science
Physics
Material Type:
Activity/Lab
Lesson Plan
Provider:
South Metro-Salem STEM Partnership
Author:
Michelle Arko
Date Added:
07/02/2015
Geometry Problems: Circles and Triangles
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This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties: solving problems by determining the lengths of the sides in right triangles; and finding the measurements of shapes by decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

Subject:
Geometry
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Grade 2 Module 3: Place Value, Counting, and Comparison of Numbers to 1,000
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In this 25-day Grade 2 module, students expand their skill with and understanding of units by bundling ones, tens, and hundreds up to a thousand with straws. Unlike the length of 10 centimeters in Module 2, these bundles are discrete sets. One unit can be grabbed and counted just like a banana?1 hundred, 2 hundred, 3 hundred, etc. A number in Grade 1 generally consisted of two different units, tens and ones. Now, in Grade 2, a number generally consists of three units: hundreds, tens, and ones. The bundled units are organized by separating them largest to smallest, ordered from left to right. Over the course of the module, instruction moves from physical bundles that show the proportionality of the units to non-proportional place value disks and to numerals on the place value chart.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
11/25/2012
Grade 5 Module 3: Addition and Subtraction of Fractions
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In Module 3, students' understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades' centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra.

Subject:
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
11/27/2012
High School Calculus
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Calculus is a year-long course that is comparable to calculus courses at the college or university level. In this course, the technological tools required for exploring, learning, and communicating calculus concepts include Microsoft Word with Microsoft Equation (or its equivalent) for typing math assignments, an approved graphing calculator (see a list of acceptable calculators at College Board AP Central) for the AP Calculus exam, and some type of grapher for creating graphs online such as Graphmatica (Windows) or Grapher (MAC) or an online graphing utility of your choice.

Subject:
Mathematics
Material Type:
Full Course
Author:
Deanna Mayers
Date Added:
06/01/2018
Math, Grade 6, Distributions and Variability
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Distributions and Variability

Type of Unit: Project

Prior Knowledge

Students should be able to:

Represent and interpret data using a line plot.
Understand other visual representations of data.

Lesson Flow

Students begin the unit by discussing what constitutes a statistical question. In order to answer statistical questions, data must be gathered in a consistent and accurate manner and then analyzed using appropriate tools.

Students learn different tools for analyzing data, including:

Measures of center: mean (average), median, mode
Measures of spread: mean absolute deviation, lower and upper extremes, lower and upper quartile, interquartile range
Visual representations: line plot, box plot, histogram

These tools are compared and contrasted to better understand the benefits and limitations of each. Analyzing different data sets using these tools will develop an understanding for which ones are the most appropriate to interpret the given data.

To demonstrate their understanding of the concepts, students will work on a project for the duration of the unit. The project will involve identifying an appropriate statistical question, collecting data, analyzing data, and presenting the results. It will serve as the final assessment.

Subject:
Mathematics
Statistics and Probability
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 6, Equations and Inequalities
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Equations and Inequalities

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Add, subtract, multiply, and divide with whole numbers, fractions, and decimals.
Use the symbols <, >, and =.
Evaluate expressions for specific values of their variables.
Identify when two expressions are equivalent.
Simplify expressions using the distributive property and by combining like terms.
Use ratio and rate reasoning to solve real-world problems.
Order rational numbers.
Represent rational numbers on a number line.

Lesson Flow

In the exploratory lesson, students use a balance scale to find a counterfeit coin that weighs less than the genuine coins. Then continuing with a balance scale, students write mathematical equations and inequalities, identify numbers that are, or are not, solutions to an equation or an inequality, and learn how to use the addition and multiplication properties of equality to solve equations. Students then learn how to use equations to solve word problems, including word problems that can be solved by writing a proportion. Finally, students connect inequalities and their graphs to real-world situations.

Subject:
Mathematics
Algebra
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 6, Expressions
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Expressions

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Write and evaluate simple expressions that record calculations with numbers.
Use parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols.
Interpret numerical expressions without evaluating them.

Lesson Flow

Students learn to write and evaluate numerical expressions involving the four basic arithmetic operations and whole-number exponents. In specific contexts, they create and interpret numerical expressions and evaluate them. Then students move on to algebraic expressions, in which letters stand for numbers. In specific contexts, students simplify algebraic expressions and evaluate them for given values of the variables. Students learn about and use the vocabulary of algebraic expressions. Then they identify equivalent expressions and apply properties of operations, such as the distributive property, to generate equivalent expressions. Finally, students use geometric models to explore greatest common factors and least common multiples.

Subject:
Mathematics
Algebra
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 6, Fractions and Decimals
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Fractions and Decimals

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Multiply and divide whole numbers and decimals.
Multiply a fraction by a whole number.
Multiply a fraction by another fraction.
Write fractions in equivalent forms, including converting between improper fractions and mixed numbers.
Understand the meaning and structure of decimal numbers.

Lesson Flow

This unit extends students’ learning from Grade 5 about operations with fractions and decimals.

The first lesson informally introduces the idea of dividing a fraction by a fraction. Students are challenged to figure out how many times a 14-cup measuring cup must be filled to measure the ingredients in a recipe. Students use a variety of methods, including adding 14 repeatedly until the sum is the desired amount, and drawing a model. In Lesson 2, students focus on dividing a fraction by a whole number. They make a model of the fraction—an area model, bar model, number line, or some other model—and then divide the model into whole numbers of groups. Students also work without a model by looking at the inverse relationship between division and multiplication. Students explore methods for dividing a whole number by a fraction in Lesson 3, for dividing a fraction by a unit fraction in Lesson 4, and for dividing a fraction by another fraction in Lesson 6. Students examine several methods and models for solving such problems, and use models to solve similar problems.

Students apply their learning to real-world contexts in Lesson 6 as they solve word problems that require dividing and multiplying mixed numbers. Lesson 7 is a Gallery lesson in which students choose from a number of problems that reinforce their learning from the previous lessons.

Students review the standard long-division algorithm for dividing whole numbers in Lesson 8. They discuss the different ways that an answer to a whole number division problem can be expressed (as a whole number plus a remainder, as a mixed number, or as a decimal). Students then solve a series of real-world problems that require the same whole number division operation, but have different answers because of how the remainder is interpreted.

Students focus on decimal operations in Lessons 9 and 10. In Lesson 9, they review addition, subtraction, multiplication, and division with decimals. They solve decimal problems using mental math, and then work on a card sort activity in which they must match problems with diagram and solution cards. In Lesson 10, students review the algorithms for the four basic decimal operations, and use estimation or other methods to place the decimal points in products and quotients. They solve multistep word problems involving decimal operations.

In Lesson 11, students explore whether multiplication always results in a greater number and whether division always results in a smaller number. They work on a Self Check problem in which they apply what they have learned to a real-world problem. Students consolidate their learning in Lesson 12 by critiquing and improving their work on the Self Check problem from the previous lesson. The unit ends with a second set of Gallery problems that students complete over two lessons.

Subject:
Mathematics
Ratios and Proportions
Material Type:
Unit of Study
Provider:
Pearson
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.

Subject:
Mathematics
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 6, Putting Math to Work
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Putting Math to Work

Type of Unit: Problem Solving

Prior Knowledge

Students should be able to:

Solve problems with rational numbers using all four operations.
Write ratios and rates.
Use a rate table to solve problems.
Write and solve proportions.
Use multiple representations (e.g., tables, graphs, and equations) to display data.
Identify the variables in a problem situation (i.e., dependent and independent variables).
Write formulas to show the relationship between two variables, and use these formulas to solve for a problem situation.
Draw and interpret graphs that show the relationship between two variables.
Describe graphs that show proportional relationships, and use these graphs to make predictions.
Interpret word problems, and organize information.
Graph in all quadrants of the coordinate plane.

Lesson Flow

As a class, students use problem-solving steps to work through a problem about lightning. In the next lesson, they use the same problem-solving steps to solve a similar problem about lightning. The lightning problems use both rational numbers and rates. Students then choose a topic for a math project. Next, they solve two problems about gummy bears using the problem-solving steps. They then have 3 days of Gallery problems to test their problem-solving skills solo or with a partner. Encourage students to work on at least one problem individually so they can better prepare for a testing situation. The unit ends with project presentations and a short unit test.

Subject:
Mathematics
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 6, Rate
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Rate

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Solve problems involving all four operations with rational numbers.
Understand quantity as a number used with a unit of measurement.
Solve problems involving quantities such as distances, intervals of time, liquid volumes, masses of objects, and money, and with the units of measurement for these quantities.
Understand that a ratio is a comparison of two quantities.
Write ratios for problem situations.
Make and interpret tables, graphs, and diagrams.
Write and solve equations to represent problem situations.

Lesson Flow

In this unit, students will explore the concept of rate in a variety of contexts: beats per minute, unit prices, fuel efficiency of a car, population density, speed, and conversion factors. Students will write and refine their own definition for rate and then use it to recognize rates in different situations. Students will learn that every rate is paired with an inverse rate that is a measure of the same relationship. Students will figure out the logic of how units are used with rates. Then students will represent quantitative relationships involving rates, using tables, graphs, double number lines, and formulas, and they will see how to create one such representation when given another.

Subject:
Mathematics
Algebra
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 6, Rational Numbers
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Rational Numbers

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Solve problems with positive rational numbers.
Plot positive rational numbers on a number line.
Understand the equal sign.
Use the greater than and less than symbols with positive numbers (not variables) and understand their relative positions on a number line.
Recognize the first quadrant of the coordinate plane.

Lesson Flow

The first part of this unit builds on the prerequisite skills needed to develop the concept of negative numbers, the opposites of numbers, and absolute value. The unit starts with a real-world application that uses negative numbers so that students understand the need for them. The unit then introduces the idea of the opposite of a number and its absolute value and compares the difference in the definitions. The number line and positions of numbers on the number line is at the heart of the unit, including comparing positions with less than or greater than symbols.

The second part of the unit deals with the coordinate plane and extends student knowledge to all four quadrants. Students graph geometric figures on the coordinate plane and do initial calculations of distances that are a straight line. Students conclude the unit by investigating the reflections of figures across the x- and y-axes on the coordinate plane.

Subject:
Mathematics
Numbers and Operations
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 6, Ratios
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Ratios

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Calculate with whole numbers up to 100 using all four operations.
Understand fraction notation and percents and translate among fractions, decimal numbers, and percents.
Interpret and use a number line.
Use tables to solve problems.
Use tape diagrams to solve problems.
Sketch and interpret graphs.
Write and interpret equations.

Lesson Flow

The first part of the unit begins with an exploration activity that focuses on a ratio as a way to compare the amount of egg and the amount of flour in a mixture. The context motivates a specific understanding of the use of, and need for, ratios as a way of making comparisons between quantities. Following this lesson, the usefulness of ratios in comparing quantities is developed in more detail, including a contrast to using subtraction to find differences. Students learn to interpret and express ratios as fractions, as decimal numbers, in a:b form, in words, and as data; they also learn to identify equivalent ratios.

The focus of the middle part of the unit is on the tools used to represent ratio relationships and on simplifying and comparing ratios. Students learn to use tape diagrams first, then double number lines, and finally ratio tables and graphs. As these tools are introduced, students use them in problem-solving contexts to solve ratio problems, including an investigation of glide ratios. Students are asked to make connections and distinctions among these forms of representation throughout these lessons. Students also choose a ratio project in this part of the unit (Lesson 8).

The third and last part of the unit covers understanding percents, including those greater than 100%.

Students have ample opportunities to check, deepen, and apply their understanding of ratios, including percents, with the selection of problems in the Gallery.

Subject:
Mathematics
Statistics and Probability
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 7
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Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Subject:
Mathematics
Material Type:
Full Course
Provider:
Pearson
Date Added:
10/06/2016
Math, Grade 7, Algebraic Reasoning
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Algebraic Reasoning

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Add, subtract, multiply, and divide rational numbers.
Evaluate expressions for a value of a variable.
Use the distributive property to generate equivalent expressions including combining like terms.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?
Write and solve equations of the form x+p=q and px=q for cases in which p, q, and x are non-negative rational numbers.
Understand and graph solutions to inequalities x<c or x>c.
Use equations, tables, and graphs to represent the relationship between two variables.
Relate fractions, decimals, and percents.
Solve percent problems included those involving percent of increase or percent of decrease.

Lesson Flow

This unit covers all of the Common Core State Standards for Expressions and Equations in Grade 7. Students extend what they learned in Grade 6 about evaluating expressions and using properties to write equivalent expressions. They write, evaluate, and simplify expressions that now contain both positive and negative rational numbers. They write algebraic expressions for problem situations and discuss how different equivalent expressions can be used to represent different ways of solving the same problem. They make connections between various forms of rational numbers. Students apply what they learned in Grade 6 about solving equations such as x+2=6 or 3x=12 to solving equations such as 3x+6=12 and 3(x−2)=12. Students solve these equations using formal algebraic methods. The numbers in these equations can now be rational numbers. They use estimation and mental math to estimate solutions. They learn how solving linear inequalities differs from solving linear equations and then they solve and graph linear inequalities such as −3x+4<12. Students use inequalities to solve real-world problems, solving the problem first by arithmetic and then by writing and solving an inequality. They see that the solution of the algebraic inequality may differ from the solution to the problem.

Subject:
Mathematics
Algebra
Material Type:
Unit of Study
Provider:
Pearson
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.

Subject:
Mathematics
Geometry
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 7, Getting Started
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Getting Started

Type of Unit: Introduction

Prior Knowledge

Students should be able to:

Understand ratio concepts and use ratios.
Use ratio and rate reasoning to solve real-world problems.
Identify and use the multiplication property of equality.

Lesson Flow

This unit introduces students to the routines that build a successful classroom math community, and it introduces the basic features of the digital course that students 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 routines of Opening, Work Time, Ways of Thinking, Apply the Learning (some lessons), Summary of the Math, Reflection, and Exercises. Students learn how to present their work to the class, the importance of students’ 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 resources and tools and to learn how to organize their work.

The mathematical work of the unit focuses on ratios and rates, including card sort activities in which students identify equivalent ratios and match different representations of an equivalent ratio. Students use the multiplication property of equality to justify solutions to real-world ratio problems.

Subject:
Mathematics
Material Type:
Unit of Study
Provider:
Pearson
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.

Subject:
Mathematics
Ratios and Proportions
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 7, Putting Math to Work
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Putting Math to Work

Type of Unit: Problem Solving

Prior Knowledge

Students should be able to:

Solve problems involving all four operations with rational numbers.
Write ratios and rates.
Write and solve proportions.
Solve problems involving scale.
Write and solve equations to represent problem situations.
Create and interpret maps, graphs, and diagrams.
Use multiple representations (i.e., tables, graphs, and equations) to represent problem situations.
Calculate area and volume.
Solve problems involving linear measurement.

Lesson Flow

Students apply and integrate math concepts they have previously learned to solve mathematical and real-world problems using a variety of strategies. Students have opportunities to explore four real-world situations involving problem solving in a variety of contexts, complete a project of their choice, and work through a series of Gallery problems.

First, students utilize their spatial reasoning and visualization skills to find the least number of cubes needed to construct a structure when given the front and side views. Then, students select a project to complete as they work through this unit to refine their problem-solving skills. Students explore the relationship between flapping frequency, amplitude, and cruising speed to calculate the Strouhal number of a variety of flying and swimming animals. After that, students explore the volume of the Great Lakes, applying strategies for solving volume problems and analyzing diagrams. Next, students graphically represent a virtual journey through the locks of the Welland Canal, estimating the amount of drop through each lock and the distance traveled. Students have a day in class to work on their projects with their group.

Then, students have two days to explore Gallery problems of their choosing. Finally, students present their projects to the class.

Subject:
Mathematics
Material Type:
Unit of Study
Provider:
Pearson
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.

Subject:
Mathematics
Statistics and Probability
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 7, Working With Rational Numbers
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Working With Rational Numbers

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Compare and order positive and negative numbers and place them on a number line.
Understand the concepts of opposites absolute value.

Lesson Flow

The unit begins with students using a balloon model to informally explore adding and subtracting integers. With the model, adding or removing heat represents adding or subtracting positive integers, and adding or removing weight represents adding or subtracting negative integers.

Students then move from the balloon model to a number line model for adding and subtracting integers, eventually extending the addition and subtraction rules from integers to all rational numbers. Number lines and multiplication patterns are used to find products of rational numbers. The relationship between multiplication and division is used to understand how to divide rational numbers. Properties of addition are briefly reviewed, then used to prove rules for addition, subtraction, multiplication, and division.

This unit includes problems with real-world contexts, formative assessment lessons, and Gallery problems.

Subject:
Mathematics
Algebra
Material Type:
Unit of Study
Provider:
Pearson
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.

Subject:
Mathematics
Geometry
Material Type:
Unit of Study
Provider:
Pearson
The Pythagorean Theorem: Square Areas
Rating

This lesson unit is intended to help teachers assess how well students are able to: use the area of right triangles to deduce the areas of other shapes; use dissection methods for finding areas; organize an investigation systematically and collect data; deduce a generalizable method for finding lengths and areas (The Pythagorean Theorem.)

Subject:
Geometry
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Repeating Decimals
Rating

This lesson unit is intended to help teachers assess how well students are able to: translate between decimal and fraction notation, particularly when the decimals are repeating; create and solve simple linear equations to find the fractional equivalent of a repeating decimal; and understand the effect of multiplying a decimal by a power of 10.

Subject:
Algebra
Ratios and Proportions
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Using Dimensions: Designing a Sports Bag
Rating

This lesson unit is intended to help you assess how well students are able to: recognize and use common 2D representations of 3D objects and identify and use the appropriate formula for finding the circumference of a circle.

Subject:
Education
Mathematics
Geometry
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Author:
http://map.mathshell.org/
Date Added:
04/26/2013
Using the Scrum Framework
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In this unit of study, students will learn about and experience the fundamentals of using the Scrum framework for product development. This unit was applied to a VEX robotics team. This unit integrates nine STEM attributes and was developed as part of the South Metro-Salem STEM Partnership's Teacher Leadership Team. Any instructional materials are included within this unit of study.

Subject:
Physical Science
Material Type:
Lecture Notes
Student Guide
Unit of Study
Provider:
South Metro-Salem STEM Partnership
Author:
Greg Smith
Date Added:
05/25/2015