Hoboken Public Schools Math Curriculum Grade Seven

Transcription

1 Hoboken Public Schools Math Curriculum Grade Seven

2 Mathematics Grade Seven HOBOKEN PUBLIC SCHOOLS Course Description Students will engage in the 5 strands of the common core math curriculum. These strands are the number system, geometry, ratio and proportional reasoning, expressions and equations, and statistics and probability. Each strand is broken down into sub categories. This program is designed to introduce and develop a foundation in the mathematical concepts necessary for college and career readiness. Students will engage in the Connected Math Series. This is divided into 8 units of study. Course Resources Connected Math o Unit Workbooks Accentuate the Negative Stretching and Shrinking Comparing and Scaling Moving Straight Ahead What Do You Expect? Filling and Wrapping Samples and Populations Shapes and Designs o Additional Practice and Skills o Dash website o Realize website Weekly Math Minutes ECRs/SCRs/Unit Assessments PARCC Released sample questions Chromebooks RICOH board Communicator / Mini Whiteboards Kuta Software Khanacademy.org NJCTL.org Math-drills.com Edmodo.com Snapshots IXL Teachertube / YouTube Videos Math-drills.com Pacing Guide Unit Accentuate the Negative Explore relationships between positive and negative numbers by modeling them on a number line Time Frame September October

3 Use appropriate notation to indicate positive and negative numbers Compare and order positive and negative rational numbers and locate them on a number line Recognize and use the relationships between a number and its opposite to solve problems Develop and use different models for representing addition, subtraction, multiplying, and dividing integers Recognize situations in which one or more operations of rational numbers are needed Use parentheses and the Order of Operations in computations Understand and use the Commutative Property for addition and multiplication Apply the Distributive Property to simplify expressions and solve problems Stretching and Shrinking Identify similar figures by comparing corresponding sides and angles Use scale factors and ratios to describe relationships among the side lengths, perimeters, and areas of similar figures Recognize the relationship between scale factor and ratio in similar figures Use informal methods, scale factors, and geometric tools to construct similar figures Compare similar figures with nonsimilar figures Distinguish algebraic rules that produce similar figures from those that produce nonsimilar figures Use algebraic rules to produce similar figures Recognize when a rule shrinks or enlarges a figure Use the properties of similarity to find distances and heights that cannot be measured directly Use scale factors or ratios to find missing side lengths in a pair of similar figures Use similarity to solve real-world problems Comparing and Scaling Use ratios, rates, fractions, differences, and percents to write statements comparing two quantities in a given situation Distinguish between and use both part-to-part and part-towhole ratios in comparisons Use percents to express ratios and proportions Recognize that a rate is a special ratio that compares two measurements with different units Write an equation to represent the pattern in a table or graph of proportionality related variables Use various strategies to solve for an unknown in a November December

4 proportion, including scaling, rate tables, percent bars, unit rates, and equivalent ratios Set up and solve proportions that arise from real-world applications, such as finding discounts and markups and converting measurement units Moving Straight Ahead Identify and describe the patterns of change between the independent and dependent variables for linear relationships represented by tables, graphs, equations, or contextual settings Construct tables, graphs, and symbolic equations that represent linear relationships Identify the rate of change between two variables and the x- and y-intercepts from graphs, tables, and equations that represent linear relationships Write equations that represent linear relationships given specific pieces of information, and describe what information the variables and numbers represent Recognize that y = mx represents a proportional relationship Solve linear equations in one variable using symbolic methods, tables, and graphs Solve linear inequalities using graphs or symbolic reasoning Show that two expressions are equivalent Write and interpret equivalent expressions What Do You Expect? Recognize that probabilities are useful for predicting what will happen over the long run For an event described in everyday language, identify the outcomes in a sample space that compose the event Interpret experimental and theoretical probabilities and the relationship between them and recognize that experimental probabilities are better estimates of theoretical probabilities when they are based on larger numbers Distinguish between outcomes that are equally likely or not equally likely by collecting data and analyzing experimental probabilities Realize that the probability of simple events is a ratio of favorable outcomes to all outcomes in the sample space Recognize that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring Filling and Wrapping Describe prisms by using their vertices, faces, and edges Estimate and calculate surface areas and volumes of polygonal prisms by relating them to rectangular prisms Explore the relationships between the surface areas and January February March

5 volumes of prisms Investigate the relationship between volumes of prisms and volumes of cylinders as well as the relationship between surface areas of prisms and surface area of cylinders Solve problems involving surface areas and volumes of solid figures Explore the relationship between circle radius (or diameter) and area Solve problems involving areas and circumferences of circles Estimate and calculate volumes of spheres and cones Solve problems involving surface areas and volumes of spheres and cones Samples and Populations Pose questions, collect data, analyze data, and interpret data to answer questions Choose appropriate measures of center (mean, median, or mode) and spread (range, IQR, or MAD) to summarize a sample Choose appropriate representations to display distributions of samples Compare summary statistics of multiple samples drawn from either the same population or from two different populations and explain how the samples vary Use the randomly generated frequencies for events to draw conclusions Use statistics from representative samples to draw conclusions and populations Use measures of center, measures of spread, and data displays from more than one random sample to compare and draw conclusions about more than one population Use mean and MAD, or median and IQR, from random samples to assess whether the differences in the samples are due to natural variability or due to meaningful differences in the underlying populations Shapes and Designs Explore the patterns among interior and exterior angles of a polygon Explore the patterns among the side lengths in a polygon Investigate the symmetries of a shape-rotation or reflection Use tools to sketch angles Reason about the properties of angles formed by parallel lines and transversals Use information about supplementary, complementary, vertical, and adjacent angles in a shape to solve for an unknown angle in a multi-step problem April-May June

6 Draw or sketch polygons with given conditions by using various tools and techniques such as freehand, use of a ruler and protractor, and use of technology Determine what conditions will produce a unique polygon, more than one polygon, or no polygon, particularly triangles and quadrilaterals Solve problems that involve properties of shapes *** For Section 7A Only: Linear Equations Find slope of lines Explore the relationship between the lines y = mx and y = mx + b Write an equation of a line in slope-intercept form Understanding graphing linear equations Sketch a linear graph by using m and b *** For Section 7A Only: Transformations Understand the concept of a translation Draw images after translations Find the coordinates of points after translations Understand the concept of a reflection Draw images after reflections Find the coordinates of points after reflections Understand the concept of a rotation Draw images after rotations Find the coordinates of points after rotations Understand the concept of a dilation Find the dimensions of figures after dilations Draw images after dilations Compare translations, reflections, rotations, and dilations May-June May-June Unit 1- Accentuate the Negative Unit 1 Description In this unit students develop an understanding that rational numbers consist of positive numbers, negative numbers, and zero. In addition, students will develop understanding of operations with rational numbers and their properties. Essential Questions How are negative numbers used in the real world context? How are rational numbers modeled on number lines? How are rational numbers used in multiple forms (in multiplication, division, addition, and subtraction)? How are opposite quantities combined in order to make 0?

7 Essential Learning Outcomes Students will be able to use appropriate notation to indicate positive and negative numbers Students will be able to recognize and use the relationship between a number and its opposite (additive inverse) to solve problems Students will be able to use models and rational numbers to represent and solve problems Students will be able to develop algorithms for adding, subtracting, multiplying, and dividing integers Students will be able to apply the distributive property to simplify expressions and solve problems Technology Infusion 8.1 Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problem individually and collaborate and to create and communicate knowledge A.5: Select and use appropriate tools and digital resources to accomplish a variety of tasks and to solve problems. Standards Addressed 7.NS.A.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.A.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 7.NS.A.3: Solve real-world and mathematical problems involving the four operations with rational numbers. 7.EE.B.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Differentiation Teach prerequisite vocabulary. Provide teacher models, multiplication tables, and calculators when necessary and appropriate.

8 Provide students with multiple options for how they can represent their understandings (e.g. multisensory techniques-auditory/visual aids; pictures, illustrations, graphs, charts, data tables, multimedia, modeling). Provide multiple grouping opportunities for students to share their ideas and to encourage work among various backgrounds and cultures (e.g. multiple representation and multimodal experiences). Provide ELL students with multiple literacy strategies. Use a variety of representations and presentations of material to students (videos, lectures, peer models, etc.) Give materials at different reading levels. Manipulate numbers to enrich or remediate for students. Collaborate with after-school programs or clubs to extend learning opportunities. Assessments Class participation Connected Math unit readiness Connected Math investigations Connected Math check ups / quizzes Connected Math unit assessments Discussions demonstrating knowledge of subject matter ECRs, SCRs, Weekly Math Minutes Edmodo snapshots 21 st Century Learning Connection "21st century skills" are the skills that today's students will need to be successful in this everchanging world. The most recognizable of these skills are the 4C's: communication, collaboration, critical thinking and creativity. However, 21st century skills also include social and emotional intelligence, technological literacy and problem solving abilities. These skills emphasize "application of knowledge" and go beyond rote memorization. Unit 2 - Stretching and Shrinking Unit 2 Description In this unit students will learn to understand what it means for figures to be similar, and develop strategies for using similar figures to solve problems Essential Questions How would you understand what it means for figures to be similar? How are strategies developed using similar figures to solve problems? How scale drawings used in the real world? Essential Learning Outcomes Students will be able to identify similar figures by comparing corresponding sides and angles

9 Students will be able to use informal methods, scale factors, and geometric figures from those that produce nonsimilar figures Students will be able to determine when a rule shrinks or enlarges a figure Students will be able to use scale factors or ratios to find missing side lengths in a pair of similar figures Technology Infusion 8.1 Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problem individually and collaborate and to create and communicate knowledge A.5: Select and use appropriate tools and digital resources to accomplish a variety of tasks and to solve problems. Standards Addressed 7.RP.A.2: Recognize and represent proportional relationships between quantities. 7.RP.A.3: Use proportional relationships to solve multistep ratio and percent problems. 7.EE.B.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 7.G.A.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.A.2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Differentiation Teach prerequisite vocabulary. Provide teacher models, multiplication tables, and calculators when necessary and appropriate. Provide students with multiple options for how they can represent their understandings (e.g. multisensory techniques-auditory/visual aids; pictures, illustrations, graphs, charts, data tables, multimedia, modeling). Provide multiple grouping opportunities for students to share their ideas and to encourage work among various backgrounds and cultures (e.g. multiple representation and multimodal experiences). Provide ELL students with multiple literacy strategies. Use a variety of representations and presentations of material to students (videos, lectures, peer models, etc.)

10 Give materials at different reading levels. Manipulate numbers to enrich or remediate for students. Collaborate with after-school programs or clubs to extend learning opportunities. Assessments Class participation Connected Math unit readiness Connected Math investigations Connected Math check ups / quizzes Connected Math unit assessments Discussions demonstrating knowledge of subject matter ECRs, SCRs, Weekly Math Minutes Edmodo snapshots 21 st Century Learning Connection "21st century skills" are the skills that today's students will need to be successful in this everchanging world. The most recognizable of these skills are the 4C's: communication, collaboration, critical thinking and creativity. However, 21st century skills also include social and emotional intelligence, technological literacy and problem solving abilities. These skills emphasize "application of knowledge" and go beyond rote memorization. Unit 3 - Comparing and Scaling Unit 3 Description In this unit students will understand ratios, rates, and percents as well as understand proportionality in tables, graphs, and equations. In addition, students will develop and use strategies for solving problems that require proportional reasoning. Essential Questions How is unit rate used in mathematics and what is the purpose? How are proportional relationships determined? How can proportional relationships be used to solve multistep ratio/percent problems? Essential Learning Outcomes Students will be able to use ratios, rates, fractions, differences, and percents to write statements comparing two quantities in a given situation Students will be able to distinguish between and use both part-to-part and part-to-whole ratios in comparisons Students will be able to write an equation to represent the pattern in a table or graph of proportionally related variables Students will be able to relate the unit rate and constant of proportionality to an equation, graph, or table describing a proportional situation Students will be able to set up and solve proportions that arise from real-world applications, such as finding discounts and markups

11 Technology Infusion 8.1 Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problem individually and collaborate and to create and communicate knowledge A.5: Select and use appropriate tools and digital resources to accomplish a variety of tasks and to solve problems. Standards Addressed 7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units 7.RP.A.2 Recognize and represent proportional relationships between quantities 7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems 7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Differentiation Teach prerequisite vocabulary. Provide teacher models, multiplication tables, and calculators when necessary and appropriate. Provide students with multiple options for how they can represent their understandings (e.g. multisensory techniques-auditory/visual aids; pictures, illustrations, graphs, charts, data tables, multimedia, modeling). Provide multiple grouping opportunities for students to share their ideas and to encourage work among various backgrounds and cultures (e.g. multiple representation and multimodal experiences). Provide ELL students with multiple literacy strategies. Use a variety of representations and presentations of material to students (videos, lectures, peer models, etc.) Give materials at different reading levels. Manipulate numbers to enrich or remediate for students. Collaborate with after-school programs or clubs to extend learning opportunities. Assessments Class participation Connected Math unit readiness Connected Math investigations Connected Math check ups / quizzes Connected Math unit assessments Discussions demonstrating knowledge of subject matter ECRs, SCRs, Weekly Math Minutes Edmodo snapshots

12 21 st Century Learning Connection "21st century skills" are the skills that today's students will need to be successful in this everchanging world. The most recognizable of these skills are the 4C's: communication, collaboration, critical thinking and creativity. However, 21st century skills also include social and emotional intelligence, technological literacy and problem solving abilities. These skills emphasize "application of knowledge" and go beyond rote memorization. Unit 4 - Moving Straight Ahead Unit 4 Description In this unit students will learn to recognize problem situations in which two variables have a linear relationship, as well as understand that the equality sign indicates that two expressions are equivalent. Essential Questions How would discovering strategies to factor and expand linear expressions with rational coefficients help in a student s understanding of equivalent expressions? How would applying properties of operation to add and subtract linear expressions with rational coefficients help in solving complex number sentences? How are equivalent forms of an expression discovered and what is the purpose? How can a solution set be represented in a graph? Essential Learning Outcomes Students will be able to construct tables, graphs, and symbolic equations that represent linear relationships Students will be able to solve problems and make decisions about linear equations using information given in tables, graphs, and equations Students will be able to solve linear equations in one variable using symbolic methods, tables, and graphs Students will be able to solve linear inequalities using graphs or symbolic reasoning Students will be able to interpret equivalent equations Technology Infusion 8.1 Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problem individually and collaborate and to create and communicate knowledge A.5: Select and use appropriate tools and digital resources to accomplish a variety of tasks and to solve problems. Standards Addressed 7.RP.A.2 Recognize and represent proportional relationships between quantities. 7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, or expand linear expressions with rational coefficients.

13 7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. 7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Differentiation Teach prerequisite vocabulary. Provide teacher models, multiplication tables, and calculators when necessary and appropriate. Provide students with multiple options for how they can represent their understandings (e.g. multisensory techniques-auditory/visual aids; pictures, illustrations, graphs, charts, data tables, multimedia, modeling). Provide multiple grouping opportunities for students to share their ideas and to encourage work among various backgrounds and cultures (e.g. multiple representation and multimodal experiences). Provide ELL students with multiple literacy strategies. Use a variety of representations and presentations of material to students (videos, lectures, peer models, etc.) Give materials at different reading levels. Manipulate numbers to enrich or remediate for students. Collaborate with after-school programs or clubs to extend learning opportunities. Assessments Class participation Connected Math unit readiness Connected Math investigations Connected Math check ups / quizzes Connected Math unit assessments Discussions demonstrating knowledge of subject matter ECRs, SCRs, Weekly Math Minutes Edmodo snapshots 21 st Century Learning Connection "21st century skills" are the skills that today's students will need to be successful in this everchanging world. The most recognizable of these skills are the 4C's: communication, collaboration, critical thinking and creativity. However, 21st century skills also include social and emotional intelligence, technological literacy and problem solving abilities. These skills emphasize "application of knowledge" and go beyond rote memorization. Unit 5 Description Unit 5 - What Do You Expect?

14 In this unit students will understand experimental and theoretical probability. In addition, students will explore and develop probability models by identifying possible outcomes, and analyze probabilities to solve problems. Essential Questions How is an event distinguished as experimental or theoretical? How is the relationship between a sample and a population determined? How can data from random samples be used to interpret information? Essential Learning Outcomes Students will be able to identify the outcomes in a sample space that compose an event Students will be able to interpret experimental and theoretical probabilities and the relationship between them and recognize that experimental probabilities are better estimates of theoretical probabilities when they are based on larger numbers Students will be able to recognize that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring Students will be able to develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events Technology Infusion 8.1 Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problem individually and collaborate and to create and communicate knowledge A.5 Select and use appropriate tools and digital resources to accomplish a variety of tasks and to solve problems. Standards Addressed 7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.C.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. 7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. 7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Differentiation Teach prerequisite vocabulary.

15 Provide teacher models, multiplication tables, and calculators when necessary and appropriate. Provide students with multiple options for how they can represent their understandings (e.g. multisensory techniques-auditory/visual aids; pictures, illustrations, graphs, charts, data tables, multimedia, modeling). Provide multiple grouping opportunities for students to share their ideas and to encourage work among various backgrounds and cultures (e.g. multiple representation and multimodal experiences). Provide ELL students with multiple literacy strategies. Use a variety of representations and presentations of material to students (videos, lectures, peer models, etc.) Give materials at different reading levels. Manipulate numbers to enrich or remediate for students. Collaborate with after-school programs or clubs to extend learning opportunities. Assessments Class participation Connected Math unit readiness Connected Math investigations Connected Math check ups / quizzes Connected Math unit assessments Discussions demonstrating knowledge of subject matter ECRs, SCRs, Weekly Math Minutes Edmodo snapshots 21 st Century Learning Connection "21st century skills" are the skills that today's students will need to be successful in this everchanging world. The most recognizable of these skills are the 4C's: communication, collaboration, critical thinking and creativity. However, 21st century skills also include social and emotional intelligence, technological literacy and problem solving abilities. These skills emphasize "application of knowledge" and go beyond rote memorization. Unit 6 - Filling and Wrapping Unit 6 Description In this unit students will understand surface areas and volumes of prisms and cylinders and how they are related, as well as determine the areas and circumferences of circles and how they are related. Lastly, students will analyze the relationships between the volumes of cylinders and the volumes of cones and spheres. Essential Questions How would the area of a figure be determined? How would surface area of a figure be configured from varying objects? How would changing the radius or diameter of a circle affect its circumference and area?

16 How can keywords be used to solve real-world problems involving volume and surface areas as well as two-dimensional objects? Essential Learning Outcomes Students will be able to describe prisms by using their vertices, faces, and edges Students will be able to investigate the relationship between volumes of prisms and volumes of cylinders as well as the relationship between surface areas of prisms and surface areas of cylinders Students will be able to solve problems involving surface areas and volumes of solid figures Students will be able to estimate and calculate areas and circumferences of circles Students will be able to estimate and calculate volumes of spheres and cones Technology Infusion 8.1 Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problem individually and collaborate and to create and communicate knowledge A.5: Select and use appropriate tools and digital resources to accomplish a variety of tasks and to solve problems. Standards Addressed 7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 7.G.A.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.A.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. 7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Differentiation Teach prerequisite vocabulary. Provide teacher models, multiplication tables, and calculators when necessary and appropriate.

17 Provide students with multiple options for how they can represent their understandings (e.g. multisensory techniques-auditory/visual aids; pictures, illustrations, graphs, charts, data tables, multimedia, modeling). Provide multiple grouping opportunities for students to share their ideas and to encourage work among various backgrounds and cultures (e.g. multiple representation and multimodal experiences). Provide ELL students with multiple literacy strategies. Use a variety of representations and presentations of material to students (videos, lectures, peer models, etc.) Give materials at different reading levels. Manipulate numbers to enrich or remediate for students. Collaborate with after-school programs or clubs to extend learning opportunities. Assessments Class participation Connected Math unit readiness Connected Math investigations Connected Math check ups / quizzes Connected Math unit assessments Discussions demonstrating knowledge of subject matter ECRs, SCRs, Weekly Math Minutes Edmodo snapshots 21 st Century Learning Connection "21st century skills" are the skills that today's students will need to be successful in this everchanging world. The most recognizable of these skills are the 4C's: communication, collaboration, critical thinking and creativity. However, 21st century skills also include social and emotional intelligence, technological literacy and problem solving abilities. These skills emphasize "application of knowledge" and go beyond rote memorization. Unit 7 - Samples and Populations Unit 7 Description In this unit students will deepen the understanding of the process of investigation and apply this to samples, as well as understand that data values in a sample vary and that summary statistics of samples taken from the same population also vary. In addition, students will understand that simulations can model real world situations. Lastly, students will understand that summary statistics of a representative sample can be used to gain information about a population. Essential Questions How can measures of center for numerical data be used to provide information about two populations? How can measures of variability for numerical data be used to provide information about two populations?

18 How is information complied in order to determine what the MAD can you share about a set of data? Essential Learning Outcomes Students will be able to pose questions, collect data, analyze data, and interpret data to answer questions Students will be able to choose appropriate measures of center (mean, median, or mode) and spread (range, IQR, or MAD) to summarize a sample Students will be able to use the randomly generated frequencies for events to draw conclusions Students will be able to use mean and MAD, or median and IQR, from random samples to assess whether the differences in the samples are due to natural variability or due to meaningful differences in the underlying populations Technology Infusion 8.1 Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problem individually and collaborate and to create and communicate knowledge A.5: Select and use appropriate tools and digital resources to accomplish a variety of tasks and to solve problems. Standards Addressed 7.SP.A.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.A.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. 7.SP.B.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. 7.SP.B.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. Differentiation Teach prerequisite vocabulary. Provide teacher models, multiplication tables, and calculators when necessary and appropriate. Provide students with multiple options for how they can represent their understandings (e.g. multisensory techniques-auditory/visual aids; pictures, illustrations, graphs, charts, data tables, multimedia, modeling).

19 Provide multiple grouping opportunities for students to share their ideas and to encourage work among various backgrounds and cultures (e.g. multiple representation and multimodal experiences). Provide ELL students with multiple literacy strategies. Use a variety of representations and presentations of material to students (videos, lectures, peer models, etc.) Give materials at different reading levels. Manipulate numbers to enrich or remediate for students. Collaborate with after-school programs or clubs to extend learning opportunities. Assessments Class participation Connected Math unit readiness Connected Math investigations Connected Math check ups / quizzes Connected Math unit assessments Discussions demonstrating knowledge of subject matter ECRs, SCRs, Weekly Math Minutes Edmodo snapshots 21 st Century Learning Connection "21st century skills" are the skills that today's students will need to be successful in this everchanging world. The most recognizable of these skills are the 4C's: communication, collaboration, critical thinking and creativity. However, 21st century skills also include social and emotional intelligence, technological literacy and problem solving abilities. These skills emphasize "application of knowledge" and go beyond rote memorization. Unit 8 - Shapes and Designs Unit 8 Description In this unit students will understand that properties of polygons that affect their shape, as well as understand special relationships among angles. In addition, students will understand the properties needed to construct polygons. Essential Questions How do certain professions utilize supplementary and complementary angles? How are lines and angles represented in our world? How do the properties of geometric figures influence their uses? Essential Learning Outcomes Students will be able to explore the patterns among interior and exterior angles of a polygon Students will be able to use tools to sketch angles Students will be able to use information about supplementary, complementary, vertical, and adjacent angles in a shape to solve for an unknown angle in a multi-step problem

20 Students will be able to draw or sketch polygons with given conditions by using various tools and techniques such as freehand, use of a ruler and protractor, and use of technology Students will be able to solve problems that involve properties of shapes Technology Infusion 8.1 Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problem individually and collaborate and to create and communicate knowledge A.5: Select and use appropriate tools and digital resources to accomplish a variety of tasks and to solve problems. Standards Addressed 7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.G.A.2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.G.B.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. Differentiation Teach prerequisite vocabulary. Provide teacher models, multiplication tables, and calculators when necessary and appropriate. Provide students with multiple options for how they can represent their understandings (e.g. multisensory techniques-auditory/visual aids; pictures, illustrations, graphs, charts, data tables, multimedia, modeling). Provide multiple grouping opportunities for students to share their ideas and to encourage work among various backgrounds and cultures (e.g. multiple representation and multimodal experiences). Provide ELL students with multiple literacy strategies. Use a variety of representations and presentations of material to students (videos, lectures, peer models, etc.) Give materials at different reading levels. Manipulate numbers to enrich or remediate for students. Collaborate with after-school programs or clubs to extend learning opportunities. Assessments Class participation Connected Math unit readiness Connected Math investigations Connected Math check ups / quizzes

21 Connected Math unit assessments Discussions demonstrating knowledge of subject matter ECRs, SCRs, Weekly Math Minutes Edmodo snapshots 21 st Century Learning Connection "21st century skills" are the skills that today's students will need to be successful in this everchanging world. The most recognizable of these skills are the 4C's: communication, collaboration, critical thinking and creativity. However, 21st century skills also include social and emotional intelligence, technological literacy and problem solving abilities. These skills emphasize "application of knowledge" and go beyond rote memorization. *** For Section 7A Only Unit 9 - Linear Equations Unit 9 Description In this unit students will cover 8th grade topics. Students will learn that slope represents unit rates, and the ratio of rise to run is the change in y-values divided by the respective change in x- values. In addition, students will learn the equations of the form y = mx pass through the origin and equations of the form y = mx + b intercept the vertical axis at b. Essential Questions How can you write an equation in slope intercept form? How can you sketch a linear graph using m and b? Essential Learning Outcomes Students will be able to find the slope of a line Students will be able to explore the relationship between the lines y = mx and y = mx + b Students will be able to write an equation of a line in slope-intercept form Students will be able to understand graphing linear equations Students will be able to sketch a linear graph by using m and b Technology Infusion 8.1 Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problem individually and collaborate and to create and communicate knowledge A.5: Select and use appropriate tools and digital resources to accomplish a variety of tasks and to solve problems. Standards Addressed 8.EE.C.7 Solve linear equations in one variable.

22 8.EE.C.8 Analyze and solve pairs of simultaneous linear equations. Differentiation Teach prerequisite vocabulary. Provide teacher models, multiplication tables, and calculators when necessary and appropriate. Provide students with multiple options for how they can represent their understandings (e.g. multisensory techniques-auditory/visual aids; pictures, illustrations, graphs, charts, data tables, multimedia, modeling). Provide multiple grouping opportunities for students to share their ideas and to encourage work among various backgrounds and cultures (e.g. multiple representation and multimodal experiences). Provide ELL students with multiple literacy strategies. Use a variety of representations and presentations of material to students (videos, lectures, peer models, etc.) Give materials at different reading levels. Manipulate numbers to enrich or remediate for students. Collaborate with after-school programs or clubs to extend learning opportunities. Assessments Class participation Connected Math unit readiness Connected Math investigations Connected Math check ups / quizzes Connected Math unit assessments Discussions demonstrating knowledge of subject matter ECRs, SCRs, Weekly Math Minutes Edmodo snapshots 21 st Century Learning Connection "21st century skills" are the skills that today's students will need to be successful in this everchanging world. The most recognizable of these skills are the 4C's: communication, collaboration, critical thinking and creativity. However, 21st century skills also include social and emotional intelligence, technological literacy and problem solving abilities. These skills emphasize "application of knowledge" and go beyond rote memorization. *** For Section 7A Only Unit 10 - Transformations Unit 10 Description In this unit students will cover 8th grade topics. Students will learn about transformations that include; rotations, reflections, translations, and dilations. Transformations can be described using coordinates.

23 Essential Questions How are transformations performed on varying figures? How do you know if the dilation is less than 1 or greater than 1? How is translations, reflections, rotations, and dilations compared? Essential Learning Outcomes Students will be able to understand the concept of translations, reflections, rotations, and dilations Students will be able to draw images after translations, reflections, rotations, and dilations Students will be able to find the coordinates of points after translations, reflections, rotations, and dilations Students will be able to compare translations, reflections, rotations, and dilations Technology Infusion 8.1 Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problem individually and collaborate and to create and communicate knowledge A.5: Select and use appropriate tools and digital resources to accomplish a variety of tasks and to solve problems. Standards Addressed 8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations 8.G.A.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. Differentiation Teach prerequisite vocabulary. Provide teacher models, multiplication tables, and calculators when necessary and appropriate. Provide students with multiple options for how they can represent their understandings (e.g. multisensory techniques-auditory/visual aids; pictures, illustrations, graphs, charts, data tables, multimedia, modeling). Provide multiple grouping opportunities for students to share their ideas and to encourage work among various backgrounds and cultures (e.g. multiple representation and multimodal experiences). Provide ELL students with multiple literacy strategies. Use a variety of representations and presentations of material to students (videos, lectures, peer models, etc.) Give materials at different reading levels.

24 Manipulate numbers to enrich or remediate for students. Collaborate with after-school programs or clubs to extend learning opportunities. Assessments Class participation Connected Math unit readiness Connected Math investigations Connected Math check ups / quizzes Connected Math unit assessments Discussions demonstrating knowledge of subject matter ECRs, SCRs, Weekly Math Minutes Edmodo snapshots 21 st Century Learning Connection "21st century skills" are the skills that today's students will need to be successful in this everchanging world. The most recognizable of these skills are the 4C's: communication, collaboration, critical thinking and creativity. However, 21st century skills also include social and emotional intelligence, technological literacy and problem solving abilities. These skills emphasize "application of knowledge" and go beyond rote memorization.