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District OverviewThe mathematics curriculum provides sequential and comprehensive K-12 instruction in a collaborative, student-centered learning environment that fosters critical thinking, creativity, skillful problem-solving, and effective communication in order to enable all students to adapt to an ever-changing, global society and increase college and career readiness. An emphasis has been placed on conceptual understanding, higher-order thinking, and problem solving skills to prepare students for 21st century careers. This is further embedded through the integrated use of technology into daily lessons. Instruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with content as they build and expand their knowledge and understanding of mathematics. Students will experience mathematics as a coherent and useful subject within the context of real-life situations. In all, the curriculum aims to reach high standards while encouraging curiosity and building confidence in a collaborative atmosphere.

Grade 7 DescriptionIn grade 7, Instructional Time should focus on 5 critical areas:

Analyze proportional relationships and use them to solve real-world and mathematical problems. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Use properties of operations to generate equivalent expressions. Solve real-life and mathematical problems using numerical and

algebraic expressions and equations. Draw, construct and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical

problems involving angle measure, area, surface area, and volume Use random sampling to draw inferences about a population. Draw informal comparative inferences about tow populations. Investigate

chance processes and develop, use, and evaluate probability models. Grade 7 Topics:

Topic 1: Integers and Rational Numbers Topic 2: Analyze and Use Proportional Relationships Topic 3: Analyze and Solve Percent Problems Topic 4: Generate Equivalent Expressions Topic 5: Solve Problems Using Equations and Inequalities Topic 6: Use Sampling to Draw Inferences About Populations Topic 7: Probability Topic 8: Solve Problems involving Geometry

Subject: Mathematics Grade: 7 Suggested Timeline: 17 – 19 days

Unit Title: Topic 1: Integers and Rational Numbers

Unit Overview/Essential Understanding: In Unit 1, students will identify integers and their opposites as additive inverses, having a sum of zero. They will express rational numbers as fractions and decimals in addition to performing addition, subtraction, multiplication and division with integers as well as fractions and decimals, both positive and negative. Students will problem solve with rational numbers by making sense of the quantities and their relationship to each other. Unit Objectives: At the end of this module, students will be able to independently use their learning to:

understand how integers and their opposites are related identify rational numbers and write them in decimal form add positive and negative integers model integer addition in real-life applications understand subtraction of integers as adding the additive inverse use properties of operations to add and subtract rational numbers multiply positive and negative integers apply integer multiplication to real-life applications find the product of rational numbers understand how to divide integers by applying the rules of multiplying the rules of multiplying integers determine equivalence among integer quotients understand how the signs of integers in a multiplication sentence relate to the signs in a related division statement decide which operations to use to solve problems use precision when solving problems with rational numbers

Focus Standards Addressed in this Unit: CC.2.1.7.E.1 – Apply and extend previous understandings of operations with fractions to operations with rational numbersImportant Standards Addressed in this Unit:N/AMisconceptions:

Students believe that negative rational numbers are calculated using the same algorithm as positive, rational numbers. Students believe that when multiplying or dividing negative, rational numbers that they have a negative product or quotient. Students are challenged by the operation rules for fractions and decimals.

Students are challenged by rules for rounding numbers (both terminating and repeating).

Concepts/Content: Rational Numbers

Competencies/Skills:

Solve real-world and mathematical problems involving the four operations with rational numbers

Description of Activities: Solve and Discuss Explore It! Guided Practice Independent Practice

Assessments: Topic Assessment Lesson Quizzes Mid Topic Checkpoint Mid Topic Performance Task Projects when appropriate for understanding

Interdisciplinary Connections: 3-Act Math Modeling Lesson STEM project

Additional Resources: www.ixl.com Teacher created supplementary material Pearson, enVisionmath2.0

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Unit Title: Topic 2: Analyze and use Proportional Relationships

Unit Overview/Essential Understanding: In Unit 2, students will be using equivalent ratios and unit rates to compare ratios and problem solve. They will find that a unit rate can be easier to use to solve problems than a ratio of fractions. Equations in the form y=kx, where k is the constant of proportionality can be used to represent proportional relationships. Students will recognize that the graph of a proportional relationship is a straight line through the origin. By recognizing proportional quantities, students can use what they know about these relationships to solve problems.Unit Objectives: At the end of this module, students will be able to independently use their learning to:

use ratios and rates to describe the relationship between two quantities find equivalent ratios and use unit rates to solve multi-step problems find unit rates with ratios of fractions use unit rates to solve multi-step problems determine whether a quantities are proportional by testing for equivalent ratios use the constant of proportionality to write equations that represent proportional relationships use equations to solve problems involving proportional relationships use mathematical modeling to represent a problem situation and to propose a solution test and verify the appropriateness of math models explain why the results from mathematical models may not align exactly to the problem situation use a graph to recognize proportionality identify a constant of proportionality from a graph interpret a point on a graph of a proportional relationship explain whether a situation represents a proportional relationship use representations to find entry points into problems

Focus Standards Addressed in this Unit: CC.2.1.7.D.1-Analyze proportional relationships and use them to model and solve real-world and mathematical problemsImportant Standards Addressed in this Unit:N/AMisconceptions:

Students are challenged by the concept of unit rates containing fractions. Students believe that any line represented on a graph represents a proportional relationship. Students believe that, when solving proportional equations, that only addition/subtraction can be used to isolate variables.

Students believe that the constant of proportionality must be a positive integer. Students are challenged by vocabulary, as in, Unit Rates and Constants of Proportionality can be represented by the same value but one

should be used over the other depending on context.Concepts/Content:

Ratios and ProportionsCompetencies/Skills:

Compute unit rates associated with ratios of fractions

Recognize and represent proportional relationships between quantities






Unit Title:

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Topic 3: Analyze and Solve Percent Problems

Unit Overview/Essential Understanding: In Unit 3, students will use equivalent ratios to find the percent of a number, and realize that a percent is a ratio out of 100. Proportional reasoning will be used to develop the percent equation, which in turn, can be used to find the percent, part, or whole. Both percent change and percent error involve finding the ratio of a difference of two values to one of those values. A mark-up is the same as a percent increase, and a markdown is the same as a percent decrease. Students will also see that the annual simple interest formula I = p x r x t corresponds to the percent equation.

Unit Objectives: At the end of this module, students will be able to independently use their learning to:

understand that equivalent rates can be used to find percents analyze percentages of numbers in a real-world context construct a percent proportion use a percent proportion to find an unknown part, whole, or percent understand the relationship between proportional reasoning and percent interpret the results of a percent equation in a real-life scenario solve real-world problems involving percent change and percent error understand the percent equation and the different ways it can be used understand and calculate markups and markdowns relate percent change to percent markup and percent markdown identify the parts of interest problems and how the values are related understand what simple interest is an how it is calculated

Focus Standards Addressed in this Unit: CC.2.1.7.D.1-Analyze proportional relationships and use them to model and solve real-world and mathematical problemsImportant Standards Addressed in this Unit:N/AMisconceptions:

Students confuse finding a fraction of a number with dividing by a fraction. Students need many exposures to percent equation to find the part, percent or whole. Students are challenged by remembering to convert percents to their decimal or fraction equivalents when using in a computation. Students believe that Interest earned can be greater than principal when using the Interest equation (I = prt).

Concepts/Content: Percents

Competencies/Skills: Use proportional relationships,

Description of Activities: Solve and Discuss

the percent and simple interest equation to solve percent problems

Explore It! Guided Practice Independent Practice



Additional Resources: www.ixl.com Teacher created supplementary materials Pearson, enVisionmath2.0


Unit Title: Topic 4: Generate Equivalent Expressions

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Unit Overview/Essential Understanding: In Unit 4, students will use algebraic expressions to represent and solve problems in real-world contexts. Rearranging or combining like terms does not change the value of an expression. All like terms must be combined in order for expressions to be simplified. The distributive property and common factors are used to factor expressions. The same rules apply for coefficients and constants when adding expressions.


understand how variables are used to represent unknown values in problems recognize when two expressions are equivalent use properties of operations to write equivalent expressions combine like integer and rational terms use the Distributive Property to expand expressions understand expanding an expression is the reverse of factoring identify the GCF of algebraic terms in expressions use properties of operations to add expressions

Focus Standards Addressed in this Unit: CC.2.2.7.B.1 – Apply properties of operations to generate equivalent expressions

Important Standards Addressed in this Unit:N/A

Misconceptions: Students are challenged by the difference between factors and terms. Students need to be reminded of basic math properties (commutative, associative and distributive). Students are challenged by taking integer rules and applying them to variable expressions. Students believe that the variable x does not have a coefficient of 1.

Concepts/Content: Algebraic Expressions

Competencies/Skills: Apply properties of operations to

generate equivalent expressions


Assessments:

Topic Assessment Lesson Quizzes Mid Topic Checkpoint Mid Topic Performance Task Projects when appropriate for understanding




Unit Title: Topic 5: Solve Problems Using Equations and InequalitiesUnit Overview/Essential Understanding: In Unit 5, students will use equations with more than one operation to represent a situation. Students will use properties of equality and

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inequality and the distributive property to solve one and two step equations and inequalities. They will use mathematical modeling to represent a situation and propose a solution. Students will also verify and test the appropriateness of their mathematical models.


analyze word problems to write two-step equations understand the relationship between the terms of the equation and the values they represent use models to solve two-step equations compare algebraic and arithmetic solutions solve equations using the Distributive Property graph the solution of inequalities on a number line solve inequalities using the Addition and Subtraction Properties of Inequality write inequalities and solve them using Multiplication and Division Properties of Inequality use mathematical modeling to represent a problem situation and to propose a solution test and verify the appropriateness of their mathematical models write and solve a two-step inequality to solve a problem solve an inequality by multiplying or dividing by a negative rational number explore the relationship between two-step inequalities and multi-step inequalities apply the Distributive Property to simplify and solve multi-step inequalities

Focus Standards Addressed in this Unit: CC.2.2.7.B.3 – Model and solve real-world mathematical problems by using and connecting numerical, algebraic, and/or graphical representationsImportant Standards Addressed in this Unit:N/AMisconceptions:

Students have difficulty converting word problems to algebraic expressions and equations. Students find it challenging solving multi-step equations involving negative rational numbers. Students have difficulty initially graphing inequalities on a number line. Students have difficulty remembering to reverse inequality signs when multiplying or dividing by negative values.

Concepts/Content: Algebraic Equations

Competencies/Skills: Model and solve real world and

mathematical problems using multiple representations such as algebraic, graphical and using


tables Solve multi-step equations or

inequalities with one variableAssessments:





Unit Title: Topic 6: Use Sampling to Draw Inferences about Populations

Unit Overview/Essential Understanding: In Unit 6, students will randomly choose samples to represent populations. They will use data from random samples to make valid inferences

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about a population. They will be able to make these inferences as well to make data displays, such as box plots to compare populations, by looking at the shapes of data displays, or the measures of center and variability. Statistical measures will also be used, such as mean, median and mode to make predictions and inferences about populations. Unit Objectives: At the end of this module, students will be able to independently use their learning to:

distinguish between a population and a sample establish whether a sample is representative of a population generate random samples make qualitative inferences from a sample data set make estimates about a population based on a sample data set, and assess whether the inferences are valid use box plots to compare and make inferences about populations use the median and IQR of datasets to informally compare and make inferences about two populations use the mode, range, mean and mean absolute deviation (MAD) to compare populations use mathematical modeling to represent a problem situation and to propose a solution test and verify the appropriateness of their math models explain why the results from their mathematical models may not align exactly to the problem situation

Focus Standards Addressed in this Unit: CC.2.4.7.B.1 – Draw Inferences about populations based on random sampling conceptsCC.2.4.7.B.2 – Draw informal comparative inferences about two populationsImportant Standards Addressed in this Unit:N/AMisconceptions:

Students believe populations and samples are interchangeable. Students still need reminders of placement of numerators and denominators when setting up proportions. Students need a lot of practice making inferences from information given. Students have difficulty remembering how to calculate central tendency.

Concepts/Content: Data, Distributions, and Random

Sampling

Competencies/Skills Draw inferences about two

populations based on random sampling concepts.

Determine and approximate relative frequencies and probabilities of events


Assessments:





Unit Title: Topic 7: Probability

Unit Overview/Essential Understanding: In Unit 7, students will use probability to find the likelihood of events. They will find theoretical probability by dividing the number of favorable

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outcomes divided by the number of possible outcomes. Students will also find experimental probability by the results of an actual experiment, finding that both probabilities are often very close, but not usually identical. The model for each of these probabilities will both have a sample space, a list of events and the probability of each event. Students will find that the possible outcomes of compound events can be represented using a tree diagram, a table or an organized list. These models can then be used to determine the probability of a favorable outcome.Unit Objectives: At the end of this module, students will be able to independently use their learning to:

use probability to describe the likelihood that an event will occur relate probability to mathematical fairness understand theoretical probability and how it can be used use theoretical probability to predict an outcome compare theoretical and experimental probability use experimental probability to make predictions explain differences between theoretical and experimental probability develop a probability model use a probability model to make an estimate use mathematical modeling to represent a problem situation and to propose a solution test and verify the appropriateness of their math models explain why the results of their mathematical models may not align exactly to the problem situation use a tree diagram, a table, or an organized list to represent the sample space for a compound event organize information about a compound event on a table, a tree diagram, or an organized list find the probability of a compound event use different tools to simulate a compound event model a real-world situation involving a compound event and predict its outcome using a simulation

Focus Standards Addressed in this Unit: CC.2.4.7.B.3 – Investigate chance processes and develop, use, and evaluate probability models


Misconceptions: Students have difficulty distinguishing between theoretical and experimental probability. Students have difficulty distinguishing between events and outcomes. Students are challenged when finding compound probabilities as opposed to simple probabilities.

Concepts/Content: Probability

Competencies/Skills: Find probabilities of independent

Description of Activities: Solve and Discuss

compound events Predict the approximate relative

frequency given the probability Find the probability of a simple

event, including the probability of a simple event not occurring

Explore It! Guided Practice Independent Practice





Unit Title: Topic 8: Solve Problems Involving Geometry

Unit Overview/Essential Understanding: In Unit 8, students will use scale drawings to calculate measurements and scale. They will understand how to construct triangles with given conditions and determine whether it’s a unique triangle, more than one triangle or no triangle. Students will find the measures of angles that are formed by intersecting lines as well as determining the relationships among these angles. They will find the diameter, radius, are and circumference of circles. Students will describe cross sections of right rectangular prisms and pyramids and solve problems involving cross

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sections. Students will find surface area of three dimensional composite shapes. They will also calculate volume of various three-dimensional figures and solve problems involving these figures.Unit Objectives: At the end of this module, students will be able to independently use their learning to:

use a scale drawing as a representation of actual lengths and areas sketch quadrilaterals with given conditions name and classify quadrilaterals according to their properties construct triangles with given conditions conclude whether or not a triangle is formed and what kind of triangle it is calculate the measures of angles by using angle relationships calculate the circumference, radius, or diameter of a circle recognize the relationship between the circumference and the diameter of a circle and pi find the area of a circle use the area of a circle use the area to find the radius and diameter solve problems involving the area of a circle use mathematical modeling to represent a problem situation and to propose a solution test and verify the appropriateness of their mathematical models describe cross sections of right rectangular prisms and pyramids solve problems involving cross sections find the surface area of two-dimensional composite shapes calculate the volume of various three-dimensional figures solve problems involving the volume of three-dimensional figures

Focus Standards Addressed in this Unit: CC.2.3.7.A.1 – Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volumeCC.2.3.7.A.2 – Visualize and represent geometric figures and describe the relationships between them


Misconceptions: Students have difficulty understanding how to determine a quadrilateral given specific conditions. Students have difficulty remembering angle relationships and congruence ie; complementary, supplementary, alternate angles, vertical

etc.

Students have difficulty using and knowing when to use given formulas to calculate area, perimeter, volume and surface area.Concepts/Content:

Area, Volume, Angles, and Circumference

Competencies/Skills: Use properties of angle types and

properties of angles formed when two parallel lines are cut by a transversal to solve problems

Solve problems involving area and circumference of a circle(s)

Solve mathematical problems involving area, volume and surface area of two-and three-dimensional objects





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