7th Math Syllabus (Ryan)

7th Grade Math Syllabus

Teacher Vincent Ryan:   ryanv@mauryk12.org

School Phone:  931-285-2300 | Fax 931-285-2612

 

School Address: 4235 Old State Road, Hampshire, TN 38461

Course Description

By the end of grade seven, students will understand and use the concept of proportional reasoning as well as pre algebraic reasoning and problems with geometric figures.

The standards are fully explained on the TnReady Common Standards website. http://tn.gov/education/article/mathematics-standards

TnReady Performance Standards

In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

 

 Content standards for Grade 7 are arranged within the following domains and clusters:

1) Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships. (2) Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. (3) Students continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity in Grade 8 they reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two- and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. (4) Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences.

Course Outline

1 Unit…  Number Systems- Part 1

..# of Days- 25

 

Adding and Subtracting Rational Numbers

       7.NS.1    

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.1a Describe situations in which opposite quantities combine to make 0.

7. NS.A.1b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real world contexts.

7.NS.A.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

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.2.b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then – (p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

 

Unit 2  Ratio and Proportional Relationships – Part 1

 

    … # of Days- 25

 

Ratio and Proportional Relationships – Part 1

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. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

7.RP.A.2a- Decide whether two quantities are in a proportional relationship (e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin).

7.RP.A.2b- Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

7.RP.A.2c- Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

7.RP.A.2d- Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

 

 

 

 

Unit 3

Number Systems – Part 2

# of Days- 15

7.NS.A.1d- Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.A.2a- Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed products of rational numbers by describing real-world contexts.

7.NS.A.2c- Apply properties of operations as strategies to multiply and divide rational numbers.

7.NS.A.2d- Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

7.NS.A.3- Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)

 

Unit 4

Equations and Expressions – part 1

# of Days- 25

7.EE.A.1- Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

7.EE.B.3a- Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers presented in any form (whole numbers, fractions, and decimals). Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.

7.EE.B.3b- Assess the reasonableness of answers using mental computation and estimation strategies.

7.EE.B.4a- 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. Solve contextual problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

7.EE.B.4b- Solve contextual problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality on a number line and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. (Note that inequalities using >, <, ≤, ≥ are included in this standard).

 

 

 

 

 

 

 

Maury County Public Schools 4/11/18 Office of Instruction Pk-12

Unit 5

Expressions and Equations – Part 2

# of Days- 20

 

7.RP.A.3- Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)

7.EE.A.2- Understand that rewriting an expression in different forms in a contextual problem can provide multiple ways of interpreting the problem and how the quantities in it are related. For example, shoes are on sale at a 25% discount. How is the discounted price P related to the original cost C of the shoes? C - .25C = P. In other words, P is 75% of the original cost for C - .25C can be written as .75C.

 

 

Unit 6

Geometry

# of Days- 20

7.G. B.4- Know and 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.

7.G.A.2- Draw 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.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.B.3- 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.5- 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.

 

 

Unit 7

Statistics and Probability

# of Days- 20

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 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

7.SP.C6- 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. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

7.SP.C.7a- 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. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the

probability that Jane will be selected and the probability that a girl will be

selected.

7.SP.C.7b- Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open end down. Do the outcomes for the

spinning penny appear to be equally likely based on the observed frequencies?

7.SP.D.8a- Summarize numerical data sets in relation to their context. Give quantitative measures of center (median and/or mean) and variability

(range and/or interquartile range), as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

7.SP.D.8b- Know and relate the choice of measures of center (median and/or mean) and variability (range and/or interquartile range) to the shape of the data distribution and the context in which the data were gathered.

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. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

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. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team; on a dot plot or box plot, the separation

 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. For example, decide whether the words in a chapter of a 7th grade science book are generally longer than the words in a chapter of a 4th grade science book.

 

 

Unit 8

TNReady Review/Wrap Up

# of Days- 25

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. For example, decide whether the words in a chapter of a 7th grade science book are generally longer than the words in a chapter of a 4th grade science book.

 

 

 

 

7th Grade Math Syllabus

Requirements: Materials and Supplies

Materials/Supplies: Students are required to bring the following items to class every day.

• Pencils (preferred)

• 3 ring binder/Folder

• Notebook paper

• Section dividers (3-5 pack)

• Composition notebook (optional)

• School-issued student agenda

Rules & Classroom Management Policies

Students are expected to come to class everyday prepared and ready to learn with a positive attitude. Students are required to act in a behavior conducive to learning, according to HUS and MCBOE Public Schools code of conduct, If students

are not able to follow the rules, they will be disciplined according to the steps and procedures detailed in the Student Handbook.

Classroom Grading & Evaluation Policy

Students will receive a grade based on the following categories:

Tests 50%

Class work/ Homework 20%

Finals 15%

Quizzes 15%

Total 100%

A 100 – 93

B 92 – 85

C 84 – 76

D 75 - 70

F 69 and below

Class work: Participation in class activities and class assignments are important to informally assess student learning and understanding. All students are expected to participate in class.

. Students are expected to take notes in their composition notebooks or 3-ring binder. The notes can be used on the standards-based quizzes. Students are responsible for any work missed during the instructional hour.

Homework: Students will receive homework Monday-Thursday to enforce key math

concepts. Students are expected to complete and turn in all homework in a timely manner.

Homework is usually due the next day, unless otherwise specified by the teacher. In most cases, homework will be graded on effort and completion. Students will be given a daily quiz based on their homework which will be considered part of their classwork/homework grade.

Quizzes: A quiz will be given in preparation for the Unit test.

Students are allowed to correct or retake quizzes.

8th Grade Math Syllabus

Tests: A test will be given at the conclusion of every Unit. Students will have an in class

review the day before the test, which will include sample test questions. Tests should be

completed independently. Using notes, talking, or cheating during a test is NOT allowed.

If a student is absent, he or she is able to make up missed quizzes or test. However, they must stay after school; unless time is given in class

Late/Make-Up Work

Students are responsible for obtaining any missed work when they are absent. All homework is due by Friday of that week unless student is absent.  In the case of absence student will have 3 school days to submit any missing homework.

Extra Credit Policy & Procedures

Extra credit assignments are given periodically, and are for all students. Students have a choice whether they would like to participate or not. Extra credit will be offered at the

teacher’s discretion. Students should not rely on extra credit as a means for getting a high grade in the class.

Tutoring

Math tutorial is available in the morning from 7 to 7:30am if a student needs homework help or remediation.  After school tutoring is available but students must arrangements in advance due to coaching and meeting responsibilities.

7th Grade Math Syllabus

Signature Acknowledgements

I acknowledge that I have read and received a copy of 7th Grade Math

Syllabus. I will govern myself according to these rules, procedures, and

expectations.

_____________________________________

Student Name

_____________________________________ ________________________

Student Signature Date

_____________________________________

Parent Name

_____________________________________ ________________________

Parent/Guardian Signature Date

_____________________________________

Cell Phone Number

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Home Number

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Work Number

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Email Address

If you have any questions or concerns regarding the course syllabus, please

contact Mr. Ryan, or set up an appointment f