Math 7 Honors Common Core

Mathematics Prince George’s County Public Schools 2014 - 2015

Course Code:

Prerequisites: Successful completion of Math 6Common Core

This course continues the trajectory towards a more formalized understanding of mathematics that occurs at the high schoollevel that began in Math 6 Common Core. Students extend ratio reasoning to analyze proportional relationships and solvereal-world and mathematical problems; extend previous understanding of the number system and operations to performoperations using all rational numbers; apply properties of operations in the context of algebraic expressions and equations;draw, construct, describe, and analyze geometrical figures and the relationships between them; apply understandings ofstatistical variability and distributions by using random sampling, making inferences, and investigating chance processesand probability models.

Students in Math 7 Honors will have assignments that reflect the inherent rigor of honors level courses. Included will be long-term projects and problem-based assignments that offer students the opportunity to directly apply mathematics at a more complex level.

In all mathematics courses, the Mathematical Practice Standards apply throughout each course and, together with the contentstandards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of theirability to make sense of problem situations.

INTRODUCTION:

Typically in a Math class, to understand the majority of the information it is necessary to continuously practice your skills. This requires a tremendous amount of effort on the student’s part. Each student should expect to dedicate 2 - 3 hours of studying for every hour in class. Some hints for success in a Math class include: attending class daily, asking questions in class, and thoroughly completing all homework problems with detailed solutions as soon as possible after each class session.

INSTRUCTOR INFORMATION:

Name:

E-Mail:

Planning:

Phone:

CLASS INFORMATION:

COURSE NUMBER:

CLASS MEETS:

ROOM:

TEXT:Big Ideas (Red), Holt McDougal

CALCULATORS:

The use of a graphing calculator is required. While participants may use any graphing calculator, the instruction in the course requires the TI-83 Plus. The TI-84 Plus is very similar and can be used as well. Knowledge and competence for use of other graphing calculators will be the sole responsibility of the student.

GRADING:

Middle School Mathematics

Overview: The goal of grading and reporting is to provide the students with feedback that reflects their progress towards the mastery of the content standards found in the Math 8 Common Core Curriculum Framework Progress Guide.

Factors / Brief Description / Grade Percentage
Per Quarter
Classwork / This includes all work completed in the classroom setting. Including:
  • Group participation
  • Notebooks
  • Vocabulary
  • Written responses
  • Group discussions
  • Active participation in math projects
  • Completion of assignments
/ 30%
Homework / This includes all work completed outside of the classroom and student’s preparation for class (materials, supplies, etc.) Assignments can included, but not limited to:
  • Problem of the Week
  • Performance Tasks
/ 20%
Assessment / This category entails both traditional and alternative methods of assessing student learning:
  • Group discussions
  • Performance Tasks
  • Problem Based Assessments
  • Exams
  • Quizzes
  • Research/Unit Projects
  • Portfolios
  • Oral Presentations
  • Surveys
An instructional rubric should be created to outline the criteria for success for each alternative assessment. / 50%

Your grade will be determined using the following scale:

90% - 100% A

80% - 89% B

70% - 79% C

60% - 69% D

59% and belowE

Math 7 Honors

Common Core Curriculum Map

Standards for Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics. / 5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Quarters 1 & 2
Unit 1
Ratios and Proportional Relationships / Unit 2
Operations with Rational Numbers / Unit 3
Expressions & Equations
Analyze proportional relationships and use them to solve real-world and mathematical problems.
7.RP.1:Compute unit ratesassociated with ratiosof fractions, including ratios of lengths, areas and other quantities measured in like and or different units.
7.RP.2: Recognize and represent proportional relationshipsbetween quantities.
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.
2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal descriptions of proportional relationships.
2c. Represent proportional relationshipsby equations.
2d. Explain what a point (x, y) on the graph of a proportional relationshipmeans in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
7.RP.3: Use proportional relationshipsto solve multistep ratio and percent problems.
7.G.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. / Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
7.NS.1:Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, and represent addition and subtraction on a horizontal or vertical number linediagram.
1a:Describe situations in which opposite quantities combine to make 0.
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 numbersby describing real-world contexts.
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 valueof their difference, and apply this principle in real-world contexts.
1d: Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.2:Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational number.
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 numbers. Interpret products of rational numbers by describing real-world contexts.
2b. 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: –(?/?) = (–?)/? = ?/(–?). Interpret quotients of rational numbers by describing real-world contexts.
2c. Apply properties of operations as strategies to multiply and divide rational numbers.
2d. Convert a rational number to a decimal using long division; and know that the decimal form of a rational number terminates in 0s or eventually repeats.
7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers. (Note: Computations with rational numbersextend the rules for manipulating fractions to complex fractions. / Use properties of operations to generate equivalent
expressions.
7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressionswith rational coefficients.
7.EE.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.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
7.EE.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.
4a: Solve word 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 solutionto an arithmetic solution, identifying the sequence of the operations used in each approach.
4b:Solve word 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 and interpret it in the context of the problem.
Supporting Standards
7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers. (Note: Computations with rational numbersextend the rules for manipulating fractions to complex fractions.) / 7.NS.1:Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, and represent addition and subtraction on a horizontal or vertical number line diagram.
1a:Describe situations in which opposite quantities combine to make 0.
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 numbersby describing real-world contexts.
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 valueof their difference, and apply this principle in real-world contexts.
7.NS.2:Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational number.
2d. Convert arational numberto a decimal using long division; and know that the decimal form of a rational number terminates in 0s or eventually repeats.
7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers. (Note: Computations with rational numbersextend the rules for manipulating fractions to complex fractions.
Honors Extended Standards
Know that there are numbers that are not rational, and approximate them by rational numbers.
8.NS.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
8.NS.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2).
Work with radicals and integer exponents.
8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions.
8.EE.2: Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. / Understand the connections between proportional relationships, lines, and linear equations.
8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.EE.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin, and the equation y = mx + b for a line intercepting the vertical axis at b.
8.F.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
Standards for Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics. / 5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Quarters 3 & 4
Unit 4
Geometry / Unit 5
Statics & Probability
Draw, construct, and describe geometrical figures and describe the relationships
between them.
7.G.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.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.4: Know the formulas for the area and circumference of a circleand use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
7.G.5: Use facts about supplementary, complementary, vertical, and adjacent anglesin a multi-step problem to write and solve simple equations for an unknown angle in a figure.
7.G.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. / Use random sampling to draw inferences about a population.
7.SP.1:Understand that statistics can be used to gain information about a populationby examining a sample of the population; generalizations about a population from a sample are validonly if the sample is representative of that population. Understand that random samplingtends to produce representative samples and support valid inferences.
7.SP.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.
Draw informal comparative inferences about two populations.
7.SP.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
7.SP.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
Investigate chance processes and develop, use, and evaluate probability models.
7.SP.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 indicates an event that is neitherunlikely nor likely, and a probability near 1 indicates a likely event.
7.SP.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.7: Develop a probability model and use it to find probabilities of events; compare probabilities from a model to observed frequencies; and if the agreement is not good, explain possible sources of the discrepancy.
7.SP.7a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
7.SP.7b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
7.SP.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
7.SP.8a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
7.SP.8b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space, which compose the event.
7.SP.8c. Design and use a simulation to generate frequencies for compound events.
Supporting Standards
7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers. (Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions. / 7.NS.2:Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational number.
7.NS.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 numbers. Interpret products of rational numbers by describing real-world contexts.
7.NS.2b: 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:

Interpret quotients of rational numbers by describing real- world contexts.
7.NS.2c: Apply properties of operations as strategies to multiply and divide rational numbers.
7.NS.2d: Convert a rational number to a decimal using long division; and know that the decimal form of a rational number terminates in 0s or eventually repeats.
7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers. (Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
Honors Extended Standards
Understand and apply the Pythagorean Theorem.
8.G.6: Explain a proof of the Pythagorean Theorem and its converse.
8.G.7: Apply the Pythagorean Theoremto determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
8.G.8: Apply the Pythagorean Theoremto find the distance between two points in a coordinate system.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
8.G.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.