GRADE 7 MATHEMATICS CURRICULUM GUIDE

Transcription

1 GRADE 7 MATHEMATICS CURRICULUM GUIDE Loudoun County Public Schools Complete scope, sequence, pacing and resources are available on the CD and will be available on the LCPS Intranet.

2 Grade 7 Mathematics Nine Weeks Overview 1 st Quarter 2 nd Quarter 3 rd Quarter 4 th Quarter a, b, d 7.1 e 7.1 a, b, c, d 7.13a, b c, d, e days 7.12 (2001 SOL) (2001 SOL) (2001 SOL) days a, b 7.6 (2001 SOL) 7.17 a, b, d, e, f (2001 SOL) 7.18 (2001 SOL) 47 days 38 days

3 Quarter 1: Academic Year Grade 7 Mathematics Topic and Essential Questions Indicators for 2009 SOLs *Deleted or moved to a different grade level Remains the same ± New content to this grade Standard(s) of Learning Essential Knowledge and Skills Essential Understandings TSWBAT: The student will be able to Additional Instructional Resources/Comments 1 st Quarter 7.3 integers Model and compute integers using Algeblocks, pictorial, and numerical representation. -How can you use the additive identity to model subtracting negative integers? TSWBAT: - Add, subtract, multiply, and divide signed numbers using the laws of arithmetic. -Model addition, subtraction, multiplication and division of integers using pictorial representations of concrete manipulatives. -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. -Simplify numerical expressions involving addition, subtraction, multiplication and division of integers using order of operations. Algeblocks Math scool Module 3 Algebra scool Module 1.2 ESS Integers Lessons p 9-14 Activity for graphing ordered pairs for absolute value NLVM Rectangle multiplication of integers NLVM Color chips addition NLVM Color chips subtraction a, b, d properties Apply commutative, associative, distributive, and additive inverse properties with the modeling and computing of integers -Solve practical problems involving addition, subtraction, multiplication, and division with integers Identify properties of operations used in simplifying expressions. -Apply the properties of operations to simplify expressions Math scool Module 1.3, 1.4 Algebra scool Module 2.3 ESS Properties of Real Numbers p Why are the commutative and associative properties limited to addition and multiplication? Justify your answer. -Generate equivalent expressions from a given expression using the laws of arithmetic and conventions of algebraic notation.

4 Quarter 1: Academic Year Grade 7 Mathematics -How can the commutative, associative and additive inverse properties be used to allow you to compute integers mentally? -How does distributing a negative number affect the expression value? ± 7.1e absolute value Describe absolute value Why is the absolute value of a number always positive? Describe real life situation revolving around absolute value. ± 7.1a, b, c, d relationships with rational numbers a) Negative exponents for powers of ten -What does a negative exponent mean when the base is ten? -What relationship occurs with negative exponents? -Describe the relationship with trend as an exponent decreases b) Scientific notation for numbers greater than zero -When should scientific notation be used? -What is the difference between scientific notation and standard form? In which situation would you use either? c) Compare and order fractions, decimals, percents, and scientific notation -How are fractions, decimals, and percents related? -When can this knowledge be helpful for Demonstrate absolute value using a number line. -Determine the absolute value of a rational number. -Recognize powers of 10 with negative exponents by examining patterns. -Write a power of 10 with a negative exponent in fraction and decimal form Write a number greater than 0 in scientific notation. -Recognize a number greater than 0 in scientific notation. -Order no more than 3 numbers greater than 0 written in scientific notation. -Compare and determine equivalent relationships between numbers larger than 0 written in scientific notation Represent a number in fraction, decimal, and percent forms. -Compare, order, and determine equivalent Math scool- Module 3.1 Algebra scool -Module 6.1 Mission Mathematics Math scool Module 5.6 Algebra scool Module Math scool Module 5.7 Algebra scool Module Math scool- Modules 4.1, 4.2, 5.2 ESS - Comparing F/D/P p 4 Activity for subsets of real

5 Quarter 1: Academic Year Grade 7 Mathematics understanding numerical relationships? d) Determine and identify square roots -How is taking the square root different from squaring a number? -Describe the subsets of the real number system -How do exponents relate to the factors of the base? -How can one number be classified in more than one subset group? -Generate negative numbers that are not classified as integers. -What is the difference between a rational and irrational number? relationships among fractions, decimals, and percents. Decimals are limited to the thousandths place, and percents are limited to the tenths place. Ordering is limited to no more than 4 numbers Determine the square root of a perfect square less than or equal to Understand informally that every number on a number line has a decimal expansion, which can be found for rational numbers using long division. -Understand that rational numbers are those with repeating decimal expansions (this includes finite decimals which have an expansion that ends in a sequence of zeros). -Informally explain why is irrational. number system NLVM - Percentages Math scool- Module 7.1 Algebra scool- Module 1.1 (Introduce 2001 SOL 7.20 and 7.21) 7.13a Translating verbal phrases into mathematic expressions and vice-versa. -What do variables represent in an expression? -Why do we use a variable(s) in an expression? Generate a real life problem and represent it using a mathematical expression. -Use rational approximations (including those obtained from truncating decimal expansions) to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions (e.g., 2). For example, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. -Use the following terms appropriately: expressions, equations, and inequalities -Write verbal expressions as algebraic expressions. Expressions will be limited to no more than 2 operations. -Write verbal sentences as algebraic equations. Equations will contain no more than 1 variable Algebra scool- Module 2.1,4.1

6 Quarter 1: Academic Year Grade 7 Mathematics term. -What is a variable expression? How can it be -Translate algebraic expressions and equations to used to represent a mathematical sequence? verbal expressions and sentences. Expressions will be limited to no more than 2 operations b Evaluate numerical expressions using order of operations Evaluating algebraic expressions given replacement values -How can algebraic expressions and equations be written? properties 7.2, 7.3 order of operations Use all the properties to simplify and evaluate expressions -Why is it important to apply properties of operations when simplifying expressions? -Why is it necessary to have an order of operations in mathematics? 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. For example, P P = 1.05P means that increased by 5% is the same as multiplied by Identify examples of expressions and equations. -Understand that an expression records operations with numbers or with letters standing for numbers. -Understand that applying the laws of arithmetic to an expression results in an equivalent expression. 3 (2 + x) = 6 + 3x Apply the order of operations to evaluate expressions for given replacement values of the variables. Limit the number of replacements to no more than 3 per expression. -Identify properties of operations used in simplifying expressions. -Apply the properties of operations to simplify expressions Algebra scool- Module Math scool- Module 1.1 Algebra scool- Module 1.5 ESS Order of Operations p NLVM Krypto Patterns in Mathematics Mystery Operations (7.19) Arithmetic and geometric sequences Analyze arithmetic and geometric sequences to discover a variety of patterns ESS Patterns, Functions, & Graphing lessons p 110 NLVM Number Patterns NLVM Fibonacci Sequence

7 Quarter 1: Academic Year Grade 7 Mathematics Assessment, Enrichment, and Remediation -Identify the common difference in an arithmetic sequence. -Identify the common ratio in a geometric sequence. -Given an arithmetic or geometric sequence, write a variable expression to describe the relationship between two consecutive terms in the sequence. -Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity, and an equation can express one quantity, thought of as the dependent variable, in terms of other quantities, thought of as the independent variables; represent a relationship between two quantities using equations, graphs, and tables; translate between any two of these representations. For example, describe the terms in a sequence t= 3, 6, 9, 12 of multiples of 3 by writing the equation t = 3n for n = 1, 2, 3, 4,. S NLVM Sieve of Eratosthenes Illuminations Limits

8 Quarter 2: Academic Year Grade 7 Mathematics Topic and Essential Questions Indicators for 2009 SOLs *Deleted or moved to a different grade level Remains the same ± New content to this grade Standard(s) of Learning Essential Knowledge and Skills Essential Understandings TSWBAT: The student will be able to Additional Instructional Resources/Comments 2 nd Quarter one-step equations only Translating verbal sentences into equations Solving one step equations Solving practical one step equations -Choose variables to represent quantities in a word problem, and construct simple equations to solve the problem by reasoning about the quantities. Algebra scool- Module 3.3 ESS Expressions and Equations p 112 -What is equality? Why is it important in equations? -How do performing identical operations on each side of the equation maintain equality? -How can the solution to an equation be graphed? -When solving an equation, why is it important to perform identical operations on each side of the equal sign? - Represent and demonstrate steps for solving one- and two-step equations in one variable using concrete materials, pictorial representations and algebraic sentences. -Solve word problems arithmetically, by using a sequence of operations on the given n umbers, and algebraically by using a variable to stand for the unknown quantity. -Understand that a linear equation in one variable might have one solution, infinitely many solutions, or no solutions. NLVM- Function Machine NLVM- Algebra Balance Scales NLVM- Algebra Balance Scales- Negatives c, d, e properties Using the inverse and identity properties to solve equations Generate equivalent expressions from a given expression using the laws of arithmetic and conventions of algebraic notation Math scool- Module 1.3 Algebra scool- Module 2.3 -Why do we need to know the identity and inverse properties in order to understand how to balance an equation? -How can the multiplicative property of zero be used to balance an equation? - Apply the properties of operations to simplify expressions

9 Quarter 2: Academic Year Grade 7 Mathematics 7.4 proportional reasoning -Write proportions that represent equivalent Solve practical problems using proportions relationships between two sets. -How are comparison used in proportional reasoning? - What makes two quantities proportional? -Solve a proportion to find a missing term. -Apply proportions to convert units of measurement between the U.S. Customary System and the metric system. Calculators may be used. -Apply proportions to solve practical problems, including scale drawings. Scale factors shall have denominators no greater than 12 and decimals no less than tenths. Calculators may be used. -Using 10% as a benchmark, mentally compute 5%, 10%, 15%, or 20% in a practical situation such as tips, tax and discounts. -Solve problems involving tips, tax, and discounts. Limit problems to only one percent computation per problem. Math scool- Module 7 ESS Ratio and Proportions p 25 ESS Proportions and Percents p 27 Illuminations- Bagel Algebra Illuminations- Mixtures Sketchpad similar figures - How do polygons that are similar compare to polygons that are congruent? -What makes something proportional? -How can proportions be solved for a missing value? -How are proportional relationships relevant to real-life situations? -What is the difference between congruent and similar figure? Identify corresponding sides and corresponding and congruent angles of similar figures using the traditional notation of curved lines for the angles. -Write proportions to express the relationships between the lengths of corresponding sides of similar figures. -Determine if quadrilaterals or triangles are similar by examining congruence of corresponding angles and proportionality of corresponding sides. -Given two similar figures, write similarity statements using symbols such as Math scool- Module 8.6 and Module 9.4 ESS Similar Figures p 48 ESS Similar Figures and Proportion p 51

10 Quarter 2: Academic Year Grade 7 Mathematics -How can you prove two figures are similar? ABC ~ DEF, A corresponds to D, and AB corresponds to DE. -How can proportions be used to solve the unknown side length? 7.14 solving two-step equations -Solve word problems leading to equations of Translating verbal sentences into two step the form px + q = r and p(x + q) = r, where p, q, linear equations and r are nonnegative rational numbers and the Solve two-step linear equations using the solution is a nonnegative rational number. identity and inverse properties Fluently solve equations of these forms, e.g. by -When solving an equation, why is it important to undoing the operations involved in producing perform identical operations on each side of the the expression on the left. equal sign? - Represent and demonstrate steps for solving one- and two-step equations in one variable using concrete materials, pictorial representations and algebraic sentences solving one step inequalities a) Solve one and two- step inequalities using the identity and inverse properties b) Graph solutions to equations and inequalities on a number line Solve real-life equations and inequalities -How are the procedures for solving equations and inequalities similar and different? -How is the solution to an inequality different from -Understand that a linear equation in one variable might have one solution, infinitely many solutions, or no solutions. -Solve linear equation with rational number coefficients, including equations that require expanding expressions using the distributive law and collecting like terms Represent and demonstrate steps in solving inequalities in one variable, using concrete materials, pictorial representations, and algebraic sentences. -Graph solutions to inequalities on the number line. -Identify a numerical value that satisfies the inequality Algebra scool- Module 3.4 Multi-step optional- Algebra scool- Module 3.5 Pythagorean Theorem optional: Math scool- 8.7, 10.3 NLVM- Pythagorean Theorem Puzzle Illuminations- Proof without words Algebra blocks ESS Expressions and Equations p 112 NLVM- Function Machine NLVM- Algebra Balance Scales NLVM- Algebra Balance Scales - Negatives Illuminations- Chairs Algebra scool- Module 5.1, 5.2, 5.3

11 Quarter 2: Academic Year Grade 7 Mathematics that of a linear equation? -How is the solution to an inequality graphed? -What is the difference between the graph of a solution to an equation and an inequality? -How do mathematical properties apply to solving multi-step equations and inequalities? -How can you use properties to justify the accuracy of your solution? Assessment, Enrichment, and Remediation

12 Quarter 3: Academic Year Grade 7 Mathematics Topic and Essential Questions Indicators for 2009 SOLs *Deleted or moved to a different grade level Remains the same ± New content to this grade Standard(s) of Learning Essential Knowledge and Skills Essential Understandings TSWBAT: The student will be able to Additional Instructional Resources/Comments 3 rd quarter coordinate plane (2001) Coordinate plane system The relationship between functions, tables, rules, and graphs -How can a coordinate plane be used to represent a relationship between two variable? -What is a function? -What are the different ways to represent a functional relationship? (explore a variety of functions linear, quadratic, cubic, absolute value etc) -What types of patterns are formed by different types of graphs? (explore a variety of functions linear, quadratic, cubic, absolute value etc) -Understand that the graph of a linear equation in two variables is a line, the set of pairs of numbers satisfying the equation. If he equation is in the form y= mx + b, the graph can be obtained by shifting the graph of y = mx by b units (upwards if b is positive, downwards if b is negative). The slope of the line is m. -Understand that a linear equation in one variable might have one solution, infinitely many solutions, or no solutions. -Solve linear equation with rational number coefficients, including equations that require expanding expressions using the distributive law and collecting like terms. Math scool- Module 10.1 Algebra scool- Module 7.1 ESS- Graphing p 54 Sketchpad NLVM- Point Plotter Illuminations- Finding your way around

13 Quarter 3: Academic Year Grade 7 Mathematics 7.8 transformations: reflection, translation, dilation, rotation Identify and sketch translations, reflections, rotation, and dilations of right triangles of rectangles -How does the size/shape/ and position change with each type of transformation (translation, rotation, reflection, and dilation)? -How do transformations affect the graph of a functional relationship? (explore a variety of functions linear, quadratic, cubic, absolute value etc) -Where can are transformations displayed in real life? -Identify the coordinates of the image of a right triangle or rectangle that has been translated either vertically, horizontally, or a combination of a vertical and horizontal translation. -Identify the coordinates of the image of a right triangle or rectangle that has been rotated 90 or 180 about the origin. -Identify the coordinates of the image of a right triangle or a rectangle that has been reflected over the x- or y-axis. -Identify the coordinates of a right triangle or rectangle that has been dilated. The center of the dilation will be the origin. -Sketch the image of a right triangle or rectangle translated vertically or horizontally. -Sketch the image of a right triangle or rectangle that has been rotated 90 or 180 about the origin. -Sketch the image of a right triangle or rectangle that has been reflected over the x- or y-axis. -Sketch the image of a dilation of a right triangle or rectangle limited to a scale factor of 1 4, 1 2, 2, 3 or 4. Math scool- Module 11 Sketchpad ESS Translations and Rotations p 55 NLVM Translations NLVM Rotations NLVM Reflection Illuminations- Algebraic Transformations

14 Quarter 3: Academic Year Grade 7 Mathematics 7.10 polygons (2001) -Identify by the number of sides Identify and draw polygons up to 10 sides or number of angles the following -What is the relationship between the number of sides polygons: pentagon, hexagon, and the number of interior/exterior angles? heptagon, octagon, nonagon, and decagon comparing quadrilaterals * Classify, compare, and contrast quadrilaterals based on their attributes -Why can some quadrilaterals be classified in more than one category? -How is deductive reasoning used to classify quadrilaterals? 7.7 area and perimeter basic and irregular (2001) Determine the area and perimeter of basic and irregular figures -What is the difference between area and perimeter? -How can irregular figures be subdivided into triangles and rectangles to find the area? -Draw a pentagon, hexagon, heptagon, octagon, nonagon, and decagon, using a variety of tools Compare and contrast attributes of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid. -Identify the classification(s) to which a quadrilateral belongs, using deductive reasoning and inference. -Understand that properties belonging to a category of plane figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. -Subdivide a polygon into rectangles and right triangles, estimate the area of the rectangles and/or right triangles to estimate the area of the polygon, and find the area of the rectangles and/or right triangles to determine the area of the polygon Math scool- Module 9.1, 9.5 Math scool- Module10.2 ESS Identifying Polygons p 51 Illuminations- Polygon Capture Math scool- Module 9.2 ESS Quadrilaterals p 49 Illuminations- Shape Sorter Math scool- Modules 13.1, 13.2, and 13.3 NLVM- Geoboard Area Illuminations- Area Tool Illuminations- Scale Factor Illuminations- Constant Dimensions Math scool- Modules 10.4, 10.5

15 Quarter 3: Academic Year Grade 7 Mathematics 7.5 solids, formulas a) describe the volume and surface area of cylinders -How are volume and surface area related? -How are area of the base and the volume of the solid related? b) solve practical problems involving volume and surface area of rectangular prisms and cylinders c) describe how changing one measured attribute of a rectangular prism affects its volume and surface area -How does the volume of a rectangular prism change when one of the attributes is increased or decreased? -What is the difference between area and surface area? Assessment, Enrichment, and Remediation -Determine if a practical problem involving a rectangular prism or cylinder represents the application of volume or surface area. -Find the surface area of a rectangular prism. -Solve practical problems that require finding the surface area of a rectangular prism. -Find the surface area of a cylinder. -Solve practical problems that require finding the surface area of a cylinder. -Find the volume of a rectangular prism. -Solve practical problems that require finding the volume of a rectangular prism. -Find the volume of a cylinder. -Solve practical problems that require finding the volume of a cylinder. -Describe how the volume of a rectangular prism is affected when one measured attribute is multiplied by a scale factor. -Describe how the surface area of a rectangular prism is affected when one measured attribute is multiplied by a scale factor. Math scool- Modules13.4, 13.5, 13.6, and 13.7 ESS Surface Area and Volume p 41 & 43 ESS Surface Area: Rect Prisms and Cylinders p 39 NLVM- Constructing 3-D Shapes NLVM- How High? (volume)

16 Quarter 4: Academic Year Grade 7 Mathematics Topic and Essential Questions Indicators for 2009 SOLs *Deleted or moved to a different grade level Remains the same ± New content to this grade Standard(s) of Learning Essential Knowledge and Skills Essential Understandings TSWBAT: The student will be able to Additional Instructional Resources/Comments 4 th Quarter Fundamental Counting Principal/Compound events *Fundamental Counting Principle *Tree diagrams *Probability for compound events (no replacement) -How do the Fundamental Counting Principle and Tree Diagrams relate to probability? -What is the role of the Fundamental Counting Principle in determining the probability of compound events? theoretical vs experimental probability -What is the difference between experimental and theoretical probability? -How is the probability of an event determined and described? -How do you analyze and test the fairness of games? -We say nothing is impossible, so why are some events considered impossible? -How can the probability of an event be represented visually? TSWBAT: -Compute the number of possible outcomes by using the Fundamental (Basic) Counting Principle. -Determine the probability of a compound event containing no more than 2 events Determine the theoretical probability of an event. Determine the experimental probability of an event. Describe changes in the experimental probability as the number of trials increases. Investigate and describe the difference between the probability of an event found through experiment or simulation versus the theoretical probability of that same event. Algebra scool- Module 20.1, 20.3 ESS- Creating Tree Diagrams p 100 Regatta Probability p Algebra scool- Module 20.2 ESS Probable Families p 87 Illuminations- Random Drawing Illuminations- The Game of Skunk -What is the difference between chance and choice? How can an understanding of probability

17 Quarter 4: Academic Year Grade 7 Mathematics affect my choices? -What careers use probability every day? How is probability applied to real-life situations? a, b - Data in practical situations - Histograms *Representing data using histograms -How can you display experimental probability in a histogram? -What is the difference between a histogram and a bar graph? 7.16 measures of central tendency (2001) *Measures of central tendency and range -Which measure of central tendency is most appropriate for a given situation? -Why is range not a measure of central tendency? Collect, analyze, display, and interpret a data set using histograms. For collection and display of raw data, limit the data to 20 items. -Determine patterns and relationships within data sets (e.g., trends). -Make inferences, conjectures, and predictions based on analysis of a set of data. -Compare and contrast histograms with line plots, circle graphs, and stem-and-leaf plots presenting information from the same data set. -Understand that measures of central tendency are types of averages for a data set. They represent numbers that describe a data set. --Understand that a set of data generated by answers to a statistical question typically shows variability-not all of the values are the same- and yet often the values show an overall pattern, often with a tendency to cluster. -A measure of center for a numerical data set summarizes all of its values using a single number. The median is a measure of center in the sense that approximately half are greater. The mean is a measure of center in the sense that it is the value that each daa point would take on if the total of the data values were redistributed fairly, and in the sense that it is the balance point of a data distribution shown on a dot plot. -Examine the range to understand spread or dispersion of the data Algebra scool- Module 19.3 NLVM- Histograms NLVM- Histogram Tool Algebra scool- Module 19.1 ESS Grab a Handful p 63 Illuminations- Mean and Median

18 Quarter 4: Academic Year Grade 7 Mathematics a, b, d, e, f (2001) *Collecting, representing and analyzing data using a variety of graphical representations (frequency tables, line plots, stem and leaf plots, box and whisker plots, and scattergrams) -What are the different types of data that can be collected? -Compare/contrast data represented in a table vs. data represented in a graph or plot. -What is the purpose of displaying data? -What are the advantages and disadvantages for each data representation? inferences and predictions (2001) *Using graphical representations to draw conclusions, make inferences and predictions about a set of data -How is data used to influence decisions? (i.e. misleading data, predictions, inferences) -How can the results of a statistical investigation be used to support or refute an argument? Assessment, Enrichment, and Remediation Understand that a statistical question is one that anticipates variability in the data related to the question and accounts for it in the answers. For example, How old am I? is not a statistical question, but How old are the students in my school? is a statistical question because one anticipates variability in students ages 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. -Understand the importance of variation in sample quantities(like means or proportions) in reasoning about how well a sample quantity estimates or predicts the corresponding population quantity Algebra scool- Module 19.2 ESS Drops on a Penny p ESS Marketing with Scattergrams p 74 NLVM- Scatterplots