Maryland Voluntary State Curriculum Mathematics: Grade 7 · PDF fileMcDougal Littell...

correlated to the

Maryland Voluntary State Curriculum

Mathematics: Grade 7

Selected exercises are referenced in parentheses, otherwise entire page is applicable. 1

McDougal Littell Pre-Algebra

correlated to the

MarylandVoluntary State Curriculum

MathematicsGRADE 7

STANDARD 1.0 KNOWLEDGE OF ALGEBRA, PATTERNS, ORFUNCTIONS–Students will algebraically represent, model, analyze, or solvemathematical or real-world problems involving patterns or functional relationships.

A. Patterns and Functions

1. Identify, describe, extend, and create linear patterns and functionsa) Identify and extend an arithmetic sequence represented as a function table

PE/TE: 693–694

• Assessment limit: Complete a function table with a given rule with twooperations (+, -, x) using whole numbers no more than 20 in the rule (0–500)

PE/TE: 693–694

b) Identify and extend a geometric sequence

PE/TE: 694–697

c) Describe how a change in one variable in a linear function affects the othervariable in a table of values

PE/TE: 694–697

B. Expressions, Equations, and Inequalities

1. Write and evaluate expressionsa) Write an algebraic expression to represent unknown quantities

PE/TE: 6–9, 80–82

McDougal Littell Pre-Algebra correlated to theMaryland Voluntary State Curriculum–Mathematics: GRADE 7


• Assessment limit: Use one unknown and one or two operations (+, -, x, ÷ with noremainders) with whole numbers (0–20), fractions with denominators as factors of100 (0- 20), or decimals with no more than three decimal places (0–20)

PE/TE: 6–9, 80–92

b) Evaluate algebraic expressions

PE/TE: 5–9, 17–20, 46, 78–83, 184–186, 191, 194–198, 211, 227–229,233–235, 239–241, 674–678

• Assessment limit: Use one unknown and no more than two operations (+, -, x, ÷with no remainders) with whole numbers (0–200), fractions with denominators asfactors of 100 (0–100), or decimals with no more than three decimal places(0–100)

PE/TE: 5–9, 17–20, 46, 78–83, 184–186, 191, 194–198, 211, 227–229,233–235, 239–241, 674–678

c) Evaluate numeric expressions using the order of operations

PE/TE: 16–21, 53, 454

• Assessment limit: Use no more than 4 operations (+, -, x, ÷ with no remainders)and 1 set of parentheses, brackets, or a division bar, with whole numbers (0–200),fractions with denominators as factors of 100 (0–100), or decimals with no morethan three decimal places (0–100)

PE/TE: 16–21, 53, 454

d) Simplify algebraic expressions represented as physical models by combining liketerms

PE/TE: 81 (#33–35), 82 (#37), 130, 656, 661 (#40)

2. Identify, write, solve, and apply equations and inequalitiesa) Write equations and inequalities to represent relationships

PE/TE: 92–95, 98–101, 104–107, 125, 127–129, 132–135, 138–142, 144–148,149–153



• Assessment limit: Use a variable, the appropriate relational symbols (>, > , <, < ,=), and one or two operational symbols (+, -, ×, ÷) on either side and use wholenumbers (0–20), fractions with denominators as factors of 100 (0–20), ordecimals with no more than three decimal places (0–20)

PE/TE: 92–95, 98–101, 104–107, 125, 127–129, 132–135, 138–142, 144–148,149–153

b) Determine the unknown in a linear equation

PE/TE: 85–89

• Assessment limit: Use one or two operations (+, -, ×) and the unknown only oncewith whole numbers (0–500), fractions with denominators as factors of 100(0–50), or decimals with no more than three decimal places (0–100)

PE/TE: 85–89

c) Solve for the unknown in an inequality

PE/TE: 138–142, 144–148, 156, 255–257

• Assessment limit: Use an inequality with one variable with a positive wholenumber coefficient and one operation (+, -, ×, ÷ with no remainders) using wholenumbers or decimals with no more than 2 decimal places (0–100)

PE/TE: 138–142, 144–148

d) Identify or graph solutions of inequalities on a number line

PE/TE: 138–142, 156

• Assessment limit: Use whole numbers (0–50)

PE/TE: 138–142, 156

e) Identify equivalent equations

PE/TE: 91

• Assessment limit: Use formulas having no more than three variables and up totwo operations, with whole numbers (0 –100), fractions with denominators asfactors of 100 (0–100), or decimals with no more than three decimal places(0–100)

PE/TE: 11, 69, 70, 73, 77, 351, 352, 363, 364, 367, 476, 478, 501, 502, 521,522, 528, 539, 540, 545, 546, 552, 553, 558, 616, 628, 629, 635. 683,704, 722, 789, 800, 818–819



C. Numeric and Graphic Representations of Relationships

1. Locate points on a number line and in a coordinate grapha) Graph rational numbers on a number line

PE/TE: 221

• Assessment limit: Use rational numbers (-100 to 100)

PE/TE: 221

b) Graph ordered pairs in a coordinate plane

PE/TE: 47–51, 55

• Assessment limit: Use no more than 4 ordered pairs of rational numbers (-20 to20)

PE/TE: 47–51, 55

c) Graph linear equations with one operation in a coordinate plane

PE/TE: 392–396, 397, 398–402

2. Analyze linear relationshipsa) Identify and describe the change represented in a table of values

PE/TE: 420–424

• Assessment limit: Identify increase, decrease, or no change

PE/TE: 420–424

b) Describe the rate of change of a linear relationship by a table of values and agraph

PE/TE: 420–424



STANDARD 2.0 KNOWLEDGE OF GEOMETRY–Students will apply theproperties of one-, two, or three-dimensional geometric figures to describe, reason,or solve problems about shape, size, position, or motion of objects.

A. Plane Geometric Figures

1. Analyze the properties of plane geometric figuresa) Identify and describe angles formed by intersecting lines, line segments, and rays

PE/TE: 709–713, 793

• Assessment limit: Use vertical, adjacent, complementary, or supplementaryangles (Include the angle symbol <m)

PE/TE: 709–713, 793

b) Identify angles formed when two parallel lines are cut by a transversal

PE/TE: 716–720

c) Identify the parts of right triangles

PE/TE: 464–469, 482–487

2. Analyze geometric relationshipsa) Determine a missing angle measure using the sum of the interior angles of

polygons.

PE/TE: 721–727, 728 (#13–15)

• Assessment limit: Use angle measures in a quadrilateral

PE/TE: 286, 518–520, 724 (Example 5), 725, 726 (#19, 20, 25), 728 (#13, 15)

b) Determine the measure of angles formed by intersecting lines, line segments, andrays.

PE/TE: 709–713

• Assessment limit: Use vertical, adjacent, complementary, or supplementaryangles

PE/TE: 709–713, 793

c) Describe the relationship between the legs and hypotenuse of right triangles

PE/TE: 464–469, 482–487



C. Representation of Geometric Figures

1. Represent plane geometric figuresa) Construct geometric figures using a variety of construction tools

PE/TE: Opportunities to address this standard can be found on the followingpages: 714, 715, 792, 794

• Assessment limit: Construct a circle using a given line segment as the radius ininches or centimeters

PE/TE: 794

b) Construct geometric figures using a variety of construction tools.


• Assessment limit: Construct a line segment congruent to a given line segment

PE/TE: 794

c) Construct geometric figures using a variety of construction tools


• Assessment limit: Construct a perpendicular bisector to a given line segment or abisector of a given angle

PE/TE: 714, 715

D. Congruence and Similarity

1. Apply the properties of congruent polygonsa) Determine the congruent parts of polygons

PE/TE: 288–292

• Assessment limit: Use the length of corresponding sides or the measure ofcorresponding angles and whole numbers (0–1000)

PE/TE: 288–292

b) Identify and describe similar polygons and their corresponding parts

PE/TE: 287–292, 293–297, 298 (#16, 17), 299–309



E. Transformations

1. Analyze a transformation on a coordinate planea) Identify, describe, and plot the results of one transformation on a coordinate plane

PE/TE: 729, 730–733, 734–739, 740–746, 747–751

• Assessment limit: Identify and plot the result of one translation (horizontal orvertical), reflection (horizontal or vertical), or rotation (90° or 180°) about a givenpoint

PE/TE: 729, 730–733, 734–739, 740–746

b) Identify and describe transformations that result in rotational and reflectionalsymmetry

PE/TE: 734–738, 740–746, 754, 755

STANDARD 3.0 KNOWLEDGE OF MEASUREMENT–Students will identifyattributes, units, or systems of measurements or apply a variety of techniques,formulas, tools or technology for determining measurements.

C. Applications in Measurement

1. Estimate and apply measurement formulasa) Estimate and determine the area of quadrilaterals

PE/TE: 69–70, 73–75, 521–526, 565, 789

• Assessment limit: Use parallelograms or trapezoids and whole numberdimensions (0–1000)

PE/TE: 521–526, 565

b) Determine the surface area of geometric solids

PE/TE: 537–539, 540–543, 557, 566

• Assessment limit: Use rectangular prisms with whole number dimensions(0–1000)

PE/TE: 552–557

c) Estimate pi using physical models

PE/TE: 527



d) Estimate and determine the volume of a triangular prism

PE/TE: 560

2. Analyze measurement relationshipsa) Determine a missing dimension for a figure using a scale.

PE/TE: 293–297, 320

• Assessment limit: Use a polygon with no more than 8 sides using whole numbers(0–1000)

PE/TE: 293–297, 320

b) Determine the distance between 2 points using a drawing and a scale

PE/TE: 288–292, 293–298, 299–304, 321

• Assessment limit: Use a scale of 1 cm: ?, _ inch: ?, _ inch: ?, or _ inch: ? andwhole numbers (0–1000)

PE/TE: 288–292, 293–298, 299–304, 321

STANDARD 4.0 KNOWLEDGE OF STATISTICS–Students will collect, organize,display, analyze, or interpret data to make decisions or predictions

A. Data Displays

1. Organize and display dataa) Organize and display data using back-to-back stem & leaf plots

PE/TE: 581–582, 584–586

• Assessment limit: Use no more than 20 data points using whole numbers (0–100)

PE/TE: 581–582, 584–586

b) Organize and display data to make circle graphs

PE/TE: 595, 607, 783



B. Data Analysis

1. Analyze dataa) Recognize misuses of data

PE/TE: 597–600

• Assessment limit: Use whether the choice of graphical display or the scale leadsto faulty interpretation or representation of data

PE/TE: 597–600

b) Analyze misleading data representation

PE/TE: 597–600

2. Describe a set of dataa) Compare measures of central tendency (mean, median, mode) to determine which

is most appropriate

PE/TE: 39–40, 44

• Assessment limit: Use no more than 10 pieces of data using whole numbers ordecimals with no more than 2 decimal places (0–100)

PE/TE: 39–40, 44

STANDARD 5.0 KNOWLEDGE OF PROBABILITY–Students will useexperimental methods or theoretical reasoning to determine probabilities to makepredictions or solve problems about events whose outcomes involve randomvariation.

A. Sample Space

1. Identify a sample spacea) Determine the number of outcomes

PE/TE: 306

• Assessment limit: Use no more than 3 independent events with a sample space ofno more than 6 outcomes in each event.

PE/TE: 306



B. Theoretical Probability

1. Determine the probability of one simple event comprised of equally likely outcomesa) Express the probability of an event as a fraction, a decimal, or a percent

PE/TE: 306–307, 635–639, 643

• Assessment limit: Use a sample space of no more than 35 outcomes

PE/TE: Opportunities to address this standard can be found on the followingpage: 308

C. Experimental Probability

1. Analyze the results of a survey or simulationa) Make predictions and express the probability of the results as a fraction, a

decimal, and a percent with no more than 2 decimal places, or a percent

PE/TE: 305, 306, 311, 608, 633

• Assessment limit: Use results of 25 or 50

PE/TE: 305, 306, 311, 608, 633

2. Conduct a probability experiment

PE/TE: 306–311

3. Compare results of theoretical probability and experimental probability

PE/TE: 305, 307–311

4. Describe the difference between theoretical and experimental probability

PE/TE: 305, 306–311



STANDARD 6.0 KNOWLEDGE OF NUMBER RELATIONSHIPS ORCOMPUTATION–Students will describe, represent, or apply numbers or theirrelationships or will estimate or compute using mental strategies, paper/pencil ortechnology.

A. Knowledge of Number and Place Value

1. Apply knowledge of rational numbers and place valuea) Read, write, and represent whole numbers

PE/TE: 770, 771

• Assessment limit: Use exponential notation with bases no more than 12 andexponents no more than 3, or in standard form (0–1000)

PE/TE: 204–209, 213

b) Express decimals using expanded form

This standard is taught in an alternate course.

• Assessment limit: Use decimals with no more than 4 decimal places (0–100)

PE/TE: 102–107

c) Determine equivalent forms of rational numbers expressed as fractions, decimal,percents, and ratios

PE/TE: 219–224, 329 -333, 340–344

• Assessment limit: Use positive rational numbers (0–100)

PE/TE: 219–224, 329–333, 340–344

d) Compare, order, and describe rational numbers with or without relational symbols(<, >, =)

PE/TE: 221, 223–224

• Assessment limit: Use no more than 4 fractions with denominators that arefactors of 300 that are less than 101, decimals with no more than 4 decimalplaces, percents or integers (0–100)

PE/TE: 221, 223–224

e) Express whole numbers and decimals in scientific notation

PE/TE: 204–209, 213



C. Number Computation

1. Analyze number relations and computea) Add, subtract, multiply, and divide integers

PE/TE: 28–33, 34–38, 41–46, 54–55

• Assessment limit: Use one operation (-100 to 100)

PE/TE: 28–33, 34–38, 41–46, 54–55

b) Add, subtract, and multiply positive fractions and mixed numbers

PE/TE: 225–242

• Assessment limit: Use no more than 2 operations and positive fractions or mixednumbers with denominators as factors of 300 less than 101 (0–2000)

PE/TE: 225–242

c) Divide fractions and mixed numbers

PE/TE: 243–243

d) Calculate powers of integers and square roots of perfect square whole numbers

PE/TE: 10–13, 52, 53, 176, 193–198, 199, 203, 212, 453, 454–457, 458–461,500, 674–678, 700

• Assessment limit: Use no more than 3 exponents for integers (–10 to 20) orsquare roots of perfect square whole numbers (0–100)

PE/TE: 10–13, 52, 53, 176, 193–198, 199, 203, 212, 453, 454–457, 458–461,500, 674–678, 700

e) Use the laws of exponents to simplify expressions

PE/TE: 193–198, 199–203, 212–213, 674–678, 700

• Assessment limit: Use the rules of exponents (power times power or powerdivided by power) with the same whole number base (0–100) and exponents(0–10)

PE/TE: 675–678



f) Identify and use the properties of addition and multiplication to simplifyexpressions

PE/TE: 30, 63–68, 71–75, 109, 125–129, 669–672

• Assessment limit: Use the commutative property of addition or multiplication,associative property of addition or multiplication, additive inverse property, thedistributive property, or the identity property for one or zero with whole numbers(0–100)

PE/TE: 30, 63–68, 71–75, 109, 125–129, 669–672

g) Determine percent of a number

PE/TE: 341–344, 345–350

2. Estimationa) Determine approximate sums, differences, products, and quotients

PE/TE: 771, 773

• Assessment limit: Use no more than 3 positive rational numbers (0–1000)

PE/TE: 771, 772

3. Analyze ratios, proportions, or percentsa) Determine equivalent ratios

PE/TE: 269–274, 275–279, 280–284, 318, 319

• Assessment limit: Use denominators as factors of 300 but less than 101 andwhole numbers (0-100)

PE/TE: 269–274, 275–279, 280–284, 318, 319

b) Determine or use ratios, unit rates, and percents in the context of a problem

PE/TE: 76–77, 269–274, 277 279, 281–284, 293–297, 318, 319 (#17, 22), 320,321

• Assessment limit: Use whole numbers (0-1000)

PE/TE: 76–77, 269–274, 277, 279, 281–284, 293–297, 318, 319 (#17, 22),320, 321



c) Determine rate of increase and decrease, discounts, simple interest, commission,sales tax

PE/TE: 352–356, 357–361, 362–366, 370 (Section 7.5), 371

d) Determine percent of a number

PE/TE: 334, 341–344, 370 (Section 3.4)

STANDARD 7.0 PROCESSES OF MATHEMATICS–Students demonstrate theprocesses of mathematics by making connections and applying reasoning to solveand to communicate their findings.

A. Problem solving1. Apply a variety of concepts, processes, and skills to solve problems

a. Identify the question in the problem

PE/TE: 18, 58–59

b. Decide if enough information is present to solve the problem

PE/TE: 58–59

c. Make a plan to solve a problem

PE/TE: 14–15, 18, 38, 160–161, 264–265, 448–449, 570–571, 704–705,795–796, 797, 798, 799, 800, 801, 802

d. Apply a strategy, i.e., draw a picture, guess and check, finding a pattern, writingan equation

PE/TE: 86–89, 92–95, 98–101, 104–107, 122–124, 125, 127–129, 132–135,264, 795, 796, 797

e. Select a strategy, i.e., draw a picture, guess and check, finding a pattern, writingan equation

PE/TE: 86–89, 92–95, 98–101, 104–107, 122–124, 125, 127–129, 132–135,264, 795, 796, 797

f. Identify alternative ways to solve a problem

PE/TE: 264–265

g. Show that a problem might have multiple solutions or no solution

PE/TE: 448–449



h. Extend the solution of a problem to a new problem situation

PE/TE: 704–705

B. Reasoning1. Justify ideas or solutions with mathematical concepts or proofs

a. Use inductive or deductive reasoning

PE/TE: Found throughout the text. See, for example, Critical Thinkingexercises on the following pages: 10, 13, 21, 28, 32, 34, 41, 45, 50, 70,95, 119, 120, 143, 148, 176, 178, 181, 186, 191

b. Make or test generalizations

PE/TE: Opportunities to address this standard can be found on the followingpages: 171, 292, 305, 310, 338, 423, 424, 425, 461, 533, 561, 613,737, 745

c. Support or refute mathematical statements or solutions

PE/TE: Opportunities to address this standard can be found in CriticalThinking exercises on the following pages: 9, 33, 38, 83, 128, 136,175, 185, 202, 224, 257, 303, 310, 334, 361, 439, 457, 480, 529, 585,600, 619, 625, 635, 671, 696, 712, 717, 726

d. Use methods of proof, i.e., direct, indirect, paragraph, or contradiction

PE/TE: 281, 402, 417, 464, 483, 484, 521, 522, 539, 540, 545, 720, 727

C. Communication1. Present mathematical ideas using words, symbols, visual displays, or technology

a. Use multiple representations to express concepts or solutions

PE/TE: Found throughout the text. See, for example, the following pages:25 (#51), 28, 42, 43, 50 (#27), 63, 65, 71, 78–82, 85–89, 90, 91, 96,119, 130, 403, 527–537, 656, 667

b. Express mathematical ideas orally

PE/TE: Found throughout the text. See, for example, Guided Practice sectionson the following pages: 7, 12, 18, 24, 31, 36, 44, 49, 66, 73, 80, 87, 93,99, 105, 122, 127, 133, 140, 151



c. Explain mathematically ideas in written form

PE/TE: Found throughout the text. See, for example, the following pages:28 (#13), 46 (#43), 50 (#27), 67 (#40), 75 (#50), 81 (#36), 88 (#36),90 (#10), 96 (#9), 101 (#37), 106 (#45a), 119 (#8), 130 (#5),135 (#33), 141 (#39), 153 (#34c), 171 (#1), 175 (#47), 181 (#50),190 (#37), 197 (#41)

d. Express solutions using concrete materials

PE/TE: Found throughout the text. See, for example, the following pages:90, 96, 119, 130, 287, 305, 403, 471, 488, 495, 506–507, 527,550–551, 656, 667, 715, 740, 794

e. Express solutions using pictorial, tabular, graphical, or algebraic methods

PE/TE: Found throughout the text. See, for example, the following pages:8 (#51), 20 (#39c), 25 (#51b), 28, 29, 47–51, 67 (#49), 85–89, 96,100 (35b), 119, 128 (#33–36), 130, 140–141, 175 (#32, 33), 190 (#36),482, 595, 608

f. Explain solutions in written form

PE/TE: Found throughout the text. See, for example, the following pages:28 (#13), 46 (#43), 50 (#27), 67 (#40), 75 (#50), 81 (#36), 88 (#36),90 (#10), 96 (#9), 101 (#37), 106 (#45a), 119 (#8), 130 (#5),135 (#33), 141 (#39), 153 (#34c), 171 (#1), 175 (#47), 181 (#50),190 (#37), 197 (#41)

g. Ask questions about mathematical ideas or problems

PE/TE: Opportunities to address this standard can be found in Error Analysisexercises throughout the text. See, for example, the following pages:8, 24, 36, 45, 152, 189, 196, 239, 255, 337, 342, 355, 365, 387, 407,474, 479, 513, 554, 560, 653, 676, 695, 736, 744

h. Give or use feedback to revise mathematical thinking

PE/TE: Opportunities to address this standard can be found in Error Analysisexercises throughout the text. See, for example, the following pages:8, 24, 36, 45, 152, 189, 196, 239, 255, 337, 342, 355, 365, 387, 407,474, 479, 513, 554, 560, 653, 676, 695, 736, 744



D. Connections1. Relate or apply mathematics within the discipline, to other disciplines, and to life

a. Identify mathematical concepts in relationship to other mathematical concepts

PE/TE: Found throughout the text. See, for example, the following pages:85–89, 90, 91–95, 172–176, 177–181, 269–274, 275–280, 385–390,391–396, 453–457, 458–461, 594–595, 596–600

b. Identify mathematical concepts in relationship to other disciplines

PE/TE: Found throughout the text. See, for example, the following pages:147 (#37), 183 (Example 3), 197 (#40, 58), 201 (Example 4), 204,207 (#39), 220 (Example 3), 225, 234 (#33), 256 (#41), 296 (#14),304 (#46), 332 (#43, 44), 354 (#6), 364 (#7), 389 (#2), 390 (#26),392 (In The Real World), 395 (#39), 396 (#41)

c. Identify mathematical concepts in relationship to life

PE/TE: Found throughout the text. See, for example, the following pages:47, 114–115, 122 (#7), 128 (#37), 141 (#38), 142 (#43),201 (Example 4), 204, 207 (#39), 217, 225, 247, 256 (#41), 274 (#46),273 (#36)

d. Use the relationship among mathematical concepts to learn other mathematicalconcepts

PE/TE: Found throughout the text. See, for example, the following pages:85–89, 90, 91–95, 172–176, 177–181, 269–274, 275–280, 385–390,391–396, 453–457, 458–461, 594–595, 596–600

MD 467/2004

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Maryland Voluntary State Curriculum Mathematics: Grade 7 · PDF fileMcDougal Littell...

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