Algebra 1 ©2004 - Holt McDougal

C15
correlated to the
New Hampshire
Mathematics Curriculum
Framework
12/2003
2004
NH 22

Goals and Standards
McDougal Littell ALGEBRA 1
correlated to the
New Hampshire
Mathematics Curriculum Framework
PROBLEM SOLVING AND REASONING
1a. K-12 Broad Goal: Students will use problem-solving strategies to investigate and
understand increasingly complex mathematical content.
PURPOSE: Problem solving should serve as the organizing feature of the mathematics
curriculum as well as other areas of study and be applied to everyday activities.
Problem-solving must not be seen as a separate topic, but rather the centerpiece
of the mathematics curriculum. Students should have many experiences in posing
and solving problems from their world, from data that are meaningful to them,
and from mathematical investigations.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Determine, collect and organize the relevant data needed to solve real-world problems.
TE: 292-299, 492, 554-559
PE: 292-299, 492, 554-559
• Determine the reasonableness of solutions to real-world problems.
TE: 27, 34, 83, 530
PE: 34, 530
• Use technology whenever appropriate to solve real-world problems which require
strategies previously learned.
TE: 209, 215, 248-249, 251, 297, 299, 317-322, 367, 382, 404, 430, 462, 492, 525,
570, 620, 663, 680, 698, 715
PE: 209, 215, 248-249, 251, 297, 299, 317-322, 367, 382, 404, 430, 462, 492, 525,
570, 620, 663, 680, 698, 715
1

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
• Use technology whenever appropriate to solve problems related to basic living skills
including, but not limited to, personal finance, wages, banking and credit, home
improvement problems, measurement, taxes, business situations, purchasing, and
transportation.
TE: 284, 317, 321, 460, 467-468, 472, 477, 478, 480, 484, 488-489, 509, 520, 545, 553
PE: 284, 317, 321, 460, 467-468, 472, 477, 480, 484, 488-489, 509, 520, 545, 553
• Apply problem solving strategies to solve problems in the natural and social sciences
and in pure mathematics.
TE: 74, 76, 147, 261, 290, 358, 373, 413, 415, 467, 506-508, 621
PE: 74, 76, 147, 261, 290, 358, 373, 413, 415, 467, 506-508
Proficiency Standards (1a):
End of Grade 10:
• Determine, collect, and organize the relevant data needed to solve real-world problems.
TE: 292-299, 492, 554-559
PE: 292-299, 492, 554-559
• Choose the appropriate technology needed to solve a real-world problem.
TE: 209, 248-249, 284, 299, 321, 367, 460, 472, 480, 492, 525, 680, 698
PE: 209, 248-249, 284, 299, 321, 367, 460, 480, 525, 698
• Translate results of a computation into solutions that fit the real-world problem (for
example, when a computation shows that one needs 3.2 gallons of paint to paint a room,
how much paint do you buy?).
TE: 34, 166, 168
PE: 34, 166, 168
• Determine if the solution of a real-world problem is reasonable.
TE: 34, 37, 83, 166, 168, 506, 530, 535, 606, 613, 627, 739
PE: 34, 166, 168, 506, 530, 535, 606, 613, 627, 739
• Use technology to solve a problem from science, social science, or mathematics.
TE: 474, 478, 489, 506-508, 510, 523
PE: 474, 478, 489, 506-508, 510, 523
2

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
1b. K-12 Broad Goal: Students will use mathematical reasoning.
PURPOSE: Students need to recognize that memorized facts, rules, and procedures are only
a part of mathematics. They need opportunities to use these facts, rules, and
procedures to make conjectures, develop and refine their reasoning abilities,
gather evidence, and produce valid rules and generalizations. Students need to be
able to justify their thinking through examples and explanations and appreciate
that how a problem is solved is as important as the answer.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Draw logical conclusions and make generalizations using deductive and inductive
reasoning.
TE: 66, 187-188, 393, 674, 739, 758-763
PE: 66, 187-188, 393, 674, 739, 758-763
• Formulate and test mathematical conjectures and arguments.
TE: 165, 455, 476, 696, 698, 723-724, 726
PE: 165, 455, 476, 696, 698, 726
• Determine the validity of an argument and /or a solution.
TE: 7, 27, 96, 103, 149, 158, 230, 312, 336, 342, 337, 343, 414, 458, 459, 467, 513,
579, 614, 621, 622, 628, 629, 654, 666, 667, 673, 679, 724, 726
PE: 7, 27, 96, 103, 149, 158, 230, 312, 337, 343, 414, 459, 467, 513, 579, 614, 622,
629, 654, 667, 673, 679, 726
• Apply mathematical reasoning skills, when appropriate, in other disciplines.
TE: 112, 150, 175, 238, 422, 506, 515, 555, 556, 601
PE: 112, 150, 175, 238, 422, 515, 556, 601
3

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
Proficiency Standards (1b):
End of Grade 10:
• Use Inductive reasoning to make generalizations from an observed pattern.
TE: 187-188
PE: 187-188
• Use logical reasoning, as well as estimation and mental computations, to determine the
validity of a solution.
TE: 34, 166, 168, 530
PE: 34, 166, 168, 530
• Justify conjectures, defend generalizations, and write logical arguments.
TE: 66, 187-188, 393, 674, 739, 758-763, 759-761
PE: 66, 187-188, 393, 674, 739, 758-763
4

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
COMMUNICATION AND CONNECTIONS
2a. K-12 Broad Goal: Students will communicate their understanding of
mathematics.
PURPOSE: Reading, writing, talking, listening, and modeling, provide students with the
opportunity to integrate the language of mathematics into their world, and help
them to develop understanding. Actively exploring, investigating, describing, and
explaining mathematical ideas promote communication which leads to a greater
comprehension of mathematical concepts.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Formulate questions, conjectures, definitions, and generalizations about, data,
information, and problem situations.
TE: 23, 71, 153, 168, 198-199, 201, 225, 240, 307, 392-393, 447, 476
PE: 23, 71, 153, 168, 198-199, 201, 225, 240, 307, 392-393, 447, 476
• Use a variety of technologies to represent and communicate mathematical ideas and
determine the appropriateness of their use.
TE: 23, 71, 99, 199, 209, 392, 570, 571, 732
PE: 23, 71, 99, 199, 209, 571, 732
• Understand, explain, analyze, and evaluate mathematical arguments and conclusions
made by others.
TE: 7, 27, 96, 103, 1439, 158, 230, 312, 337, 414, 429, 459, 467, 514, 579, 610, 614,
622, 629, 667, 673, 679, 726
PE: 7, 27, 96, 103, 1439, 158, 230, 312, 337, 414, 429, 459, 467, 514, 579, 610, 614,
622, 629, 667, 673, 679, 726
• Understand the efficiency and power of mathematical notation.
TE: 369-375, 396-405
PE: 369-375, 396-405
5

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
Proficiency Standards (2a):
End of Grade 10:
• Evaluate given information and determine appropriate questions suggested by the
situation.
TE: 23, 31, 71, 78, 131, 153, 225, 240, 397, 425, 476, 603, 698, 737
PE: 23, 31, 71, 78, 131, 153, 225, 240, 397, 425, 476, 603, 698, 737
• Evaluate given information and determine appropriate generalizations suggested by the
situation.
TE: 71, 78, 93, 456, 470, 511
PE: 71, 78, 93, 456, 470, 511
• Describe orally and/or in writing how various technologies can be used to communicate
about a specific situation.
TE: 198, 209, 392, 447, 501, 517
PE: 198, 209, 392, 447, 501, 517
• Use mathematical symbols and notation to communicate mathematically.
TE: 23, 99, 199, 315, 392-393, 483, 540, 571, 732
PE: 23, 99, 199, 315, 392-393, 483, 540, 571, 732
• Justify conjectures, defend generalizations and write logical arguments.
TE: 31, 61, 93, 225, 240, 292, 374, 397, 425, 449, 470, 476, 517, 775
PE: 31, 61, 93, 225, 240, 292, 374, 397, 425, 449, 470, 476, 517, 775
6

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
2b. K-12 Broad Goal: Students will recognize, develop, and explore mathematical
connections.
PURPOSE: Mathematical topics, ideas, and procedures must be connected to each other and
to the students’ everyday experiences, both in and out of school. In particular,
mathematics must be connected to all other curriculum areas. Mathematical
connections will help students become aware of the usefulness of mathematics,
serve to bridge the concrete and the abstract, and enable deeper understanding of
important ideas.
7-12 Building upon the K-6 experiences, in grades 7-12:
• View mathematics as an integrated whole. (Be able to synthesize the varied branches.)
TE: 23, 47, 161-162, 173, 204-209, 292-299, 348, 351, 398-404, 506, 520, 526-532
PE: 23, 47, 161-162, 173, 204-209, 292-299, 348, 351, 398-404, 506, 520, 526-532
• Explain the relationship between a real-world problem and an appropriate mathematical
model.
TE: 316-321, 543-545, 554-559
PE: 316-321, 543-545, 554-559
• Explain in oral or written form how mathematics connects to other disciplines, to daily
life, careers, and society.
TE: 238, 271, 293, 318, 338, 423, 430, 509, 522, 545, 621
PE: 238, 271, 293, 318, 338, 423, 430, 509, 522, 545, 621
• Use models and calculators or other technologies to develop equivalent representations
of the same mathematical concept.
TE: 71, 78, 99, 131, 153, 526-531, 575, 603, 610, 683, 729
PE: 71, 78, 99, 131, 153, 526-531, 575, 603, 610, 683, 729
• Recognize the logical development of mathematics from basic assumptions and
definitions, and understand that mathematics frequently arises out of real-world
applications.
TE: 16-21, 32-38, 63-70, 72-77, 79-84, 93-98, 108-113, 450-460, 463-468
PE: 16-21, 32-38, 63-70, 72-77, 79-84, 93-98, 108-113, 450-460, 463-468
7

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
• Recognize that many real world applications require an understanding of use of
mathematical concepts (for example: personal finance, running a business, building a
house, following a recipe, or sending a rocket to the moon).
TE: 140, 171, 175, 306, 313, 343, 413, 434, 454, 545, 592, 711
PE: 140, 171, 175, 306, 313, 343, 413, 434, 454, 545, 592, 711
Proficiency Standards (2b):
End of Grade 10:
• Explain in oral or written form the relationships among various mathematical concepts
(for example, the relationship between exponentiation and multiplication).
TE: 450-455, 503-505, 526-532, 745
PE: 450-455, 503-505, 526-532, 745
• Translate among equivalent representations of the same concept (for example, a table of
values, an equation, and a graph may all be representations of the same function).
TE: 71, 78, 99, 131, 153, 521-531, 575, 603, 610, 683, 729
PE: 71, 78, 99, 131, 153, 521-531, 575, 603, 610, 683, 729
• Explain in oral or written form the relationships between a real-world problem and an
appropriate mathematical model.
TE: 316-321, 543-545, 554-559
PE: 316-321, 543-545, 554-559
• Explain in oral or written form how mathematics connects to other areas (for example:
geometry in art and architecture, data analysis in social studies and exponential growth
in finance).
TE: 13, 42, 74, 271, 274, 306, 331, 338, 402, 454, 651, 711
PE: 13, 42, 74, 271, 274, 306, 331, 338, 402, 454, 651, 711
8

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
NUMBERS, NUMERATION, OPERATIONS, AND NUMBER THEORY
3a. K-12 Broad Goal: Students will develop number sense and an understanding of
our numeration system.
PURPOSE: Students must understand numbers if they are to make sense of the ways
numbers are used in their everyday world. Numbers are used to describe and
interpret real-world phenomena. Students need to use numbers to quantify, to
identify location, to identify a specific object in a collection, to name, to
measure, and to model real-world situations. They need to understand relative
magnitude in order to make sense of everyday situations.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Read and write rational numbers.
The McDougal Littell High School series assumes that reading, writing, and modeling
rational numbers has been treated in earlier courses.
• Use physical models to represent rational numbers.
The McDougal Littell High School series assumes that reading, writing, and modeling
rational numbers has been treated in earlier courses.
• Recognize and demonstrate the difference in magnitude of rational numbers.
TE: 2, 62, 64, 67, 70, 81
PE: 2, 62, 64, 67
• Compare magnitudes of integers, rational, and irrational numbers.
TE: 2, 62, 64, 67, 70, 81, 779-780
PE: 2, 62, 64, 67, 779-780
• Develop and use order relations for integers, rational and irrational numbers.
TE: 2, 62, 64, 67, 70, 81, 779-780
PE: 2, 62, 64, 67, 779-780
9

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
Proficiency Standards (3a):
End of Grade 10:
• Read and write rational numbers.
The McDougal Littell High School series assumes that reading, writing, and modeling
rational numbers has been treated in earlier courses.
• Use physical models to represent rational numbers.
The McDougal Littell High School series assumes that reading, writing, and modeling
rational numbers has been treated in earlier courses.
• Compare and order real numbers.
TE: 2, 62, 64, 67, 70, 81, 779-780
PE: 2, 62, 64, 67, 779-780
10

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
3b. K-12 Broad Goal: Students will understand the concepts of number operations.
PURPOSE: Students need to build an awareness of the properties of an operation, see
relationships among operations, and acquire insight into the effects of operations
on real numbers. Students need to recognize conditions in real-world situations
where the use of these operations is indicated and useful.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Demonstrate an understanding of the operations of addition, subtraction, multiplication,
and division of rational numbers, and the effect of performing these operations (for
example, what can one say about the quotient when dividing by a fraction between 0
and 1?).
TE: 21, 25, 32, 71-75, 79-82, 93-96, 108-111
PE: 32, 71-75, 79-82, 93-96, 108-111
• Understand the standard algebraic order of operations.
TE: 16-21, 68, 104
PE: 16-21
• Understand the properties of exponents.
TE: 5, 9-21, 450-454, 463-469, 477-490
PE: 9-21, 450-454, 463-469, 477-490
• Recognize when to use and how to apply the field properties.
TE: 39, 73, 74, 78, 81, 94, 99-107, 113, 124, 139, 643-644, 759
PE: 39, 73, 94, 99-107, 113, 124, 139, 643-644, 759
11

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
Proficiency Standards (3b):
End of Grade 10:
• Examine the four basic operations from a functional perspective: that is, as operations
on ordered pairs.
TE: 73, 79, 93-99, 758
PE: 73, 79, 93-99, 758
• Connect the properties of operations on real numbers to common uses (for example, the
distributive property is used in each of the following cases: 2x + 3x = 5x ; 2/7 + 3/7 =
5/7; and 2(3x + 4) = 6x + 8).
TE: 95, 101-106
PE: 101-106
12

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
3c. K-12 Broad Goal: Students will compute.
PURPOSE: The purpose of computation is to solve problems. While computation remains
important in mathematics and in everyday life, advances of technology require us
to rethink how computation is done today. Students must recognize that
estimation, mental computation, use of calculators, and paper and pencil
calculation are all appropriate ways to compute solutions to problems. Basic fact
memorization should be incorporated into a rich curriculum rather than be its
primary focus.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Apply the standard algebraic order of operations with real numbers.
TE: 16-22, 68, 104
PE: 16-22
• Apply the properties of exponents with real numbers.
TE: 9-15, 449-469
PE: 9-15, 449-469
• Simplify expressions involving the use of grouping symbols such as parentheses.
TE: 10, 16-21
PE: 10, 16-21
Proficiency Standards (3c):
End of Grade 10:
• Perform the four basic operations with rational numbers.
TE: 21, 25, 32, 71-75, 79-82, 93-96, 108-111
PE: 32, 71-75, 79-82, 93-96, 108-111
• Simplify expressions containing rational numbers, integer exponents, and grouping
symbols using conventional methods and technology.
TE: 102-106, 109, 111, 151, 450-453, 457, 459, 463-466
PE: 102-106, 109, 111, 450-453, 457, 459, 463-466
13

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
• Evaluate numerical expressions containing scientific notation.
TE: 470-475
PE: 470-475
• Use the order of operations to evaluate expressions.
TE: 16-21, 68, 104
PE: 16-21
• Use the field properties to simplify expressions.
TE: 73, 74, 78, 81, 94, 99-107, 113, 124, 139, 758, 643-644
PE: 73, 94, 99-107, 113, 124, 139, 758, 643-644
14

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
3d. K-12 Broad Goal: Students will use mental computation and estimation skills
and strategies and know when it is appropriate to do so.
PURPOSE: Students should know what is meant by estimation and mental computation,
when they are appropriate, and how close an estimate is required in a given
situation. Students should be encouraged to estimate the solution of problems
before computation or measurement is done, and to use estimation to determine
the reasonableness of answers, and to recognize when an estimate is sufficient as
an answer.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Determine the reasonableness of answers for problems involving arithmetic operations
on real numbers.
TE: 34, 37, 83, 166, 168, 506, 530, 606, 613, 627, 739
PE: 34, 166, 168, 506, 530, 606, 613, 627, 739
Proficiency Standards (3d):
End of Grade 10:
• Use estimation and mental computation to determine the reasonableness of answers
obtained from the four basic operations on real numbers.
TE: 526-531, 534
PE: 526-531, 534
• Select and use appropriate mental computation and estimation strategies in problem
situations when exact answers are not needed.
TE: 1, 25, 37, 83, 181, 287, 315-320, 645, 647
PE: 1, 25, 181, 287, 315-320, 645, 647
15

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
GEOMETRY, MEASUREMENT, AND TRIGINOMETRY
4a. K-12 Broad Goal: Students will name, describe, model, classify, and compare
geometric shapes and their properties with an emphasis on their wide
applicability in human activity.
PURPOSE: Geometry helps students represent and describe the world in which they live.
Students need to investigate, experiment, and explore geometric properties using
both technology and hands on materials.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Explore the relationship among definitions, postulates, and theorems.
See McDougal Littell Geometry, pages: 10-12, 17, 79-81
• Investigate the properties of two- and three-dimensional shapes.
See McDougal Littell Geometry, pages: 196-201, 236-242, 272-284, 286-300, 322-370,
535-556, 595-634, 660-698,719-771
• Deduce properties of and relationships among figures from given assumptions.
See McDougal Littell Geometry, pages: 196, 229, 237, 289, 294-295, 302-307, 535,
551-556
• Use compass and straightedge, manipulatives, and technology to explore geometric
constructions.
See McDougal Littell Geometry, pages: 43, 77, 110, 115, 155, 159, 161, 163, 218, 264,
286, 294, 297, 329, 354, 361, 411, 497, 514, 542, 547, 564, 618, 641, 647, 667, 673-674
• Deduce properties and relationships among congruent figures and similar figures.
TE: 139-144, 428, 708, 750
PE: 140-144, 428, 708, 750
• Explore basic transformations (for example: reflections, translations, rotations, or
dilations).
See McDougal Littell Geometry, pages: 395-443, 506-514
16

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
• Use basic transformations to demonstrate similarity, symmetry, and congruence of
figures.
See McDougal Littell Geometry, pages: 395-443
• Explore relationships between synthetic and coordinate representations.
See McDougal Littell Geometry, pages: 165-177, 243-249, 254, 343, 360, 426, 429, 646
• Apply principles of coordinate geometry, i.e., graph lines and circles and determine the
slope and intercept of a line, mid-point of a line segment, the center and radius of a
circle.
TE: 203-255, 747-750
PE: 203-255, 747-750
• Understand the interrelationships between algebraic and geometric representations of the
same mathematical concept.
See McDougal Littell Geometry, pages: 166-176, 243-249
Proficiency Standards (4a):
End of Grade 10:
• Represent and solve problems using the properties of two- and three- dimensional
geometric figures.
See McDougal Littell Geometry, pages: 273, 277, 280, 285, 291, 298, 357, 378, 474,
478, 482, 487, 528, 532, 685, 688, 745
• Use technology, manipulatives, and/or coordinate geometry to deduce and explain the
properties of and the relationships among geometric figures.
See McDougal Littell Geometry, pages 39, 43, 228, 249, 270, 286, 291, 294, 326-317,
329, 354, 361, 547, 618, 628
• Translate between synthetic and coordinate representations.
See McDougal Littell Geometry, pages: 165-177, 243-249, 254, 343, 360, 426, 429, 646
17

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
4b. K-12 Broad Goal: Students will develop spatial sense.
PURPOSE: We live in a three dimensional world. To interpret, understand, and appreciate
that world, students need to develop an understanding of space. Research
suggests that there is a high correlation between spatial abilities and success in
mathematics. Spatial skills include making and interpreting drawings, forming
mental images, visualizing changes, and generalizing about perceptions in the
environment.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Explore two-dimensional and three-dimensional geometry using shadows, perspectives,
projections, and maps.
See McDougal Little Geometry, pages: 15, 129, 132, 141, 188-189, 508, 512
• Explore the effects of reflections, translations, rotations, and dilations in the study of
congruent and similar geometric shapes and tessellations.
See McDougal Little Geometry, pages: 395-443
• Understand, model, describe, analyze, and apply patterns produced by processes of
geometric change, formally connecting iteration, approximations, limits, self-similarity,
and fractals.
See McDougal Little Geometry, pages: 133, 291, 293, 556, 590-591
• Use manipulatives and computer graphics to enhance spatial sense and to increase
understanding of geometry and to explore its connections to other parts of mathematics,
science, and art.
See McDougal Little Geometry, pages: 39, 43, 228, 249, 270, 286, 291, 294, 316-317,
329, 354, 361, 547, 618, 628
• Explore other geometries and their applications (for example, non-Euclidean geometries
have significant applications in science).
See McDougal Little Geometry, pages: 714-715
18

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
Proficiency Standards (4b):
End of Grade 10:
• Sketch specific two-dimensional figures, given definitions and/or properties.
See McDougal Little Geometry, pages: 188-189, 720, 724-726, 728, 732-732
• Demonstrate that the conditions necessary for congruence or the conditions necessary
for similarity are met.
See McDougal Little Geometry, pages: 228, 488-495, 766
• Use technology, manipulatives, and/or coordinate geometry to explain properties of
transformations (for example: translations, line reflections, rotations, dilations, and the
composition of these transformations).
See McDougal Little Geometry, pages: 396, 399, 400, 403-404, 409, 411, 414, 416-417,
422-435
• Demonstrate an understanding of properties among two- and three-dimensional figures.
See McDougal Little Geometry, pages: 162, 273-278, 285, 288-293, 302-307, 341-345,
561-565
19

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
4c. K-12 Broad Goal: Students will develop an understanding of measurement and
systems of measurement through experiences which enable them to use a variety
of techniques, tools, and units of measurement to describe and analyze
quantifiable phenomena.
PURPOSE: Measurement is used in many ways throughout our lives. Students must be
introduced to the standard units of measure used in both the metric and English
Systems. Students should estimate and measure length, area, capacity, volume,
weight, time and temperature, as well as discover practical uses of these skills.
High school students must develop more mature insights into the essential role of
measurement as a link between the abstractions of mathematics and the
concreteness of the real-world. By using various techniques and tools, we
describe and analyze quantifiable phenomena to understand and organize our
world.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Explore linear and area measures of two-dimensional figures.
TE: 11, 13, 21, 100, 163, 177-179, 344, 558, 578, 595, 666-669, 688
PE: 11, 13, 21, 163, 177-179, 344, 558, 578, 595, 666-669, 688
• Explore the volume, surface area and linear measures of three-dimensional figures.
TE: 11, 13, 14, 177, 454, 630, 660
PE: 11, 14, 177, 454, 630, 660
• Apply the Pythagorean Theorem to real-world situations.
TE: 738-743, 746, 763
PE: 738-743, 763
• Enhance, extend, apply, and formalize understandings and applications of measurement
including strategies for determining perimeters, areas, and volumes by using formulas,
approximations, and computer-geometry programs.
TE: 11, 23, 13-14, 29, 174, 175, 177
PE: 11, 23, 13-14, 29, 174, 177
20

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
.
• Use ratio and proportions to explore the properties of similar figures and use these
properties to solve problems.
TE: 140-141, 143, 159, 750-751
PE: 140-141, 143, 159, 750-751
• Choose appropriate techniques and tools to measure quantities in order to achieve
specified degrees of precision, accuracy, and error (or tolerance) of measurement.
The McDougal Littell High School series assumes that measurement and related topics
have been covered in earlier courses.
• Choose an appropriate unit of measure and use appropriate formulas to find perimeter
and circumference, area of polygons and circles, the volume and surface area of selected
solids, and the measure of angles.
See McDougal Littell Geometry, pages: 145, 371-380, 669-675, 691-698, 729-749, 752-765
• Choose appropriate units for measuring size, rates, and energy.
The McDougal Littell High School series assumes that measurement and related topics
have been covered in earlier courses.
• Select and use appropriate formulas and procedures to determine a measure when a
direct measurement is not available.
TE: 141, 641, 754, 756
PE: 141, 641, 754, 756
• Understand and apply measurement in career-based contexts and in interdisciplinary
situations.
TE: 34, 48, 74, 140, 147, 168, 171, 271, 313, 318, 413, 415, 481, 606, 608, 645, 672, 711
PE: 34, 48, 74, 140, 147, 168, 171, 271, 313, 318, 413, 415, 481, 606, 608, 645, 672, 711
21

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
Proficiency Standards (4c):
End of Grade 10:
• Identify and use appropriate units of measurement.
The McDougal Littell High School series assumes that measurement and related topics
have been covered in earlier courses.
• Approximate areas of irregular shapes drawn on a grid.
The McDougal Littell High School series assumes that measurement and related topics
have been covered in earlier courses
• Convert commonly used measurements to equivalent ones within a measurement system.
The McDougal Littell High School series assumes that measurement and related topics
have been covered in earlier courses:
• Apply the formulas for and choose an appropriate unit of measurement to find the linear
and area measures associated with two-dimensional figures and the volume and surface
area of three-dimensional figures.
TE: 11, 13, 21, 29, 174, 175, 177
PE: 11, 13, 21, 29, 174, 177
• Apply the Pythagorean theorem to problem solving situations.
TE: 738-743, 746
PE: 738-743
• Select an appropriate procedure to determine a measure when a direct measurement
cannot be made.
TE: 141, 641, 754, 756
PE: 141, 641, 754, 756
• Use ratio and proportion to find the measure of all sides of similar figures.
TE: 140-141, 143-144
PE: 140-141, 143-144
22

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
4d. K-12 Broad Goal: Students will know the basic concepts of trigonometry and
apply these concepts to real-world problems.
PURPOSE: all students should explore real-world phenomena which involve right triangle
trigonometry. These experiences should include the use of the sine, cosine, and
tangent ratios. Technology should be used to facilitate the learning of
trigonometry, allowing students more time and power to explore realistic
applications.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Explore the sine, cosine, and tangent ratios in right triangles.
TE: 752-753, 755-757
PE: 752-753, 755, 757
• Use the sine, cosine, and tangent ratios to solve real-world problems.
TE: 754, 756
PE: 754, 756
Proficiency Standards
End of Grade 10:
• Use technology or manipulatives to apply basic trigonometric ratios to solve practical
real-world problem.
TE: 753-757
PE: 753-757
23

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
DATA ANALYSIS, STATISTICS, AND PROBABILITY
5a. K-12 Broad Goal: Students will use data analysis, statistics and probability to
analyze given situations and the outcomes of experiments.
PURPOSE: Collecting, organizing, displaying, and interpreting data, as well as using the
information to make decisions and predictions, have become very important in
our society. Statistical instruction should be carried out in a spirit of investigation
and exploration so students can answer questions about data. Probability must be
studied in familiar contexts encouraging students to model situations. Students
need to investigate fairness, chances of winning, and uncertainty. Technology
should be used as a tool throughout the investigation process.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Collect, organize, describe and interpret data from familiar contexts.
TE: 41-45, 84, 185, 204-209, 292-298, 368-373, 375-382, 392-393, 570-571, 792-794
PE: 41-45, 84, 185, 204-209, 292-298, 368-373, 375-380, 382, 392-393, 570-571, 792-
794
• Use a variety of techniques which include but are not limited to spreadsheets, tables,
stem and leaf plots, box and whisker plots, to analyze data and make predictions.
TE: 375-382
PE: 375-382
• Understand sampling and recognize its role in statistical claims.
TE: 181-183-184, 645, 647-648, 653-654
PE: 181, 183-184, 645, 647-648, 653-654
• Understand and apply measures of central tendency, dispersion and correlation.
TE: 369-370
PE: 369-370
• Design a statistical experiment to study a problem, conduct the experiment, interpret,
and communicate the outcomes.
TE: 392-393
PE: 392-393
24

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
• Use graphics technology to analyze real world data.
TE: 382
PE: 382
• Apply the normal curve and its properties to familiar contexts.
See McDougal Littell Algebra 2, pages: 746-751
• Use relative frequency and probability, as appropriate, to represent and solve problems
involving uncertainty.
TE: 114-119, 170, 345, 452, 454, 465, 468, 596, 666, 668, 675
PE: 114-119, 170, 345, 452, 454, 465, 468, 596, 666, 668, 675
• Use simulations to estimate probabilities.
See McDougal Littell Algebra 2, pages: 723, 728, 738
• Create, interpret, and understand applications of discrete and continuous probability
distributions.
See McDougal Littell Algebra 2, pages: 737-751
• Make predictions based on interpolation and extrapolation from data.
TE: 297, 318-322, 570
PE: 297, 318-322, 570
• Make decisions based on interpretation of data.
TE: 370, 372, 373, 377, 379
PE: 372, 373, 377, 379
25

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
Proficiency Standards (5a):
End of Grade 10:
• Given a bar, line, circle or picture graph, interpret and analyze the data.
TE: 41-45, 115, 373, 651-654
PE: 41-45, 115, 373, 651-654
• Choose an appropriate scale and construct a graph or diagram using a set of numerical
data in a variety of mediums.
TE: 651-652, 654, 793
PE: 651-652, 654, 793
• Calculate the common measures of central tendency: mean, median and mode.
TE: 369-374
PE: 369-374
• Use appropriate measure of central tendency in problem situations.
TE: 370-372
PE: 370-372
• Given a set of numerical data, determine the ordered pairs and make a scatter plot.
TE: 292-299, 525, 570-571
PE: 292-299, 525, 570-571
• Use sample sets to make appropriate inferences and predictions.
TE: 181, 184, 645, 647-648, 653-654
PE: 181, 184, 645, 647, 653-654
• Predict and find the probability of outcomes of a simple probability experiment.
TE: 115-119
PE: 115, 117-118
• Interpret probabilities in real world situations (for example: lotteries, or medical testing.
TE: 115, 118
PE: 115, 118
26

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
FUNTIONS, RELATIONS, AND ALGEBRA
6a. K-12 Broad Goal: Students will recognize patterns and describe and represent
relations and functions with tables, graphs, equations and rules, and analyze how
a change in one element results in a change in another.
PURPOSE: One of the central themes of mathematics is the study of patterns, relations, and
functions. This study requires students to recognize, describe, and generalize
patterns and build mathematical models to predict the behavior of real-world
phenomenon that exhibit the observed pattern. This study of patterns leads to an
exploration of functions, a concept which is an important unifying idea in all
aspects of mathematics.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Analyze functions and relations to describe how a change in one quantity results in a
change in another.
TE: 23, 34, 51, 240, 452, 480-481, 488, 508, 523, 658, 711, 714, 718-720, 726, 755, 757
PE: 23, 51, 240, 480-481, 488, 508, 523, 658, 711, 714, 718-720, 726, 755, 757
• Use polynomial, rational, trigonometric, and exponential functions to model real-world
relationships.
TE: 48-49, 51, 237, 239, 242, 274-275, 278, 281-284, 287, 289-290, 292-299, 302,
304, 483-485, 488-489, 492, 506, 508, 513, 535, 538, 545
PE: 48-49, 51, 237, 274-278, 281-284, 287, 289-290, 292-299, 302, 304, 483-485,
488-489, 492, 506, 508, 513, 535, 538, 545
• Use charts and tables to organize and represent data.
TE: 46-52, 237, 256-260, 273-321, 479-490, 506, 518-525, 554-560, 657-658
PE: 46-51, 237, 256-260, 273-321, 479-490, 506, 518-525, 554, 556-559, 657
27

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
Proficiency Standards (6a):
End of Grade 10:
• Develop algebraic formulas to express relationships which occur in other disciplines (for
example: science, or economics).
TE: 147, 207, 238, 287, 293, 297, 419, 423, 428, 454, 478, 489, 515, 522, 550, 645,
713
PE: 147, 207, 238, 287, 293, 297, 419, 423, 428, 454, 478, 489, 515, 522, 550, 645,
713
• Recognize and describe relationships within a set of data.
TE: 14, 23, 80, 554-560
PE: 14, 23, 80, 554-560
28

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
6b. K-12 Broad Goal: Students will use algebraic concepts and processes to
represent situations that involve variable quantities with expressions, equations,
inequalities, matrices and graphs.
PURPOSE: Algebra is the language through which much of mathematics is communicated. It
provides a means of representing concepts at an abstract level and then applying
those concepts. Students in grades K-6 should explore algebraic concepts in an
informal way, emphasizing physical models, data, graphs and other mathematical
representations. Formal algebraic manipulation may be deferred to later grades.
The understanding of algebraic representation is a prerequisite to formal work in
virtually all of mathematics. Algebraic processes are important tools in the study
of natural sciences and social sciences.
K-12 Curriculum Standards (6b):
7-12 Building upon the K-6 experiences, in grades 7-12:
• Simplify algebraic expressions using the standard order of operations.
TE: 96, 104, 109, 111, 453, 459, 460, 464, 466, 467, 469, 576-587
PE: 96, 104, 109, 111, 453, 459, 464, 466, 576-587
• Perform polynomial operations with manipulatives.
TE: 575, 603, 610
PE: 575, 603, 610
• Model and solve problems that involve varying quantities with variables, expressions,
equations, inequalities, absolute values, vectors, and matrices.
TE: 48, 141, 147, 161-162, 168, 216, 220, 258, 274-275, 310, 342, 400, 418, 506, 592,
651, 672, 678
PE: 48, 141, 147, 161-162, 168, 216, 220, 258, 274-275, 310, 342, 400, 418, 506, 592,
651, 672, 678
• Evaluate algebraic expressions for given values of the variable.
TE: 3-6, 10, 15, 17, 19-21, 24, 76, 79-80, 83, 84, 96, 109, 112, 113, 202, 502, 504
PE: 3-6, 10, 15, 19-21, 76, 83, 96, 109, 112, 202, 502, 504
• Write an equation, using one or two variables, which represents a real-world problem.
TE: 273-321
PE: 273-321
29

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
• Write an inequality, using one or two variables, which represents a real world problem.
TE: 334-335, 347-338, 351, 355, 357, 550
PE: 334, 338, 355, 357, 550
• Solve equations and inequalities in one or two variables, by informal and formal
algebraic methods.
TE: 24, 26, 132-159, 210, 250-255, 503-509, 510, 526-538, 541
PE: 24, 26, 132-159, 210, 250-255, 503-509, 526-538, 541
• Use tables and graphs as tools to interpret expressions, equations, and inequalities.
TE: 80, 156, 161, 211-255, 360-367, 458, 476. 483, 486-490, 517-525
PE: 80, 156, 161, 211-255, 360-367, 458, 476. 483, 486-490, 517-525
• Develop, explain, use, and analyze, procedures for operating on algebraic expressions
and matrices.
TE: 86-92, 102-105, 130, 145-146, 155, 396
PE: 86-92, 102-105, 130, 145-146, 155, 396
• Solve equations and inequalities of varying degrees using graphing calculators and
computers as well as appropriate paper-and-pencil techniques.
TE: 132-173, 175, 250-255, 505-510, 526-539, 643-648
PE: 132-173, 250-255, 505-510, 526-539, 643-648
• Model real-world problems with systems of equations or inequalities.
TE: 399, 404-407, 411-424, 434
PE: 405-407, 411-424, 434
• Solve systems of equations or inequalities using technology as well as pencil-and-paper
techniques.
TE: 398-402, 404-409, 411-424, 432
PE: 411-424, 432
• Use technology to explore the use of matrices in the solution of systems of equations.
TE: 92
PE: 92
30

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
• Understand the logic and purposes of algebraic procedures.
TE: 23, 71-73, 78-79, 93, 99-100, 102, 132, 138, 267, 250, 450, 463, 526-527
PE: 23, 71-73, 78-79, 93, 99-100, 102, 132, 138, 267, 250, 450, 463, 526-527
• Interpret algebraic equations and inequalities geometrically and describe geometric
objects algebraically.
TE: 203-256, 398-432, 518-526, 690
PE: 203-256, 398-432, 518-526, 690
Proficiency Standards (6b):
End of Grade 10:
• Evaluate simple algebraic expressions for given values of the variable.
TE: 3-6, 10, 15, 17, 19-21, 24, 76, 79-80, 83, 84, 96, 109, 112, 113, 202, 502, 504
PE: 3-6, 10, 15, 19-21, 76, 83, 96, 109, 112, 202, 502, 504
• Perform simple operations on matrices.
TE: 86-92
PE: 86-92
• Write an equation or inequality in one variable which represents a real-world problem.
TE: 5, 6, 25, 29, 33-34, 37
PE: 5, 6, 25, 33-34, 37
• Solve equations and inequalities in one variable.
TE: 24-30
PE: 24-30
• Graph the solution set of equations and inequalities in one variable.
TE: 334-338, 339, 346-349, 355-357, 359
PE: 334-338, 346-349, 355-357, 359
31

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
• Use appropriate graphing technology (for example: a graphing calculator, or graphing
software) to graph an equation or inequality in two variables.
TE: 248-251
PE: 248-249, 251
• Use appropriate graphing technology (such as a graphing calculator or graphing
software) to solve systems of linear equations in two variables.
TE: 404, 409
PE: 404, 409
• Solve and justify, orally or in writing, the algebraic solution to a real-world problem.
TE: 105, 183, 223, 365, 392-393, 461, 570-571
PE: 105, 183, 223, 365, 392-393, 461, 570-571
32

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
MATHEMATICS OF CHANGE
7a. K-12 Broad Goal: Students will be able to use concepts about mathematical
change in analyzing patterns, graphs, and applied situations.
PURPOSE: All natural phenomena are characterized by change. Mathematics is a tool for
representing and describing this change, and a preliminary understanding of
change is an important precursor to the more formal ideas of calculus. Through
explorations of patterns, tables, graphs, functions, and situations which focus on
the nature of change, representation, understanding, and recognition of types of
change can be promoted. Real-world examples of change can be examined.
Proportional reasoning and experience with rates should be part of this process.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Use proportional reasoning strategies to solve problems about rates.
TE: 140-143, 645, 647-648
PE: 140-143, 645, 647-648
• Extend patterns and predict nth terms in number sequences.
See McDougal Littell Algebra 2, pages: 652, 656, 659-660, 662-663, 666-667, 671
• Extend patterns and predict nth terms in sequences of geometric figures.
See McDougal Littell Geometry, pages: 5-9, 590-591
• Examine tables of numbers from familiar contexts to determine if patterns exist.
TE: 292-299, 483, 525, 554-559, 663
PE: 292-299, 483, 525, 554-559, 663
• Recognize and describe different types of change (for example: arithmetic, geometric,
periodic, damped, or oscillating).
TE: 293, 297, 423, 460, 467, 477-478, 481-482, 621
PE: 297, 423, 460, 467, 477-478, 481-482, 621
• Calculate and describe change in continuous and discrete contexts which are familiar.
TE: 293, 297, 423, 460, 467, 477-478, 481-482, 621
PE: 297, 423, 460, 467, 477-478, 481-482, 621
33

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
• Interpret and analyze information about change in familiar situations (for example:
percent change, average change, or rates such as distance per unit time).
TE: 161, 229, 232, 274-275, 478-482, 484-489
PE: 161, 229, 274-275, 478-482, 484-489
• Recognize and interpret information about change in graphs of functions.
TE: 232, 460, 480-482, 488, 489, 490
PE: 460, 480-482, 488, 490
Proficiency Standards (7a):
End of Grade 10:
• Solve rate problems that involve proportional reasoning.
TE: 140-141, 143, 645, 647-648
PE: 140-141, 143, 645, 647-648
• Extend patterns and predict nth terms in number sequences, using words and/or
symbols.
See McDougal Littell Algebra 2, pages: 651-663, 666-671
• Extend patterns and predict nth terms in sequences of geometric figures, using words
and/or symbols.
TE: 3, 5-7, 9
PE: 3, 5-7, 9
• Examine tables of numbers from familiar contexts to determine if patterns exist.
TE: 292-299, 483, 492, 555-557, 559
PE: 292-299, 483, 492, 555-557, 559
• Differentiate among different types of change (for example: arithmetic, geometric, or
periodic).
TE: 554-560
PE: 554-559
34

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
• Calculate and describe change in continuous and discrete contexts which are familiar.
TE: 293, 297, 423, 460, 467, 477-478, 481-482, 515, 601, 621
PE: 297, 423, 460, 467, 477-478, 481-482, 515, 601, 621
• Interpret and analyze information about change in familiar situations (for example:
percent change, average change, or rates such as distance per unit time).
TE: 161, 229, 232, 274-275, 478-482, 484-489
PE: 161, 229, 274-275, 478-482, 484-489
35

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
DISCRETE MATHEMATICS
Discrete mathematics is defined as the study of topics which involve items that can be counted,
rather than continuous amounts which can only be measured. Discrete mathematics is actually
an umbrella term which includes such topics as: counting techniques, sets, relations, functions,
logic and reasoning, patterning (iteration and recursion), algorithms, and induction. Probability,
networks, graph theory, social decision making, and matrices should also be included in a
discrete mathematics curriculum. Embedded in these areas are the three main themes of discrete
mathematics: existence (Is there a solution?), counting (How many solutions are there?), and
efficiency (What is the best solution?).
8a. K-12 Broad Goal: Students will use a variety of tools from discrete mathematics
to explore and model real-world situations.
PURPOSE: Information and communication continue to impact the modern world and
require the understanding of discrete mathematics. Decision making involving
sets and systems having a countable number of elements needs to be integrated
throughout the curriculum. Students should have experiences with finite graphs,
matrices, sequences, recursion and the development and testing of algorithms.
7-12 Building upon the K-6 experiences, in grades 7-12:
• Represent data and solve problem situations using graphs, trees and matrices.
TE: 86-91
PE: 86-91
• Use algebraic and geometric iteration to explore patterns and solve problems.
TE: 187, 315
PE: 187, 315
• Use combinations and permutations to solve a variety of problems.
See McDougal Littell Algebra 2, pages: 701-714, 717
• Use algorithms for finding optimal paths and circuits in graphs.
TE: 285, 405
PE: 285, 405
• Solve optimization problems.
See McDougal Littell Algebra 2, pages: 163-168
36

McDougal Littell ALGEBRA 1 correlated to the
New Hampshire Mathematics Curriculum Framework
• Analyze different algorithms for efficiency
The McDougal Littell high school series leaves this topic for a more specialized
advanced course.
• Create and interpret discrete probability distributions using technologies whenever
appropriate.
See McDougal Littell Algebra 2, pages: 738-745
• Use linear programming to solve problems.
TE: 437
PE: 437
• Use the counting principle to solve problems.
TE: 788-789
PE: 788-789
Proficiency Standards (8a):
End of Grade 10:
• Use combinations and permutations to solve a variety of problems.
See McDougal Littell Algebra 2, pages: 703-714, 717
37