group mathematics assessment and diagnostic...

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GROUP MATHEMATICS ASSESSMENT AND DIAGNOSTIC EVALUATION (G•MADE) ©2004

Correlated to

CONNECTICUT MATHEMATICS CURRICULUM FRAMEWORKS

GRADES K – 12

Pearson AGS Globe Pearson Learning Group

TABLE OF CONTENTS

GRADE K ............................................................................................................................................ 1

GRADE 1............................................................................................................................................. 3

GRADE 2............................................................................................................................................. 5

GRADE 3............................................................................................................................................. 7

GRADE 4............................................................................................................................................. 9

GRADE 5........................................................................................................................................... 11

GRADE 6........................................................................................................................................... 13

GRADE 7........................................................................................................................................... 15

GRADE 8........................................................................................................................................... 17


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CONNECTICUT AGS/GLOBE PUBLISHING CONTENT STANDARDS For MATHEMATICS GRADE K GMADE LEVEL R – Form A

Algebraic Reasoning: Patterns And Functions – Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Students should… 1.1 Understand and describe patterns and functional relationships. a. Sort and classify objects using attributes.

Concepts and Communication 6, 16, 18, 28 Process and Applications 7, 13

b. Identify a pattern and describe the rule using the physical attributes or position of objects in a sequence. Identify/Continue pattern: Process and Applications 5, 9, 21

Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.How are quantitative relationships represented by numbers? 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. a. Use numbers to count, order, compare, label, locate and measure.

Concepts and Communication 4, 5, 8, 10, 20, 22, 24, 27 Process and Applications 1, 2-6, 8-11, 16-19, 20-28

b. Share equal parts of an object. This content standard is not assessed within the multiple-choice format.

c. Share a set of objects that is divided into groups with equal amounts. This content standard is not assessed within the multiple-choice format.

2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. a. Count, adding one more to the previous number and group and count by ones and tens.

Process and Applications 9, 21, 23, 25

Geometry and Measurement – Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. How do geometric relationships and measurements help us to solve problems and make sense of our world? 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. a. Identify and sort shapes and solids by physical characteristics.

Identify: Concepts and Communication 15, 19

3.2 Use spatial reasoning, location and geometric relationships to solve problems. a. Use positional language to describe location, direction and position of objects.

Concepts and Communication 9, 21

3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure a. Use calendars and clocks to measure and record time.

Identify clock: Concepts and Communication 13 Tell time: Process and Applications 14

b. Use nonstandard units to estimate measures of length, area, temperature, weight and capacity. Length: Process and Applications 13


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CONNECTICUT AGS/GLOBE PUBLISHING CONTENT STANDARDS For MATHEMATICS GRADE K GMADE LEVEL R – Form A

Working with Data: Probability and Statistics – Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies. How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions? 4.1 Collect, organize and display data using appropriate statistical and graphical methods. a. Visualize information and make comparisons about information displayed in real and picture graphs.

This content standard is not assessed within the multiple-choice format.

4.2 Analyze data sets to form hypotheses and make predictions. a. Extend different types of patterns and make predictions.


4.3 Understand and apply basic concepts of probability. a. Observe the frequency of real-world events and identify the likelihood of future events.



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CONNECTICUT AGS/GLOBE PUBLISHING CONTENT STANDARDS For MATHEMATICS GRADE 1 GMADE LEVEL 1 – Form A

Algebraic Reasoning: Patterns And Functions – Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Students should… 1.1 Understand and describe patterns and functional relationships. a. Examine attributes of objects and describe the relationships.

Concepts and Communication 13, 18, 26 Process and Applications 25

1.2 Represent and analyze quantitative relationships in a variety of ways. a. Represent the result of counting, combining and separating sets of objects using number sentences.

Number sentences: Process and Applications 21 Solving, combining, separating: Concepts and Communication 23 Process and Applications 3, 9, 12, 17, 18, 20, 26

1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems. a. Identify quantities as equivalent or nonequivalent.

‘Same’: Concepts and Communication 6 ‘Equal’: Process and Applications 23

Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.How are quantitative relationships represented by numbers? 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. a. Represent and order two-digit numbers as groups of tens and ones in the base ten place value system.

Sequence two-digit numbers: Concepts and Communication 2, 8, 12, 20, 24 Process and Applications 1 Identify tens place: Concepts and Communication 15 Count 10s & 1s: Process and Applications 3, 17, 23

b. Identify and compare equal parts of a whole. Process and Applications 13, 25 c. Partition a set of objects into smaller groups with equal amounts. This content standard is not assessed within the multiple-

choice format. d. Describe relationships between quantities using ratios. This content standard is not assessed within the multiple-

choice format. 2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. a. Count by groups, add one more to the grouping and compare values of groups.

Counting by groups: Concepts and Communication 11 Process and Applications 3, 17

b. Add by counting and combining and subtract by separating, comparing or counting on. Adding: Concepts and Communication 17, 21, 23 Operations and Computation 1, 3, 5, 7, 8, 10, 13, 16, 19, 20, 22, 24 Process and Applications 6, 12, 15, 17-19, 23, 26 Subtracting: Operations and Computation 2, 4, 6, 9, 11, 12, 14, 15, 17, 18, 21, 23 Process and Applications 20, 21


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Geometry and Measurement – Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. How do geometric relationships and measurements help us to solve problems and make sense of our world? 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. a. Classify shapes and solids by common characteristics.

Identify shapes: Concepts and Communication 1, 26 Process and Applications 28 Patterns with shapes: Process and Applications 5, 11

3.2 Use spatial reasoning, location and geometric relationships to solve problems. a. Describe, name and interpret direction and position of objects.


3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure a. Plan and sequence events.


b. Estimate length, area, volume, weight and temperature using nonstandard units. Volume: Concepts and Communication 18 Length: Process and Application 7, 22

c. Use standard units of measure to communicate measurement in a universal manner. Process and Applications 7, 22 Working with Data: Probability and Statistics – Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies. How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions? 4.1 Collect, organize and display data using appropriate statistical and graphical methods. a. Collect, organize, record and describe data.

Process and Applications 2, 14, 24

4.2 Analyze data sets to form hypotheses and make predictions. a. Organize data in tables and graphs and make comparisons of the data.


4.3 Understand and apply basic concepts of probability. a. Determine the likelihood of certain events through simple experiments and observations of games.



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Algebraic Reasoning: Patterns And Functions – Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Students should… 1.1 Understand and describe patterns and functional relationships. a. Describe and extend patterns.

Concepts and Communication 17, 28 Process and Applications 10, 17

b. Analyze change in terms of quantity and quality using patterns. This content standard is not assessed within the multiple-choice format.

1.2 Represent and analyze quantitative relationships in a variety of ways. a. Represent real-life situations using number sentences.

Student solves real-life situations but is not asked to write number sentences: Process and Applications 1-28

1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems. a. Represent quantities that have the same value with an equal sign.

Solving: Operations and Computation 3, 15

Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.How are quantitative relationships represented by numbers? 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. a. Represent three-digit numbers as groups of hundreds, tens and ones in the base ten place value system.

Identify a 3-digit number: Concepts and Communication 12

b. Represent fractions by sharing portions of equal size as parts of a whole or parts of a set. Concepts and Communication 1 c. Recognize that the denominator of a fraction tells how many equal parts an object or a set has been divided into, and the numerator indicates how many of the parts are being considered.


d. Describe relationships between quantities using ratios. This content standard is not assessed within the multiple-choice format.

2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. a. Develop fact families of basic facts using the inverse relationship of addition and subtraction.


b. Explore the relationship of multiplication and division through a variety of methods. Process and Applications 3, 19 c. Identify and use equivalent representations of numbers to estimate and compute. This content standard is not assessed within the multiple-

choice format.


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Geometry and Measurement – Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. How do geometric relationships and measurements help us to solve problems and make sense of our world? 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. a. Identify shapes as the same when there are changes in position.


3.2 Use spatial reasoning, location and geometric relationships to solve problems. a. Recognize and use geometric relationships to solve problems.

Process and Applications 2

3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure a. Estimate and measure the length of time to complete activities and tasks.


b. Measure through direct comparison and through repetition of units. Estimate shortest/longest: Concepts and Communication 9, 14, 26

Working with Data: Probability and Statistics – Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies. How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions? 4.1 Collect, organize and display data using appropriate statistical and graphical methods. a. Construct graphs from data, then make comparisons and draw conclusions.

Draw conclusions from data: Process and Applications 22

4.2 Analyze data sets to form hypotheses and make predictions. a. Determine patterns and make predictions from data displayed in tables and graphs.


4.3 Understand and apply basic concepts of probability. a. Analyze data gathered from experiments and identify the likelihood of future events.



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Algebraic Reasoning: Patterns And Functions – Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Students should… 1.1 Understand and describe patterns and functional relationships. a. Create and describe patterns using different objects and symbols.

Concepts and Communication 10, 22, 26

1.2 Represent and analyze quantitative relationships in a variety of ways. a. Identify mathematical relationships as equations.

Identify and solve: Concepts and Communication 3, 13, 20, 26 Operations and Computation 4, 11, 17, 21

1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems. a. Represent quantities that have the same value with an equal sign.


Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.How are quantitative relationships represented by numbers? 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. a. Represent numbers in expanded and regrouped forms in the base ten place value system.


b. Recognize that a fraction with the same numerator and denominator represents the whole object or an entire set.


c. Use fractions to measure and to represent points on a ruler or number line. This content standard is not assessed within the multiple-choice format.

2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. a. Use strategies that involve place value patterns and algebraic properties to estimate, add and subtract.


b. Approximate solutions to problems involving computation through the use of efficient methods. Problem Solving: Process and Applications 1-28 c. Solve multiplication and division problems using rectangular arrays, number patterns, skip counting and repeated addends.

Solving: Operations and Computation 1, 4, 6, 8, 11, 14, 15, 17, 21 Process and Applications 4, 6, 8, 14, 15, 21, 23

d. Compare fractions, identify equivalent fractions, add and subtract fractions with like and unlike denominators using models and pictures.



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Geometry and Measurement – Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. How do geometric relationships and measurements help us to solve problems and make sense of our world? 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. a. a. Classify and compare polygons and solids using various attributes.

Concepts and Communication 25, 27 Process and Applications 20

3.2 Use spatial reasoning, location and geometric relationships to solve problems. a. Represent location on simple maps.


3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure a. Plan events and make schedules.


b. Determine and use different tools and units appropriate for specific measurement tasks. Concepts and Communication 7, 12, 16, 19 Process and Applications 5, 22, 28

Working with Data: Probability and Statistics – Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies. How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions? 4.1 Collect, organize and display data using appropriate statistical and graphical methods. a. Design surveys for the collection of data and justify conclusions drawn from the data.


4.2 Analyze data sets to form hypotheses and make predictions. a. Analyze data to identify a typical element or event.


4.3 Understand and apply basic concepts of probability. a. Use samples and simulations to determine probability, and to make and test predictions.



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Algebraic Reasoning: Patterns And Functions – Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Students should… 1.1 Understand and describe patterns and functional relationships. a. Classify patterns as repeating or growing.

Sequence: Process and Applications 9

1.2 Represent and analyze quantitative relationships in a variety of ways. a. Demonstrate the equivalence of both sides of an equation.

Operations and Computation 2, 6, 15, 17

1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems. a. Represent possible values using symbols.


Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.How are quantitative relationships represented by numbers? 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. a. Extend whole number place value patterns, models and notations to include decimals, which are fractions that have denominators that are multiples of ten.

Process and Applications 9, 21

b. Use models and pictures to reveal patterns about equivalent fractions and ratios. Problem Solving: Process and Applications 25 c. Use fractions to represent a ratio or a division problem. Process and Applications 10, 25 d. Make comparisons and describe quantitative relationships using ratios. This content standard is not assessed within the multiple-

choice format. 2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. a. Use place value concepts and commutative and associative properties to estimate and compute.


b. Use number patterns, basic facts, rectangular arrays, place value models and the distributive property to multiply and divide.

Concepts and Communication 26 Operations and Computation 2, 4, 6, 8, 10, 11, 13, 15, 17, 18, 20, 23, Process and Applications 3, 4, 8, 14, 16, 17, 22, 23, 26

c. Add and subtract fractions and mixed numbers with like and unlike denominators using models, pictures and number sentences.

Solving +, - fractions: Operations and Computation 9 Process and Applications 24


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Geometry and Measurement – Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. How do geometric relationships and measurements help us to solve problems and make sense of our world? 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. a. Describe geometric properties of polygons and solids.


3.2 Use spatial reasoning, location and geometric relationships to solve problems. a. Find possible pathways between two points using maps that are based on the rectangular coordinate system.


3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure a. Recognize that patterns exist between measurements of length, perimeter and area of squares and rectangles.


b. Make precise measurements and use benchmarks to estimate measures. Concepts and Communication 10, 13, 19, 25 Process and Applications 32, 26

Working with Data: Probability and Statistics – Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies. How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions? 4.1 Collect, organize and display data using appropriate statistical and graphical methods. a. Organize and analyze categorical and numerical data.

Analyze: Process and Applications 1

4.2 Analyze data sets to form hypotheses and make predictions. a. Describe what is “average” about the characteristics in a data set.


4.3 Understand and apply basic concepts of probability. a. Determine fair situations and good choices based upon the likelihood of an occurrence.



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Algebraic Reasoning: Patterns And Functions – Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Students should… 1.1 Understand and describe patterns and functional relationships. a. Identify trends and make predictions based upon patterns and data displayed in different formats.

Concepts and Communication 24 Process and Applications 30

1.2 Represent and analyze quantitative relationships in a variety of ways. a. Recognize that a change in one variable may relate to a change in another variable.


1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems. a. Describe the general relationship between two sets of data using an equation or inequality.


Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.How are quantitative relationships represented by numbers? 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. a. Extend whole number place value patterns, models and notations to include decimals, which are fractions that have denominators that are multiples of ten.

Concepts and Communication 2, 7, 8, 14, 17, 23

b. Classify numbers by their factors. Concepts and Communication 3, 26 c. Express numbers as equivalent fractions, decimals or percents. Operations and Computation 13, 22 d. Represent ratios and proportions and solve problems using models and pictures. Operations and Computation 13, 22 2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. a. Estimate and compute using models and pictures.

Solving computations: Concepts and Communication 1-24 Process and Applications 2-15, 17-26, 28, 29

Geometry and Measurement – Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. How do geometric relationships and measurements help us to solve problems and make sense of our world? 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. a. Use geometric relationships to describe polygons and solids.


b. Recognize that changes in the perimeter of a polygon may affect its area, and changes in area may affect the perimeter.



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3.2 Use spatial reasoning, location and geometric relationships to solve problems. a. Identify, describe and build nets for solid figures and objects.


b. Determine geometric relationships through spatial visualization. This content standard is not assessed within the multiple-choice format.

3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure a. Solve problems in the measure of time and in converting units of length in the customary and metric systems using specific ratios.

Process and Applications 2, 4, 7, 10, 12, 18, 23, 28

Working with Data: Probability and Statistics – Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies. How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions? 4.1 Collect, organize and display data using appropriate statistical and graphical methods. a. Differentiate between numerical and categorical data and their appropriate representations.


4.2 Analyze data sets to form hypotheses and make predictions. a. Examine different data collection methods and their effects.


4.3 Understand and apply basic concepts of probability. a. Relate the likelihood of an event to a numerical value.



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Algebraic Reasoning: Patterns And Functions – Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Students should… 1.1 Understand and describe patterns and functional relationships. a. Identify relationships and make generalizations through the use of patterns.

Concepts and Communication 11, 24 Process and Applications 3, 24

1.2 Represent and analyze quantitative relationships in a variety of ways. a. Represent and analyze mathematical relationships with the help of tables, graphs, equations and inequalities.


1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems. a. Solve real-world problems using algebraic methods.

The opportunity to solve real-world problems using algebraic methods can be found in Process and Applications 3, 5-7, 8-10, 12-18, 20-25, 27-30.

b. Demonstrate how to maintain equivalence in equations. This content standard is not assessed within the multiple-choice format.

Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.How are quantitative relationships represented by numbers? 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. a. Relate whole numbers, fractions, decimals and integers to number lines, scales, the coordinate plane and problem- solving situations.

Process and Applications 1-30

b. Express place value patterns using exponents to write powers of ten. This content standard is not assessed within the multiple-choice format.

c. Interpret and connect fraction notation to division. Concepts and Communication 14 d. Compare quantities and solve problems using ratios, rates and percents. Process and Applications 7, 8, 16, 23, 29, 30 2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. a. Solve problems using a variety of computational strategies, including the use of calculators.

Paper/pencil: Concepts and Communication 3, 8, 10, 11, 13, 14, 17, 18, 24, 26 Operations and Computation 1-24 Process and Applications 1-30

b. Describe when products or quotients with fractions and decimals can yield a larger or smaller result than either factor.



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Geometry and Measurement – Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. How do geometric relationships and measurements help us to solve problems and make sense of our world? 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. a. Classify polygons according to their properties.

Concepts and Communication 7, 9, 16, 21, 25

b. Examine the relationships between the measures of area of 2-dimensional objects and volumes of 3-dimensional objects.


3.2 Use spatial reasoning, location and geometric relationships to solve problems. a. Construct similar polygons on coordinate grids.


3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure a. Solve problems involving measurement through the use of a variety of tools, techniques and strategies.

Concepts and Communication 1, 15 Process and Application 6, 8, 22

b. Use specific ratios to convert between measures of length, area, volume, mass and capacity in the customary and metric systems.

Concepts and Communication 1, 4, 6, 7, 12, 15, 19, 20, 28 Process and Applications 6, 10, 18, 22, 27

Working with Data: Probability and Statistics – Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies. How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions? 4.1 Collect, organize and display data using appropriate statistical and graphical methods. a. Display and compare sets of data using various systematic or graphical representations.


4.2 Analyze data sets to form hypotheses and make predictions. a. Describe the shape of data sets using the measures of spread and central tendency.


4.3 Understand and apply basic concepts of probability. a. Understand that probabilities are more reliable to use as predictors when there is a large number of trials.


b. Express probability using various numerical representations. Process and Applications 8, 20


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CONNECTICUT AGS/GLOBE PUBLISHING CONTENT STANDARDS For MATHEMATICS GRADE 7 GMADE LEVEL M – Form A

Algebraic Reasoning: Patterns And Functions – Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Students should… 1.1 Understand and describe patterns and functional relationships. a. Analyze physical phenomena and patterns to identify relationships and make generalizations.


1.2 Represent and analyze quantitative relationships in a variety of ways. a. Describe the effects of characteristics of mathematical relationships on the way the relationships are represented.


1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems. a. Solve problems using a variety of algebraic methods.

Operations and Computation 3, 9, 18, 21, 22, 24 Process and Applications 2, 19-28, 30

b. Maintain equivalence in equations to determine solutions. This content standard is not assessed within the multiple-choice format.

Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.How are quantitative relationships represented by numbers? 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. a. Represent real-world situations and solutions to problems using the appropriate symbolic form (fractions, decimals or percents).

Problem Solving: Process and Applications 1-30

b. Understand the use of scientific notation as related to powers of ten as an efficient method for writing and comparing very large numbers.

Concepts and Communication 11, 13, 15 Operations and Computation 23

c. Use percents to make comparisons between groups of unequal size. Concepts and Communication 25 Operations and Computation 5, 11, 18 Process and Applications 2, 7, 15, 25

2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. a. Extend the operations of addition, subtraction, multiplication and division to negative numbers.

Concepts and Communication 3, 6, 7, 9, 11, 14-16, 18, 20, 22, 23, 25 Operations and Computation 1-24 Process and Applications 2, 5-9, 11-16, 19-23, 25, 27, 28, 30


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Geometry and Measurement – Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. How do geometric relationships and measurements help us to solve problems and make sense of our world? 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. a. Describe and classify polygons according to their transformational properties.


3.2 Use spatial reasoning, location and geometric relationships to solve problems. a. Understand how 3-dimensional objects can be represented in 2 dimensions using base plans (footprints), orthogonal views, nets and isometric drawings.


3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure a. Solve geometric and measurement problems through the use of a variety of tools, techniques and strategies.

Concepts and Communication 1, 4, 8, 10, 12, 24, 26 Process and Applications 5, 9, 15, 20

Working with Data: Probability and Statistics – Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies. How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions? 4.1 Collect, organize and display data using appropriate statistical and graphical methods. a. Select the appropriate visual representation of data based on the kind of data collected and the purpose for their use.


4.2 Analyze data sets to form hypotheses and make predictions. a. Understand that measures of central tendency and spread can be used to describe data sets and justify conclusions.


4.3 Understand and apply basic concepts of probability. a. Compare and determine experimental and theoretical probabilities.



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Algebraic Reasoning: Patterns And Functions – Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Students should… 1.1 Understand and describe patterns and functional relationships. a. Analyze physical phenomena, functions and patterns to identify relationships and make generalizations.


1.2 Represent and analyze quantitative relationships in a variety of ways. a. Describe the effects of characteristics of linear relationships on the way the relationships are represented verbally and in tables, graphs and equations.


1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems. a. Solve problems using various algebraic methods and properties.

Operations and Computation 3, 9, 18, 21, 22, 24 Process and Applications 2, 19-28, 30

Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.How are quantitative relationships represented by numbers? 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. a. Compare and order integers, powers and roots using number lines and grids.


b. Extend the understanding of scientific notation to very small numbers. Concepts and Communication 23 2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. a. Solve problems involving fractions, decimals, ratios and percents.

Concepts and Communication 5, 6, 16-18, 22, 25, 27, 28 Operations and Computation 2, 4-6, 10, 11, 13, 14, 16-20, 22 Process and Applications 2, 4, 6-8, 14, 15, 17, 19, 21, 22, 25, 26, 30

b. Make generalizations about operations with very large and very small numbers. This content standard is not assessed within the multiple-choice format.

c. Connect the exponential growth and decay models to repeated multiplication by the same factor. This content standard is not assessed within the multiple-choice format.

Geometry and Measurement – Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. How do geometric relationships and measurements help us to solve problems and make sense of our world? 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. a. Explore the relationships among sides, angles, perimeters, areas, surface areas and volumes of congruent and similar polygons and solids.



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3.2 Use spatial reasoning, location and geometric relationships to solve problems. a. Model geometric relationships in a variety of ways.

Concepts and Communication 10, 26 Process and Applications 5, 9, 20

3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure a. Use a variety of concrete methods, including displacement, to find volumes of solids.


b. Solve problems involving measurement through the use of appropriate tools, techniques and strategies. Concepts and Communication 1, 4, 8, 10, 12, 24, 26 Process and Applications 5, 9, 15, 20

Working with Data: Probability and Statistics – Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies. How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions? 4.1 Collect, organize and display data using appropriate statistical and graphical methods. a. Construct appropriate representations of data based on the size and kind of data set and the purpose for their use.

Interpret representation of data: Process and Applications 18

4.2 Analyze data sets to form hypotheses and make predictions. a. Make and evaluate statistical claims and justify conclusions with evidence.


4.3 Understand and apply basic concepts of probability. a. Determine possible outcomes using a variety of counting techniques.



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CONNECTICUT AGS/GLOBE PUBLISHING CONTENT STANDARDS For MATHEMATICS GRADES 9-12 CORE GMADE LEVEL H – Form A

Algebraic Reasoning: Patterns And Functions – Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Students should… 1.1 Understand and describe patterns and functional relationships. a. Describe relationships and make generalizations about patterns and functions.

Process and Applications 6, 13, 22, 30

1.2 Represent and analyze quantitative relationships in a variety of ways. a. Represent and analyze linear and nonlinear functions and relations symbolically and with tables and graphs.

Process and Applications 13, 30

1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems. a. Manipulate equations, inequalities and functions to solve problems.

The opportunity to use operations, properties and algebraic symbols can be found in Operations and Computation 1-24 and Process and Applications 3-12, 14-21, 23-25, 27, 28.

Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.How are quantitative relationships represented by numbers? 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. a. Extend the understanding of number to include integers, rational numbers and real numbers.

The opportunity to use this standard can be found in Concepts and Communication 6, 17, 23, 27 Operations and Computation 1-24 Process and Applications 1-30.

b. Interpret and represent large sets of numbers with the aid of technologies. Use of technology (calculator, etc.) when taking the GMADE will invalidate the normative scores.

2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. a. Develop strategies for computation and estimation using properties of number systems to solve problems.

The opportunity to use this standard can be found in Concepts and Communication 6, 17, 23, 27 Operations and Computation 1-24 Process and Applications 1-30.

b. Solve proportional reasoning problems. Concepts and Communication 14 Process and Applications 9, 11, 16

Geometry and Measurement – Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. How do geometric relationships and meas. help us to solve prob. and make sense of our world? 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. a. Investigate relationships among plane and solid geometric figures using geometric models, constructions and tools.

Geometric terms/problem solving: Concepts and Communication 3, 8, 16, 21 Process and Applications 8, 18, 20, 24


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CONNECTICUT AGS/GLOBE PUBLISHING CONTENT STANDARDS For MATHEMATICS GRADES 9-12 CORE GMADE LEVEL H – Form A

b. Develop and evaluate mathematical arguments using reasoning and proof. This content standard is not assessed within the multiple-choice format.

3.2 Use spatial reasoning, location and geometric relationships to solve problems. a. Verify geometric relationships using algebra, coordinate geometry, and transformations.


3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure a. Solve a variety of problems involving 1-, 2- and 3-dimensional measurements using geometric relationships and trigonometric ratios.

Concepts and Communication 13 Process and Applications 8, 18, 20, 24

Working with Data: Probability and Statistics – Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies. How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions? 4.1 Collect, organize and display data using appropriate statistical and graphical methods. a. Create the appropriate visual or graphical representation of real data.

Interpret: Process and Applications 5, 13, 22, 30

4.2 Analyze data sets to form hypotheses and make predictions. a. Analyze real- world problems using statistical techniques.

Process and Applications 3, 5, 9, 13, 16, 17, 21, 22, 26, 27, 30

4.3 Understand and apply basic concepts of probability. a. Understand and apply the principles of probability in a variety of situations.


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