athematics c · athematics c urriculum colchester ... make estimates and approximations, ... be...

MATHEMATICS

CURRICULUM

COLCHESTER PUBLIC SCHOOLS

PRESENTED TO THE BOARD OF EDUCATION MAY, 2007

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COLCHESTER PUBLIC SCHOOLS MATHEMATICS CURRICULUM

This report was compiled by the Colchester Public School District’s

Mathematics Curriculum Committee, under the guidance and support of the district’s math leadership team. The document sets the expectation that all students in the Colchester Public School system will become proficient in mathematics. In order to achieve these goals, students must be active participants in a “planned, ongoing, and systematic” mathematics curriculum. Colchester educators provide an encouraging environment where students can satisfy their innate curiosity and maximize their individual mathematical abilities. Prepared by: Central Office Personnel Greg Plunkett Barbara Gilbert CES Teachers Jackie Somberg Kathleen Sheridan Erin Hermann Beth Pepin Julia Broad Karen Gambolati JJIS Teachers Deb Sandberg Linda Stoddard Judy Sullivan Sharon Falcone Lori Joyce

WJJMS Teachers Paul Weston Amanda LaSaracina Frank Gionfriddo Maddalena Scrivano Tammy Burton Frank Newman BA Teachers Diane Hover Donna Bonin Teri Schlosser Carol Hale Michele Berardo John Lecce Bruce McCubrey

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“If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.”

- GALILEO

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http://thinkexist.com/quotation/if_i_were_again_beginning_my_studies-i_would/143628.html

TABLE OF CONTENTS

I. Philosophy, Vision, Program Goals, and Content Standards… … 5 II. Colchester Mathematics Curriculum……………………………… 8

III. Sample Pacing Guides and Assessments …………………………. 106 IV. Connecticut State Standards and Position Statement on Mathematics

Education and Curriculum Framework….…………………….…..246 V. Program Evaluation……………………………………………….…314

VI. CMT and CAPT Grade Level Blueprint, Vocabulary Lists and

Calculator Use Policy……………………………………………..…327 VII. Resources, Web Sites and Strategies ……………………………… 366 VIII. Budget…………………………………………………………………388

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PHILOSOPHY

We believe that mathematics is a fundamental component of a high quality education, designed to develop our students' ability to reason and solve problems. Our mathematics curriculum encompasses clear mathematical communication, data analysis/ probability, problem solving, reasoning and representation. All students will be proficient in mathematical skills and possess a highly developed number sense. We are committed to providing a math program that is an effective combination of concepts, skills and applications, providing confident and independent problem solvers. An exemplary math experience will be provided to all students. This program will be developmentally appropriate, sequential, and connected through all grade levels. Various instructional practices will be implemented to meet the diverse needs of all learners and to nurture the innate curiosity of students. Mathematics is relevant and will be integrated with other disciplines to foster real world connections. Students need to value math and realize it is an ongoing component of life. Our math program will prepare students to succeed in a technologically sophisticated world. All students will be provided the essential instruction necessary to reach their math potential.

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GOALS

As a result of education in grades K-12, each student should be able to:

1. Demonstrate developmentally appropriate skills in the content standards of numbers and operations, algebra, geometry, measurement, and data analysis/probability.

2. Communicate mathematically using oral, written, concrete,

pictorial, graphic, and symbolic representations.

3. Use mathematical reasoning to make, defend, and evaluate

predictions and to justify and verify conclusions. 4. Use mathematical concepts, techniques, and technology to

represent, analyze and solve problems.

5. Identify connections and equivalent representations to

illuminate and understand the structure of mathematics. 6. Integrate mathematical skills and concepts to solve problems in

other disciplines.

7. Use mathematical understanding to make connections with

confidence and appreciate the relevance of mathematics.

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CONTENT STANDARDS In order to achieve the Colchester K-12 mathematical goals, our students should be able to:

1. understand and use the addition, subtraction, multiplication, and

division of whole numbers, fractions, decimals, and integers. 2. make estimates and approximations, and judge whether the results

are reasonable. 3. demonstrate quantitative sense by using numbers to count,

measure, compare, and order.

4. understand and use ratios, proportions, percents, exponents.

5. make and use measurements in both US Customary and metric units to approximate and measure length, area, volume, weight, temperature, and time.

6. demonstrate an understanding of spatial relationships and basic

concepts of geometry to construct and describe geometric models and patterns.

7. understand and use basic concepts of probability and statistics to

collect, organize, display, and analyze data, simulate events and test hypotheses.

8. understand and use algebraic concepts and functions to analyze

situations, develop models, and verify solutions.

9. use technology to interpret, understand, and solve mathematical problems.

10. solve and explain multi step problems.

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STATE FRAMEWORKS / COLCHESTER CONTENT STANDARDS

Algebraic Reasoning: Patterns and Functions How do patterns and functions help us describe data and physical phenomena and solve a variety of problems?

• Patterns • Algebra and Functions

1. Understand and use algebraic concepts and functions to analyze situations, develop models, and verify solutions.

2. Solve and explain multi-step problems.

Numerical and Proportional Reasoning How are the base ten number system and fractions, decimals, percents and ratios related?

• Number Sense • Operations • Estimation and Approximation • Ratio, Proportion and Percent

3. Understand and use the addition, subtraction, multiplication, and division of whole numbers, fractions, decimals, and integers.

4. Make estimates and approximations, and judge whether the results are reasonable.

5. Demonstrate quantitative sense by using numbers to count, measure, compare, and order.

6. Understand and use ratios, proportions, percents, and exponents.

Geometry and Measurement How do geometric relationships and measurements help us to solve problems and make sense of our world?

• Measurement • Spatial Relationships and Geometry

7. Make and use measurements in both US Customary and metric units to approximate and measure length, area, volume, weight, temperature, and time.

8. Demonstrate an understanding of spatial relationships and basic concepts of geometry to construct and describe geometric models and patterns.

Working with Data How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions?

• Probability and Statistics • Discrete Mathematics

9. Understand and use basic concepts of probability and statistics to collect, organize, display, and analyze data, simulate events and test hypotheses.

10. Use technology to interpret, understand, and solve mathematical problems.

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State Framework: ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS Patterns and functional relationships can be represented and analyzed using a variety of strategies and tools. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Grade Pre K – Math Colchester Content

Standard Students will… Performance Expectation Exploration/Application Assessment

1. Understand and describe patterns and functional relationships.

a. Sort and classify objects by an attribute. b. Describe and extend patterns using the attributes of various objects.

• Sort and classify objects by a single attribute (size, shape, color, texture, orientation and position) and describe the rule used.

• Describe qualitative changes such as hotter, cooler, taller, cooler, less, equal.

• Recognize, copy, extend and create simple auditory and physical patterns using a variety of materials in different contexts.

See pacing guide

See pacing guide

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State Framework: 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 and tools. How are quantitative relationships represented by numbers? Grade Pre K – Math Colchester Content


2 Understand that a variety of numerical representations can be used to describe quantitative relationships.

a. Use numbers to count, order and compare. b. Share equal parts of a whole object.

• Count and identify the number of objects in a set.

• Compare sets and identify those with more, less and the same amounts.

• Describe the position of objects using the terms ‘first’ and ‘last’.

• Recognize numbers in real life situations.

• Explore a whole and half of an object.

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Use numbers and their properties to compute flexibly and fluently and reasonably estimate measures and quantities.

a. Count, adding one or more to the previous amount.

• Count by rote, 1 to 10. • Count as one more object is added to

a set of objects.

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State Framework: GEOMETRY AND MEASUREMENT Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies and tools. How do geometric relationships and measurements help us to solve problems and make sense of our world? Grade Pre K – Math Colchester Content


8. 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 by physical characteristics.

• Identify and sort simple shapes such as square, rectangle, triangle and circle.

• Use a variety of materials to construct various shapes and describe their physical attributes.

Use spatial reasoning, location and geometric relationships to solve problems.

a. Use positional language to describe location, direction and position of objects.

• Use positional language - e.g., under, over, inside, next, near, in front – to describe position and order.

• Complete simple shape and jigsaw puzzles.

Develop and apply units, systems, formulas and appropriate tools to estimate and

a. Sequence events during a limited time period.

• Describe time periods or a sequence of events using terms such as morning, afternoon and night, yesterday, today and tomorrow, 1st, next, then, and last.

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measure. b. Use nonstandard units to estimate measures of length, area and capacity.

• Use nonstandard units and body

referents to compare and estimate length, area and capacity.

• Sort, estimate and order objects by length or area using comparative language such as more, longer, shorter, taller or bigger to describe relationships.

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State Framework: ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS Patterns and functional relationships can be represented and analyzed using a variety of strategies and tools. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Grade: Kindergarten – Math Colchester Content



a. Sort and classify objects by an attributes. b. Identify a pattern and describe the rule using the physical attributes or position of objects in a sequence.

• Sort and classify objects by size, shape, color, texture, use, orientation and position and describe the rule used.

• Recognize, copy and extend patterns

of sounds, colors, shapes, textures and numbers in a variety of contexts and describe the rule of the pattern.

• Make comparisons and describe qualitative and quantitative changes of a given pattern (more, less, bigger, smaller, longer, one more, one less and equal).

Everyday Math 3 See pacing chart

Regular formative assessments as indicated in pacing chart

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State Framework: 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 and tools. How are quantitative relationships represented by numbers? Grade: Kindergarten – Math Colchester Content


2.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. b. Share equal parts of a whole object.

• Use numbers to locate, order, label and measure.

• Identify the numerals 1-10 and match sets of objects to the numerals.

• Compare sets using the terms more, less, and the same, and order sets from least to greatest.

• Identify ordinal position of objects, first through fifth, and last.

• Act out story problems and solve practical problems using objects.

• Recognize and name penny, nickel, dime.

• Recognize numbers in ‘real-life’ situations.

• Use a variety of models to identify a

whole and a half of an object.

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• Compare two parts of a whole and describe the parts as closer to a whole, or closer to very little.

• Recognize that two halves can be put together to make a whole.

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State Framework: 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 and tools. How are quantitative relationships represented by numbers? Grade: Kindergarten – Math Colchester Content


c. Share a set of objects that is divided into groups with equal amounts.

• Share a set of objects considered to be a whole by forming two smaller sets that have equal amounts.

Use numbers and their properties to compute flexibly and fluency and to reasonable estimate measures and quantities.

a. Count, adding one more to the previous number, and group and count by ones, fives, and tens.

• Count to and past 10 to 20, then to 30, and group and count objects by 10.

• Estimate the amount of objects in a set using 10 as a benchmark, and then count to determine if the amount is more or less than 10.

• Identify sets and numbers, which are equal and one more.

• Count backward from 10. • Count and trade pennies for objects.

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State Framework: 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? Grade: Kindergarten – Math Colchester Content


8. 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.

(1) Sort, order, compare and use comparative language to describe small sets of objects sequenced by size, length, area and volume. (2) Identify, sort and compare two-and three-dimensional shapes and solids in the environment, such as triangles, squares, rectangles, circles, cubes, spheres, cylinders, cones and prisms. (3) Use a variety of materials to create geometric shapes and solids and build copies of simple shapes and designs by direct observation and by visual memory.

Use spatial reasoning, location and geometric relationships to solve problems

a. Use positional language to describe location, direction and position of objects.

(1) Describe the position, location and direction of objects, or parts of objects, using terms such as inside, outside, top, bottom, close, closer, etc. (2) Complete simple & jigsaw puzzles.

Develop and apply units, systems, formulas and appropriate tools to estimate and measure.

a. Use calendars and clocks to measure and record time. b. Use nonstandard units to estimate measures of length,

(1) Located a date on the calendar (yesterday, today and tomorrow) and sequence events using terms like before and after. (1) Estimate the number of objects in a handful, and then count to verify.

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area, temperature, weigh and capacity.

(2) Estimate the amount of objects in a set using benchmarks of 10, and count to determine if the estimate is more or less. (3) Explore, describe and discuss strategies to estimate length, area, temperature and weight using nonstandard units to compare. (4) Explore using everyday objects as nonstandard units to measure length, area and capacity. (5) Compare the weight of two objects using a balance scale and identify which is heavier.

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State Framework: ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS Patterns and functional relationships can be represented and analyzed using a variety of strategies and tools. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Grade: 1st – Math Colchester Content


1 Understand and describe patterns and functional relationships.

a. Examine attributes of objects and describe their relationships.

• Sort, classify and order objects and numbers based on one and two attributes and describe the rule used.

• Recognize, extend, describe and create a variety of patterns, and translate the same pattern from one representation (such as color) to another representation (such as shape).

• Describe counting patterns and number patterns.

• Develop and test generalizations based on observations of patterns and relationships.

Everyday Math 3 See pacing chart

Benchmark and formative assessments as indicated in pacing chart

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.

• Model real-life situations that involve addition and subtraction of whole numbers using objects, pictures and open sentences.

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2.Use operations, properties and algebraic symbols to determine equivalence and solve problems.

a. Identify quantities as equivalent or non-equivalent.

• Demonstrate balance or equivalence using models.

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State Framework: 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 and tools. How are quantitative relationships represented by numbers? Grade: 1st – Math Colchester Content


5. 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. b. Identify and compare equal parts of a whole. c. Partition a set of

• Estimate and describe quantity with benchmark amounts such as 0, 10 and 100.

• Represent two-digit numbers on number lines and using models.

• Determine and compare values and trade with sets of pennies, nickels and dimes & quarters.

• Identify ordinal position of objects, first through tenth.

• Identify and represent 1/2, 1/3, and

1/4 of a whole and identify portions that are not halves, thirds, or fourths.

• Compare parts of a whole object and estimate whether they are closer to a very little, one half or one whole.

• Make a whole of equal-sized parts of familiar objects.

• Identify half of a small set of objects

considered to be the whole.

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objects into smaller groups with equal amounts. d. Describe relationships between quantities using ratios.

• Describe patterns with simple ratios using familiar contexts, such as 1 cat has 4 legs, 2 cats have 8 legs.

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State Framework: 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 and tools. How are quantitative relationships represented by numbers? Grade: 1st – Math Colchester Content


3. Use numbers and their properties to compute flexibly and fluently, and to reasonable estimate measures and quantities.

a. Count by groups, add one more to the grouping and compare values of groups. b. Add by counting and combining and subtract by separating, comparing or counting on.

• Count whole numbers to 100. • Identify, read and write numerals to

100 and beyond. • Group and skip count by 2s, 5s, and

10s. • Count on from a given amount,

orally and with models, and count back from 20.

• Identify one more and one less and explore ten more and ten less.

• Write number sentences and use objects and pictures to model and solve addition and subtraction story problems.

• Develop, describe and use a variety of strategies to add and subtract one-digit numbers.

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• Explore finding the sum of two two-digit numbers using models and counting strategies.

• Identify reasonable answers to problems that reflect real-world experiences.

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State Framework: GEOMETRY AND MEASUREMENT Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies and tools. How do geometric relationships and measurements help us to solve problems and make sense of our world? Grade: 1st – Math Colchester Content



a. Classify shapes and solids by common characteristics.

• Sort, build, name and draw two- and three- dimensional objects.

• Use a variety of materials to create two- and three-dimensional designs and copy them from visual memory.

• Create and explore shapes and designs with a line of symmetry.


a. Describe, name and interpret direction and position of objects.

• Indicate relative position, direction and location with terms such as inside, outside, top, bottom, left and right.

7. Develop and apply units, systems, formulas and appropriate tools to estimate and measure.

a. Plan and sequence events.

• Estimate and compare the length of time needed to complete tasks using terms such as longer or shorter.

• Use the calendar to identify dates, days, weeks and months and to plan and sequence events.

• Tell time to the hour with analog and digital clocks.

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State Framework: GEOMETRY AND MEASUREMENT Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies and tools. How do geometric relationships and measurements help us to solve problems and make sense of our world? Grade: 1st – Math Colchester Content


b. Estimate length, area, volume, weight and temperature using nonstandard units. c. Use standard units of measure to communicate measurement in a universal manner.

• Use physical referents to make estimates and to determine and describe the reasonableness of answers to measurement problems.

• Use estimation, physical referents and nonstandard units to sort and compare objects.

• Explore using the standard units of inch and centimeter to estimate and measure length.

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State Framework: ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS Patterns and functional relationships can be represented and analyzed using a variety of strategies and tools. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Grade: 2nd – Math Colchester Content



a. Describe and extend patterns. b. Analyze change in terms of quantity and quality using patterns.

• Describe and classify data and objects based on more than one attribute.

• Use patterns and the rules that describe them to identify a missing object, objects with common or different attributes, and the complement of a set of objects.

• Explore a variety of ways to describe and write rules for patterns.

• Explore and describe number patterns including odd and even numbers, counting by 2s, 5s, 10s, 100s, and counting on by 10.

• Make comparisons of data and analyze observable changes using qualitative and quantitative descriptions.

Everyday Math 3 See Pacing chart

Benchmark and formative assessments as indicated in pacing chart.

Represent and analyze quantitative

a. Represent real-life situations using

• Model situations involving addition and subtraction of whole numbers

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relationships in a variety of ways.

number sentences. using objects, pictures, symbols and open sentences.

2. Use operations, properties and algebraic symbols to determine equivalence and solve problems.

a. Represent quantities that have the same value with an equal sign.

• Demonstrate understanding of the = sign as an equality symbol.

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State Framework: 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 and tools. How are quantitative relationships represented by numbers? Grade: 2nd – Math Colchester Content


5. 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. b. Represent fractions by sharing portions of equal size as parts of a whole or parts of a set.

• Use place value models and pictures to represent two- and three-digit numbers and write numbers in expanded and regrouped forms.

• Locate, label and order two- and three-digit numbers using place value models, pictures and number lines to identify 10 more and 10 less and 100 more and 100 less than a number.

• Count with and trade pennies, nickels, dimes, quarters and dollars and determine and compare values

• Model and describe equal parts of a whole as unit fractions 1/2 through 1/10.

• Use models and familiar objects to estimate, compare and order unit fractions (1/2, 1/3, 1/4) of a whole.

• Estimate and use counting and grouping of objects to find equal parts of a small set of counting objects, such as 1/2, 1/3 or 1/4 of 12

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cookies. • Explore equivalent fractions using

models.

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c. Recognize that the denominator of a fraction tells how may equal parts an object or a set has been divided into, and that the numerator indicates how many of the parts are being considered. d. Describe relationships between quantities using ratios.

• Identify and build models of fractional parts of a whole (such as ¾), other than unit fractions.

• Describe simple ratios in patterns using models and pictures (e.g., in a pattern of green, green, red blocks, there are always two green blocks for each red block).

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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. c. Identify and use equivalent representations of

• Recall basic addition and subtraction facts.

• Identify reasonable answers and solve addition and subtraction problems involving real-world experiences.

• Explore multiplication by extending number patterns, skip counting, combining repeated addends, building models of groups the same size and using arrays and pictures.

• Explore the connection between multiplication and division using models and pictures of groups and arrays.

• Compare and round numbers to the nearest 10 using place value models

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numbers to estimate and compute.

and number lines. • Explore and describe strategies for

representing, estimating, adding and subtracting two two-digit numbers with and without regrouping.

• Recognize when an estimate is appropriate and use estimation strategies that result in identifying a reasonable answer to a problem.

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State Framework: GEOMETRY AND MEASUREMENT Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies and tools. How do geometric relationships and measurements help us to solve problems and make sense of our world? Grade: 2nd – Math Colchester Content



a. Identify shapes as the same when there are changes in position.

• Explore translations (slides), reflections (flips) and rotations (turns) of simple polygons using manipulative materials.

• Build and identify shapes that have one or more lines of reflective symmetry or that can be divided into two congruent parts.

• Explore filling a two-dimensional region with different shapes.


a. Recognize and use geometric relationships to solve problems.

• Explore combining and subdividing polygons and solids with manipulative materials and reconstruct them from visual memory.

• Build, describe, draw and identify polygons, solids and other two- and three-dimensional objects found in the environment.

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State Framework: GEOMETRY AND MEASUREMENT Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies and tools. How do geometric relationships and measurements help us to solve problems and make sense of our world? Grade: 2nd – Math Colchester Content



a. Estimate and measure the length of time to complete activities and tasks. b. Measure through direct comparison and through repetition of units.

• Use the calendar to write and solve problems involving time.

• Tell time to the half-hour, and explore time to the quarter-hour (analog and digital).

• Develop and use nonstandard referents and standard benchmarks to estimate and measure length, area, weight, capacity and volume.

• Identify reasonable estimates and describe the strategies used to determine the estimates.

• Explore using measurement tools such as thermometers, basic rulers and balance scales to measure temperature, length and weight.

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State Framework: ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS Patterns and functional relationships can be represented and analyzed using a variety of strategies and tools. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Grade: 3rd – Math Colchester Content


1 Understand and describe patterns and functional relationships.

a. Create and describe patterns using different objects and symbols.

• Use a variety of materials to construct, reproduce, describe and extend numerical and spatial patterns.

• Explore and describe patterns and sequences using tables, graphs and charts.

• Sort and classify the same set of objects in more than one way and explain the reason for each sort.

Everyday Math 3—see pacing chart

Benchmark and formative assessments as indicated in pacing chart.

Represent and analyze quantitative relationships in a variety of ways.

a. Identify mathematical relationships as equations.

• Model situations that reflect mathematical relationships involving addition, subtraction, multiplication and division as open number sentences and match number sentences to story problems.

2. Use operations, properties and algebraic symbols to determine

a. Represent quantities that have the same value with an equal sign.

• Demonstrate understanding of the = sign as an equality symbol and explore inequalities and the = symbol.

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equivalence and solve problems.

• Demonstrate equivalence using the commutative and associative properties of whole numbers.

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State Framework: 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 and tools. How are quantitative relationships represented by numbers? Grade: 3rd – Math Colchester Content


5.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

• Use models and expanded and regrouped forms to represent two- and three-digit numbers.

• Locate, label, compare and order whole numbers to 1000, including multiples of 10 and 100, using place value models, number patterns and the number line.

• Name and state the value of pennies, nickels, dimes, quarters, and half-dollars and show different ways to make a given amount.

• Determine and compare the values of sets of coins and write the values using decimal notation.

• Use models and pictures to represent

fractions and label the parts with words and fraction symbols.

• Identify a whole as a fraction with the same numerator and denominator.

• Use counting and grouping of

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set.

objects to find equal parts of a set of objects and use models and number patterns to identify amounts such as 2/3 of 12 is 8.

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c. Use fractions to measure and to represent points on a ruler or number line.

• Estimate fractional values and measure to the nearest half unit with the aid of number lines and rulers.

• Explore and describe addition of fractions with like denominators and write matching fraction sentences using models.


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.

• Identify 10 and 100 more and less than a number.

• Compare and round numbers to the nearest 10 and 100.

• Use commutative and associative properties to solve problems.

• Estimate, add and subtract with two-

and three-digit numbers using a variety of strategies.

• Use estimation strategies to determine and justify the reasonableness of a computational answer.

• Recognize when an estimate is

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appropriate and determine whether an estimation strategy will result in an over- or underestimate.

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c. Solve multiplication and division problems using rectangular arrays, number patterns, skip counting and repeated addends. d. Compare fractions, identify equivalent fractions and add and subtract fractions with like and unlike denominators using models and pictures.

• State the multiplication and division facts with factors as 1, 2, 3, 4, 5 and 10.

• Explore division problems with and without remainders.

• Write and solve multiplication and division story problems and match to number sentences (equations).

• Use models and pictures of sets and arrays to represent multiplication and division of two- and three-digit numbers by one-digit numbers.

• Construct and use models to identify equivalent fractions and to compare and order fractions with like and unlike denominators of 2, 3, 4, 5, 6 and 8.

• Identify patterns with equivalent ratios such as 3 out of 6 crayons are red or 4 out of 8 crayons are red and the same as 1 out of 2 crayons.

• Construct and use models to add and subtract fractions with like and unlike denominators and write

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fraction sentences to match the models.

• Write and solve story problems that involve fractions.

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State Framework: GEOMETRY AND MEASUREMENT Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies and tools. How do geometric relationships and measurements help us to solve problems and make sense of our world? Grade: 3rd – Math Colchester Content



a. Classify and compare polygons and solids using various attributes.

• Sort polygons and solids through use of characteristics such as the relationship of sides (parallel, perpendicular), kinds of angles (acute, right and obtuse), symmetry and congruence.

• Describe similarities and differences of two- and three-dimensional shapes in the environment using physical features such as number of sides, number of angles, lengths of sides and straight and curved parts.

• Investigate ways to tile or tessellate a region or shape using various polygons.


a. Represent location on simple maps.

• Draw and interpret simple maps using coordinate systems and shapes or pictures.

• Identify and recognize two-dimensional geometric shapes and figures, including number of angles

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and sides of polygons. • Draw two-dimensional geometric

shapes and figures.

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State Framework: GEOMETRY AND MEASUREMENT Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies and tools. How do geometric relationships and measurements help us to solve problems and make sense of our world? Grade: 3rd – Math Colchester Content



a. Plan events and make schedules. b. Determine and use different tools and units appropriate for specific measurement tasks.

• Tell time to the minute, using analog and digital clocks, and identify AM and PM.

• Use calendars and clocks to plan and sequence events.

• Develop and explain strategies for using nonstandard and standard referents to estimate measurements of length, area, weight, temperature, volume and capacity.

• Explore strategies for estimating and measuring the perimeters, areas and volumes of irregular shapes and solids.

• Describe and use estimation strategies that can identify a reasonable answer to a measurement problem when an estimate is appropriate.

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State Framework: 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 and tools. How are quantitative relationships represented by numbers? Grade 4 – Math Colchester Content



a. Extend whole number place value patterns, models and notations to include decimals, which are fractions that have denominators that are multiples of ten. b. Use models and pictures to reveal patterns about equivalent fractions and ratios.

• Identify, round, order, and compare whole numbers and decimals to 100,000.

• Build place value models, draw diagrams and show equivalent representations for

two-, three-, and four-digit numbers in expanded and regrouped forms. • Build models and describe tenths

and hundredths using equivalent ratio, fraction and decimal notation.

• Express a division problem as a fraction and describe the relationship between the divisor and the remainder written as a fraction.

Everyday Math 3—see pacing guide.

Formative and benchmark assessments as indicated in pacing guides.

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State Framework: NUMERICAL AND PROPORTIONAL REASONING - Continued Grade 4 – Math Colchester Content



c. Use number patterns, basic facts, rectangular arrays, place value models and the distributive property to multiply and divide. d. Add and subtract factions and mixed numbers with like denominators using models, pictures and

• Develop fluency with multiplication and division fact families for all factors 1 through 12.

• Relate multiplication and division to models with groups and rectangular arrays.

• Explore the property of zero in multiplication and its implication in division.

• Identify the appropriate operation and write a word problem to match a given addition, subtraction or multiplication sentence and write the matching number sentence to solve a word problem.

• Use arrays and explore using the distributive property 10 x (5 + 4) = (10 x 5) + (10 x 4) to estimate, multiply and divide two- and three-digit numbers by one-digit factors.

• Solve problems involving the

addition and subtraction of fractions with like denominators.

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number sentences. • Use models and pictures to estimate a reasonable answer when adding or subtracting decimals, fractions and mixed numbers.

• Write and solve word problems involving decimals, fractions and mixed numbers, identify reasonable answers, and match equations to the problems.

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State Framework: NUMERICAL AND PROPORTIONAL REASONING – Continued Grade 4 – Math Colchester Content


3. Demonstrate quantitative sense by using numbers to count, measure, order and compare.

a. Use place value concepts and commutative and associative properties to estimate and compute.

• Use place value models, diagrams, number pattern and number lines to identify, order, round, and compare two-, three-, and four-digit whole numbers up to 10,000.

• Solve practical problems and extend patterns involving 10 and 100 more and less than a number.

• Use place value concepts, number patterns, the number line and the commutative and associative properties to develop estimation and computation strategies.

• Apply and explain a variety of estimation strategies in problem-solving situations to add and subtract money amounts less than $10.00 and two- and three-digit numbers with and without regrouping.

• Determine and discuss the reasonableness of an answer and explain why a particular estimation strategy will result in an over- or under-estimate.

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State Framework: GEOMETRY AND MEASUREMENT Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies and tools. How do geometric relationships and measurements help us to solve problems and make sense of our world? Grade 4 – Math Colchester Content


4. Understand and use ratios, proportions, percents, exponents.

a. Use fractions to represent a division problem.

• Estimate locations and label fractions on number lines and rulers.

• Build and label a variety of models to represent, compare and order fractional parts of a whole and mixed numbers and to identify ratios and equivalent fractions.

• Use counting, number patterns and grouping to identify parts of a set.

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State Framework: GEOMETRY AND MEASUREMENT - continued Grade 4 – Math Colchester Content


5. Make and use measurements in both US Customary and metric units to approximate and measure length, area, volume, weight, temperature, and time.

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.

• Explore converting inches to feet and feet to yards.

• Solve practical problems that involve estimation and measurement of length, perimeter, area, volume, capacity, weight and temperature.

• Explore relationships between the lengths of sides of rectangles and their areas and perimeters and generalize the patterns as simple formulas.

• Identify and use the appropriate customary and metric units and tools for measuring length, perimeter, area, weight, time, temperature and capacity.

• Explore converting from one unit to another when measuring time and solve problems that involve elapsed time using clocks and calendars.

• Use estimation to predict reasonable answers to measurement problems.

• Estimate, draw and measure length to the nearest inch, half-inch and centimeter.

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a. Describe geometric properties of polygons and solids. b. Find possible pathways between two points using maps that are based on the rectangular coordinate system.

• Build, draw, describe and classify two- and three-dimensional figures.

• Analyze two-dimensional shapes and determine lines of symmetry and congruence.

• Create and read maps and use coordinate systems to specify locations.

54

State Framework: 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? Grade 4 – Math Colchester Content



a. Organize and analyze categorical and numerical data. b. Describe what is “average about the characteristics in data. c. Determine fair situations & good choices based on the likelihood of an occurance.

• Explore a variety of ways to collect, organize, record, analyze and interpret data.

• Construct and interpret broken line graphs, line plots, bar graphs, picture graphs, glyphs and simple circle graphs.

• Make predictions and defend conclusions based on data.

• Use the range, mode, median and mean to describe features of a data set. • Identify possible outcomes of events using combinations (where order does not matter) & explore situations using permutations (where order does matter). • Conduct probability experiments & express the probability based on possible outcomes.

55

State Framework: ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS Patterns and functional relationships can be represented and analyzed using a variety of strategies and tools. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Grade 4 – Math Colchester Content



a. Classify patterns as repeating or growing. b. Demonstrate the equivalence of both sides of an equation. c. Represent possible values using symbols.

• Recognize a variety of patterns and trends including repeating and growing patterns.

• Explore extending and comparing arithmetic and geometric sequences.

• Develop and test generalizations of patterns and relationships.

• Use equations to describe the rules for number patterns and to model word problems.

• Demonstrate equivalence with the commutative, associative and distributive properties of whole numbers.

• Use variables to represent quantities in expressions and number sentences.

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State Framework: Algebraic Reasoning Grade 4 – Math Colchester Content


9. Use technology to interpret, understand and solve mathematical problems

a. Use instructional software to solve problems Use calculators to solve problems Use smart board to manipulate data and number lines

Use smart board to display symmetry, group numbers, graph data

All Units See Pacing Guide

10. Solve and explain multi step problems.

a. Use written language to explain process of using mathematical understanding.

● build mathematical knowledge through problem solving

• Apply and adapt a variety of appropriate strategies to solve problems.

• solve problems that arise in mathematics and in other contents

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a. Classify numbers by their factors.

• Use rectangular arrays to identify factor pairs and to classify numbers as prime, composite and perfect squares.

• Develop strategies, using place value relationships, inverse operations and commutative, associative and distributive properties, to simplify computations with two-, three-, and four-digit numbers and money amounts.

• Explore divisibility rules & patterns w/ remainders.

Everyday Math 3—see pacing guide

Formative and benchmark assessments as indicated in pacing guide.


a. Estimate and compute using models and pictures.

• Choose and use benchmarks to approximate locations on number lines and coordinate grids.

• Estimate and use counting, grouping of objects, number patterns, equivalent ratios and division to find fractional parts of a set of objects.

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• Use estimation to predict results and to recognize when an answer is or is not reasonable.

• Explain when an estimation strategy will result in an over- or underestimate.

• Estimate products and missing factors using multiples of 10, 100, and 1000.

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3. Demonstrate quantitative sense by using numbers to count, measure, compare and order.

a. Extend whole number place value patterns, models and notations to include decimals, which are fractions that have denominators that are multiples of 10.

• Identify, round, order and compare whole numbers to 1,000,000 using diagrams and number lines.

• Express numbers in expanded and regrouped forms and use the numbers to support computational strategies.

• Solve problems involving finding 10,100 and 1000 more and less than a number.

• Use models to extend whole number place value concepts and patterns to decimals.

• Explore numbers less than zero and extend the number line to introduce the concept of integers within practical applications.

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4. Understand and use ratios, proportions, percents and exponents.

a. Express numbers as equivalent fractions, decimals or percents. b. Represent ratios and proportions and solve problems using models and pictures.

• Represent a rational number in its equivalent fraction, decimal, and percent forms with models, number patterns and common factors.

• Construct and use models and pictures to add and subtract fractions, decimals and mixed numbers with like and unlike denominators.

• Use equivalence and substitution with common denominators when adding and subtracting.

• Build models to identify and compare ratios and describe quantitative relationships using fraction and decimal equivalents.

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Colchester Public Schools



5. Make and use measurements in both US customary and metric units to approximate and measure length, area, volume, weight, temperature, and time.

a. Recognize that changes in the perimeter of a polygon may affect its area, and changes in area may affect the perimeter. b. Solve problems in the measure of time and in the conversion of units of length in the customary and metric systems using specific rations.

• Explore the relationship between area and perimeter when the dimensions of a polygon change.

• Develop formulas to find the perimeter and area of squares, rectangles and triangles.

• Solve length problems involving conversion of measure within the customary and metric systems.

• Solve problems involving the conversion of measure of time and elapsed time (days, hours, minutes and seconds).

• Estimate and choose appropriate units and tools to measure and solve a variety of problems involving length, perimeter, area, volume, capacity, mass, time, angle and temperature.

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a. Use geometric relationships to describe polygons and solids. b. Identify, describe and build nets for solid figures and objects. c. Determine geometric relationships through spatial visualization.

• Use geometric relationships such as parallel, perpendicular and congruent to describe the attributes of sets and subsets of shapes and solids.

• Make and test conjectures about geometric relationships.

• Represent the surface of three-dimensional objects through the use of two-dimensional nets.

• Investigate and develop strategies to determine the volume of rectangular solids.

• Plot points on the rectangular coordinate system and estimate and determine the distance between points.

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State Framework: WORKING WITH DATA: PROBABILITY AND STATISTICS Data can be analyzed to make informed decisions using a variety of strategies and tools. How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions? Grade 5 – Math Colchester Content



a. Differentiate between numerical and categorical data and their appropriate representations. b. Examine different data collection methods and their effects. c. Relate likelihood of an event to a numerical value.

• Construct and interpret broken line graphs, line plots, bar graphs, picture graphs, simple circle graphs, and stem and leaf plots and evaluate how well each kind of display represents the features of the data.

• Design and conduct surveys and samplings to collect data that represent a general population.

• Explore how a change is an outlier can change the measures of central tendency.

• Identify possible outcomes & • express likelihood of events in a

fraction. • Design & conduct probability

experiments & games if chance. • Make & test predictions of

probability & fairness.

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a. Identify trends and make predictions based upon patterns and data displayed in different formats. b. Recognize that a change in one variable may relate to a change in another variable. c. Describe the general relationship between two sets of data using an equation or inequality.

• Extend and compare arithmetic and geometric sequences.

• Represent geometric and numeric patterns using words, tables, graphs, and equations.

• Analyze patterns and data to make generalizations and predictions.

• Describe how a change in one variable relates to a change in a second variable in context.

• Represent mathematical relationships using variables in expressions, equations and inequalities.

• Model and solve one-step equations using materials that model equivalence.

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State Framework: ALGEBRAIC REASONING Grade 5 – Math Colchester Content


9. Use technology to interpret, understand and solve mathematical problems.

Use instructional software to solve problems Use calculators to solve problems Use Smart boards to manipulate data .

Solve problems that arise in mathematics and in other contexts.

All Units

66


State Framework: ALGEBRAIC REASONING Grade 5 – Math Colchester Content


10. Solve and explain multi step problems.

a. Build new mathematical knowledge through problem solving.

● Write division problems in fraction form and round the fraction form to estimate an answer to a division problem. ● Create & solve multistep problems & explore order of operations in the context of practical situations. ● Solve problems that arise in mathematics ● Apply and adapt a variety of appropriate strategies to solve problems.

All Units See Pacing Guide

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1. Understand & use algebraic concepts & functions to analyze sets, develop models, verify solutions.

a. Identify relationships and make generalizations through the use of patterns.

Describe, analyze and extend numeric, geometric and statistical patterns and use them to justify predications.

MSM chp. 4 MSM chp. 10

Quarterly Benchmark

2. Solve & explain multi-step problems.

Solve real-world problems.

Use specific strategies, such as guess & check, make a table, draw a diagram, work backward to solve word problems.

Infused throughout curriculum

Quarterly benchmark DOM problems

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a. Identify and understand fractions in their various forms and relate them to decimals and percents.

• Use models and common factors to identify equivalent fractions and their decimal representations.

• Determine the decimal equivalents of fracions.

CMP Bits & Pieces I Kaleidos activity (fraction match game, fraction decimal match, fraction loop cards) Scott Foresman Middle School Math Ch 5B

Quarterly benchmarks & Chp. tests

b. Add, subtract, multiply and divide fractions and decimals and apply them to real-life situations c. Express numbers as equivalent fractions, decimals or percents.

• Add, subtract, multiply & divide fractions and decimals using a variety of computational strategies.

• Create and solve a variety of problems involving fractions, decimals, mixed numbers, money and simple percents.

• Represent a rational number in its equivalent fraction, decimal, ratio and percent forms with models, number patterns and common factors.

• Construct and use models and

Middle School Math Ch 3, 6, 7 CMP Bits & Pieces I

Quarterly benchmarks & Chp. tests

69


pictures to add and subtract fractions, decimals and mixed

numbers with like and unlike denominators.

70




4. Make estimates &

approximations & judge whether the results are reasonable

5. Demonstrate quantitative sense by using numbers to count, measure, compare and order

6. Understand and use ratios, proportions, percents, exponents

a. Use estimation to decide if answers are reasonable

a. Solve problems using a variety of computational strategies, including the use of calculators. a. Compare quantities and solve problems using ratios and percentages

(1) Estimate and predict reasonable answers and recognize and explain when an estimate will be more or less than an exact answer. (1) Use a variety of computational strategies (mental computation, paper-and-pencil and calculator) to add, subtract, multiply and divide multidigit numbers in the context of multistep word and practical problems. (2) Locate, order and compare whole numbers, fractions, decimals and integers on number lines, scales and the coordinate grid.

• Estimate and find percents using benchmarks and number patterns.

• Convert between rates using ratios and proportions.

• Solve problems involving rations, proportions and percents

Infused throughout curriculum 1) Infused, with special instruction on strategies during 2 days prior to extended task benchmark Chapter 10 MSM M & M ratio-proportion activity.

Ongoing Extended tasks benchmarks Chp. 10 Benchmark

71




7. Make and use measurements in both U.S. custom & Metric units to approximate and measure length, area, volume, weight, temperature & time.

8. Demonstrate an

understanding of spatial relationships and basic

concepts of geometry to

a. Solve problems involving measurement through the use of a variety of tools, techniques and strategies. b. Use specific ratios to convert between measure of length, area, mass and capacity in the customary and metric systems. a. Find perimeter and area of parallelograms, triangles, circles and irregular figures. b. Use spatial

(1) Estimate and determine length, area, mass and angle measures. (2) Select and use appropriate units, strategies and tools to measure and solve problems involving length, perimeter, area, capacity, weight, mass temperature and angles. (1) Use different ratios to convert between units of length, area and volume in the customary and metric systems. (2) Recognize and use powers of ten as conversion ratios in the metric system

• Use the rectangle as a basic shape to model and develop formulas for the area of triangles, parallelograms, trapezoids and circles.

MSM Ch. 4 DOM problems MSM Ch. 4 Pi week activities Ch. 4 (MSM) Geometer sketch pad activities MSM Ch. 4 & Ch. 10 (similar figures) Geometer sketch pad

Homework class discussions Quarterly benchmarks

72


construct and describe geometric models and patterns

reasoning, location and geometric relationships to solve problems.

• Recognize the relationships among radius, diameter, circumference and area of circles. • Explore similarity of polygons as a result of dilations (a reduction or enlargement) and their effects on their measurements. • Explore transformations of geometric figures.

73


State Framework: Working with Data 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? Grade 6 – Math Colchester Content


9. Understand and use basic concepts of probability and statistics to collect, organize, display and analyze data, simulate events and test hypotheses. 10. Use technology used throughout entire curriculum to interpret, understand, and solve mathematical problems.

a. Collect, organize and display data using appropriate graphical methods and make predictions base don the data from the graphs. b. Analyze data using measures of central tendency. Use calculators, including graphing calculators and EXCEL program to manipulate data.

• Compare sets of data graphically using histograms, double bar graphs, back-to-back stem and leaf plots and scatter plots.

• Describe the shape of data sets

using measure of spread (range and outliers) and central tendency (mode, median and mean).

• Recognize that changes in a data set can affect the mode, median, mean and range.

• Construct circle graphs and recognize that they represent data proportionally.

Use calculators to determine mean.

Chp. 1 MSM M&M Circle Graph Activity Chap. 1 MSM

Chp.1 Test Chp.1 Test

74


State Framework: ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS Grade: 7 Colchester Content


1. Understand & use algebraic concepts & functions to analyze situations, develop models, & verify solutions.

a. Solve problems using a variety of algebraic methods. b. Maintain equivalence in equations to determine solutions.

(1) Generalize mathematical situations and patterns with algebraic expressions, equations and inequalities. (2) Identify the independent and dependent variables in a given situation.

MSM 7 Chp. 2 CMP – variables & patterns CMP Bits & Pieces 2

• Chp. 2 Quarterly benchmark – MSM 7

CMP Variables & Patterns • Benchmark -

quarterly


a. Use strategies, such as making a table, working backwards, etc. to solve multi-step problems.

(1) Solve problems using concrete, verbal, symbolic, graphical and tabular representations. (2) Model and solve one-step and two-step linear equations using a variety of methods.

CMP Variables & Patterns, Bits & Pieces II & MSM 7 – Chp. 2

Same as above

75


State Framework: 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 and tools. How are quqntitative relationships represented by numbers? Grade: 7 Colchester Content


Numerical & Proportional Reasoning 3. Understand and use the addition, subtraction, multiplication & division of whole numbers, fractions, decimals & integers.

a. Solve problems using the four basic units of operators with fractions and decimals.

(2) Identify and classify fractions as terminating or repeating decimals (3) Estimate and perform computations with fractions, decimals, mixed numbers, improper fractions, ratios, proportions and percents. (4) Multiply and divide mixed numbers and decimals using the distributive property. (5) Use and describe appropriate methods to divide by a decimal.

CMP – Bits & Pieces 2 CMP Bits & Pieces Quarterly Benchmark

4. Make estimates & Approximations & judge Whether the results are

a. Make estimates before problem solving to judge whether final result is reasonable.

(7) Estimate to predict outcomes and determine reasonableness of results, and describe whether an estimate is an over-or underestimate

• Daily Oral Math Problems

• Interwoven throughout each unit.

Daily oral math Quarterly Benchmarks

76


Reasonable. 5. Demonstrate quantitative sense by using numbers to count, measure, compare & order

a. Represent real-world situations & solutions to problems using the appropriate symbolic form (fractions, decimals, or percents)

(1) Rewrite a rational number in its equivalent fraction, decimal, ratio and percent forms with number patterns and common factors. (2) Identify and classify fractions as terminating or repeating decimals. (3) Estimate and perform computations with fractions, decimals, mixed numbers, improper fractions, ratios, proportions and percents. (4) Multiply and divide mixed numbers and decimals using the distributive property. (5) Use and describe appropriate methods

to divide by a fraction or a decimal.

CMP Bits & Pieces II

77


State Framework: 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 and tools. How are quqntitative relationships represented by numbers? Grade: 7 Colchester Content


c. Use percents to make comparisons between groups of unequal size

(1) Estimate and find percents, including percents greater than 100 percent and less than 1 percent using number patterns and the distributive property. (2) Find what percent one amount is of another amount using a variety of strategies.

6. Understand & use ratios, proportions, percents & exponents.

a. Use ratios, proportions, percents, & exponents to solve problems and real world applications.

1) Rewrite a rational number in its equivalent fraction, decimal, ratio and percent forms with number patterns and common factors. (2) Use the order of operations to compute and solve a variety of multi-step problems, including those with parentheses and exponents.

Bits & Pieces II CMP Comparing & Scaling

B & P Benchmark Comp & Scal.. Benchmark

78


State Framework: GEOMETRY AND MEASUREMENT Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies and tools. How do geometric relationships and measurements help us solve problems and make sense of our world? Grade: 7 Colchester Content


7. Make & use measurements in both U.S. customary and metric units to approximate & measure length, area volume, weight, temperature and time. 8. Demonstrate an understanding of spatial relationships & basic concepts of geometry to construct & describe geometric models & patterns

a. Compute area & measure weight a. Describe and classify polygons according to their transformational properties.

Approximate and accurately measure objects using the U.S. customary and metric systems. Identify congruent & similar figures & draw & classify geometric figures.

MSM Chp. 5 & 11

Chp 5 & 11 Test

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State Framework: Working with Data Data can be analyzed to make informed decisions using a variety of strategies, tools and technology. How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions? Grade: 7 Colchester Content


9. Understand & use basic concepts of probability & statistics to collect, organize, display & analyze data, simulate events and test hypotheses

4.1 Collect, organize and display data using appropriate statistical and geographical methods.

(1) Formulate questions, design surveys and samplings, organize and analyze gathered data and defend the analysis. (2) Organize and display data using appropriate graphical representations and make and defend predications based on patterns and trends.

Chp. 1 (MSM) 7) (CMP) Variable & Pattern

Quarterly Benchmark & Chp Test

4.2 Analyze data sets to form hypotheses and make predictions.

(1) Find, use and interpret measures of central tendency and spread, including mode, median, mean, range and outliers. (2) Compare two sets of data based on their distributions and measures of central tendency.

Chp. 1 (MSM) 7) (CMP) Variable & Pattern

Quarterly Benchmark & Chp Test

10. Use technology throughout entire curriculum to interpret,

Use scientific calculators, including graphing calculators and EXCEL

• Input statistical data to construct graphs. • Use calculator to determine measure of

central tendency.

Variables & Patterns Chp. 1

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understand, and solve mathematical problems.

program to manipulate data. Use interactive white boards.

• Utilize white board to explain & demonstrate concepts throughout the curriculum

81


State Framework: ALGEBRAIC REASONONG: 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? Grade 8 Math Colchester Contest

Strand Students will … Performance Expectation Exploration/Application Assessment

1. Understand & use algebraic concepts.

a. Analyze data, functions and patterns to identify relationships and make generalizations.

b. Analyze linear relationships using tables, graphs, and equations.

• Write equations to generalize patterns.

• Identify linear relationships and compare and contrast their properties using tables and equations.

• Recognize and solve problems of direct variation.

• Determine the constant rate of change in a linear relationship and recognize this as the slope of a line.

• Interpret slope and y-intercepts contextual situations, graphs, and linear equations.

• Given two linear relationships in context, recognize that they may have a common solution.

Middle School Mathematics – Chapter 3 Connected Math Program – Moving Straight Ahead

Algebra Extended Task benchmark


a. Solve problems using various algebraic methods and properties.

b. Analyze linear

• Solve multi-step equations using algebraic properties.

• Use tables, graphs, and equations to represent mathematical relationships and solve real-world

Middle School Mathematics – Chapter 3 Connected Math Program – Moving

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relationships using tables, graphs, and equations.

problems. Straight Ahead

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State Framework: 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 techniques. How are the base ten number system and fractions, decimals, percents, and ratios related? Grade 8 Math

Colchester Contest Strand

Students will … Performance Expectation Exploration/Application Assessment


a. Compare and order integers, powers and roots using number lines and grids.

• Solve a variety of problems involving integers, powers, roots, and scientific notation.

• Use powers of ten and negative exponents to write decimal fractions.

Connected Math Program – Accuate the Negative

Middle School Mathematics – Chapter 2 benchmark


a. Use estimation to decide if answers are reasonable.

• Estimate and solve problems involving percent of increase and decrease.

• Develop, describe, and use a variety of methods to estimate and calculate mentally with very large and very small numbers.

Middle School Mathematics – Chapter 6 Connected Math Program – Moving Straight Ahead

5. Demonstrate quantitative sense by using numbers to count, measure, compare, and order.

a. Solve problems using a variety of computational strategies.

• Compare, locate, and order rational numbers on number lines, scales, and coordinate grids.

• Identify another rational number between any two rational numbers.

• Use powers of ten and positive and negative exponents to express and compare magnitude of very large

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and very small numbers and connect to scientific notation.

85


State Framework: 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 techniques. How are the base ten number system and fractions, decimals, percents, and ratios related? Grade 8 Math



6. Understand and use ratios, proportions, percents, and exponents.

a. Solve problems involving fractions, decimals, ratios, and percents.

• Find the results of multiplication and division with powers of ten using patterns in operating with exponents.

• Develop, describe, and use a variety of methods to operate with very large and very small numbers.


86


State Framework: 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 measurement help us to solve problems and make sense of our world? Grade 8 Math Colchester Contest

Strand Students will … Performance Expectation Exploration/Application Assessment

7. Make and use measurements in both US customary and metric units to approximate and measure length, area, volume, weight, temperature, and time.

a. Explore the relationships among sides, angles, perimeters, areas, and volumes.

b. Solve problems involving measurements in both metric and customary units.

• Solve problems involving area and volume.

• Analyze relationships among angles, sides, perimeters, and areas of congruent and similar polygons, including Pythagorean Theorem.

• Select and use appropriate units , strategies, and tools to measure and solve problems involving length, perimeter, area, weight, mass, temperature and angles.

RM Lessons with interactive whiteboard


8. Demonstrate an understanding of special relationships and basic concepts of geometry to construct and describe geometric models and patterns.

a. Model geometric relationships in a variety of ways.

• Use coordinate geometry to explore and test geometric relationships of parallel and perpendicular lines and polygons and their transformations.

87


State Framework: WORKING WITH DATA – PROBABILTY 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. Grade 8 Math




a. Construct representations of data.

b. Make and evaluate statistical claims and justify conclusions with evidence.

• Collect, organize, display, compare, and analyze large data sets.

• Construct a variety of data displays, identify where measures of central tendency are found in graphical displays.

• Make predictions from scatter plots. • Analyze and interpret data using

descriptive statistics, including range, mode, median, outliers, and mean.

10. Use technology to interpret, understand, and solve mathematical problems.

a. Use scientific and graphing calculators and Excel program to manipulate data.

b. Use interactive whiteboard to demonstrate and practice data analysis skills.

• Use scientific and graphing calculators to find mean, median, mode, range.

• Use graphing calculators to show linear representations.

• Manipulate interactive whiteboard software programs and computer technologies, ie. Excel, to practice data skills and related math concepts.

Interactive whiteboard

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Bacon Academy Content Standard

Concepts

Introduce =I Developing=D Mastery = M Reinforce=R

Understand and use algebraic concepts and functions to analyze situations, develop models, and verify solutions. (Algebraic Reasoning: Patterns and Functions)

Understand and apply the concepts of relations, functions, and independent vs. dependent variables. Use functions to model real phenomena and to make predictions. Identify appropriate values for the domain and range based upon the data the variables model. Use tables, graphs and equations to analyze linear functions. Calculate and interpret constant rate of change (slope). Use tables, graphs and equations to analyze non-linear functions. Calculate and interpret non-constant rate of change. Perform operations with polynomials. Perform operations with functions.

- I I I I - - I -

I

D

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D I I

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Concepts


Understand and use addition, subtraction, multiplication, and division of whole numbers, fractions, decimals and integers. (Numerical and Proportional Reasoning)

Understand and use integers. Understand and use rational numbers. Understand and use irrational numbers. Understand and use complex numbers. Apply the properties of real numbers to develop strategies for computation. Understand and use proportional reasoning. Use technology to perform difficult computations. Understand and use matrices and vectors.

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Make estimates and approximations, and judge whether results are reasonable. (Numerical and Proportional Reasoning)

Apply the properties of real numbers to develop strategies for estimation. Apply proportional reasoning as a strategy to make geometric estimates. Apply proportional reasoning as a strategy to make algebraic estimates.

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Demonstrate quantitative sense by using numbers to count, measure, compare, order. (Numerical and Proportional Reasoning)

Construct number lines and grids to order and compare the real numbers. Extend the measurement of angles and arcs to include radian measure.

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Understand and use ratios, proportions, percents, exponents. (Numerical and Proportional Reasoning)

Rewrite a rational number in equivalent fraction, decimal and percent forms and apply them to practical application. Apply the concepts of ratio and proportion to algebraic and geometric models. Understand and define real number exponents and their properties. Use exponents to model and solve problems involving exponential growth and decay.

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Make and use measurements in U.S. Customary and metric units to approximate and measure length, area, volume, weight, temperature, and time. (Geometry and Measurement)

Select appropriate units, scales, degree of precision and strategies to determine length, angle measure, perimeter, circumference and area of plane geometric figures. Solve a variety of problems involving one, two, and three dimensional measurements using geometric relationships and trigonometric ratios. Solve a variety of application problems involving temperature and time.

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Demonstrate an understanding of spatial relationships and basic concepts of geometry to construct and describe geometric models and patterns. (Geometry and Measurement)

Investigate and verify geometric relationships using algebra, coordinate geometry and transformations. Develop and evaluate mathematical arguments using reasoning and proof.

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Understand and use basic concepts of probability and statistics to collect, organize, display, and analyze events and test hypotheses. (Working with Data)

Obtain real data and create meaningful graphical representations of the data. Analyze data to make inferences about a population and to make predications. Determine an appropriate linear and non-linear regression model from given data. Determine outcomes and solve problems involving the probabilities of events. Apply theoretical and experimental probabilities appropriately to solve problems and predict results. Understand and use permutations, combinations, recursion and mathematical induction to solve problems.

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Use technology to interpret, understand, and solve mathematical problems. (Working with Data)

Use a calculator, where appropriate, to solve practical problems and graph functions. Use technologies to analyze characteristics and behaviors of graphs and the relationships between graphs. Use geometric modeling software to investigate properties of geometric figures and spatial relationships.

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Solve and explain multi-step problems. (Algebraic Reasoning: Patterns and Functions)

Use patterns and numerical methods to solve multi-step problems. Identify and solve multi-step problems involving geometry. Identify and solve multi-step problems modeled using linear functions. Identify and solve multi-step problems modeled using non-linear functions.

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BACON ACADEMY MATHEMATICS

Three (3) credits of Mathematics are required for graduation. It should also be noted that a minimum of Algebra 1, Geometry, and Algebra II are required for admission to most 4-year colleges and many 2-year colleges or technical schools. A fourth year of mathematics is recommended.

Recommended Course Sequences 9th Foundations of Math (0310) / \ 10th Consumer Math (0331) Algebra 1A (0311) | | 11th Applied Math (0321) Algebra 1B (0312) | 12th Informal Geometry (0314) ____________________________________________________________________ 9th Algebra 1A (0311) / \ 10th Consumer Math (0331) Algebra 1B (0312) | | 11th Applied Math (0321) Informal Geometry (0314) | 12th Integrated College (0324) ____________________________________________________________________ 9th Algebra 1 (0315) | 10th Geometry (0322) / \ 11th Integrated College (0324) Algebra II (0332) / \ 12th Algebra II (0332) Advanced Math (0336) _____________________________________________________________________

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9th Honors Geometry (0323) | 10th Honors Algebra II (0333) | -AP Statistics (0355) 11th Pre-Calculus (0343) | -Discrete Math (0335) 12th AP Calculus (0353) _____________________________________________________________________

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FOUNDATIONS OF MATH 1 (0310)

Level 1 Year 1 Credit

This course is designed to provide a freshman alternative for those students needing additional preparation before electing to take Algebra IA next year. Students will be required to utilize mathematical methods and concepts to solve problems involving basic operations with whole numbers, fractions, decimals, and integers. Students will be encouraged to effectively analyze and evaluate information to solve problems and will be required to demonstrate an ability to communicate clearly and concisely using appropriate mathematical vocabulary and notation when responding to questions and explaining their work. Manipulatives will be used to provide a hands-on learning experience. Technological literacy will be developed using the scientific calculator to perform routine computations and to facilitate problem solving.

Prerequisite: Open only to recommended grade 9 students.

CONSUMER MATH (0331) Level 1 Year 1 Credit This course is designed to provide a year of general mathematics for those sophomores and juniors who have completed either Foundations of Math or Algebra IA and are not continuing in the college prep program. Students will develop an ability to effectively analyze and evaluate information to solve problems involving Number and Quantity, Measurement and Geometry, Statistics, Probability and Discrete Math and Algebra and Functions, in preparation for the CAPT test. Students will be required to utilize mathematical methods and concepts to solve problems involving basic operations with whole numbers, fractions, decimals, and integers. A review of computational skills will be integrated with a variety of practical, consumer and career related application problems. Students will also work to develop an ability to communicate clearly and concisely using appropriate mathematical vocabulary and notation when responding to questions and explaining their work. Technological literacy will be developed using the scientific calculator to perform routine computations and to facilitate problem solving. The focus of the applications studied will be on consumer related applications of mathematics such as measurement, income, spending, taxation, budgeting, and banking. Prerequisite: Foundations of Math or Algebra IA

APPLIED MATH (0321) Level 1 Year 1 Credit

This course is designed to provide a year of general mathematics for those students who have not yet mastered the mathematical processes and content areas defined by the State of Connecticut as part of Connecticut’s Common Core of Learning. Students will develop an ability to effectively analyze and evaluate information to solve problems involving Number and Quantity, Measurement and Geometry, Statistics,

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Probability and Discrete Math and Algebra and Functions. Students will be required to utilize mathematical methods and concepts to solve problems involving basic operations with whole numbers, fractions, decimals, and integers. A review of computational skills will be integrated with a variety of practical, consumer and career related application problems. Students will also work to develop an ability to communicate clearly and concisely using appropriate mathematical vocabulary and notation when responding to questions and explaining their work. Technological literacy will be developed using the scientific calculator to perform routine computations and to facilitate problem solving. The applied topics may include data collection, table and chart reading, graphing, statistics, measurement, taxation, and banking in addition to applied algebra and geometry. Prerequisite: Open to grade 11-12 students.

ALGEBRA 1A (0311) Level 1 Year 1 Credit

This course is the first in a two-year Algebra I program for students who have experienced an introduction to, but not yet mastered, the skills and concepts of pre-algebra. The program provides an opportunity to pursue the study of basic Algebra at a slower pace, by doing so over a two-year period of time. A review of basic math skills and a variety of selected pre-algebra topics will be integrated with a study of the traditional skills and concepts of Algebra. Students will be required to utilize mathematical methods and concepts to solve problems including operations with integers, algebraic expressions, and solving equations. Students will be encouraged to effectively analyze and evaluate information to solve problems and will be required to demonstrate an ability to communicate clearly and concisely using appropriate mathematical vocabulary and notation when responding to questions and explaining their work. Manipulatives will be used to provide a hands-on learning experience. Technological literacy will be developed using the scientific calculator to perform routine computations and to facilitate problem solving.

Note: The second course in the program, Algebra IB (312), must be completed to provide the equivalent program of Algebra I (315). Prerequisite: Open to grade 9-11 students.

ALGEBRA 1B (0312) Level 1 Year 1 Credit

This course is a continuation of Algebra 1A and is the second part in a two-year Algebra 1 program. Upon successful completion, students may elect to take Geometry in the following year.

Prerequisite: Open to grade 10-12 students, with a 70 or better in Algebra 1A.

ALGEBRA 1 (0315) Level 2 Year 1 Credit

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This course is designed to provide an innovative approach to the study of algebra and extends the traditional skills and concepts. Students

will be required to utilize mathematical methods and concepts to solve problems including linear equations, word problems with an introduction to quadratics. Students will be encouraged to effectively analyze and evaluate information to solve problems and will be required to demonstrate an ability to communicate clearly and concisely using appropriate mathematical vocabulary and notation when responding to various questions and explaining work. Technological literacy will be developed by regularly using a scientific calculator to solve equations, simplify expressions, evaluate linear equations, create graphs and to perform routine computations to facilitate problem solving. Students will also use computer software to investigate and reinforce the equation of a line and the concept of slope. Graphing calculators will be introduced to investigate tables of values and to discover the properties of graphs.

INFORMAL GEOMETRY (0314) Level 1 Year 1 Credit

This course is designed to provide a third year of study for those students who have completed the two-year algebra program. An informal approach to the study of geometry will be used to develop the student’s ability to utilize mathematical and scientific methods to solve problems. Students will be encouraged to effectively analyze and evaluate problems involving measurement and classification of geometric shapes and figures. Technological literacy will be developed by regularly using calculators to facilitate problem solving. The students will also develop an awareness of world culture and society through the study of real world application problems. Students will be required to communicate clearly and concisely with the appropriate mathematical vocabulary and notation when responding to various questions and explaining work. Prerequisite: Algebra IB or Algebra I (315) with teacher recommendation.

GEOMETRY (0322) Level 2 Year 1 Credit

This course is designed to provide an understanding of the basic structures of geometry and to develop spatial visualizations, while building a knowledge of the relationships among geometric elements. Students will be required to effectively analyze and evaluate information from a variety of sources using inductive and deductive reasoning, and to communicate clearly, concisely, and persuasively using correct geometric vocabulary and notation. Students will be required to utilize mathematical methods and concepts to solve problems involving measurement and classification of geometric shapes and figures. Right triangle trigonometry and the properties of circles and polygons will be used to solve application problems. Students will develop technological literacy through the use of scientific and graphing calculators, Geometer’s Sketchpad software, and the Internet.

Prerequisite: Grade of 70 or better in Algebra I (315).

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GEOMETRY (0323)


This course is designed to offer a challenging and extensive approach to the study of geometry. Students will be required to effectively analyze and evaluate information from a variety of sources using inductive and deductive reasoning, and to communicate clearly, concisely, and persuasively using correct geometric vocabulary and notation. Students will be required to utilize mathematical methods and concepts to solve problems involving measurement and classification of geometric shapes and figures. Right triangle trigonometry and the properties of circles and polygons will be used to solve application problems. Students will develop technological literacy through the use of scientific and graphing calculators, Geometer’s Sketchpad software, and the Internet. Prerequisite: Open to grade 9 students with a 80 or better in grade 8 Algebra 1.

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INTEGRATED COLLEGE MATH (0324)


This course is intended for those students who have completed both Algebra 1 and Geometry, but have not yet mastered the skills necessary for success in Algebra 2. A review of the basic skills and concepts from algebra and geometry will be provided using an integrated with a preview of selected topics from Algebra 2. Students will be required to use mathematical and scientific methods and concepts to solve problems involving number sense, algebra, geometry, statistics and logic. Technological literacy will be developed using graphing calculators, Geometer’s Sketchpad, and various other computer programs to explore principles of geometry and algebra. Students will be encouraged to effectively analyze and evaluate information from a variety of sources and to communicate clearly, concisely, and persuasively the findings of their mathematical work. Students will present data using various visual techniques including graphs, spreadsheets, charts, tables, and diagrams which will be used to support their work.

Prerequisite: Open only to grades 11-12 students who have completed both Algebra 1 and Geometry and who do not meet the prerequisite for Algebra 2.


This course is the third in the traditional college preparatory math sequence, beginning with Algebra 1 and Geometry. A comprehensive review of basic algebraic and geometric skills and concepts will be integrated with a study of more advance topics. Students will be required to utilize mathematical methods and concepts to solve problems involving linear, quadratic, exponential, logarithmic and polynomial functions. Students will be encouraged to effectively analyze and evaluate information to solve problems and will be required to demonstrate an ability to communicate clearly and concisely using appropriate mathematical vocabulary and notations when responding to various questions and explaining work. Technological literacy will be developed through daily use of the graphing calculator to solve equations, create and investigate the properties of graphs, and to facilitate problem solving.

Prerequisite: Grade of 70 or better in Algebra 1 and Geometry.


This course is designed to offer a challenging and extensive approach to the study of advanced algebra. Students will be required to utilize mathematical methods and concepts to solve problems involving linear, quadratic, exponential, logarithmic and polynomial functions. Additional topics will include rational functions, matrices, and trigonometry. Students will be encouraged to effectively analyze and evaluate information to

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solve in-depth problems and will be required to demonstrate an ability to communicate clearly and concisely using appropriate mathematical vocabulary and notations when responding to various questions and explaining work. Technological literacy will be developed through daily use of the graphing calculator to solve equations, create and investigate the properties of graphs, and to facilitate problem solving.

Prerequisite: Open to grade 10-11 students with a B or better in Algebra 1 and Geometry 323. ADVANCED MATH (0336)


This course is designed to provide a junior/senior alternative to Pre-calculus for those students who do not intend to take Calculus next year. Students will be required to utilize mathematical and scientific methods and concepts to solve problems involving advanced algebra, trigonometry, and exponential growth and decay. Students will be encouraged to effectively analyze and evaluate information to solve problems, and will be required to demonstrate an ability to communicate clearly and concisely using appropriate mathematical vocabulary and notation when responding to questions and explaining work. Technological literacy will be developed as the graphing calculator will be used daily to investigate and discover properties of graphs and to perform routine computations to facilitate problem solving.

Prerequisite: Open only to grade 11-12 students with a 70 or better in Algebra 2 and teacher recommendation.

PRE-CALCULUS (0343) Level 3 Year 1 Credit

This course is a combination of advanced algebra and trigonometry, and is designed to provide the student with an understanding of the advanced mathematics required for calculus. Students will be required to utilize mathematical and scientific methods and concepts in the study of functions, relations and their graphs, coordinate geometry, conic sections, solutions of higher degree equalities and inequalities, circular functions and their inverses, trigonometric functions, identities, formulas and their applications, exponential and logarithmic functions, and other topics as time allows. Students will effectively analyze and evaluate information to solve problems, and will be required to demonstrate an ability to communicate clearly and concisely using appropriate mathematical vocabulary and notation when responding to questions and explaining work. Students will develop technological literacy through daily use of the graphing calculator.

Prerequisite: Grade of 80 or better in Algebra 1, Geometry and Algebra 2 (333) and teacher recommendation.

*DISCRETE MATH (0335) Level 3 Year 1 Credit This course is designed to be taken as an elective math credit for those students who are planning to pursue the study of mathematics, computer science, or engineering at the college level. The curriculum is designed to introduce students to discrete math ideas and concepts that

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underlie the science and technology of the computer age. Students will develop an ability to think abstractly and develop algorithms to solve problems using logically valid forms of argument. Course topics will include but are not limited to elementary number theory, methods of proof, symbolic logic, mathematical induction, set theory, digital logic circuits, and graph theory. Students will be encouraged to demonstrate an ability to communicate clearly and concisely using appropriate mathematical vocabulary and notation when responding to questions and explaining work. Students will develop technological literacy through the investigation of computer algorithms.

Prerequisite: Grade of 80 or better in Pre-calculus or may be taken concurrently with Pre-calculus with consent of instructor.

A.P. CALCULUS (0353) AP Year 1 Credit

This Advanced Placement course is designed to prepare students for the AP Calculus AB exam. Students will be required to utilize mathematical and scientific methods and concepts in the study of analytic geometry, functions, limits, derivatives, and integrals of algebraic, trigonometric, inverse trigonometric, and logarithmic and exponential functions. Students will effectively analyze and evaluate information to solve problems involving applications of the derivative and integral, and will be required to demonstrate an ability to communicate clearly and concisely using appropriate mathematical vocabulary and notation when responding to questions and explaining their work. Students will develop technological literacy through daily use of the graphing calculator, which is required on the AP exam.

The Advanced Placement Exam of the College Board will be offered at the completion of the course and will provide the student with an opportunity for college credit.

Prerequisite: Grade of 80 or better in Pre-calculus.

A.P. STATISTICS (0355) AP Year 1 Credit

This Advanced Placement course is designed to prepare students for the AP Statistics exam, and provides an excellent option for any student planning to pursue a post-high school education, regardless of the student’s intended college major. AP Statistics may be taken alone or as a second math credit. The curriculum is designed to introduce students to the major concepts and tools for collecting and analyzing data. Students will be required to utilize mathematical methods and concepts to draw conclusions from data, then effectively analyze and evaluate the data to solve problems. Students will also be required to demonstrate an ability to communicate clearly and concisely using appropriate mathematical and statistical vocabulary and notation when responding to questions and explaining their work. Students will develop technological literacy through daily use of the graphing calculator and computer applications software. The Advanced Placement Exam of the College Board will be offered at the completion of the course and will provide the student with an opportunity for college credit.

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Prerequisite: Grade of 80 or better in Pre-calculus, Advanced Math or consent of instructor.

COMPUTER PROGRAMMING 1A (0352)

Level 2 Semester 1/2 Credit

This course is designed to provide an introduction to the skills of computer programming. Students will be encouraged to effectively analyze and evaluate information to solve problems and will be required to demonstrate an ability to communicate clearly and concisely using appropriate vocabulary. Technological literacy will be developed through individual projects that are focused on gaming. Students will be encouraged to create and build their own computer games. Students will write programs using a variety of programming languages including, but not limited to, PASCAL, Visual Basic, and HTML.

Prerequisite: Grades 9-12 with a 80 or better in Algebra I.

COMPUTER PROGRAMMING 1B (0356) Level 2 Semester 1/2 Credit

This course is a continuation of Computer Programming 1A. Students will continue to develop their ability to write programs using PASCAL, Visual Basic, and HTML while utilizing programming methods and concepts to solve problems involving basic computer operations. The emphasis on gaming will continue with the development of more advanced programming techniques. Technological literacy will be further developed through daily use of the computer.

Prerequisite: Computer Programming IA.

COMPUTER PROGRAMMING 2 (0362) Level 3 Year 1 Credit

This course is a continuation of Computer Programming 1. Students will continue to develop their ability to write programs with an emphasis on the C++ programming language. Students will be required to effectively analyze and evaluate information to develop program algorithms, then utilize programming methods and concepts to design and write a computer game. Technological literacy will be further developed through daily use of the computer.

Prerequisite: Grade of 80 or better in Computer Programming IB.

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A.P. COMPUTER SCIENCE (0357) AP Year 1 Credit

This Advanced Placement course is designed to prepare students for the AP Computer Science exam. Students will develop advanced programming skills and write programs using the JAVA programming language. Prerequisite: Grade of 80 or better in Computer Programming 2.

*WEBPAGE DESIGN IA (0358) Level 2 Semester 1/2 Credit This beginning course in webpage design will provide students with the basic skills used in the design and creation of webpages. Students will have the opportunity to create their own webpage as well as the experience of editing the existing www.baconacademy.org and www.colchesterct.org webpages Topics will include HTML, Javascript, Falsh, Mysql and other database languages as well as the Dreamweaver webeditor. Prerequisite: Grades 9-12 with a 80 or better in Algebra I.

*WEBPAGE DESIGN IB (0359) Level 2 Semester 1/2 Credit This course is a continuation of Webpage Design IA. Students will continue to develop their ability to design, create and edit webpages. Prerequisite: Webpage Design IA. *Not offered in 2007-2008 due to insufficient staffing.

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athematics c · athematics c urriculum colchester ... make estimates and approximations, ... be...

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