New Hampshire Framework Correlations: Eddie Files

THE EDDIE FILES features East Harlem teacher, Kay Toliver, and her innovative approach to teaching mathematics. The series follows "Eddie," a fictional student in Miss Toliver's classroom, as he investigates the world of careers by meeting real people in real jobs. Students discover the application of math concepts in the real world. The teacher's guide contains a synopsis of each episode describing the three major elements: Toliver's classroom lesson, Eddie's fictional experiences, and interviews with professionals; activities, including hands-on math; and resources for more information about the careers highlighted.
Problem Solving and Reasoning
Communication and Connections
Numbers, Numeration, Operations, and Number Theory
Geometry, Measurement, and Trigonometry
Data Analysis, Statistics, and Probability

Problem Solving and Reasoning

Broad Goal 1a:
Students will use problem-solving strategies to investigate and understand increasingly complex mathematical content.

Purpose: Problem solving should serve as the organizing feature of the mathematics curriculum as well as other areas of study and be applied to everyday activities. Problem-solving must not be seen as a separate topic, but rather the centerpiece of the mathematics curriculum. Students should have many experiences in posing and solving problems from their world, from data that are meaningful to them, and from mathematical investigations.

Proficiency Standards 1a
By the end of Grade 6 students will:

• Solve problems that require the use of strategies (for example: working backwards; looking for patterns and relationships; guess and check; making tables, charts, and graphs; solving a simpler version of a problem; looking for similar problems; drawing a diagram; or creating a model).
  
  
• Formulate, solve, and verify problems from every-day and mathematical situations and interpret the results.
  
  
• Solve multi-step problems, solve problems with multiple solutions, recognize when a problem has no solution, and recognize problems where more information is needed.
  
  
• Solve problems using manipulatives, graphs, charts, diagrams, and calculators.

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Broad Goal 1b

Students will use mathematical reasoning.

Purpose: Students need to recognize that memorized facts, rules, and procedures are only a part of mathematics. They need opportunities to use these facts, rules, and procedures to make conjectures, develop and refine their reasoning abilities, gather evidence, and produce valid rules and generalizations. Students need to be able to justify their thinking through examples and explanations and appreciate that how a problem is solved is as important as the answer.

Curriculum Standards 1b

In grades 4-6 students will:

• Draw conclusions using inductive reasoning, elementary deductive reasoning, and reasoning by analogy.
  
  
• Use models, known facts, properties, and relationships to explain their thinking.
  
  
• Explain conjectures, solutions processes, and answers.
  
  
• Appreciate the pervasive use and power of reasoning as a part of mathematics.
  
  
• Show increasing ability to understand and apply reasoning processes and spatial reasoning (symmetry, reflections, motions in the plane, and identifying three-dimensional objects from two-dimensional drawings).

Proficiency Standards 1b
By the end of Grade 6 students will:

• Continue a pattern involving integers and positive rational numbers.
  
  
• Solve problems involving two-and three-dimensional geometric shapes and explain one's reasoning.
  
  
• Use elementary deductive reasoning to solve word problems.
  
  
• Use models, known facts, properties, and relationships to explain thinking and to justify answers and solution processes.

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Communication and Connections

Broad Goal 2a
Students will communicate their understanding of mathematics.

Purpose: Reading, writing, talking, listening, and modeling, provide students with the opportunity to integrate the language of mathematics into their world, and help them to develop understanding. Actively exploring, investigating, describing, and explaining mathematical ideas promote communication which leads to a greater comprehension of mathematical concepts.

Curriculum Standards 2a

In grades 4-6 students will:

• Relate everyday language to mathematical language and symbols.
  
  
• Discuss, illustrate, and write about mathematical concepts and relationships.
  
  
• Use language to reflect on, clarify, and articulate thinking about mathematical ideas and situations.
  
  
• Demonstrate mathematical communication through discussion, representation, reading, writing, listening, and responding, individually and in groups.
  
  
• Use a variety of technologies (for example: computers, calculators, video, CD-ROM, or laser disc, to represent and communicate mathematical ideas).
  
  
• Understand and appreciate the economy and power of mathematical symbolism and its role in the development of mathematics.
  

Proficiency Standards 2a
By the end of Grade 6 students will:

• Demonstrate an understanding of mathematical concepts and relationships through a variety of methods (for example: writing, graphing, charts, diagrams, number sentences, or symbols)
  
  
• Explain, analyze, and evaluate mathematical arguments and conclusions presented by others.
  
  
• Explain conclusions, thought processes, and strategies in problem-solving situations.
  
  
• Make conjectures and defend generalizations.
  
  
• Evaluate the validity of a mathematical statement.

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Broad Goal 2b
Students will recognize, develop, and explore mathematical connections.

Purpose: Mathematical topics, ideas, and procedures must be connected to each other and to the students' everyday experiences, both in and out of school. In particular, mathematics must be connected to all other curriculum areas. Mathematical connections will help students become aware of the usefulness of mathematics,serve to bridge the concrete and the abstract, and enable deeper understanding of important ideas.

Curriculum Standards 2b

In grades 4-6 students will:

• Understand the mathematical processes and procedures of addition, subtraction, multiplication, and division and relate them to one another.
  
  
• Recognize equivalent representations of concepts and procedures and translate among them as appropriate (for example, understand how the addition of whole numbers, fractions, and decimals are related).
  
  
• Recognize relationships among different topics in mathematics.
  
  
• Recognize and use mathematics in other curriculum areas and in their daily lives.
  
  
• Link concepts and procedures (for example, know why you "invert and multiply"when dividing two fractions).

Proficiency Standards 2b
By the end of grade 6 students will:

• Identify the relationships among the four basic operations on rational numbers.
  
  
• Identify the relationship among the basic operations as applied to whole numbers and to positive rational numbers.
  
  
• Use mathematical skills, concepts, and applications in other disciplines (for example: graphs in social studies, patterns in art, or music and geometry in technology education).

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Numbers, Numeration, Operations, and Number Theory

Broad Goal 3a
Students will develop number sense and an understanding of our numeration system.

Purpose: Students must understand numbers if they are to make sense of the ways numbers are used in their everyday world. Numbers are used to describe and interpret real-world phenomena. Students need to use numbers to quantify, to identify location, to identify a specific object in a collection, to name, to measure, and to model real-world situations. They need to understand relative magnitude in order to make sense of everyday situations.

Curriculum Standards 3a

In grades 4-6 students will:

• Read and write integers and positive rational numbers.
  
  
• Represent and identify whole numbers, fractions, and decimals using physical models.
  
  
• Use physical models to represent integers and positive rational numbers.
  
  
• Explore the relationship of simple decimals to fractions.
  
  
• Explore the operations of addition, subtraction, multiplication, and division of integers using manipulatives or representational models.
  
  
• Demonstrate an understanding of denominate numbers (numbers involving units of measure, such as 3 in.) through applications to real-life situations.
  
  
• Explore the meaning of 10%, 25%, 50%, 75%, and 100% and their fraction and decimal equivalents.
  
  
• Demonstrate an understanding of prime and composite numbers.
  
  
• Identify multiples and factors of whole numbers.
  
  
• Demonstrate an understanding of the periodicity of numbers.

Proficiency Standards 3a
By the end of grade 6 students will:

• Name and identify a fraction or decimal, given a physical representation.
  
  
• Given a decimal representation in tenths or hundredths, write an equivalent fraction.
  
  
• Given an integer or a positive rational number, represent the number with the use of physical models or diagrams.
  
  
• Explain the use of numbers in various every-day contexts (for example: calendars, clocks, signs, or literature).
  
  
• Given a set of fractional models, name and write those that represent equivalent fractions.
  
  
• Given a pair of fractions, determine which is larger by using physical models or illustrations.
  
  
• Develop and use order relations for integers and positive rational numbers.
  
  
• Apply number theory to the factoring of whole numbers and the equivalency of positive rational numbers.

Broad Goal 3b
Students will understand the concepts of number operations.

Purpose: Students need to build an awareness of the properties of an operation, see relationships among operations, and acquire insight into the effects of operations on real numbers. Students need to recognize conditions in real-world situations where the use of these operations is indicated and useful.

Curriculum Standards 3b

In grades 4-6 students will:

• Develop meaning for multiplication and division of whole numbers, fractions, and decimals by modeling and discussing a rich variety of problem situations
  
  
• Demonstrate and explain the relationship among the four basic operations and, when appropriate, use the associative, commutative, and distributive properties to simplify computations
  
  
• Explore and develop the concepts of addition and subtraction of fractions and decimals using manipulatives.

Proficiency Standards 3b
By the end of grade 6 students will:

• Apply the associative, commutative, and distributive properties in a problem solving situation
  
  
• Apply the multiplicative and additive properties of zero and the multiplicative property of one
  
  
• Demonstrate an understanding of multiplication as repeated addition and of division as repeated subtraction
  
  
• Demonstrate an understanding that the product of two whole numbers greater than 1 is greater than either of the factors
  
  
• Demonstrate an understanding that when dividing two whole numbers that are greater than one, the quotient will be smaller than the dividend.

Broad Goal 3d
Students will use mental computation and estimation skills and strategies and know when it is appropriate to do so.

Purpose: Students should know what is meant by estimation and mental computation, when they are appropriate, and how close an estimate is required in a given situation. Students should be encouraged to estimate the solution of problems before computation or measurement is done, and to use estimation to determine the reasonableness of answers, and to recognize when an estimate is sufficient as an answer.

Curriculum Standards 3d

In grades 4-6 students will:

• Use a variety of mental computation techniques in appropriate situations
  
  
• Demonstrate estimation skills through a variety of strategies
  
  
• Determine the reasonableness of answers
  
  
• Recognize and use estimation and mental computation to solve problems where exact answers are not required.

Proficiency Standards 3d
By the end of grade 6 students will:

• Use estimation and mental computation to determine the reasonableness of answers obtained from the four basic operations on rational numbers
  
  
• Select and use appropriate mental computation and estimation strategies in problem situations when exact answers are not needed.

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Geometry, Measurement, and Trigonometry

Broad Goal 4a
Students will name, describe, model, classify, and compare geometric shapes and their properties with an emphasis on their wide applicability in human activity. Purpose: Geometry helps students represent and describe the world in which they live. Students need to investigate, experiment, and explore geometric properties using both technology and hands on materials.

Curriculum Standards 4a

In grades 4-6 students will:

• Explore, discuss, and describe properties of common two and three dimensional figures.
  
  
• Explore congruence and similarity of two dimensional figures.
  
  
• Investigate rotational and reflective symmetry. (Point and line symmetry.)

Proficiency Standards 4a
By the end of grade 6 students will:

• Identify, describe, and name properties of triangles, quadrilaterals, and other polygons.
  
  
• Identify point and line symmetry in given polygons.
  
  
• Measure and classify angles.
  
  
• Identify and draw congruent and similar figures using graph paper.

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Broad Goal 4b
Students will develop spatial sense.

Purpose: We live in a three dimensional world. To interpret, understand, and appreciate that world, students need to develop an understanding of space. Research suggests that there is a high correlation between spatial abilities and success in mathematics. Spatial skills include making and interpreting drawings, forming mental images, visualizing changes, and generalizing about perceptions in the environment.

Curriculum Standards 4b

In grades 4-6 students will:

• Explore transformational geometry through the use of slides, flips, and turns and the relations to tessellation's.
  
  
• Explore classification of two and three dimensional figures based upon properties.
  
  
• Enhance spatial sense using manipulatives and computer graphics.
  
  
• Explore the relationships and properties of two dimensional and three dimensional figures using manipulatives and technology.

Proficiency Standards 4b
By the end of grade 6 students will:

• Tessellate (tile) a plane with a given figure and create a figure that will tile the plane.
  
  
• Describe the shadow of certain figures.

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Broad Goal 4c
Students will develop an understanding of measurement and systems of measurement through experiences which enable them to use a variety of techniques, tools, and units of measurement to describe and analyze quantifiable phenomena.

Purpose: Measurement is used in many ways throughout our lives. Students must be introduced to the standard units of measure used in both the metric and English Systems. Students should estimate and measure length, area, capacity, volume, weight, time and temperature, as well as discover practical uses of these skills. High school students must develop more mature insights into the essential role of measurement as a link between the abstractions of mathematics and the concreteness of the real-world. By using various techniques and tools, we describe and analyze quantifiable phenomena to understand and organize our world.

Curriculum Standards 4c

In grades 4-6 students will:

• Investigate and compare standard and nonstandard units of measurement for length, area volume, capacity, weight, time, and temperature.
  
  
• Explore and discover formulas for area and volume.
  
  
• Explore estimation strategies for finding areas and volumes.
  
  
• Explore conversion of units within a measurement system and between systems.

Proficiency Standards 4c
By the end of grade 6 students will:

• Find and/or estimate the perimeter and area of a given quadrilateral or triangle.
  
  
• Demonstrate an understanding of the use of maps, scale drawings, and timelines.
  

Data Analysis, Statistics, and Probability

Broad Goal 5a
Students will use data analysis, statistics and probability to analyze given situations and the outcomes of experiments.

Purpose: Collecting, organizing, displaying, and interpreting data, as well as using the information to make decisions and predictions, have become very important in our society. Statistical instruction should be carried out in a spirit of investigation and exploration so students can answer questions about data. Probability must be studied in familiar contexts encouraging students to model situations. Students need to investigate fairness, chances of winning, and uncertainty. Technology should be used as a tool throughout the investigation process.

Curriculum Standards 5a

In grades 4-6 students will:

• Collect, organize, describe, represent, and interpret data in both simulations and real world situations.
  
  
• Simulate, display, graph, and analyze data using technology and other means.
  
  
• Investigate and explore mean, median, and mode.
  
  
• Investigate and explore the basic elements of sampling.
  
  
• Make predictions, inferences, and decisions based on interpretation of data.
  
  
• Demonstrate an ability to read and interpret statistical data presented in text.
  
  
• Explore situations involving probability.

Proficiency Standards 5a
By the end of grade 6 students will:

• Construct and interpret line plots, stem and leaf plots, frequency distributions, and graphs.
  
  
• Use multiple representations to display equivalent data.
  
  
• Select appropriate data to solve simulations and real world problems.
  
  
• Simulate, display, graph and analyze data in a variety of mediums.
  
  
• Determine and explore various uses of mean, median, and mode.
  
  
• Use sampling techniques to make predictions.
  
  
• Given a sample space find probabilities of events.