ScholDistrict: Beekmantown
Building: Cumberland Head Elementary
Author: Simone Lutz, Judy Quint
Email: kmurdock@mum.neric.org
Title: Treasure MathStorm
Platform: PC
Curriculum_Area: Mathematics
Grade_Level: 1-3
Standard 3 - Mathematics (Elementary)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
* use critical thinking abilities to solve real-life math problems
Students will use Treasure MathStorm to reinforce math skills introduced during class instruction. They will create a set of four math problems for their peers to solve. Students will write and illustrate each problem on a 5 X 7 index card that will be clipped together as a set. Each card will have the answer written on the back. Students will trade sets with classmates and will be responsible for explaining the solution if necessary.
District: Cobleskill-Richmondville
Building: HS
Author: Jim Meigel
Email: meigelj@crcs.k12.ny.us
Title: Geometer's SketchPad
Platform: PC
Curriculum_Area: Math
Grade_Level: 10
NYS_Standard_Referenced
Standard 3 - Math (Commencement)
Students will understand mathematics by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Modeling/Multiple Representation
4) Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
* represent problem situations symbolically by using algebraic expressions, sequences, tree diagrams, geometric figures and graphs.
* use learning technologies to make and verify geometric conjectures.
* use graphing utilities to create and explore geometric and algebraic models.
Students use the software to test various hypotheses and geometric constructs.
District: Guilderland
Building: Altamont
Author: Beth Bini
Email: bethbini@yahoo.com
Title: Math Blaster 1
Platform: MAC
Publisher: Davidson
Curriculum_Area: math
Grade_Level: K-6
Standard 3 - Mathematics
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability and trigonometry.
Number and Numeration
2) Students use number sense and numeration to develop an understanding of the multiple use of numbers to communicate mathematically and the use of numbers in the development of mathematical ideas.
Operations
3) Operations students use math operations and relationships to understand mathematics.
* Students will use problem solving skills to analyze numbers and operation signs to make correct equations.
* Students will add, subtract, multiply, or divide whole numbers, as well as use estimation, fractions, or number patterns.
* Students will use mental math skills to sequence numbers correctly.
* Students will use problem solving strategies such as decision making, cause and effect, identifying patters and risk taking.
Students answer a series of problems, (addition, subtraction, multiplication, division, estimation, fractions or patterns) in a timed setting.
This program has very good graphics and a variety of mathematical activities for students to choose from. Lots of variations and options to reinforce and practice mathematical skills.
District: Harrisville Central School
Building: High School
Author: Steven Pike
Email:
Title: The Geometer's Sketchpad
Platform: PC
Curriculum_Area: Mathematics
Grade_Level: 7 - 9
Standard 3 - Mathematics (Intermediate)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Mathematical Reasoning
1) Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.
* explore and solve problems generated from school, home, and community situations, using concrete objects or manipulative materials where possible.
Students will use the software to create triangles, pentagons, and other polygons. They will measure all interior and exterior angles and find the sum of each for the different polygons. Students will then describe the different polygons and their characteristics in a report.
District: New Lebanon Central School
Building: Walter B. Howard Elementary School
Author: Janet Haley and Carolyn Tinger
Email: NLCSWBHE@taconic.net
Title: Number Munchers
Platform: MAC
Curriculum_Area: Mathematics
Grade_Level: 3
Standard 3 - Mathematics (Elementary)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
3) Students use mathematical operations and relationships among them to understand mathematics.
*Add, subtract, multiply, and divide whole numbers.
Students practice recognizing and identifying basic facts of addition, subtraction, multiplication and division, factors for numbers up to 99 and multiples of numbers 2 to 20.
District: New Lebanon Central School
Building: Walter B. Howard Elementary School
Author: Janet Haley and Carolyn Tinger
Email: NLCSWBHE@taconic.net
Title: Troggle Trouble Math
Platform: MAC
Curriculum_Area: Mathematics
Grade_Level: 3
Standard 3-Mathematics (Elementary)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
3) Students use mathematical operations and relationships among them to understand mathematics.
*Explore and solve problems generated from school, home and community situations, using concrete objects or manipulative materials when possible.
*Add, subtract, multiply, and divide whole numbers.
Students will practice addition, subtraction, multiplication and division of whole numbers and use these skills to solve story problems.
District: Ogdensburg City School District
Building: Lincoln/Sherman
Author: Sharon Roe, Mary Toole, Patty Winters
Email: mtoole@mum.neric.org
Title: Mega Math Blaster
Platform: PC
Curriculum_Area: Math
Grade_Level: K-4
Standard 3 - Math (Elementary)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically: by applying mathematics in real-world setting, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Number and Numeration
2) Students use number sense and numeration to develop an understanding of the multiple use of numbers to communicate mathematically, and the use of numbers in he development of mathematical ideas.
Operations
3) Students use mathematical operations and relationships among them to understand mathematics.
* Add, subtract, multiply, and divide whole numbers.
* Know single digit addition, subtraction, multiplication, and division facts.
Students answer series of addition, subtraction, multiplication and division problems in a timed setting.
District: Ogdensburg City School District
Building: Lincoln/Sherman Elementary Schools
Author: Sharon Roe, Mary Toole, Patty Winters
Email: mtoole@mum.neric.org
Title: Money Town
Platform: PC
Curriculum_Area: Math
Grade_Level: K-3
Standard 3 - Math (Elementary)
Students will understand mathematics and become mathematically confident communicating and reasoning mathematically: by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems ,geometry, algebra, data analysis, probability, and trigonometry.
Number and Numeration
2) Students use number sense and numeration to develop an understanding of the multiple use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.
* Relate counting to grouping and to place-value
* Recognize the order of whole numbers and commonly used fractions and decimals.
Using the money match, students will match money of equal amounts.
Given an amount of money, students will select coins to make appropriate change.
District: Ogdensburg City School District
Building: Lincoln Elementary, Sherman Elementary
Author: Sharon Roe, Mary L. Toole, and Patty Winters
Email: mtoole@mum.neric.org
Title: Ms. Infinity's Math Mansion
Platform: PC
Curriculum_Area: Math
Grade_Level: 2
Standard 3 - Math (Elementary)
Students will understand mathematics and become mathematically confident communicating and reasoning mathematically: by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability and trigonometry.
Mathematical Reasoning
1) Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence and construct an argument.
Patterns/Functions
7) Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics and construct generalizations that describe patterns simply and efficiently.
* Use models, facts and relationships to draw conclusions about mathematics and explain
their thinking.
* Recognize, describe, extend, and create a wide variety of patterns.
Find patterns in sequences of numbers, such as triangular numbers 1,3,6,10...
Continue simple and complex patterns.
District: Ogdensburg City School District
Building: Lincoln Elementary, Sherman Elementary
Author: Sharon Roe, Mary L. Toole, Patty Winters
Email: mtoole@mum.neric.org
Title: Sonic's Schoolhouse
Platform: PC
Curriculum_Area: Math
Grade_Level: K-4
Standard 3 - Mathematics (Elementary)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically: by applying mathematics in real-world setting, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Number and Numeration
2) Students use number sense and numeration to develop an understanding of the multiple uses numbers.
Operations
3) Students use mathematical operations and relationships among them to understand mathematics.
* Relate counting to grouping and to place value.
* Recognize the order of whole numbers.
* Add subtract, multiply and divide whole numbers.
* Know single digit addition, subtraction, multiplication and division facts.
Will successfully master addition, subtraction, multiplication and division of whole
numbers, by attempting to score a perfect ten on each lesson.
Will be able to fill in the blank in a given number sentence again while attempting to
score a perfect ten.
District: Plattsburgh City School District
Building: All
Author: Marye Howard
Email: mhoward@mum.neric.org
Title: Computer Curriculum Corporation
Platform: MAC
Curriculum_Area: MST
Grade_Level: 3-5
Standard 3 - Mathematics (Elementary)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Operations
3) Students use mathematical operations and relationships among them to understand mathematics.
* add, subtract, multiply and divide whole numbers.
* develop strategies for selecting the appropriate computational and operational method in
problem-solving situations.
* know single digit addition, subtraction, multiplication, and division facts.
* understand the commutative and associate properties.
Students will achieve a 85% Mastery of the Problem Solving course and the Mathematical Concepts and Skills Course.
District: Plattsburgh City School District
Building: All
Author: Mr. Gilles Fortin
Email: gmfortin@northnet.org
Title: TesselMania!
Platform: PC & MAC
Curriculum_Area: Mathematics
Grade_Level: 3-12
Standard 3 - Mathematics
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Patterns/Functions
7) Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.
* analyze data by making tables and graphs and looking for patterns of change.
* observe patterns of change in trends or cycles and make predictions on what might happen
in the future.
* Use sophisticated mathematical models such as graphs and equations of various algebraic
or trigonometric functions.
* recognize, describe, and generalize a wide variety of patterns and functions.
Students will create their own tessellation at appropriate age level using computer programs and vocabulary. Project must reflect understanding of principles needed for shapes to tessellate. Presentations would be completed for demonstration at Tessellation Fair.
District: Potsdam Central
Building: HS
Author: Terry Remmington
Email: tremming@potsdam.k12.ny.us
Title: KidPix
Platform: MAC
Curriculum_Area: Math
Grade_Level: 5
Standard 3 - Mathematics (Elementary)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Modeling/Multiple Representation
Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
* use concrete materials to model spatial relationships.
* construct tables, charts, and graphs to display and analyze real-world data.
* use multiple representations (simulations, manipulative materials, pictures, and
diagrams) as tools to explain the operation of everyday procedures.
Students will create a multitude of triangles of different proportions on screen and measure the angles, and reporting the results.
Students will use an actual protractor on screen to determine that no matter how a triangle is represented, the sum of all angles is 180 degrees.
District: Saranac Central School
Building: All
Author: Larry Garrow
Email: lgarrow@mum.neric.org
Title: EasyBook
Platform: MAC
Curriculum_Area: Math
Grade_Level: K
Standard 3 - Mathematics (Elementary)
Number and Numeration
Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world and the use of numbers in the development of mathematical ideas.
* use whole numbers and fractions to identify locations, quantify groups of objects, and measure distances.
Students will create a book using EasyBook - “My Book of 100 Things.” Students will stamp 10 objects on each of 10 pages to total 100 objects.
District: Saranac Central School
Building: All
Author: Larry Garrow
Email: lgarrow@mum.neric.org
Title: KidPix
Platform: MAC
Curriculum_Area: Math
Grade_Level: 6
Standard 3 - Mathematics (Intermediate)
Modeling/Multiple Representation
4) Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
* visualize, represent and transform two- and three- dimensional shapes.
Draw one two-dimensional geometric figure and show all lines of symmetry. Draw two pairs of congruent geometric shapes and label each shape.
District: Scotia-Glenville Central School District
Building: Scotia-Glenville Junior High School
Author: Fred Parker
Email: FPARKER294@AOL.COM
Title: Algebra Plotter (Josten's)
Platform: MAC
Curriculum_Area: Mathematics
Grade_Level: 7-9
Standard 3 - Mathematics (Intermediate)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Modeling/Multiple Representation
4) Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
Patterns/Functions
7) Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.
* represent numerical relationships in one and two dimensional graphs. * develop methods to solve basic linear and quadratic equations.
Students use software to graph linear and quadratic equations. Graphs can be analyzed for slope, y-intercept, and the solution of linear systems.
District: Scotia-Glenville Central School District
Building: Scotia-Glenville High School
Author: Ellen Law
Email: ejlaw@capital.net
Title: Analyzer
Platform: MAC
Curriculum_Area: Mathematics and Science
Grade_Level: 11-12
Standard 3 - Mathematics (Commencement)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Patterns and Functions
7) Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics and construct generalizations that describe patterns simply and efficiently.
* model real-world problems with systems of equations and inequalities.
* use graphing utilities to create and explore geometric and algebraic models.
Students can then use this exploration and their findings to make generalizations about the behavior of these trigonometry functions under given conditions.
Students are given a template to construct a box. The base of the box must be kept square. The length of the cut, which represents the height of the box, needs to be determined so that the box constructed will be of maximum volume. Students will determine the polynomial that models the volume of the box, use the appropriate software to graphically represent the volume, and then use features of the software to find the extreme of the function. The ordered pair will represent the cut and the corresponding maximum volume.
District: Scotia-Glenville Central Schools
Building: Scotia-Glenville Junior High School
Author: James Hartlage
Email: jmhartlage@aol.com
Title: Canvas (Deneba Software)
Platform: PC & MAC
Curriculum_Area: Technology Education
Grade_Level: 7-8
Standard 3 - Mathematics (Intermediate)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
* add, subtract, multiply, and divide fractions, decimals, and integers. (Standard 3)
* visualize, represent, and transform two-and three-dimensional shapes. (Standard 3)
* develop measurement skills and informally derive and apply formulas in direct measurement activities. (Standard 3)
Students will: investigate commercially produced cereal boxes and identify how the five elements of design (balance, proportion, contrast, tie between elements, and rhythm) were used.
Students will use paper and colored pencils to generate alternatives and a final solution which incorporporate the five elements of design.
Students will use drafting tools to create a development on heavy card stock - - this will be cut out, folded, and glued to form a box.
Students will reproduce their final solution on the computer using CANVAS.
Students will attach print-out to their box.
Students will evaluate their solution using the five elements of design as a criterion.
Author: Sherry McGaughan
Email: jkavanau@aol.com
Title: The Geometer's Sketchpad
Platform: MAC
Curriculum_Area: Mathematics
Grade_Level: 7
Standard 3 - Mathematics (Intermediate)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Modeling/Multiple Representation
4) Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
Measurement
5) Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.
* use appropriate tools to construct and verify geometric relationships.
* develop measurement skills and informally derive and apply formulas in direct measurement activities.
Students will identify parts of a circle. Students will examine relationship between the measure of a central angle and its intercepted arc.
Students will state the relationship between the radius and diameter of a circle.
District: Scotia-Glenville Central School District
Building: Scotia-Glenville High School
Author: Joseph Kavanaugh
Email: jkavanau@aol.com
Title: The Geometer's Sketchpad
Platform: MAC
Curriculum_Area: Mathematics
Grade_Level: 9-12
Standard 3 - Mathematics (Intermediate)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Mathematical Reasoning
1) Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.
* make and evaluate conjectures and arguments using appropriate language
* make conclusions based on inductive reasoning.
Students will create a triangle and measure each of the interior angles. They will then transform the triangles and the angle measures will change. The students will observe their examples and conclude that in each case, the sum of the interior angles of the triangle is 180 degrees.
District: Scotia-Glenville Central School District
Building: Scotia-Glenville High School
Author: Ellen Law
Email: ejlaw@capital.net
Title: Mac Numerics
Platform: MAC
Curriculum_Area: Math, Science
Grade_Level: 11-12
Standard 3 - Mathematics (Commencement)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Modeling/Multiple Representation
4) Students use mathematical/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
Patterns/Functions
7) Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and effectively.
* use graphing utilities to create and explore geometric and algebraic models.
* use computers and graphing calculators to analyze mathematical phenomena
Students will, given the basic definitions and formulas for the conic sections, use MacNumeric to study the effect of changing the lead coefficients on the conics. Students can then use this exploration and their findings to make generalizations about the findings to make generalizations about the behavior of the conics under given conditions.
Students will, given the basic definitions and formulas for the sine and cosine functions (y=As in(Bx+C) and y=Acos(Bx+C) students use MacNumerics to study the effect of changing the coefficients on the functions.
District: Scotia-Glenville Central School District
Building: Scotia-Glenville Junior High
Author: Richard Putorti
Email: songman@concentric.net
Title: Music Time
Platform: MAC
Curriculum_Area: Math, Science, Technology
Grade_Level: 8
Standard 3 - Mathematics (Intermediate)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Numbers and Numeration
2) Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.
* understand, represent, and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, expanded and scientific notation.)
* add, subtract, multiply, and divide fractions, decimals, and integers.
* demonstrate an understanding of operational algorithms (procedures for adding, subtracting, etc.).
* develop appropriate proficiency with facts and algorithms.
Students will apply their knowledge of fractions to music as they complete incomplete measures, correct incorrect measures and compose music using Music Time.
District: Scotia-Glenville Central School District
Building: Scotia-Glenville Junior High
Author: Richard Putorti
Email: songman@concentric.net
Title: True Basic
Platform: MAC
Curriculum_Area: Math, Science, Technology
Grade_Level: 8
Standard 3 - Mathematics (Intermediate)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Operations
3) Students use mathematical operations and relationships among them to understand mathematics.
* understand, represent, and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, expanded and scientific notation.)
* develop an understanding of number theory (primes, factors, and multiples.)
* add, subtract, multiply, and divide fractions, decimals, and integers.
* use grouping symbols (parentheses) to clarify the intended order of operations.
* demonstrate an understanding of operational algorithms (procedures for adding, subtracting, etc.).
* develop appropriate proficiency with facts and algorithms.
Students will communicate mathematics by translating mathematical expressions into BASIC expressions. They will compare paper and pencil answers with programmed answers and discuss discrepancies.
District: Ticonderoga Central School
Building: Elementary
Author: Robert Porter
Email: rporter@mum.neric.org
Title: Computer Curriculum Corporation Math
Concepts and Skills
Platform: MAC
Curriculum_Area: Math, Technology
Grade_Level: K-8
Standard 3 - Mathematics (Elementary)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Mathematical Reasoning
1) Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.
Number and Numeration
2) Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.
Operations
3) Students use mathematical operations and relationships among them to understand mathematics.
Modeling/Multiple Representation
4) Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
Measurement
5) Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.
Uncertainty
6) Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations.
Patterns/Functions
Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.
* use models, facts, and relationships to draw conclusions about mathematics and explain their thinking.
* use patterns and relationships to analyze mathematical situations.
* justify their answers and solution processes.
* use logical reasoning to reach simple conclusions.
* use whole numbers and fractions to identify locations, quantify groups of objects, and measure distances.
* use concrete materials to model numbers and number relationships for whole numbers and common fractions, including decimal fractions.
* relate counting to grouping and to place-value.
* recognize the order of whole numbers and commonly used fractions and decimals.
* demonstrate the concept of percent through problems related to actual situations.
* add, subtract, multiply, and divide whole numbers.
* develop strategies for selecting the appropriate computational and operational method in problem solving situations.
* know single digit addition, subtraction, multiplication, and division facts.
* understand the commutative and associative properties.
* use concrete materials to model spatial relationships.
* construct tables, charts, and graphs to display and analyze real-world data.
* use multiple representations (simulations, manipulative materials, pictures and diagrams) as tools to explain the operation of everyday procedures.
* use variables such as height, weight, and hand size to predict changes over time.
* use physical materials, pictures, and diagrams to explain mathematical ideas and processes and to demonstrate geometric concepts.
* understand that measurement is approximate, never exact.
* select appropriate standard and nonstandard measurement tools in measurement activities.
* understand the attributes of area, length, capacity, weight, volume, time, temperature, and angle.
* estimate and find measures such as length, perimeter, area, and volume using both nonstandard and standard units.
* collect and display data.
* use statistical methods such as graphs, tables, and charts to interpret data.
* make estimates to compare to actual results of both formal and informal measurement.
* make estimates to compare to actual results of computations.
* recognize situations where only an estimate is required.
* develop a wide variety of estimation skills and strategies.
* determine the reasonableness of results.
* predict experimental probabilities.
* make predictions using unbiased random samples.
* determine probabilities of simple events.
* recognize, describe, extend, and create a wide variety of patterns.
* represent and describe mathematical relationships.
* explore and express relationships using variables and open sentences.
* solve for an unknown using manipulative materials.
* use a variety of manipulative materials and technologies to explore patterns.
* interpret graphs.
* explore and develop relationships among two and three dimensional geometric shapes.
* discover patterns in nature, art, music, and literature.
* use a variety of equipment and software packages to enter, process, display, and communicate information in different forms using text, tables, pictures, and sound.
* describe the uses of information systems in homes, schools, and businesses.
* understand that computers are used to store personal information.
* demonstrate ability to evaluate information.
* use the computer as a tool for generating and drawing ideas.
* use special mathematical notation and symbolism to communicate in mathematics and to compare and describe quantities, express relationships, and relate mathematics to their immediate environments.
* use simple logical reasoning to develop conclusions, recognizing that patterns and relationships present in the environment assist them in reaching these conclusions.
This is evident, for example when students:
—think algebraically using addition, multiplication, number concepts, equation problem solving strategies, subtraction, and word problems. These concepts will be applied by students building geometric figures using the mouse. The figures the students create will show similarity and congruency.
—Find patterns in sequences of numbers.
—Explore numbers with a computer’s calculator to show relationships.
—Number lines will be displayed where students will shade in portions to build and understand fractions and their relationship to decimals.
—Explore the relationship between bar graphs and circle graphs and then create their own using a given set of data.
—Solve multiple step problems that are designed for students to visualize answers with out pencil and paper.
—Use estimation to show height and width using non-standard means of measurement such as paper clips or a persons height.
—calculate perimeter, width, length, area of a fence around a house.
—make predictions using a bag of colored marbles or a spinner.
District: Ticonderoga Central School
Building: Elementary
Author: Robert Porter
Email: rporter@mum.neric.org
Title: Computer Curriculum Corporation Math
Investigations
Platform: MAC
Curriculum_Area: Math Technology
Grade_Level: 6-8
Standard 3 - Mathematics (Intermediate)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Mathematical Reasoning
1) Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.
Number and Numeration
2) Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.
Operations
3) Students use mathematical operations and relationships among them to understand mathematics.
Modeling/Multiple Representation
4) Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
Measurement
5) Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.
Uncertainty
6) Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations.
Patterns/Functions
Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.
* apply a variety of reasoning strategies.
* make and evaluate conjectures and arguments using appropriate language.
* make conclusions based on inductive reasoning.
* justify conclusions involving simple and compound (i.e., and/or) statements.
* understand, represent, and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, expanded and scientific notation).
* understand and apply ratios, proportions, and percents through a wide variety of hands-on explorations.
* develop an understanding of number theory (primes, factors, and multiples).
* recognize order relations for decimals, integers, and rational numbers.
* add, subtract, multiply, and divide fractions, decimals, and integers.
* use grouping symbols (parentheses) to clarify the intended order of operations.
* apply the associative, commutative, distributive, inverse, and identity properties.
* demonstrate an understanding of operational algorithms (procedures for adding, subtracting, etc.).
* develop appropriate proficiency with facts and algorithms.
* apply concepts of ratio and proportion to solve problems.
* visualize, represent, and transform two and three dimensional shapes.
* use maps and scale drawings to represent real objects or places.
* use the coordinate plane to explore geometric ideas.
* represent numerical relationships in one and two dimensional graphs.
* use variables to represent relationships.
* use concrete materials and diagrams to describe the operation of real world processes and systems.
* develop and explore models that do and do not rely on chance.
* investigate both two and three dimensional transformations.
* use appropriate tools to construct and verify geometric relationships.
* develop procedures for basic geometric constructions.
* estimate, make, and use measurements in real-world situations.
* select appropriate standard and nonstandard measurement units and tools to measure to a desired degree of accuracy.
* develop measurement skills and informally derive and apply formulas in direct measurement activities.
* use statistical methods and measures of central tendencies to display, describe, and compare data.
* explore and produce graphic representations of data using calculators/computers.
* develop critical judgment for the reasonableness of measurement.
* use estimation to check the reasonableness of results obtained by computation, algorithms, or the use of technology.
* use estimation to solve problems for which exact answers are inappropriate.
* estimate the probability of events.
* use simulation techniques to estimate probabilities.
* determine probabilities of independent and mutually exclusive events.
* recognize, describe, and generalize a wide variety of patterns and functions.
* describe and represent patterns and functional relationships using tables, charts and graphs, algebraic expressions, rules, and verbal descriptions.
* develop methods to solve basic linear and quadratic equations.
* develop and understanding of functions and functional relationships: that a change in one quantity (variable) results in change in another.
* verify results of substituting variables.
This is evident, for example, when students:
Use problem solving in real world applications, geometry; measurement, problem solving strategies, and word problems, work with mystery numbers and age problems, number systems, time, rate and distance.
Use on-line math tools to solve problems to apply technology in mathematics problem solving.
Understand, represent and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, expanded, and scientific, notation).
Understand and apply ratios, proportions, and percents.
Develop and understanding of number theory (primes, fractors, and multiples).
Use grouping symbols (parentheses) to clarify the intended order of operations.
District: Voorheesville
Building: Elementary
Author: Kim Greiner
Email: kgreiner@mail.neric.org
Title: Clock
Platform: PC
Curriculum_Area: Mathematics
Grade_Level: 1-4
Standard 3 - Mathematics (Elementary)
Measurement
5) Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.
* understand that measurement is approximate, never exact
* select appropriate standard and nonstandard measurement tools in measurement activities
* understand the attributes of area, length, capacity, weight, volume, time, temperature, and angle
* estimate and find measures such as length, perimeter, area, and volume using both nonstandard and standard units
* collect and display data
* use statistical methods such as graphs, tables, charts to interpret data
Students will use the manipulative clocks, both digital and analog, to set the times as assigned by the teacher, another student, activity cards or the software. They will create problems about real-world events, such as train schedules. They will use the software to practice these skills and get ideas for their own problems.
District: Voorheesville
Building: Elementary
Author: Kim Greiner
Email: kgreiner@mail.neric.org
Title: Exploring Math with Manipulatives II
Platform: PC
Curriculum_Area: Mathematics
Grade_Level: 2-4
Standard 3 - Mathematics (Elementary)
Patterns and Functions
7) Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.
* recognize, describe, extend, and create a wide variety of patterns
* represent and describe mathematical relationships
* explore and express relationships using variables and open sentences
* solve for an unknown using manipulative materials
* use a variety of manipulative materials and technologies to explore patterns
* interpret graphs
* explore and develop relationships among two- and three-dimensional geometric shapes
* discover patterns in nature, art, music, and literature
Students will use colored tiles (pattern blocks) to create a geometric design from a picture of a real-world object. They will trace the outside of the figure. Another student will then re-create the design with the computer software with at least two solutions.
District: Voorheesville
Building: Elementary
Author: Kim Greiner
Email: kgreiner@mail.neric.org
Title: Math Practice I
Platform: PC
Curriculum_Area: Mathematics
Grade_Level: 1-2
Standard 3- Mathematics (Elementary)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Operations
3) Students use mathematical operations and relationships among them to understand mathematics.
* add, subtract, multiply, and divide whole numbers
* develop strategies for selecting the appropriate computational and operational method in problem solving situations
* know single digit addition, subtraction, multiplication, and division facts
* understand the commutative and associative properties
Students will use concrete objects to solve subtraction problems. They will each present a solution, to a problem they created from a "real-world" situation, orally to the class by demonstrating the "take away" process to justify their solution.
District: Voorheesville
Building: Elementary
Author: Kim Greiner
Email: kgreiner@mail.neric.org
Title: Measurement, Time & Money III
Platform: PC
Curriculum_Area: Mathematics
Grade_Level: 4-6
Standard 3 - Mathematics (Elementary)
Mathematics
1) Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.
4) Students use mathematical modeling/ multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
* use models, facts, and relationships to draw conclusions about mathematics and explain their thinking
* use patterns and relationships to analyze mathematical situations
* justify their answers and solution processes
* use logical reasoning to reach simple solutions
* use concrete tables, charts, and graphs to display and analyze real-world data
* use multiple representations as tools to explain the operation of everyday procedures
* use variable such as height, weight, and hand size to predict changes over time
* use physical materials, picture, and diagrams to explain mathematical ideas and processes and to demonstrate geometric concepts
Students will choose a topic of interest or concern in the community. They will design a survey or monitor a phenomenon. They will gather data and organize it in a chart. They will choose an appropriate type of graph to display their data. They will write letters to community officials to persuade them to modify the situation. They will use their data and graphs to support their position.
District: Watervliet School District
Building: Elementary
Author: Sue Heid, Christine Sheridan, Jean Dowling
Email: jdowling@mum.neric.org
Title: Base Ten Blocks
Platform: MAC
Curriculum_Area: Mathematics
Grade_Level: 4-5
Standard 3 - Mathematics (Elementary)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Operations
3) Students use mathematical operations and relationships among them to understand mathematics.
* add, subtract, multiply, and divide whole numbers.
* develop strategies for selecting the appropriate computational and operational method in problem-solving situations.
Reinforce student understanding of numbers, patterns and abstract number concepts and operations.
District: Watervliet School District
Building: Elementary
Author: Susan Heid, Christine Sheridan, Jean Dowling
Email: jdowling@mum.neric.org
Title: Math Shop
Platform: MAC
Curriculum_Area: Math
Grade_Level: 4-6
Standard 3 - Mathematics (Elementary)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Number and Numeration
2) Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.
* use whole numbers and fractions to identify locations, quantity groups of objects, and measure distances.
* demonstrate the concept of percent through problems related to actual situations.
Students will use a newspaper advertisement that gives prices and identify the smallest bill they could use to buy an item. Then students will calculate the change they would get.
Students will use a recipe book to change the proportions of some of the ingredients by increasing or reducing the number of servings (i.e. 8 people require - 1 cup of sugar ; 12 people 1 1/2 cups, 16 people 2 cup, etc.)
Students will use a tape measure to determine differences between length of certain objects in the classroom.
Students will conduct a survey and create a circle graph using data gathered. Students will create a pie chart using the results of the number of times they flipped a coin and record heads/tails.