|
|
|
Web Resources Supporting the Maryland Voluntary State Curriculum
|
Mathematics - Grade 7
Algebra | Geometry | Measurement | Statistics | Probability | Number | Process |
ALGEBRA
Standard 1.0 Knowledge of Algebra, Patterns, and Functions |
| Students will algebraically represent, model, analyze, or solve mathematical or real-world problems involving patterns or functional relationships. |
Topic
A. Patterns and Functions |
Indicator
1.Identify, describe, extend, and create linear patterns and functions
Objectives
a. Complete a function table with a given two-operation rule Sample Assessments Assessment limit: Use the operations (+, -, x), numbers no more than 20 in the rule and whole numbers (0-500)
b. Identify and extend a geometric sequence
c. Describe how a change in one variable in a linear function affects the other variable in a table of values
|
Rectangle Pattern Challenges
This activity presents a growing rectangle that is colored in a particular pattern of colors. The first three stages are shown, and the students are asked to look at how the pattern grows. A range of interesting questions are posed related to the rectangle, including comparing the rates of growth of the numbers of squares of different colors and predicting numbers of each color at different stages. Students are also directed to develop recursive and closed forms for the numbers of squares of each color; the formulas are either linear or quadratic.
Introduction to Sequences
This activity introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on. |
Topic
B. Expressions, Equations, and Inequalities |
Indicator
1. Write and evaluate expressions
Objective
a. Write an algebraic expression to represent unknown quantities Assessment limit: Use one unknown and one or two operations (+, -, ×, ÷ with no remainders) with whole numbers, fractions with denominators as factors of 100, or decimals with no more than three decimal places (0-500)
b. Evaluate algebraic expressions Sample Assessments Assessment limit: Use one unknown and no more than two operations (+, -, ×, ÷ with no remainders) with whole numbers (0 – 200), fractions with denominators as factors of 100 (0 – 100), or decimals with no more than three decimal places (0 – 100)
c. Evaluate numeric expressions using the order of operations Assessment limit: Use no more than 4 operations (+, -, ×, ÷ with no remainders) with or without up to 2 sets of parentheses, brackets, or a division bar, with whole numbers (0 – 200), fractions with denominators as factors of 100 (0 – 100), or decimals with no more than three decimal places (0 – 100)
d. Simplify algebraic expressions represented as physical models by combining like terms
Indicator
2. Identify, write, solve, and apply equations and inequalities
Objectives
a. Write equations and inequalities to represent relationships Assessment limit: Use a variable, the appropriate relational symbols (>, ≥, <, ≤, =), and one or two operational symbols (+,-,×,÷) on either side and use whole numbers, fractions with denominators as factors of 100, or decimals with no more than three decimal places (0 – 500)
b. Determine the unknown in a linear equation Sample Assessments Assessment limit: Use one or two operations (+, -, ×) and the unknown only once with whole numbers (0 – 500), fractions with denominators as factors of 100 (0 – 50), or decimals with no more than three decimal places (0 – 100)
c. Solve for the unknown in an inequality Assessment limit: Use an inequality with one variable with a positive whole number coefficient and one operation (+, -, ×, ÷ with no remainders) using whole numbers or decimals with no more than 2 decimal places (0 – 500)
d. Identify or graph solutions of inequalities on a number line Assessment limit: Use whole numbers (0 – 50)
e. Apply given formulas to a problem solving situation Assessment limit: Use formulas having no more than three variables and up to two operations, with whole numbers, fractions with denominators as factors of 100, or decimals with no more than three decimal places (0 – 100)
|
Astronomical Scales
Students will understand how scaling factors can be used to make representations of astronomical distances; learn how to write and solve equations that relate real distance measurements to scaled representations of the distances; and understand how the use of scientific notation makes calculations involving large numbers easier to manage.
Lesson Tutor: A Beginning Look at Basic Algebra, Lesson 1 - Evaluating algebra expressions
By the end of this lesson the student will be able to define these terms: variable; algebraic expression; signs of operation; order of operations.
SpeedMath - Multiply and Divide
The goal of SpeedMath - Multiply and Divide is to create an equation, as quickly as possible, from the four digits that are provided by the computer. Players can use multiplication and division to create their equation, but are not allowed to rearrange the digits. Players can chose from two game types: single player to practice SpeedMath Deluxe and tournament play if they want to challenge their classmates. Single players can choose games consisting of 5, 10 or 15 questions. All tournaments are 10 questions long. Requires a JavaScript enabled web browser (Netscape Navigator 4 or Internet Explorer 4 or higher).
Order of Operations Idea Bank
The Order of Operations Idea Bank offers math activities and resources for teachers, parents, and others as suggested by teachers. This Idea Bank offers creative suggestions for teaching order of operations.
Solving Systems of Equations
This applet is used to calculate the solution set to a linear system of equations. Type in the number of equations (this should be the same as the number of unknowns) and then press "Enter Equations." A window pops up with blank text fields where you may enter the coefficients for each variable in the system of equations. The column on the right is for adding the solution values for each of the equations. This table will contain the same values as the coefficient matrix. After you have filled out each of the text fields, press "done." Finally, a new window will pop up providing that all of the fields had values entered. This window will contain the values of each of the unknowns for which the computer solved.
Understanding Equations
This is a set of interactive graphing exercises that demonstrates Linear Equations, Quadratic Equations and Third-degree Polynomials.
Formulas
This resource is an on-line interactive math quiz covering formulas: working with commonly used formulas to solve for an unknown and to isolate a designated variable.
Graphing Solutions on a Number Line
In Mastering Algebra I: Course 1, students focus on the symbols and rules of algebra and how they are used to represent relationships. They use these concepts to learn how to solve linear equations in one variable and apply these skills to solve real-life problems. Students progress through the course by graphing linear functions and linear systems, and solve the latter both graphically and algebraically. A study of linear inequalities in one and two variables parallels the study of linear equalities with an exploration of absolute value. Practice problems and interactions within every tutorial provide ample opportunities for students to master the skills and concepts presented.
Calculus: Differential Equations and Initial Value Problems
Graphs solution functions y(x) to the differential equation y'=f (x,y), with initial value given by y(x0)=y0. Java applet and accompanying HTML pages for basic exploration. Mathlets work best using Netscape Communicator version 4.75 or later. |
Topic
C. Numeric and Graphic Representations of Relationships |
Indicator
1. Locate points on a number line and in a coordinate plane
Objective
a. Represent rational numbers on a number line Sample Assessments
Assessment limit: Use rational numbers (-100 to 100)
b. Graph ordered pairs in a coordinate plane Assessment limit: Use no more than 4 ordered pairs of rational numbers (-20 to 20)
c. Graph linear equations with one operation in a coordinate plane
Indicator
2. Analyze linear relationships
Objectives
a. Identify and describe the change represented in a table of values Assessment limit: Identify increase, decrease, or no change
b. Describe the rate of change of a linear relationship by a table of values and a graph
|
Functions and the Vertical Line Test
The following discussions and activities are designed to lead the students to explore the vertical line test for functions. Plotting points and drawing simple piecewise functions are practiced along the way.
Lines, Rays, Line Segments, and Planes
This lesson is designed to introduce students to lines, rays, line segments and planes.
Graphing Solutions on a Rectangular Coordinate Plane
In Mastering Algebra I: Course 1, students focus on the symbols and rules of algebra and how they are used to represent relationships. They use these concepts to learn how to solve linear equations in one variable and apply these skills to solve real-life problems. Students progress through the course by graphing linear functions and linear systems, and solve the latter both graphically and algebraically. A study of linear inequalities in one and two variables parallels the study of linear equalities with an exploration of absolute value. Practice problems and interactions within every tutorial provide ample opportunities for students to master the skills and concepts presented. |
GEOMETRY
Standard 2.0 Knowledge of Geometry |
| Students will apply the properties of one-, two-, or three-dimensional geometric figures to describe, reason, or solve problems about shape, size, position, or motion of objects. |
Topic
A. Plane Geometric Figures |
Indicator
1. Analyze the properties of plane geometric figures
Objectives
a. Identify and describe angles formed by intersecting lines, line segments, and rays Assessment limit: Use vertical, adjacent, complementary, or supplementary angles (Include the angle symbol ∠ m)
b. Identify angles formed when two parallel lines are cut by a transversal
c. Identify the parts of right triangles
Indicator
2. Analyze geometric relationships
Objectives
a. Determine a missing angle measurement using the sum of the interior angles of polygons. Assessment limit: Use angle measures in a quadrilateral
b. Determine the measure of angles formed by intersecting lines, line segments, and rays. Assessment limit: Use vertical, adjacent, complementary, or supplementary angles
c. Describe the relationship between the legs and hypotenuse of right triangles
|
Lines, Rays, Line Segments, and Planes
This lesson is designed to introduce students to lines, rays, line segments and planes.
Web of Lines
This lesson describes a hands-on way for students to learn about lines, rays, segments, and points. Students use yarn to create a "web" of parallel and perpendicular lines.
Types of Angles
This site from Math Cove is an on-line tutorial that steps students through a number of concepts in geometry, including angle measure, types of angles, complementary and supplementary angles, and the sum of angles. The tutorial includes a collection of applets which either illustrate an idea or provide a forum for students to explore the concept. This activity might prove useful as a review for students, or a teacher might want to use the applets in a class demonstration for a particular concept.
Classifying Triangles by Sides
This course prepares students for the more formal study of mathematics in high school. Students continue their study of numbers and their operations by exploring ratios, proportions, and irrational numbers. They also begin a study of the fundamental Skills & concepts found in algebra, geometry, statistics, and probability. In each workout that follows a tutorial, students apply what they have learned to solve sets of questions at varying levels of difficulty. In this unit, students will learn to dissect a quadrilateral into sets of triangles, define a right triangle, define an isosceles triangle, and define a scalene triangle. |
Topic
C. Representation of Geometric Figures |
Indicator
1. Represent plane geometric figures
Objective
a. Construct geometric figures using a variety of construction tools Assessment limit: Construct a circle using a given line segment as the radius in whole number inches or centimeters
b. Construct geometric figures using a variety of construction tools. Assessment limit: Construct a line segment congruent to a given line segment
c. Construct geometric figures using a variety of construction tools Clarification Assessment limit: Construct a perpendicular bisector to a given line segment or a bisector of a given angle
|
Shape Tool
This Illuminations resource is an interactive shape tool applet, which can be used to create various polygons and other geometric figures such as lines and segments. Shapes can be manipulated in a variety of ways, including stretching or shrinking, rotating, or creating a mirror image. Clicking on an individual tool makes instructions appear. Illuminations java applets work best using Internet Explorer 5 or better.
What's in a Shape?
The purpose of this lesson, from Science NetLinks, is to explore characteristics of shapes by making and using tangram sets; to discover how the tangram pieces are related to one another; and to determine how many different combinations of the triangles, squares, and parallelograms in tangram sets can make a given shape. By using tangram shapes children learn the relationships between shapes, for instance, that two identical right isosceles triangles fit together to form a square. Additionally, children learn that three basic shapes - triangles, squares, and parallelograms, each composed of one or more small right triangles - can be fit together to form many other shapes and figures. One line of research on how people learn emphasizes the helpfulness of making multiple representations of the same idea and translating from one to another. When a student can begin to represent a relationship in tables, graphs, symbols, and words, one can be confident that the student has really grasped its meaning. |
Topic
D. Congruence |
Indicator
1. Apply the properties of congruent polygons
Objective
a. Determine the congruent parts of polygons Sample Assessments Assessment limit: Use the length of corresponding sides or the measure of corresponding angles and whole numbers (0 – 1000)
b. Identify and describe similar polygons and their corresponding parts
|
Congruent Triangles
This Manipulatives allows students to construct two triangles from various combinations of sides and angles. You can choose to work with any one of four different cases: SSS, SAS, ASA, SSA.
Relations and Sizes
Students will learn the concepts of congruent figures, similar figures, squares and square roots, right triangle fact and practice their mathematic skills.
|
Topic
E. Transformations |
Indicator
1. Analyze a transformation on a coordinate plane
Objectives
a. Identify, describe, and plot the results of one transformation on a coordinate plane Clarification | Seeds | Sample Assessments Assessment limit: Identify or plot the result of one translation (horizontal or vertical), reflection (horizontal or vertical), or rotation about a given point (90° or 180°)
b. Identify and describe transformations that result in rotational and reflectional symmetry |
TransmoGrapher
In this activity, students explore the world of translations, reflections, and rotations in the Cartesian coordinate system by transforming squares, triangles and parallelograms.
Perfectly Puzzling Pentominoes
Students utilize manipulatives (pentominoes) to demonstrate knowledge of: lines of symmetry, slides, reflections(flips), rotations(turns), area, and perimeter.
Symmetry Around the World
During 1999 & 2000 the students of 6B, St Kieran's, Manly Vale, Sydney, Australia worked on a collection of web pages to help others around the world explore the concepts of line symmetry and rotational symmetry in the world around us. |
MEASUREMENT
Standard 3.0 Knowledge of Measurement |
| Students will identify attributes, units, or systems of measurements or apply a variety of techniques, formulas, tools or technology for determining measurements. |
Topic
C. Applications in Measurement
|
Indicator
1.Estimate and apply measurement formulas
Objectives
a. Estimate and determine the area of quadrilaterals Seeds Assessment limit: Use parallelograms or trapezoids and whole number dimensions (0 – 1000)
b. Determine the surface area of geometric solids Seeds | Sample Assessments
Assessment limit: Use rectangular prisms with whole number dimensions (0 – 1000)
c. Estimate pi using physical models
d. Estimate and determine the volume of a triangular prism Technology
Indicator
2. Analyze measurement relationships
Objectives
a. Determine a missing dimension for a figure using a scale. Assessment limit: Use a polygon with no more than 8 sides using whole numbers (0 – 1000)
b. Determine the distance between 2 points using a drawing and a scale Sample Assessments Assessment limit: Use a scale of 1 cm=?, ¼ inch=?, or ½ inch=?, and whole numbers (0 – 1000)
|
Polygons
Students will learn polygon basics, triangles, quadrilaterals, and area of polygons and circles, and practice their mathematic skills.
Surface Area
This printable teacher sheet, from Illuminations, features equations for finding the ratios for computing the surface area of cylinders and rectangular prisms. Teachers can copy this sheet onto a transparency to use with an overhead projector.
How Does the Surface Area of a Rectangular Prism Change with its Linear Dimensions?
In this lesson, students assume that the computer inside the Personal Satellite Assistant (PSA) is in the shape of a rectangular prism. The prism must be made smaller in order to fit into a PSA with an 8-inch (20-cm)diameter. Students discover that the surface area of a rectangular prism changes as its length, width, and height change. They find that the surface area increases as you flatten the prism, and that the width of the 8-inch (20-cm) sphere in which it must fit restricts the length, width, and height of the prism. They also discover that there is more than one solution to this problem.
MATHLINE - Iditarod: Checkpoints
Students use maps and charts of the Iditarod trail in Alaska to measure to scale and calculate distances between locations. |
STATISTICS
Standard 4.0 Knowledge of Statistics |
| Students will collect, organize, display, analyze, or interpret data to make decisions or predictions. |
Topic
A. Data Displays |
Indicator
1. Organize and display data
Objectives
a. Organize and display data using back-to-back stem-and-leaf plots Clarification | Sample Assessments Assessment limit: Use no more than 20 data points using whole numbers (0–999)
b. Organize and display data to make circle graphs |
Creating Circle Graphs using Excel
Description Students evaluate data from a circle graph that compares time spent on various activities. They will use the computer to manipulate their own data as they compare, examine, create and evaluate data using circle graphs.
Stem and Leaf Plotter
Description In this activity, students view stem-and-leaf plots of their data, and then get to practice finding means, medians, and modes. |
Topic
B. Data Analysis |
Indicator
1. Analyze data
Objectives
a. Recognize and analyze faulty interpretation or representation of data Sample Assessments Assessment limit: Use the choice of graphical display or the scale as leading to faulty interpretation or representation of data
b. Determine the best choice of a data display Assessment limit: Use a given data set
c. Analyze misleading data representation
Indicator
2. Describe a set of data
Objectives
a. Analyze measures of central tendency to determine or apply mean, median, mode Sample Assessments Assessment limit: Use no more than 15 pieces of data for the mean or median; or 15 to 30 pieces of data for the mode, using whole numbers or decimals with no more than 2 decimal places (0 – 100)
|
Interpreting Data
The way data is presented can mean that it either consciously or unconsciously gives the wrong impression. The major advantage of using graphs and charts to represent data is that it gives an instant visual picture of the relationship between the variables but this picture can easily be altered by using different scales and ways of presentation.
Mission 2: Drive-Through Deceit
Dr. Eugene Wick I.D. and his associate Platypus have decided to brainwash an army of children by buying a fast food franchise - Yummy's! - and putting a subliminal message in the kids meals. As a double agent working for the Anti-Villainy Unit (AVU), the student must follow AVU orders to thwart Dr. Wick's plans for fast food domination.
Mean, Median, and Mode
Description The goal of this lesson is to introduce the concepts of mean, median and mode and to develop understanding and familiarity with these ideas. The Mean and Median Activity lets students explore mean and median in an efficient way; the Mean, Median and Mode Discussion helps them to formalize their knowledge.
Central Tendency
Description In this lab, students will collect data and find the range and three measures of central tendency (mode, median and mean). They will construct frequency tables, bar graphs, and line plots. They will use data from a small sample to make predictions about both smaller and larger samples. They will also be introduced to the graphing calculator. |
PROBABILITY
Standard 5.0 Knowledge of Probability |
| Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation. |
|
Indicator
1. Identify a sample space
Objectives
a. Determine the number of outcomes Clarification | Sample Assessments Assessment limit: Use no more than 3 independent events with a sample space of no more than 6 outcomes in each event.
|
Combinations
This unit focuses on combinations, a subject related to the probability-and-statistics strand of mathematics. Students will be encouraged to discover all the combinations for the given problem-solving skills (including elimination and collection of organized data) and drawing conclusions. The use of higher-level thinking skills (synthesis, analysis, and evaluations) is the overall goal. |
Topic
B. Theoretical Probability |
Indicator
1. Determine the probability of an event comprised of no more than 2 independent events
Objectives
a. Express the probability of an event as a fraction, a decimal, or a percent Clarification | Sample Assessments Assessment limit: Use a sample space of no more than 35 outcomes and decimals with no more than 2 decimal places
|
Random Drawing Tool
This tool, from Illuminations, allows students to explore the relationship between theoretical and experimental probabilities. Students use this "box model" as a statistical device to simulate standard probability experiments such as flipping a coin or rolling a die.
|
Topic
C. Experimental Probability |
Indicator
1. Analyze the results of a survey or simulation
Objectives
a. Make predictions and express the probability of the results as a fraction, a decimal with no more than 2 decimal places, or a percent Clarification Assessment limit: Use results of 25 or 50
Indicator
2. Conduct a probability experiment
Indicator
3. Compare outcomes of theoretical probability with the results of experimental probability
Indicator
4. Describe the difference between theoretical and experimental probability
|
Probability by Surprise
This resource, from Susan P. Holmes at Stanford University, features a collection of applets demonstrating probability. For example, in the Birthday Problem Applet, students can randomly generate a number of dates representing birthdays and track when two of the generated dates match. The other applets explore similar themes. Use this link to access the Probability by Surprise website through the Illuminations resource review for grades 6-8.
Selected Web Resources: Data Analysis and Probability / All Grades
This resource, from Illuminations, features a collection of links to their Selected Web Resources for the Data Analysis and Probability Standard for all grades. Selected Web Resources are useful online mathematics education resources--games, activities, lessons, and more--each of which has been approved by an editorial board. |
NUMBER
Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic |
| Students will describe, represent, or apply numbers or their relationships or will estimate or compute using mental strategies, paper/pencil or technology. |
Topic
A. Knowledge of Number and Place Value |
Indicator
1. Apply knowledge of rational numbers and place value
Objectives
a. Read, write, and represent whole numbers Assessment limit: Use exponential notation with bases no more than 12 and exponents no more than 3 in standard form (0 – 1000)
b. Express decimals using expanded form Assessment limit: Use decimals with no more than 4 decimal places (0 – 100)
c. Determine equivalent forms of rational numbers expressed as fractions, decimal, percents, and ratios Assessment limit: Use positive rational numbers (0 – 100)
d. Compare, order, and describe rational numbers with or without relational symbols (<, >, =) Sample Assessments Assessment limit: Use no more than 4 fractions with denominators that are factors of 300 that are less than 101 (0-100), decimals with no more than 4 decimal places (0-100), percents (0-100) or integers (-100 to 100)
e. Express whole numbers and decimals in scientific notation
|
Birthdays and the Binary System: A Magical Mixture
This lesson, from Illuminations, revolves around patterns and place value in the binary system. Students are drawn into mathematics by the "magical" ability to guess an unknown number and by the use of birthdays.
Money Bags
Students explore different combinations of coins that can be used for specified amounts of money using paper money and tree diagrams. Students write money amounts in different forms (expanded, standard, decimal).
SpeedMath - Inequalities
The goal of SpeedMath - Inequalities is to determine, as quickly as possible, if one expression is larger than, smaller than, or equal to another expression. Players can chose from two game types: single player to practice SpeedMath Deluxe and tournament play if they want to challenge their classmates. Single players can choose games consisting of 5, 10 or 15 questions. All tournaments are 10 questions long. Requires a JavaScript enabled web browser (Netscape Navigator 4 or Internet Explorer 4 or higher).
|
Topic
C. Number Computation |
Indicator
1. Analyze number relations and compute
Objectives
a. Add, subtract, multiply, and divide integers Assessment limit: Use one operation (-100 to 100)
b. Add, subtract, and multiply positive fractions and mixed numbers Assessment limit: Use no more than 2 operations and positive fractions or mixed numbers with denominators as factors of 300 less than 101 (0 – 2000)
c. Divide fractions and mixed numbers
d. Calculate powers of integers and square roots of perfect square whole numbers Sample Assessments Assessment limit: Use exponents of no more than 3 for integers (-10 to 20) or square roots of perfect square whole numbers (0–100)
e. Use the laws of exponents to simplify expressions Assessment limit: Use the rules of exponents (power times power or power divided by power) with the same whole number base (0 – 100) and exponents (0 – 10)
f. Identify and use the properties of addition and multiplication to simplify expressions Assessment limit: Use the commutative property of addition or multiplication, associative property of addition or multiplication, or the identity property for one or zero with whole numbers (0 – 100)
g. Determine percent of a number
Indicator
2. Estimation
Objectives
a. Determine approximate sums, differences, products, and quotients Assessment limit: Use no more than 3 positive rational numbers (0 – 1000)
Indicator
3. Analyze ratios, proportions, and percents
Objectives
a. Determine equivalent ratios Assessment limit: Use denominators as factors of 300 but less than 101 and whole numbers (0-100)
b. Determine and use rates, unit rates, and percents as ratios in the context of a problem Sample Assessments Assessment limit: Use whole numbers (0-1000)
c. Determine rate of increase and decrease, discounts, simple interest, commission, sales tax
d. Determine percent of a number
|
How Much Does It Cost?
In this activity from Figure This!, reviewed for grades 6-8 by Illuminations, students explore the mathematics behind calculating the actual savings on "percent-off" sales. They look at a variety of real-life situations involving percentages and discounts. Students can access hints to help figure out this challenge, and try some additional related activities. Links to a printable version of this challenge and additional related facts and web resources are included on the page. Read the full review on the Illuminations site, where you can access this resource directly.
Pascal's Triangle
This lesson, from the Shodor Education Foundation, Inc., is designed to lead students to explore the number patterns and fractal properties of Pascal's Triangle. Basic arithmetic operations of multiplication and long division are practiced in a novel way.
Evaluating & Simplifying Expressions
In Mastering Algebra I: Course 1, students focus on the symbols and rules of algebra and how they are used to represent relationships. They use these concepts to learn how to solve linear equations in one variable and apply these skills to solve real-life problems. Students progress through the course by graphing linear functions and linear systems, and solve the latter both graphically and algebraically. A study of linear inequalities in one and two variables parallels the study of linear equalities with an exploration of absolute value. Practice problems and interactions within every tutorial provide ample opportunities for students to master the skills and concepts presented.
Simplify
Enter an expression and click the Simplify button, the simplify command tries to rewrite a given expression in the 'simplest' form possible.
Square Roots
Students will learn the concept and properties of square roots. They also learn how to do operations on square roots.
Estimation
This activity introduces students to making estimations.
How Many Pearls?In this activity, students estimate the number of pearls in a treasure chest.
Scientific American Frontiers - Alien Invasion: Estimating a Snake Population
In this activity, students will estimate populations using capture/recapture statistics calculate estimated population, and critically analyze sampling techniques.
Computing Costs
Students are expected to calculate the money out of pocket needed to purchase a discounted item taxed at a certain percentage of sales tax.
What Does Percent Have to Do with It?
Confused about percentages at the mall? Students go shopping for a true real-life experience involving percent. Exposure to percent relative to sales tax and discount prices is experienced in this lesson. |
PROCESS
Standard 7.0 Process of Mathematics |
| Students demonstrate the processes of mathematics by making connections and applying reasoning to solve problems and to communicate their findings. |
Topic
A. Problem Solving |
Indicator
1. Apply a variety of concepts, processes, and skills to solve problems
Objectives
a. Identify the question in the problem
b. Decide if enough information is present to solve the problem
c. Make a plan to solve a problem
d. Apply a strategy, i.e., draw a picture, guess and check, finding a pattern, writing an equation
e. Select a strategy, i.e., draw a picture, guess and check, finding a pattern, writing an equation
f. Identify alternative ways to solve a problem
g. Show that a problem might have multiple solutions or no solution
h. Extend the solution of a problem to a new problem situation |
Selected Web Resources: Problem Solving / All Grades
This resource, from Illuminations, features a collection of links to their Selected Web Resources for the Problem Solving Standard for all grades. Selected Web Resources are useful online mathematics education resources--games, activities, lessons, and more--each of which has been approved by an editorial board.
Finding Satisfactory Solutions
The purpose of this Science NetLinks lesson is to explore the creative aspects of problem solving and practice creative problem solving strategies in the context of a story problem. In this activity, students decide where to locate ice cream stands in a town so that no one has to travel too far to buy a treat. The problem-solving strategies for this problem give students a chance to grapple with the notion of proof and to decide what makes a solution satisfactory.
|
Topic
B. Reasoning |
Indicator
1. Justify ideas or solutions with mathematical concepts or proofs
Objectives
a. Use inductive or deductive reasoning
b. Make or test generalizations
c. Support or refute mathematical statements or solutions
d. Use methods of proof, i.e., direct, indirect, paragraph, or contradiction |
Off the Scale
In this lesson, the eighth of a nine-part unit from Illuminations titled "Measuring Up: Concepts in Measurement," students use real-world examples to solve problems involving scale as they examine maps of their home states and calculate distances between cities.
A Thousand Lockers
This resource from the Math Forum, reviewed for grades 6-8 by Illuminations, provides a problem-solving activity and lesson plan. Students investigate the problem and try to discover patterns. They make a graph of their data and construct a data table. The activity provides suggestions for the use of both manipulatives and spreadsheets in solving the problem. Students gain experience in working with others,
communicating mathematics, and problem solving. |
Topic
C. Communications |
Indicator
1. Present mathematical ideas using words, symbols, visual displays, or technology
Objectives
a. Use multiple representations to express concepts or solutions
b. Express mathematical ideas orally
c. Explain mathematically ideas in written form
d. Express solutions using concrete materials
e. Express solutions using pictorial, tabular, graphical, or algebraic methods
f. Explain solutions in written form
g. Ask questions about mathematical ideas or problems
h. Give or use feedback to revise mathematical thinking |
Spreadsheet and Graphing Tool
This interactive math applet combines the features of a spreadsheet and a graphing calculator. It can be used as a general tool or customized for specific purposes. For example, see how this tool can be used to investigate rational functions in the whelk i-Math Investigation, or exponential functions in the decay of light i-Math or the trout population i-Math.
Creating Circle Graphs using Excel
Description Students evaluate data from a circle graph that compares time spent on various activities. They will use the computer to manipulate their own data as they compare, examine, create and evaluate data using circle graphs.
Graphing Solutions on a Number Line
students focus on the symbols and rules of algebra and how they are used to represent relationships. They use these concepts to learn how to solve linear equations in one variable and apply these skills to solve real-life problems. Students progress through the course by graphing linear functions and linear systems, and solve the latter both graphically and algebraically. A study of linear inequalities in one and two variables parallels the study of linear equalities with an exploration of absolute value. Practice problems and interactions within every tutorial provide ample opportunities for students to master the skills and concepts presented. |
Topic
D. Connections |
Indicator
1. Relate or apply mathematics within the discipline, to other disciplines, and to life
Objectives
a. Identify mathematical concepts in relationship to other mathematical concepts
b. Identify mathematical concepts in relationship to other disciplines
c. Identify mathematical concepts in relationship to life
d. Use the relationship among mathematical concepts to learn other mathematical concepts |
|
|
|
|
|
