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Web Resources Supporting the Maryland Voluntary State Curriculum
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Mathematics - Grade 8
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 patterns, functions and sequences
Objectives
a. Determine the recursive relationship of arithmetic sequences represented in words, in a table or in a graph
Assessment limit: Provide the nth term no more than 10 terms beyond the last given term using common differences no more than 10 with integers (-100 to 5000)
b. Determine the recursive relationship of geometric sequences represented in words, in a table, or in a graph
Clarification | Seeds | Sample Assessments Assessment limit: Provide the nth term no more than 5 terms beyond the last given term using the recursive relationship of geometric sequences with whole numbers and a common ratio of no more than 5:1 (0 – 10,000)
c. Determine whether relationships are linear or nonlinear when represented in words, in a table, symbolically, or in a graph
Assessment limit: Use a graph to determine if a relationsip is linear or nonlinear
d. Determine whether relationships are linear or nonlinear when represented symbolically
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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.
Geometric Sequence
Students will learn the geometric sequence and find the sum of an geometric sequence.
Exploring Linear Functions: Representational Relationships
Technology allows the linking of multiple representations of mathematical situations and the exploration of the relationships that emerge. This example presents a series of explorations based on two linked representations of linear functions. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.
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Topic
B. Expressions, Equations, and Inequalities |
Indicator
1. Write, simplify, and evaluate expressions
Objective
a. Write an algebraic expression to represent unknown quantities Assessment limit: Use one unknown and no more than 3 operations and rational numbers (-1000 to 1000)
b.Evaluate an algebraic expression Assessment limit: Use one or two unknowns and up to three operations and rational numbers (-100 to 100)
c. Evaluate numeric expressions using the order of operations Assessment limit: Use no more than 5 operations including exponents of no more than 3 and 2 sets of parentheses, brackets, a division bar, or absolute value with rational numbers (-100 to 100)
d. Simplify algebraic expressions by combining like terms Sample Assessments Assessment limit: Use no more than 3 variables with integers (-50 to 50), or proper fractions with denominators as factors of 20 (-20 to 20)
e. Describe a real-world situation represented by an algebraic expression
Indicator
2. Identify, write, solve, and apply equations and inequalities
Objectives
a. Write equations or inequalities to represent relationships Thinking skills Assessment limit: Use a variable, the appropriate relational symbols (>, ≥, <, ≤, and no more than 3 operational symbols (+, -, ×, ÷) on either side and rational numbers (-1000 to 1000)
b. Solve for the unknown in a linear equation Thinking Skills Assessment limit: Use one unknown no more than 3 times on one side and up to three operations (same or different but only one division) and rational numbers (-2000 to 2000)
c. Solve for the unknown in an inequality
Assessment limit: Use a one- or two-operation inequality with one variable on one side no more than 3 times whose result after combining coefficients is a positive whole number coefficient with integers (-100 to 100)
d. Identify or graph solutions of inequalities on a number line Assessment limit: Use one variable once with a positive whole number coefficient and integers (-100 to 100)
e. Identify equivalent equations Assessment limit: Use one unknown no more than 3 times on one side and up to three operations (same or different but only one division) and integers (-2000 to 2000)
f. Apply given formulas to a problem-solving situation Assessment limit: Use no more than four variables and up to three operations with rational numbers (-500 to 500)
g. Write equations and inequalities that describe real-world problems
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Using Variables to Express Relationships
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 choose variables to represent each of the unknown quantities in a problem, use algebraic expressions to show the relationship between variables, and substitute one variable for another and writing an equation containing only one variable term.
Like Terms
This lesson will show how to distinguish algebraic terms. Like terms can be combined by adding or subracting the coefficients of each term...the variables themselves do not change.
Simplifying Algebraic Expressions
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 simplify one side of an equation using the distributive property of multiplication over addition and following the order of operations, combine like terms, and investigate the elements of an algebraic expression.
Combining Like Terms
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 apply the commutative property of multiplication, apply the distributive property of multiplication over addition, simplify expressions by combining like terms, simplify expressions by using the order of operations.
Solving Inequalities
Student will solve and graph inequalities and absolute values.
Graphing Inequalities
This is an activity I use when I need to get my students into groups of two and review inequalties and perpendicular slopes.
Graphing Equations and Inequalities
Students will learn the concepts of the coordinate plane, slope and y-intercept, and graphing linear equations.
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Topic
C. Numeric and Graphic Representations of Relationships |
Indicator
1. Locate points on a number line and in a coordinate plane
Objective
a. Graph linear equations in a coordinate plane
Assessment limit: Use two unknowns having integer coefficients (-9 to 9) and integer constants (-20 to 20)
Indicator
2. Analyze linear relationships
Objectives
a. Determine the slope of a graph in a linear relationship Clarification | Sample Assessments Assessment limit: Use an equation with integer coefficients (-9 to 9) and integer constants (-20 to 20) and a given graph of the relationship
b. Determine the slope of a linear relationship represented numerically or algebraically
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Solving Absolute Value Equations
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.
Exploring the Point — Slope Equation of a 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. |
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 geometric relationships between angles formed when parallel lines are cut by a transversal. Assessment limit: Use alternate interior, alternate exterior, or corresponding angles
b. Identify and describe the relationship among the parts of a right triangle Assessment limit: Use the hypotenuse or the legs of right triangles
Indicator
2. Analyze geometric relationships
Objectives
a.Determine the measurements of angles formed by parallel lines cut by a transversal Assessment limit: Use alternate interior, alternate exterior, and corresponding angles
b.Apply right angle concepts to solve real-world problems Sample Assessments Assessment limit: Use the Pythagorean Theorem
c. Determine whether three given side lengths form a right triangle
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Fun with Angles
This lesson plan will help the students visualize the different angles (corresponding, alternate interior, and same-side interior) when coplanar lines are cut by a transversal.
Noodles Away
This lesson will assist students to see angle relationships and the relationship of parallel lines and transversals. This exercise is good for visual and tactile learners, since it is of a concrete nature. Students of all academic levels can enjoy this.
Geometry Rules! (Symmetry of Polyhedra)
The great diversity of models that can be constructed with Polymorf panels is due in large part to the relationship of the legs to the hypotenuse of the right triangle. In the most general form this is expressed by the Pythagorean theorem. What this means is that the area of a square with an edge length equal to the hypotenuse of a right triangle is equal to the sum of the areas of two squares whose edge lengths are equal to the length of each leg. The design of the Polymorf panels is based on a special case of this, the isosceles right triangle, where both legs are equal in length. This family of shapes can be used to model some important structural types that constantly recur in natural and man-made systems. This is demonstrated through the lessons in this resource. |
Topic
C. Representation of Geometric Figures |
Indicator
1. Represent plane geometric figures
Objective
a. Draw quadrilaterals Assessment limit: Provide given whole number dimensions in inches or centimeters or angle measurements
b. Construct perpendicular line segments Assessment limit: Provide a given point on a given line segment
c. Construct triangles Clarification Assessment limit: Construct a triangle congruent to a given triangle
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Quadrilaterals
This lesson is designed to introduce students to quadrilaterals. Included in this lesson are discussions of parallelograms, rectangles, and trapezoids.
Quadrilateral Relations
Students are asked to show diagrammatically how the various quadrilaterals are related. This is a nifty little activity.
A Perpendicular Pilgrimage
Students examine the concept of perpendicularity both geometrically and algebraically. Students apply their knowledge by designing safe passage through a two-dimensional obstacle course using only perpendicular line segments. |
Topic
D. Congruence |
Indicator
1. Apply the properties of similar polygons
Objective
a. Determine similar parts of polygons Thinking Skills | Sample Assessments Assessment limit: Use the length of corresponding sides or the measure of corresponding angles and rational numbers with no more than 2 decimal places (0 – 1000)
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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.
Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures
The interactive figures in this four-part example allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations. |
Topic
E. Transformations |
Indicator
1. Analyze a transformation on a coordinate plane
Objectives
a. Identify, describe, and plot the results of multiple transformations on a coordinate plane Seeds | Sample Assessments Assessment limit: Identify or plot the result of two transformations on one figure using translations (horizontal or vertical), reflections (horizontal or vertical), or rotations about a given point (90° or 180°) |
Congruent Cafe
Congruency, Math Standard 1B, 4H - Modeling/Multiple Representation - Students investigate both two- and three-dimensional transformations. This is a play for three actors (or groups) and chorus in about 3 lessons (or more) based on work with pattern blocks.
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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
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Indicator
1.Estimate and apply measurement formulas
Objectives
a. Estimate and determine the circumference or area of a circle Assessment limit: Include circles using rational numbers with no more than 2 decimal places (0 – 10,000)
b. Estimate and determine area of a composite figure Sample Assessments
Assessment limit: Include composite figures with no more than 6 polygons (triangles, rectangles, or circles) by measuring, partitioning, or using formulas with whole number dimensions (0 - 10,000)
c. Estimate and determine the volume of a cylinder
Assessment limit: Use cylinders, given the formula, and whole number dimensions (0-10,000)
d. Determine the volume of cones, pyramids, and spheres
e. Determine the surface area of cylinders, prisms, and pyramids
Indicator
2. Analyze measurement relationships
Objectives
a. Use proportional reasoning to solve measurement problems Clarification | Seeds | Sample Assessments Assessment limit: Use proportions, scale drawings with scales as whole numbers, or rates using whole numbers or decimals (0 – 1000)
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Comparison of circles and their areas-problem centered
This is a problem centered lesson that will help the student compare the circumference and area of circles that will fit into a fixed square. As the number of equally sized circles that fill the square changes, how does the total area of the circles change? How does the sum of the circumferences change?
Circle Fun
Students will label the parts of a circle as a review. they will then complete a chart on finding circumference and area of circles. When they finish their chart, students will create their own circumference and area tests.
Fill It Up!
Estimation is the focus of this Figure This! activity, reviewed for grades 6-8 by Illuminations. The question is to estimate which cylinder will hold the most popcorn. The two cylinders are each made from an 8 ½ by 11 sheet of paper. Each cylinder is made with one side of the sheet, so that one cylinder is tall and skinny and the other cylinder is short and round. The "Answer" section shows two ways of determining the answer. One way to determine the answer is by actually making the cylinders and filling them up with popcorn to see which has the most popcorn. The other way is to calculate the volume of each cylinder to see which has the largest volume. The formula for volume is given. In the "Try These" and "Think About This" section, some interesting and challenging questions are asked that could be good discussion questions on estimation, or you just might want to use the problem during your class! The site is a bit slow at times, so be patient. |
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 to make circle graphs Sample Assessments Assessment limit: Use no more than 5 categories with data in whole number percents
b. Organize and display data to make box-and-whisker plots Assessment limit: Use no more than 12 pieces of data and whole numbers (0 – 1000)
c. Organize and display data to make a scatter plot Assessment limit: Use no more than 10 points and whole numbers (0 – 1000) |
Human Box and Whisker Plot
Students will learn how to construct box and whisker plots as they actively participate in being a part of one based upon their heights. As an extension of the lesson, students will learn how to interpret a graph of this type.
Scatterplot
A scatterplot can be used to visually represent the relationship between two variables. Using this virtual Manipulatives students can add data points, view graph information, move a data point, delete a data point, change the display region, and clear the graph.
Simple Plot
Students can plot ordered pairs of numbers, either as a scatter plot or with the dots connected. |
Topic
B. Data Analysis |
Indicator
1. Analyze data
Objectives
a. Interpret tables Assessment limit: Use no more than 5 categories having no more than 2 quantities per category and whole numbers or decimals with no more than 2 decimal places (0 – 100)
b. Interpret box-and-whisker plots Thinking Skills | Sample Assessments Assessment limit: Use minimum, first (lower) quartile, median (middle quartile), third (upper) quartile, or maximum and whole numbers (0 – 100)
c. Interpret scatter plots Thinking Skills Assessment limit: Use no more than 10 points using whole numbers or decimals with no more than 2 decimal places (0 – 100)
d. Interpret circle graphs Assessment limit: Use no more than 8 categories (0 – 1000)
e. Analyze multiple box-and-whisker plots using the same scale
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Data Analysis: Interpreting Tables and Graphs
In this unit, students learn how to create and analyze mathematical data, and chart this data on graphs. Additionally, students write both friendly and business letters in the context of a local business.
Usage and Interpretation of Graphs
In this lesson, students will receive a review on graphs. It also involves problem solving and prediction, and will require the student to use his/her processing skills. The lesson will also demonstrate to the student how useful graphs are, and that graphs can summarize.
What's in a Graph?
The purpose of this lesson is to help students learn how to use and interpret graphs. The graphs will be pulled from a variety of sources, and the activities ask the students to interpret graphs. The students need to start this lesson with the knowledge of what a graph is. They should also know how to observe and collect data. |
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. |
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Indicator
1. Identify a sample space
Objectives
a. Describe the difference between independent and dependent events
b. Determine the number of outcomes Sample Assessments Assessment limit: Use no more than 5 dependent events with no more than 10 outcomes in the first event
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Unders and Overs
Students have to place bets on one of three outcomes - Under 7, Seven, or Over 7. Two dice are tossed and the numbers added. If Unders or Overs wins, the payout is even money. If Seven wins, the payout is 4 to 1. Students are asked to analyse this game to determine which is the best bet.
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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
Sample Assessments Assessment limit: Use a sample space of 36 to 60 outcomes
Indicator
2. Determine the probability of a second event that is dependent on a first event of equally likely outcomes
Objectives
a. Express the probability as a fraction, a decimal, or a percent Clarification | Sample Assessment Assessment limit: Use a sample space of no more than 60 outcomes
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Probability Spaces
This site provides students interactive, web-based resources of probability theory. Some important contents such as random experiments, sets and events, functions and random variables, probability measures, conditional probability, independence, and convergence are introduced. Requires Microsoft Windows with Internet Explorer (version 6.0 or later), with the MathPlayer plug-in (version 2.0b or later), and the Java plug-in (version 1.5 or later).
Probability Equations
A collection of four probability equations ranging from simple probability to binomial distribution. The student reads the problem, observes the formula used to solve the problem and then clicks to see the complete solution explained. Requires Microsoft Windows with Internet Explorer (version 6.0 or later), with the MathPlayer plug-in (version 2.0b or later), and the Java plug-in (version 1.5 or later). |
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 | Sample Assessments Assessment limit: Use 20 to 500 results
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
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Spinning Nickels
Students will make predictions to figure out the probability of a spun nickel landing on either heads or tails. Students will then test their predictions through experimentation.
Plinko! Probability from a TV Game
Plinko is the most popular game of chance on the TV game show The Price is Right. This demo uses Plinko to illustrate how mathematics is useful for predicting a strategy that gives the highest probability for a big win.
Sabermetrics
Sabermetrics, on the Baseball Archive website, contains information about this branch of statistics that is devoted to answering objective questions about baseball and making predictions based on probability. It includes background information, reports on actual studies, and software tools that can be downloaded. This page is featured in the Science NetLinks lesson, Baseball Stats. |
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 rational numbers Sample Assessments Assessment limit: Use exponential notation or scientific notation from (-10,000 to 1,000,000,000)
b. Compare, order, and describe rational numbers with and without relational symbols (<, >, =) Assessment limit: Use no more than 4 integers(-100 to 100) or positive rational numbers (0–100) using equivalent forms or absolute value
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Order in the Classroom
Students define and identify integers, rational, irrational, real, and complex numbers. They find examples of each and write them on note cards. They work in small groups to put each card in ascending or descending order.
Scientific Notation
This resource is an on-line interactive math quiz covering scientific notation: converting between standard and scientific notation, performing operations, significant digits, and applications.
MATHLINE - Language and Literature: How Big Is It?
Using the children's story "Is a Blue Whale the Biggest Thing There Is?" by Robert E. Wells, students will learn to: --Develop an understanding of large numbers, including benchmarks to comprehend their magnitude --Recognize, understand, and appropriately use various representations for large numbers (e.g., exponential, scientific, and calculator notation) |
Topic
C. Number Computation |
Indicator
1. Analyze number relations and compute
Objectives
a. Add, subtract, multiply and divide integers Assessment limit: Use one operation (-1000 to 1000)
b. Calculate powers of integers and square roots of perfect square whole numbers Assessment limit: Use powers with bases no more than 12 and exponents no more than 3, or square roots of perfect squares no more than 144
c. Identify and use the laws of exponents to simplify expressions Assessment limit: Use the rules of power times power or power divided by power with the same integer as a base (-20 to 20) and exponents (0-10)
d. Use properties of addition and multiplication to simplify expressions Assessment limit: Use the commutative property of addition or multiplication, associative property of addition or multiplication, additive inverse property, the distributive property, or the identity property for one or zero with integers (-100 to 100)
Indicator
2. Estimation
Objectives
a. Estimate the square roots of whole numbers Assessment limit: Use whole numbers (0 – 100)
Indicator
3. Analyze ratios, proportions, and percents
Objectives
a. Determine unit rates Assessment limit: Use positive rational numbers (0 – 100)
b. Determine or use percents, rates of increase and decrease, discount, commission, sales tax, and simple interest in the context of a problem Sample Assessments Assessment limit: Use positive rational numbers (0 - 10,000)
c. Solve problems using proportional reasoning Assessment limit: Use positive rational numbers (0 – 1000)
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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.
Combining Like Terms
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 apply the commutative property of multiplication, apply the distributive property of multiplication over addition, simplify expressions by combining like terms, simplify expressions by using the order of operations.
Percents
This resource is an on-line interactive math quiz covering percents: conversions between fractions, decimals, and percents, percent applications, and simple interest.
What's Your Rate?
In this lesson, the third of a nine-part unit from Illuminations titled "Measuring Up: Concepts in Measurement," students calculate unit rates and set up proportions. The students gather data to write and solve their own proportions. |
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 |
Towers of Hanoi
The goal of the towers of hanoi problem is to move a stack of disks from one peg to another in as few a moves as possible.
Adjacent Circles
In this lesson, part of a set of four related Illuminations lessons on combinations, students are encouraged to discover all the combinations that can be made from three colors. This activity strengthens the students' problem-solving skills (including elimination and collection of organized data) and their ability to draw conclusions. The use of higher-level thinking skills (synthesis, analysis, and evaluations) is the overall goal.
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.
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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 |
Improving Deductive Reasoning Skills
This activity was designed to enhance student problem solving strategies and increase student ability to solve deductive reasoning problems as well as to bring a sense of fun and accomplishment to math problem solving. Heterogeneous groups of students can produce their own deductive reasoning puzzles for other students to solve, and an example of one student's puzzle is included.
Just a Usual Day at Unusual School
This activity, from Los Alamos National Lab, deals with logical analysis. Students perform a play which takes place in a school where some of the students always lie and the rest always tell the truth. Terry, the protagonist, is trying to find out which students are which, but at the beginning, there is no way of knowing whom to believe. Background information, key concepts, and vocabulary are included, along with teacher information. |
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
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h. Give or use feedback to revise mathematical thinking |
National Library of Virtual Manipulatives for Interactive Math
This is a NSF supported project that began in 1999 to develop a library of uniquely interactive, web-based virtual manipulatives or concept tutorials, mostly in the form of Java applets, for mathematics instruction (K-12 emphasis). The project includes dissemination and extensive internal and external evaluation.
Educational JAVA Programs
This site was started in November of 1997 with the purpose of providing Java™ Applets that can be used as tools to help and enhance the education of children both at school and at home.
Math: Virtual Manipulatives
This is a collection of interactive math manipulative sites. Move the manipulatives to demonstrate mathematical problems and concepts. The concepts that are covered include addition, subtraction, graphing, geometry, fractions, and more. Some sites include animated tutorials, printable math manipulatives, information about Base 10 Blocks and how to use them. There are links to eThemes Resources on tessellations, pattern blocks, and tangrams. |
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 |
Hummingbird Mathematics Activities
Too often students fail to see relevance between math and everyday life. Math can be integrated with science, reading, logic, and other basic skills in ways that will excite students on a daily basis. Students that are involved in observations of the Hummingbird or that undertake a research project that deals with the species will collect data that can be manipulated, graphed, and interpreted. Mathematical analysis often helps us understand what we have seen in the hummingbird garden or at the feeder. With the Hummingbird by the Numbers activity you and your students can develop some interesting word problems that polish their math skills.
The Mathematics of Saving
THE MATHEMATICS OF SAVING is a workbook designed to give students practical skills in mathematics used in daily life. This workbook deals with simple and compound interest, effective yield, annuities and careers in banking. Includes a section on careers in banking. Part of a series of workbooks titled "Mathematics for Everyday Living". Ordering information for this resource is provided by the Jump$tart Personal Finance Clearinghouse. |
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