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Web Resources Supporting the Maryland Voluntary State Curriculum
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Mathematics - Grade 6
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 numeric patterns and functions
Objectives
a. Identify and describe sequences represented by a physical model or in a function table
b. Identify and describe sequences represented by a physical model or in a function table Assessment limit: Use whole numbers or decimals with no more than two decimal places (0 – 10,000)
c. Complete a function table with a given two-operation rule Assessment limit: Use the operations of (+, -, x), numbers no more than 10 in the rule, and whole numbers (0 - 50)
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An Introduction to Arithmetic and Geometric Sequences
This resource from the Shodor Education Foundation, reviewed for grades 6-8 by Illuminations, is a lesson plan designed to introduce students to the idea of an arithmetic sequence. The plan links to an interactive sequencer activity that allows students to see the effect of changing the initial values for the starting number, multiplier, and add-on. The lesson also includes a discussion of recursion, iteration, and fractals.
The Fibonacci Series
The purpose of this lesson, from Science NetLinks, is to appreciate and investigate a numerical pattern; to look for evidence of mathematical patterns in nature. In this lesson, students will explore the Fibonacci series. They will identify the pattern among the Fibonacci numbers, look for applications of these numbers, and explore the ways that this pattern can be related to objects and shapes in both the natural and designed world. Science and technology are rich and especially important contexts in which to learn the value of mathematics and to develop mathematical problem solving skills, but they are not the only ones. (Benchmarks, p. 32) This lesson uses examples from art and architecture, as well as nature, to reinforce the ideas in the central benchmarks. In grades 3-5, students should be encouraged to describe all sorts of things mathematically -- in terms of numbers, shapes, and operations. In middle school, students should continue to have opportunities to reflect on the nature of patterns and relationships in a purely abstract way. |
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 operation (+, -) with whole numbers, fractions with denominators as factors of 24, or decimals with no more than two decimal places (0-200)
b. Evaluate an algebraic expression Assessment limit: Use one unknown and one operation (+, -) with whole numbers (0 – 200), fractions with denominators as factors of 24 (0 – 50), or decimals with no more than two decimal places (0 – 50)
c. Evaluate numeric expressions using the order of operations Clarification | Sample Assessments Assessment limit: Use no more than 4 operations (+, -, x, ÷ with no remainders) with or without 1 set of parentheses or a division bar and whole numbers (0-100)
d. Represent algebraic expressions using physical models, manipulatives, and drawings
Indicator
2. Identify, write, solve, and apply equations and inequalities
Objectives
a. Identify and write equations and inequalities to represent relationships Assessment limit: Use a variable, the appropriate relational symbols (>, <, =), and one operational symbol (+, -, ×, ÷) on either side and use fractions with denominators as factors of 24 (0 – 50) or decimals with no more than two decimal places (0 – 200)
b. Determine the unknown in a linear equation Sample Assessments Assessment limit: Use one operation (+, -, ×, ÷ with no remainders) and use positive whole number coefficients using decimals with no more than two decimal places (0 – 100)
c. Solve for the unknown in a one-step inequality
d. Identify or graph solutions of a one-step inequality on a number line
e. Apply given formulas to a problem solving situation
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Pan Balance - Expressions
Students can use this interactive pan balance from Illuminations to "weigh" numeric or algebraic exressions. They can practice arithmetic and algebraic skills, and investigate the important concept of "equivalence." Mathlets are math applets you can use to explore math and create interactive lessons.
Equations
The equations section of QuickMath allows you to solve and plot virtually any equation or system of equations. In most cases, you can find exact solutions to your equations. Even when this is not possible, QuickMath may be able to give you approximate solutions to almost any l&sevel of accuracy you require. It also contains a number of special commands for dealing with quadratic equations.
Inequalities
The inequalities section of QuickMath allows you to solve virtually any inequality or system of inequalities in a single variable. In most cases, you can find exact solutions. Even when this is not possible, QuickMath may be able to give you approximate solutions to almost any level of accuracy you require. In addition, you can plot the regions satisfied by one or more inequalities in two variables, seeing clearly where the intersections of those regions occur.
Algebra
The algebra section of QuickMath allows you to manipulate mathematical expressions in all sorts of useful ways. At the moment, QuickMath can expand, factor or simplify virtually any expression, cancel common factors within fractions, split fractions up into smaller ('partial') fractions and join two or more fractions together into a single fraction. More specialised commands are on the way.
Linear Equations in One Variable
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.
Using Addition or Subtraction to Eliminate a Variable
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
C. Numeric and Graphic Representations of Relationships |
Indicator
1. Locate points on a number line and in a coordinate grid
Objective
a. Represent rational numbers on a number line
Assessment limit: Use integers (-20 to 20)
b. Graph ordered pairs in a coordinate plane. Assessment limit: Use no more than 3 ordered pairs of integers (-20 to 20) or no more than 3 ordered pairs of fractions/mixed numbers with denominators of 2 (-10 to 10)
c. Graph linear data from a function table
Indicator
2. Analyze linear relationships
Objectives
a. Identify and describe the change represented in a graph Clarification | Sample Assessments Assessment limit: Identify increase, decrease, or no change
b. Translate the graph of a linear relationship onto a table of values that illustrates the type of change
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Exploring Linear Data
In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit. Pages for four activities are provided.
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.
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. |
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, describe, and label points, lines, rays, line segments, vertices, angles, and planes using correct symbolic notation
b. Identify and describe line segments Sample Assessments Assessment limit: Use diagonal line segments
c. Identify and describe the parts of a circle Assessment limit: Use radius, diameter, or circumference
Indicator
2. Analyze geometric relationships
Objectives
a. Compare and classify triangles by sides Thinking Skills Assessment limit: Use scalene, equilateral, or isosceles
b. Compare and classify triangles by angle measure Assessment limit: Use equiangular, obtuse, acute, or right
c. Determine a third angle measure of a triangle given two angle measures Sample Assessments Assessment limit: Use the concept of the sum of angles in any triangle is 180° without using a diagram
d. Identify and compare the relationship between parts of a circle Seeds Assessment
limit: Use radius, diameter and circumference
(=3.14)
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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.
Creating and Understanding Circles and Their Parts
This lesson will offer a hands-on opportunity to explore and construct circles. Students will develop a definition for identifying the parts of a circle such as the center, radius, diameter, chord, and circumference. Students will use compasses and rulers in constructing these parts of a circle.
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. Draw geometric figures using a variety of tools Assessment limit: Draw triangles given the measures of 2 sides and one angle or 2 angles and 1 side using whole numbers (0-20) and angle measures (0°-179°)
b. Identify, describe, or draw a polygon Sample Assessments Assessment limit: Use the first quadrant given no more than six coordinates
c. Identify or describe angle relationships Assessment limit: Use perpendicular bisectors or angle bisectors
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How Many Triangles Can You Construct?
In this lesson, the last in a four-part unit from Illuminations titled "Triangles," students identify patterns in a geometrical figure, build a foundation for the understanding of fractals, and develop experiments to test hypotheses. They then communicate their work in the form of a news report.
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. |
Topic
D. Congruence |
Indicator
1. Analyze congruent figures
Objective
a. Identify and describe congruent polygons and their corresponding parts
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Congruent Triangles
Description 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. |
Topic
E. Transformations |
Indicator
1. Analyze a transformation on a coordinate plane
Objectives
a. Plot the result of one transformation (translation, reflection, rotation) on a coordinate plane |
Graphing and the Coordinate Plane
This lesson, from the Shodor Education Foundation, Inc., is designed to introduce students to graphing ordered pairs of numbers on the coordinate plane. |
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
A. Measurement Units |
Indicator
1. Measure in customary and metric units
Objectives
a. Select and use appropriate tools and units Assessment limit: Measure length to the nearest 1/16 inch with a rule
Indicator
2. 2. Measure angles in polygons
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Measuring Up: Concepts in Measurement
This unit includes concepts related to proportional reasoning, ratio, and indirect measurement. Students engage in a variety of activities that involve taking their own measurements, exploring different ratios, and examining similar figures. Students convert measurements into customary and metric units. These activities immerse students in problem solving, reasoning, and making connections to real-life situations. |
Topic
C. Applications in Measurement
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Indicator
1.Estimate and apply measurement formulas
Objectives
a. Estimate and determine the area of a polygon Assessment limit: Use triangles and whole number dimensions (0 – 200)
b. Estimate and determine the volume of a rectangular prism Prerequisite
Assessment limit: Use rectangular prisms and whole number dimensions (0 – 1000)
c. Estimate and determine the area of a composite figure Clarification | Seeds | Thinking Skills | Sample Assessments Assessment limit: Use composite figures with no more than four polygons (triangles or rectangles) and whole number dimensions (0 – 500)
d. Determine missing dimension of a quadrilateral given the perimeter length Sample Assessments Assessment limit: Find length in a quadrilateral given the perimeter with whole number dimensions (0 – 200)
e. Determine the missing dimension of rectangles Sample Assessments Assessment limit: Find length in a square or rectangle given the area and whole number dimensions (0 – 200)
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Finding the Area of Irregular Figures
In this lesson, one of a multi-part unit from Illuminations, students estimate the areas of highly irregular shapes and use a process of decomposition to calculate the areas of irregular polygons. Click "Display Full Record" and see the Relation field for a link to the unit overview.
Area Formula Lab
This resource from Dr. Margo Lynn Mankus, reviewed for grades 6-8 by Illuminations, is a series of activities that explore the area of a variety of geometric shapes. Using these activity worksheets, students derive the area formulas of shapes including squares, rectangles, triangles, and more. The worksheets are "hands on," allowing students to cut out shapes and manipulate them on a grid. Read the full review on the Illuminations site, where you can access this resource directly.
Quadrilaterals
Description This lesson is designed to introduce students to quadrilaterals. Included in this lesson are discussions of parallelograms, rectangles, and trapezoids.
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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 frequency tables Thinking Skills | Sample Assessments Assessment limit: Use no more than 5 categories or ranges of numbers and total frequencies of no more than 25
b. Organize and display data to make stem-and-leaf plots Thinking Skills | Sample Assessments Assessment limit: Use no more than 20 data points and whole numbers (0–99)
c. Organize and display data using a back-to-back stem-and-leaf plot
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Games, Measurement, and Statistics: Unit Overview
In this unit of 5 lessons from Illuminations, students participate in games and activities that develop concepts of measurement and statistics. Students are asked to measure distances using standard and nonstandard units and to record their measurements in various tables. They are then asked to use descriptive statistics to report the results. These lessons include an individual activity for four different levels plus one for parents to complete with their child at home.
State Names: Investigating Real-World Data
Determine the number of times that each letter of the alphabet is used when writing the names of all 50 states. Understand how various representations, including steam-and-leaf plots, box-and-whisker plots, and histograms, can be used to organize the data. |
Topic
B. Data Analysis |
Indicator
1. Analyze data
Objectives
a. Interpret frequency tables Assessment limit: Use no more than 5 categories or ranges of numbers and frequencies of no more than 25
b. Read and analyze circle graphs Sample Assessments Assessment limit: Use no more than 5 categories using data in whole numbers or percents (0 – 1000)
c. I Interpret data from a stem-and-leaf plot
Indicator
2. Describe a set of data
Objectives
a. Apply measures of central tendency (mean, median, mode)
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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.
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.
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. |
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. |
Topic
B. Theoretical Probability |
Indicator
1. Determine the probability of one simple event comprised of equally likely outcomes
Objectives
a. Express the probability of an event as a fraction.
b. Express the probability of an event as a decimal Clarification | Sample Assessments Assessment limit: Use a sample space of 10, 20, 25, or 50 outcomes
c. Express the probability of an event as a percent
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Simulating Probability Situations Using Box Models
In this lesson, from Illuminations, students explore the relationship between theoretical and experimental probabilities. They use an interactive "box model" that allows them to simulate standard probability experiments such as flipping a coin or rolling a die.
The Game of SKUNK: Choice and Chance in Life
In this lesson, from Illuminations, students practice decision-making skills while playing a dice game called "Skunk." This allows them to develop a better understanding of mathematical probability and of the concept of choice versus chance. |
Topic
C. Experimental Probability |
Indicator
1. Analyze the results of a probability experiment.
Objectives
a. Make predictions and express the experimental probability as a fraction, a decimal, or a percent Clarification | Sample Assessments Assessment limit: Use no more than 30 results in the sample space
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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Adjustable Spinner
This tool, from Illuminations, allows students to create their own spinners and examine the outcomes given a specified number of spins. Students learn that experimental probabilities differ according to the characteristics of the model. They also grapple with the idea of variability, the concept that two identical spinners or dice may not produce identical experimental data. This interactive math applet can be used to explore math and create interactive lessons.
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. |
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 form with powers of 10 (0 - 100,000)
b. Read, write, and represent integers Assessment limit: Use integers from (-100 to 100)
c. Identify and determine equivalent forms of fractions as decimals, as percents, and as ratios Sample Assessments Assessment limit: Use proper fractions with denominators as factors of 100, decimals, percents, or ratios (0 – 1000)
d. Compare and order fractions, decimals alone or mixed together, with and without relational symbols (<, >, =) Assessment limit: Include no more than 4 fractions with denominators with factors of 100 or decimals with up to 2 decimal places (0 – 100)
e. Compare and order integers
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Base Ten Blocks
Simple applet lets students explore whole decimal numbers, place value, and even algebra with blocks.
Decimal Roundup!
Students will show an understanding of place value by rounding decimals to the place value of ones, whole, tenths, hundredths, and thousandths place.
Fractions - Equivalent
Using this Manipulatives, students recognize and generate equivalent forms of commonly used fractions and show multiple representations of equivalent fractions.
Fractions - Comparing
Using this Manipulatives, students use models and equivalent forms to judge the size of fractions, recognize and generate equivalent forms of commonly used fractions, and identify fraction values using a number line.
Fraction - Percent Equivalents
Essential Question: To what extent is it important for students to represent and use numbers in a variety of equivalent forms? Content Knowledge: Students will understand proportions and cross products. Students will understand how to convert any fraction to a percent. Procedural Knowledge: Students will learn how to convert any fraction to a percent using proportions and cross products. |
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Indicator
1.Apply number relationships
Objectives
a. Determine prime factorizations for whole numbers and express them using exponential form
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Factorize
This tool, from Illuminations, allows students to practice the factorizations of given numbers. Students also build arrays to represent each factorization.
The Factor Game
Students can exercise their factoring ability in this interactive math-let from Illuminations, based on the Factor Game from the Prime Time unit of the Connected Mathematics Project. This interactive activity engages students in a friendly contest in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. |
Topic
C. Number Computation |
Indicator
1. Analyze number relations and compute
Objectives
a. Add and subtract fractions and mixed numbers and express answers in simplest form
Sample Assessments Assessment limit: Use a 3-digit factor by another factor with no more than 2-digits and whole numbers (0 - 10,000)
b. Multiply fractions and mixed numbers and express in simplest form Assessment limit: Use denominators as factors of 24 not including 24 (0 – 20)
c. Multiply decimals Assessment limit: Use a decimal with no more than 3 digits multiplied by a 2-digit decimal (0 – 1000)
d. Divide decimals Assessment limit: Use a decimal with no more than 5 digits divided by a whole number with no more than 2 digits without annexing zeros (0 – 1000)
e. Determine a percent of a whole number Assessment limit: Use 10%, 20%, 25% or 50% of a whole number (0 – 1000)
f. Simplify numeric expressions using the properties of addition and multiplication Assessment limit: Use the distributive property to simplify numeric expressions and whole numbers (0 – 1000)
Indicator
2. Estimation
Objectives
a. Determine the approximate products and quotients of decimals Assessment limit: Use a decimal with no more than a 3 digits multiplied by a 2-digit whole number, or the quotient of a decimal with no more than 4 digits in the dividend divided by a 2-digit whole number (0 – 1000)
Indicator
3. Analyze ratios, proportions, and percents
Objectives
a. Represent ratios in a variety of forms
b. Use ratios and unit rates to solve problems
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Fraction Game Tool
This interactive one-person game is a fun way to practice your skills while you explore relationships among fractions and ways of combining fractions. You can play a two-person fraction game on the E-Standards Web site.
Fractions in Everyday Life
This activity, from the Math Forum at Drexel University, focuses on students' working knowledge of fraction multiplication and division. Students are asked to adjust a cookie recipe by multiplying and dividing to change the yield.
Multiplying Decimals and Mixed Numbers
This lesson is designed to reinforce skills associated with multiplying decimals and mixed numbers and allow students to visualize the effects of multiplying by a decimal or mixed number.
Lesson Tutor: Turn Around Addition: Number Sense and Numeration - Lesson 2
By the end of this lesson the student will be able to remember the rule of operations. These problems demonstrate the associative property of addition. The property is also true of multiplication. Teaching this as a foundational truth now will facilitate pre-algebra concepts that your child will meet with in the future.
Percents
This resource is an on-line interactive math quiz covering percents: conversions between fractions, decimals, and percents, percent applications, and simple interest.
Measure 4 Measure
This site is a collection of interactive sites on the Web that estimate, calculate, evaluate, translate, etc.... The links are categorized as follows: science/math; health; finance; and everything else. Nearly 100 links are included. Under science, math, and health one can find links to a body surface area calculator, various density converters, a heat index calculator, and a target heart rate calculator. The everything else category includes, among others, a bowling score calculator, a grass seed estimator, and an Internet statistics generator.
Percent Problem Solving
Students apply their knowledge of fractions, decimals, and percents in order to understand the relationship amongst the three. Students will solve basic percent number problems using the percent proportion or other methods and play a game using a resource of the Shodor Education Foundation, Inc. Permission has been granted to use the materials as part of the Interactivate Your Bored Math Students workshop. Students will also analyze and explain the results of their game by answering two exploration questions. |
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. Students should be encouraged to state their own criteria for what is a satisfactory result and to discuss their judgments in terms of their purposes. Science for All Americans and Benchmarks take the approach that mathematics can be characterized as a cycle of investigation that is intended to lead to the development of mathematical ideas. (See essay) Students should have the opportunity to use this cycle of investigation in their own work. Ideas in this lesson are also related to concepts found in the following Benchmark chapters: The Mathematical World; Common Themes: Models; and Habits of Mind: Computation and Estimation. |
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 |
Train Riddles
Children write and solve riddles about Cuisenaire Rod trains. In this activity, children have the opportunity to understand how Cuisenaire Rods are related to one another, assign numerical values to the rods, and use logical reasoning.
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. Students should be encouraged to state their own criteria for what is a satisfactory result and to discuss their judgments in terms of their purposes. Science for All Americans and Benchmarks take the approach that mathematics can be characterized as a cycle of investigation that is intended to lead to the development of mathematical ideas. (See essay) Students should have the opportunity to use this cycle of investigation in their own work. Ideas in this lesson are also related to concepts found in the following Benchmark chapters: The Mathematical World; Common Themes: Models; and Habits of Mind: Computation and Estimation. |
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.
The Math-Science Quest for Solutions: Scientific Problem-Solving for Individuals
The Math-Science Quest for Solutions Puzzles about beginning mathematics are intriguing challenges for youngsters and adults alike. The complexity of the puzzles is determined by the operation signs that are used in the Solutions. This page provides the Math-Science Quest for Solutions at three levels designed for individual problem-solvers.
Fill and Pour
Each problem presents two containers of specified volume, with a target volume of juice to be delivered exactly in one of the two containers. The user can fill or empty either container as often as desired, and can pour juice from either container into the other. There is no unique solution for this puzzle, but the applet keeps track of the amount of juice in each container after each action, and a correct solution is recognized by a message of congratulations and either a cherry or a "rubber duckie." |
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 |
Mathematical Metaphors in Art
In this lesson, students investigate the role of mathematics in their everyday lives. They then discover, through reading a Times article and through analyzing a specific example of art, that mathematics exists on a deeper 'metaphoric' level in art. This lesson is found on the New York Times Learning Network.
Electronic Bookshelf of Materials that Feature an Interdisciplinary Approach to Mathematics
This site, part of The National Numereacy Network, provides web links to sixteen different disciplines showing how math relates to other disciplines.
Making Beds
In the following lesson, students participate in activities in which they focus on connections between mathematics and children's literature. |
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