ALEX Lesson Plans
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Title: Inequalities: Solving and Graphing
Description:
The students will extend their knowledge from solving equalities to solving inequalities. They will also learn to graph the solutions of inequalities.
Standard(s): [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4]
Subject: Mathematics (7)
Title: Inequalities: Solving and Graphing
Description: The students will extend their knowledge from solving equalities to solving inequalities. They will also learn to graph the solutions of inequalities.
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Title: It's Around There Somewhere! Perimeter, and Circumference
Description:
The purpose of this lesson is to review the concepts of perimeter, and circumference.Students will also use their knowledge to apply perimeter, and circumference formulas within practical applications such as in spatial design.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] GEO (912) 35: Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [GGMD1] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4]
Subject: Mathematics (7  12)
Title: It's Around There Somewhere! Perimeter, and Circumference
Description: The purpose of this lesson is to review the concepts of perimeter, and circumference.Students will also use their knowledge to apply perimeter, and circumference formulas within practical applications such as in spatial design.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: New York with $1200
Description:
CONGRATULATIONS!!! You are Demopolis Middle School’s first –place winner of the annual MATHATHON!!!!!!!!!! You and three of your classmates have been awarded an exciting trip to NEW YORK CITY! You will each be given $1200 to cover all your expenses during your three day stay. You must use only your $1200 prize to cover all expenses (transportation costs, hotel accommodations, food, gratuities (tips), souvenirs, and entertainment). Please budget your money carefully – decide which purchases are most important and budget these first. Don’t forget to have fun!!
Standard(s): [T1] CIT (7) 8: Apply principles of money management to the preparation of a personal budget that addresses housing, transportation, food, clothing, medical expenses, and insurance as well as checking and savings accounts, loans, investments, credit, and comparison shopping. [TC2] (68) 2: Publish digital products that communicate curriculum concepts. [TC2] (68) 5: Use basic features of word processing, spreadsheets, databases, and presentation software. [TC2] (68) 6: Select specific digital tools for completing curriculumrelated tasks. [TC2] (68) 8: Identify safe uses of social networking and electronic communication. [TC2] (68) 9: Practice responsible and legal use of technology systems and digital content. [TC2] (68) 11: Use digital tools and strategies to locate, collect, organize, evaluate, and synthesize
information. [MA2013] (7) 4: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. [7NS1] [MA2013] (7) 8: Understand that rewriting an expression in different forms in a problem context can shed light on the problem, and how the quantities in it are related. [7EE2] [MA2013] (7) 9: Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. [7EE3] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
Subject: Mathematics (7), or Social Studies (7), or Technology Education (6  8)
Title: New York with $1200
Description: CONGRATULATIONS!!! You are Demopolis Middle School’s first –place winner of the annual MATHATHON!!!!!!!!!! You and three of your classmates have been awarded an exciting trip to NEW YORK CITY! You will each be given $1200 to cover all your expenses during your three day stay. You must use only your $1200 prize to cover all expenses (transportation costs, hotel accommodations, food, gratuities (tips), souvenirs, and entertainment). Please budget your money carefully – decide which purchases are most important and budget these first. Don’t forget to have fun!!
Thinkfinity Lesson Plans
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Title: On Fire
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This unit of five lessons, from Illuminations, introduces the components of a firesafe and firewise environment. Students create a firewise location through calculations and measurement of percent slope, defensible space distance and various vegetation separation distances. The unit plan culminates with students designing a firewise property and testing their firewise IQ.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 17: Use variables to represent numbers, and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6EE6] [MA2013] (6) 20: Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. [6EE9] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [MA2013] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5] [MA2013] (8) 8: Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. [8EE6] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3]
Subject: Mathematics Title: On Fire
Description: This unit of five lessons, from Illuminations, introduces the components of a firesafe and firewise environment. Students create a firewise location through calculations and measurement of percent slope, defensible space distance and various vegetation separation distances. The unit plan culminates with students designing a firewise property and testing their firewise IQ. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Square Circles
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This Illuminations lesson allows students to use a variety of units when measuring the side length and perimeter of squares, as well as the diameter and circumference of circles. They draw conclusions about the relationship of side/perimeter in squares and diameter/circumference in circles based on collected data. Then, through physical representations, they develop the idea of a constant that relates a circle s diameter to its circumferencenamely pi.
Standard(s): [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4]
Subject: Mathematics Title: Square Circles
Description: This Illuminations lesson allows students to use a variety of units when measuring the side length and perimeter of squares, as well as the diameter and circumference of circles. They draw conclusions about the relationship of side/perimeter in squares and diameter/circumference in circles based on collected data. Then, through physical representations, they develop the idea of a constant that relates a circle s diameter to its circumferencenamely pi. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Constant Dimensions
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In this Illuminations lesson, students measure the length and width of a rectangle using both standard and nonstandard units of measure. In addition to providing measurement practice, this lesson allows students to discover that the ratio of length to width of a rectangle is constant, in spite of the units. For many middle school students, this discovery is surprising.
Standard(s): [MA2013] (6) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6RP1] [MA2013] (6) 2: Understand the concept of a unit rate ^{a}/_{b} associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. [6RP2] [MA2013] (6) 3: Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6RP3] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [MA2013] (7) 1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7RP1] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (7) 3: Use proportional relationships to solve multistep ratio and percent problems. [7RP3] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4]
Subject: Mathematics Title: Constant Dimensions
Description: In this Illuminations lesson, students measure the length and width of a rectangle using both standard and nonstandard units of measure. In addition to providing measurement practice, this lesson allows students to discover that the ratio of length to width of a rectangle is constant, in spite of the units. For many middle school students, this discovery is surprising. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Balancing Shapes
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In this lesson, one of a multipart unit from Illuminations, students balance shapes using an interactive pan balance applet to study equality, essential to understanding algebra. Equivalent relationships are recognized when the pans balance, demonstrating the properties of equality.
Standard(s): [MA2013] (6) 12: Write and evaluate numerical expressions involving wholenumber exponents. [6EE1] [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3] [MA2013] (6) 15: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). [6EE4] [MA2013] (6) 16: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. [6EE5] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4]
Subject: Mathematics Title: Balancing Shapes
Description: In this lesson, one of a multipart unit from Illuminations, students balance shapes using an interactive pan balance applet to study equality, essential to understanding algebra. Equivalent relationships are recognized when the pans balance, demonstrating the properties of equality. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Patterns and Function
Description:
In this lesson, from Illuminations, students investigate properties of perimeter, area, and volume related to various geometric two and threedimensional shapes.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9]
Subject: Mathematics Title: Patterns and Function
Description: In this lesson, from Illuminations, students investigate properties of perimeter, area, and volume related to various geometric two and threedimensional shapes. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Graphing What
Description:
This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs.
Standard(s): [MA2013] (6) 17: Use variables to represent numbers, and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6EE6] [MA2013] (6) 20: Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. [6EE9] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [MA2013] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5] [MA2013] (8) 11: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.) [8F1] [MA2013] (8) 13: Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8F3] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 15: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [8F5] [MA2013] AL1 (912) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL1 (912) 25: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [FIF1] [MA2013] AL1 (912) 26: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [FIF2] [MA2013] AL1 (912) 28: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 39: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [FLE3] [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] PRE (912) 16: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.)* [FIF4] (Alabama) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics Title: Graphing What
Description: This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Web Resources
Podcasts
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Title: Math in Fashion
Description:
In this video, student teams used algebra to modify Chloe Dao’s garment design to meet the target price required by the buyer.
Standard(s): [MA2013] (6) 16: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. [6EE5] [MA2013] (6) 19: Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [6EE8] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4]
Math in Fashion
http://www.thirteen....
In this video, student teams used algebra to modify Chloe Dao’s garment design to meet the target price required by the buyer.
Interactives/Games
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Title: Math Makes a Connection: The Locker Problem
Description:
In this interactive game, students use their knowledge of multiples to solve a locker problem. Students will manually open or close a locker by clicking on the lockers. They must answer the following question: Which of the 1000 locker doors are open when every student finishes?
Standard(s): [MA2013] (6) 17: Use variables to represent numbers, and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6EE6] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4]
Math Makes a Connection: The Locker Problem
http://connectedmath...
In this interactive game, students use their knowledge of multiples to solve a locker problem. Students will manually open or close a locker by clicking on the lockers. They must answer the following question: Which of the 1000 locker doors are open when every student finishes?
Thinkfinity Learning Activities
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Title: Pan Balance  Numbers
Description:
This student interactive, from Illuminations, can be used to find numerical expressions that are equivalent to one another. If equivalent expressions are placed in the blue and red pans on the virtual scale, it will balance.
Standard(s): [MA2013] (6) 16: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. [6EE5] [MA2013] (6) 18: Solve realworld and mathematical problems by writing and solving equations of the form
x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers. [6EE7] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [MA2013] (7) 15: Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. [7G5] [MA2013] (8) 9: Solve linear equations in one variable. [8EE7]
Subject: Mathematics Title: Pan Balance  Numbers
Description: This student interactive, from Illuminations, can be used to find numerical expressions that are equivalent to one another. If equivalent expressions are placed in the blue and red pans on the virtual scale, it will balance. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: Calculation Nation
Description:
Become a citizen of Calculation Nation! Play online math strategy games to learn about fractions, factors, multiples, symmetry and more, as well as practice important skills like basic multiplication and calculating area! Calculation Nation uses the power of the Web to let students challenge themselves and opponents from anywhere in the world. The element of competition adds an extra layer of excitement.
Standard(s): [MA2013] (3) 1: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. [3OA1] [MA2013] (3) 2: Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. [3OA2] [MA2013] (3) 13: Understand a fraction ^{1}/_{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction ^{a}/_{b} as the quantity formed by a parts and size ^{1}/_{b}. [3NF1] [MA2013] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3NF3] [MA2013] (4) 12: Explain why a fraction ^{a}/_{b} is equivalent to a fraction ^{nxa}/_{nxb} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4NF1] [MA2013] (4) 13: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as ^{1}/_{2}. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [4NF2] [MA2013] (4) 28: Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. [4G3] [MA2013] (6) 2: Understand the concept of a unit rate ^{a}/_{b} associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. [6RP2] [MA2013] (6) 4: Interpret and compute quotients of fractions, and solve word problems involving division of fractions, e.g., by using visual fraction models and equations to represent the problem. [6NS1] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [MA2013] (7) 1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7RP1] [MA2013] (7) 4: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. [7NS1] [MA2013] (7) 5: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. [7NS2] [MA2013] (7) 6: Solve realworld and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) [7NS3] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [MA2013] (8) 17: Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. [8G2] [MA2013] (8) 18: Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. [8G3] [MA2013] DM1 (912) 1: Analyze topics from elementary number theory, including perfect numbers and prime numbers, to determine properties of integers. (Alabama)
Subject: Mathematics Title: Calculation Nation
Description: Become a citizen of Calculation Nation! Play online math strategy games to learn about fractions, factors, multiples, symmetry and more, as well as practice important skills like basic multiplication and calculating area! Calculation Nation uses the power of the Web to let students challenge themselves and opponents from anywhere in the world. The element of competition adds an extra layer of excitement. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8,9
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Title: Pan Balance  Expressions
Description:
This interactive pan balance, from Illuminations, allows students to enter and compare numeric or algebraic expressions. They can '' weigh'' the expressions they want to compare by entering them on either side of the balance, allowing them to practice arithmetic and algebraic skills, as well as to investigate the concept of equivalence.
Standard(s): [MA2013] (6) 12: Write and evaluate numerical expressions involving wholenumber exponents. [6EE1] [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3] [MA2013] (6) 15: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). [6EE4] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 12: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8F2]
Subject: Mathematics Title: Pan Balance  Expressions
Description: This interactive pan balance, from Illuminations, allows students to enter and compare numeric or algebraic expressions. They can '' weigh'' the expressions they want to compare by entering them on either side of the balance, allowing them to practice arithmetic and algebraic skills, as well as to investigate the concept of equivalence. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8,9,10,11,12

