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is a shift transformation. The first known shift transformation is attributed to Julius Caesar, and is now called the Caesar cipher. The cipher works in the following way. Each letter in the alphabet is replaced by another letter using a predef...
Interactivate: Interactive Math Activities
Determine the value of two fractions you have chosen (which are represented as points on a number line). Then find a fraction whose value is between your two fractions (using an arrow on the number line as a guide) and determine its value. Bounded Fraction Pointer...
Drexel Math Forum Lesson Plans
investigate the problem of air pollution in a given location and research possible solutions using a variety of tools (laboratory technology, Internet resources, multimedia technology, etc.). Mathematics goals include estimating, making, and ...more>> Al...
 Caesar Shifter
© 2008 National Council of Teachers of Mathematics http://illuminations.nctm.org Caesar Shifter To use the Caesar substitution cipher, create a Caesar shifter as follows: 1. Remove the circles at the bottom of this sheet. 2. Place the smaller circle over the larger circle, ...
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© 2008 National Council of Teachers of Mathematics http://illuminations.nctm.org Caesar Shifter To use the Caesar substitution cipher, create a Caesar shifter as follows: 1. Remove the circles at the bottom of this sheet. 2. Place the smaller circle over the larger circle, and place a paper fastener through the center of both circles. 3. To encode a message, rotate the smaller circle the appropriate number of units. Then, replace plaintext letters from the smaller circle with ciphertext
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http://illuminations.nctm.org/Lessons/Codes/Caesar-AS-Shifter.pdf#page=1
illuminations.nctm.org/Lessons/Codes/Caesar-AS-Shifter.pdf#page=1
© 2008 National Council of Teachers of Mathematics http://illuminations.nctm.org Caesar Shifter To use the Caesar substitution <span class="highlight">cipher</span>, create <span class="highlight">a</span> Caesar shifter as follows: 1. Remove the circles at the bottom of this sheet. 2. Place the smaller circle over the larger circle, <span class="highlight">and</span> place <span class="highlight">a</span> paper fastener through the center of both circles. 3. To encode <span class="highlight">a</span> message, rotate the smaller circle the appropriate number of units. Then, replace plaintext letters from the smaller circle with ciphertext
Microsoft Word - K-8 Mathematics Curriculum Framework.doc
solving a problem Supplementary angles Two angles whose measures total 180 degrees Surface area The total area of the faces (including the bases) and curved surfaces of a three-dimensional figure Symmetry (See line symmetry or rotational symmetry.) Technology Tools used to enhan...
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solving a problem Supplementary angles Two angles whose measures total 180 degrees Surface area The total area of the faces (including the bases) and curved surfaces of a three-dimensional figure Symmetry (See line symmetry or rotational symmetry.) Technology Tools used to enhance teaching: calculators, interactive graphics programs, spreadsheets, Smart-Board, etc. Theoretical probability Identifying, using mathematical expectations, the number of possible ways an event can happen compared to all of the
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http://arkansased.org/teachers/pdf/k8_math_may05.pdf#page=26
arkansased.org/teachers/pdf/k8_math_may05.pdf#page=26
demonstrate <span class="highlight">and</span> describe congruent figures within <span class="highlight">a</span> two- dimensional figure Ex. Letter, shapes, environmental print <span class="highlight">and</span> polygons G.9.2.2 Demonstrate the motion of <span class="highlight">a</span> single <span class="highlight">transformation</span> G.9.3.1 Draw one or more lines of symmetry in <span class="highlight">a</span> polygon G.9.3.2 Describe the motion (<span class="highlight">transformation</span>) of <span class="highlight">a</span> two-dimensional figure as <span class="highlight">a</span> flip (reflection), slide (translation) or turn (rotation) G.9.4.1 Determine the result of <span class="highlight">a</span> <span class="highlight">transformation</span> of <span class="highlight">a</span>
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http://arkansased.org/teachers/pdf/k8_math_may05.pdf#page=57
arkansased.org/teachers/pdf/k8_math_may05.pdf#page=57
recognizing the size <span class="highlight">and</span> shape do not change G.9.7.1 Examine the congruence, similarity, <span class="highlight">and</span> line or rotational symmetry of objects <span class="highlight">using</span> transformations G.9.7.2 Perform translations <span class="highlight">and</span> reflections of two-dimensional figures <span class="highlight">using</span> <span class="highlight">a</span> variety of methods (paper folding, tracing, graph paper) G.9.8.1 Determine <span class="highlight">a</span> transformation’s line of symmetry <span class="highlight">and</span> compare the properties of the figure <span class="highlight">and</span> its <span class="highlight">transformation</span> G.9.8.2 Draw the results of translations <span class="highlight">and</span> reflections about the x- <span class="highlight">and</span> y-axis <span class="highlight">and</span>
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http://arkansased.org/teachers/pdf/k8_math_may05.pdf#page=73
arkansased.org/teachers/pdf/k8_math_may05.pdf#page=73
the square of the length of the hypotenuse (<span class="highlight">a</span> 2 + b 2 )= c 2 . Quadrilateral <span class="highlight">A</span> polygon with four sides Quadrant Any of the four sections into which <span class="highlight">a</span> rectangular coordinate grid is divided by the intersection of the x- <span class="highlight">and</span> y-axes (The quadrants are numbered I, II, III, <span class="highlight">and</span> IV, beginning at the upper right (where x- <span class="highlight">and</span> y-coordinates are positives) <span class="highlight">and</span> continuing counterclockwise.) Qualitative change Relating to or involving comparisons <span class="highlight">based</span> on qualities Quantitative change Involving
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http://arkansased.org/teachers/pdf/k8_math_may05.pdf#page=74
arkansased.org/teachers/pdf/k8_math_may05.pdf#page=74
solving <span class="highlight">a</span> problem Supplementary angles Two angles whose measures total 180 degrees Surface area The total area of the faces (including the bases) <span class="highlight">and</span> curved surfaces of <span class="highlight">a</span> three-dimensional figure Symmetry (See line symmetry or rotational symmetry.) Technology Tools used to enhance teaching: calculators, interactive graphics programs, spreadsheets, <span class="highlight">Smart</span>-Board, etc. Theoretical probability Identifying, <span class="highlight">using</span> mathematical expectations, the number of possible ways an event can happen compared to all of the
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methods of proof. D.8.1 Use truth tables to determine truth values of compounded propositional statements. D.8.2 Find the converse, inverse, and contrapositive of a statement. D.8.3 Determine whether two propositions are logically equivalent. D.8.4 Identify and give exam...
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methods of proof. D.8.1 Use truth tables to determine truth values of compounded propositional statements. D.8.2 Find the converse, inverse, and contrapositive of a statement. D.8.3 Determine whether two propositions are logically equivalent. D.8.4 Identify and give examples of undefined terms, definitions, axioms, and theorems. D.8.5 Construct logical arguments using laws of detachment (modus ponens), syllogism, tautology, and contradiction; judge the validity of
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http://www.ode.state.or.us/teachlearn/real/documents/maaks.pdf#page=5
www.ode.state.or.us/teachlearn/real/documents/maaks.pdf#page=5
methods of proof. D.8.1 Use truth tables to determine truth values of compounded propositional statements. D.8.2 Find the converse, inverse, <span class="highlight">and</span> contrapositive of <span class="highlight">a</span> statement. D.8.3 Determine whether two propositions are logically equivalent. D.8.4 Identify <span class="highlight">and</span> give examples of undefined terms, definitions, axioms, <span class="highlight">and</span> theorems. D.8.5 Construct logical arguments <span class="highlight">using</span> laws of detachment (modus ponens), syllogism, tautology, <span class="highlight">and</span> contradiction; judge the validity of
Microsoft Word - Math GLE K-8 8-08.doc
placing them side by side • Find items that are longer than or shorter than a given measure (e.g., longer than 10 linker cubes) • Talk about time using calendar (e.g., today, Classification: • Name and sort plane figures by size and shape • Identify t...
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placing them side by side • Find items that are longer than or shorter than a given measure (e.g., longer than 10 linker cubes) • Talk about time using calendar (e.g., today, Classification: • Name and sort plane figures by size and shape • Identify the new shape formed by combining two shapes • Recognize and compare attributes and parts of two- dimensional and three- dimensional shapes Location and transformation: • Explore symmetry through drawings and use of manipulatives • Describe
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http://www.doe.k12.de.us/infosuites/staff/ci/content_areas/files/Math%20GLE%20K-8%208-08.pdf#page=6
www.doe.k12.de.us/infosuites/staff/ci/content_areas/files/Math%20GLE%20K-...
August 2008 2 Mathematics Design Team – Understanding by Design (UbD) Enduring Understandings <span class="highlight">and</span> Essential Questions Enduring Understandings: Numeric Reasoning 1. Numbers can be represented in multiple ways. 2. The same operations can be applied in problem situations that seem quite different from one another. 3. Being able to compute fluently means making <span class="highlight">smart</span> choices about which tools to use <span class="highlight">and</span> when to use them. 4. Knowing the reasonableness of an answer comes from <span class="highlight">using</span> good number sense
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http://www.doe.k12.de.us/infosuites/staff/ci/content_areas/files/Math%20GLE%20K-8%208-08.pdf#page=8
www.doe.k12.de.us/infosuites/staff/ci/content_areas/files/Math%20GLE%20K-...
computers. Enduring Understandings: Numbers can be represented in multiple ways. The same operations can be applied in problem situations that seem quite different from one another. Being able to compute fluently means making <span class="highlight">smart</span> choices about which tools to use <span class="highlight">and</span> when to use them. Knowing the reasonableness of an answer comes from <span class="highlight">using</span> good number sense <span class="highlight">and</span> estimation strategies. Essential Questions: What makes an estimate reasonable? What makes an answer exact? What makes <span class="highlight">a</span> strategy both effective
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http://www.doe.k12.de.us/infosuites/staff/ci/content_areas/files/Math%20GLE%20K-8%208-08.pdf#page=11
www.doe.k12.de.us/infosuites/staff/ci/content_areas/files/Math%20GLE%20K-...
computers. Enduring Understandings: Numbers can be represented in multiple ways. The same operations can be applied in problem situations that seem quite different from one another. Being able to compute fluently means making <span class="highlight">smart</span> choices about which tools to use <span class="highlight">and</span> when to use them. Knowing the reasonableness of an answer comes from <span class="highlight">using</span> good number sense <span class="highlight">and</span> estimation strategies. Essential Questions: What makes an estimate reasonable? What makes an answer exact? What makes <span class="highlight">a</span> strategy both
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http://www.doe.k12.de.us/infosuites/staff/ci/content_areas/files/Math%20GLE%20K-8%208-08.pdf#page=18
www.doe.k12.de.us/infosuites/staff/ci/content_areas/files/Math%20GLE%20K-...
placing them side by side • Find items that are longer than or shorter than <span class="highlight">a</span> given measure (e.g., longer than 10 linker cubes) • Talk about time <span class="highlight">using</span> calendar (e.g., today, Classification: • Name <span class="highlight">and</span> sort plane figures by size <span class="highlight">and</span> shape • Identify the new shape formed by combining two shapes • Recognize <span class="highlight">and</span> compare attributes <span class="highlight">and</span> parts of two- dimensional <span class="highlight">and</span> three- dimensional shapes Location <span class="highlight">and</span> <span class="highlight">transformation</span>: • Explore symmetry through drawings <span class="highlight">and</span> use of manipulatives • Describe
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http://www.doe.k12.de.us/infosuites/staff/ci/content_areas/files/Math%20GLE%20K-8%208-08.pdf#page=30
www.doe.k12.de.us/infosuites/staff/ci/content_areas/files/Math%20GLE%20K-...
August 2008 26 slide: See translation. solve: To find all values of <span class="highlight">a</span> variable that make <span class="highlight">a</span> sentence true. stem-<span class="highlight">and</span>-leaf plot: <span class="highlight">A</span> method of organizing data <span class="highlight">using</span> the digits of the greatest place value to group the data. strategies: Methods used to solve problems. symmetry: <span class="highlight">A</span> figure has symmetry if it remains the same after some operation or <span class="highlight">transformation</span> is done to it. T theoretical (<span class="highlight">a</span> priori) probability: <span class="highlight">A</span> probability formulated <span class="highlight">using</span> prior or intuitive knowledge of the sample space
Standard 1: Number and Operation
North Dakota Mathematics April 2005 Content and Achievement Standards 46 Standard 2: Students understand and apply geometric concepts and spatial relationships to represent and solve problems in mathematical and nonmathematical situations. PROFICIENCY DESCRIPTOR...
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North Dakota Mathematics April 2005 Content and Achievement Standards 46 Standard 2: Students understand and apply geometric concepts and spatial relationships to represent and solve problems in mathematical and nonmathematical situations. PROFICIENCY DESCRIPTOR Benchmark Expectations ADVANCED PROFICIENT PROFICIENT PARTIALLY PROFICIENT NOVICE 7.2.5. Draw the result of a transformation in the coordinate
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http://www.dpi.state.nd.us/standard/content/math/math.pdf#page=45
www.dpi.state.nd.us/standard/content/math/math.pdf#page=45
6.2.6. Draw basic geometric figures <span class="highlight">using</span> appropriate tools, i.e., circle with <span class="highlight">a</span> compass, triangle <span class="highlight">and</span> rectangle with <span class="highlight">a</span> ruler or straight edge Students select <span class="highlight">a</span> tool <span class="highlight">and</span> draw basic geometric figures with no errors. Students select <span class="highlight">a</span> tool <span class="highlight">and</span> draw basic geometric figures with no significant errors. Students select <span class="highlight">a</span> tool <span class="highlight">and</span> draw basic geometric figures with <span class="highlight">a</span> few significant errors. Students select <span class="highlight">a</span> tool <span class="highlight">and</span> draw basic geometric figures with many significant errors. Grade 7
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http://www.dpi.state.nd.us/standard/content/math/math.pdf#page=46
www.dpi.state.nd.us/standard/content/math/math.pdf#page=46
North Dakota Mathematics April 2005 Content <span class="highlight">and</span> Achievement Standards 46 Standard 2: Students understand <span class="highlight">and</span> apply geometric concepts <span class="highlight">and</span> spatial relationships to represent <span class="highlight">and</span> solve problems in mathematical <span class="highlight">and</span> nonmathematical situations. PROFICIENCY DESCRIPTOR Benchmark Expectations ADVANCED PROFICIENT PROFICIENT PARTIALLY PROFICIENT NOVICE 7.2.5. Draw the result of <span class="highlight">a</span> <span class="highlight">transformation</span> in the coordinate
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http://www.dpi.state.nd.us/standard/content/math/math.pdf#page=88
www.dpi.state.nd.us/standard/content/math/math.pdf#page=88
linear, quadratic, polynomial, absolute value, <span class="highlight">and</span> exponential), <span class="highlight">using</span> technology when appropriate Students generate graphs of <span class="highlight">a</span> variety of functions with no errors. Students generate graphs of <span class="highlight">a</span> variety of functions with no significant errors. Students generate graphs of <span class="highlight">a</span> variety of functions with <span class="highlight">a</span> few significant errors. Students generate graphs of <span class="highlight">a</span> variety of functions with many significant errors. NUMERIC <span class="highlight">AND</span> ALGEBRAIC REPRESENTATIONS 11-12.5.3. Solve quadratic equations involving
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http://www.dpi.state.nd.us/standard/content/math/math.pdf#page=93
www.dpi.state.nd.us/standard/content/math/math.pdf#page=93
North Dakota Mathematics 93 April 2005 Content <span class="highlight">and</span> Achievement Standards Recursion - The process of applying an algebraic formula to <span class="highlight">a</span> previously acquired number in order to obtain <span class="highlight">a</span> sequence of numbers. Recursive formula - <span class="highlight">A</span> formula for <span class="highlight">a</span> sequence in which the definition for each term in the sequence is <span class="highlight">based</span> on the previous term or terms. In <span class="highlight">a</span> recursive formula, the value of at least one term must be given; for example, the sequence 3, 6, 12, 24,… is defined recursively by the following
Microsoft Word - mathstd20038g.docmathstd20038g.pdf
standing next to the building. By using the person as a frame of reference adjust your original estimate. 2. estimates to check whether or not the result of a real-world problem using rational numbers and/or simple algebraic expressions is reasonable and ma...
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standing next to the building. By using the person as a frame of reference adjust your original estimate. 2. estimates to check whether or not the result of a real-world problem using rational numbers and/or simple algebraic expressions is reasonable and makes predictions based on the information (2.4.A1a) ($), e.g., you have a $4,000 debt on a credit card. You pay the minimum of $30 per month. Is it reasonable to pay off the debt in 10 years? 3. determines a reasonable range for the estimation of a
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http://www.ksde.org/LinkClick.aspx?fileticket=VJee7vha%2bsQ%3d&tabid=141&mid=8017&forcedownload=true#page=5
www.ksde.org/LinkClick.aspx?fileticket=VJee7vha%2bsQ%3d&tabid=141&mid=801...
standing next to the building. By <span class="highlight">using</span> the person as <span class="highlight">a</span> frame of reference adjust your original estimate. 2. estimates to check whether or not the result of <span class="highlight">a</span> real-world problem <span class="highlight">using</span> rational numbers <span class="highlight">and</span>/or simple algebraic expressions is reasonable <span class="highlight">and</span> makes predictions <span class="highlight">based</span> on the information (2.4.A1a) ($), e.g., you have <span class="highlight">a</span> $4,000 debt on <span class="highlight">a</span> credit <span class="highlight">card</span>. You pay the minimum of $30 per month. Is it reasonable to pay off the debt in 10 years? 3. determines <span class="highlight">a</span> reasonable range for the estimation of <span class="highlight">a</span>
Microsoft Word - mathstdrev0703.docmathstdrev0703.pdf
standing next to the building. By using the person as a frame of reference adjust your original estimate. 2. estimates to check whether or not the result of a real-world problem using rational numbers and/or simple algebraic expressions is reasonable and ma...
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standing next to the building. By using the person as a frame of reference adjust your original estimate. 2. estimates to check whether or not the result of a real-world problem using rational numbers and/or simple algebraic expressions is reasonable and makes predictions based on the information (2.4.A1a) ($), e.g., you have a $4,000 debt on a credit card. You pay the minimum of $30 per month. Is it reasonable to pay off the debt in 10 years? 3. determines a reasonable range for the estimation of a
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http://www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=8017&forcedownload=true#page=268
www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=801...
standing next to the building. By <span class="highlight">using</span> the person as <span class="highlight">a</span> frame of reference adjust your original estimate. 2. estimates to check whether or not the result of <span class="highlight">a</span> real-world problem <span class="highlight">using</span> rational numbers <span class="highlight">and</span>/or simple algebraic expressions is reasonable <span class="highlight">and</span> makes predictions <span class="highlight">based</span> on the information (2.4.A1a) ($), e.g., you have <span class="highlight">a</span> $4,000 debt on <span class="highlight">a</span> credit <span class="highlight">card</span>. You pay the minimum of $30 per month. Is it reasonable to pay off the debt in 10 years? 3. determines <span class="highlight">a</span> reasonable range for the estimation of <span class="highlight">a</span>
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http://www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=8017&forcedownload=true#page=302
www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=801...
real numbers <span class="highlight">and</span>/or algebraic expressions is reasonable <span class="highlight">and</span> makes predictions <span class="highlight">based</span> on the information (2.4.A1a) ($), e.g., if you have <span class="highlight">a</span> $4,000 debt on <span class="highlight">a</span> credit <span class="highlight">card</span> <span class="highlight">and</span> the minimum of $30 is paid per month, is it reasonable to pay off the debt in 10 years? 3. determines if <span class="highlight">a</span> real-world problem calls for an exact or approximate answer <span class="highlight">and</span> performs the appropriate computation <span class="highlight">using</span> various computational strategies including mental math, paper <span class="highlight">and</span> pencil, concrete objects, <span class="highlight">and</span>/or appropriate technology
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http://www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=8017&forcedownload=true#page=320
www.ksde.org/LinkClick.aspx?fileticket=9Of%2f53hRla8%3d&tabid=141&mid=801...
▲ analyzes the impact of transformations on the perimeter <span class="highlight">and</span> area of circles, rectangles, <span class="highlight">and</span> triangles <span class="highlight">and</span> volume of rectangular prisms <span class="highlight">and</span> cylinders (2.4.A1f), e.g., reducing by <span class="highlight">a</span> factor of ½ multiplies an area by <span class="highlight">a</span> factor of ¼ <span class="highlight">and</span> multiplies the volume by <span class="highlight">a</span> factor of 1/8, whereas, rotating <span class="highlight">a</span> geometric figure does not change perimeter or area. 2. describes <span class="highlight">and</span> draws <span class="highlight">a</span> simple three-dimensional shape after undergoing one specified <span class="highlight">transformation</span> without <span class="highlight">using</span> concrete objects to perform the <span class="highlight">transformation</span>
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