Similarities and Differences Or Compare and Contrast

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1 Similarities and Differences Or Compare and Contrast Research has shown that identifying similarities and differences can produce significant gains in student achievement. For it to be effective it must be more than mere mention of similarities and differences during the instruction. It should be overt, written, discussed, and summarized. Examples of strategies include the following: 1. If you are comparing two concepts, draw a line down the center of a piece of paper. For this example, let s use adding fractions versus adding decimals. It is often helpful to fold the paper in half.. Write everything you and students can think of to say about the first concept.. Then write everything you and students can think of to say about the second concept. 4. Look for links and similarities. Add additional statements as they come up. Identify and summarize. 5. Look for differences. Add additional statements as they come up. Identify and summarize. 6. Summarize the comparisons in sentence form. Adding fractions Adding decimals 1 1 To add fractions with common denominator, add the numerator and keep the denominator Compare Contrastb //009

2 Concept: Concept: Compare Contrastb //009

3 Concept: Concept: Compare Contrastb //009

4 Examples of concepts for compare/contrast - Algebra Math Homework English Homework O Solving an equation for a given variable Rational numbers Irrational numbers Product of powers power of a product (exponential functions) Direct variation slope intercept form of linear equation System of linear equations one linear equation Solve system by substitution solve by linear combination (elimination) Exponential growth exponential decay function x Scientific notation regular number notation Quotient of powers power of a quotient n n 5 Solution to a system of linear equations Properties of real numbers (e.g. properties of multiplication) Evaluate Slope y-intercept Slope of parallel lines Box-Whisker plot Solution of a system of linear equations y Probability Number line y x 4 Graph linear equation Axis of symmetry of quadratic Quadratic formula Discriminant Exponential function 5 Solution to one linear equation properties of equality (multiplication property of equality) solve rate of change the point on the graph slope of perpendicular lines Stem-Leaf plot solution of a system of linear inequalities y Odds Coordinate plane y x 4 Graph quadratic equation Vertex of quadratic Graph of quadratic equation Quadratic formula Quadratic function Compare Contrastb //009

5 Whole Numbers & Patterns: estimate exact answer product quotient expanded form standard form exponential form word form sum difference associative property commutative property distributive property division evaluate simplify exponent base numerical expression order of operations solving an equation sequence term dividend divisor underestimate overestimate Introduction to Algebra algebraic expression numerical expression constant variable equation inequality addend subtrahend multiplier multiplicand solution extraneous solution factor quotient inverse operations order of operations inequality equality expression sentence Number Theory and Fractions Numerator denominator Factors multiples prime factorization factor tree common denominator common factor composite prime greatest common factor common denominator common denominator least common multiple least common denominator improper fraction proper fraction mixed number improper fraction divisible divisibility rules simplify reduce equivalent simplest form like fractions unlike fractions Collecting and Displaying Data Horizontal vertical bar graph line graph mean median mode median ordered pair coordinate range outlier stem-and-leaf plot box-and-whiskers plot x-axis y-axis double-bar graph row column frequency table stem-and-leaf plot cell interval origin quadrants functions relations input output x-coordinate y-oordinate positive number negative Ratios & Proportions indirect measurement direct measurement percent proportion rate ratio Compare Contrastb //009 scale scale drawing corresponding sides corresponding angles tip sales tax interest principal

6 Clockwise counterclockwise Horizontal vertical Protractor ruler triangle angle congruent equal line of symmetry parallel perpendicular polygon regular polygon quadrilateral polygon reflection line of reflection transformation translation vertex point Geometric Relationships line segment plane plane figure line segment ray acute angle right angle obtuse angle straight angle vertical angles adjacent angles complementary angles supplementary angles acute triangle obtuse triangle right triangle scalene triangle isosceles triangles equilateral triangle parallelogram rectangle rhombus square edge face cone prism Capacity weight Length width proportion ratio celcius fahrenheit weight mass circle circumference Measurement radius diameter pi.14 customary system metric system perimeter area center interior Probability volume surface area base vertex edge face cubic unit square unit Probability odds experimental theoretical probability outcome prediction sample space event permutations combinations population sample independent events dependent events Compare Contrastb //009

7 Examples of concepts for compare/contrast MS Math Compare Contrastb

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