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Harrison County Schools Curriculum Guide for Math Department Course Name: ___General Math________ Grade Level Targeted: 7th Grade Unit (s): ___________ Essential Questions How is coordinate geometry used in the real world? Kentucky Core Content Version 4.1 MA-07-3.3.1 Students will identify and graph ordered pairs on a coordinate system, correctly identifying the origin, axes and ordered pairs; and will apply graphing in the coordinate system to solve realworld and mathematical problems. DOK 2 Key Vocabulary 1. 2. 3. 4. 5. 6. 7. Ordered Pairs X-Axis Y-Axis Vertical Horizontal Origin Four Quadrants Activities and Assessments Week One: Review axes, identify components of ordered pairs. Identify and label all four quadrants, plot points and label in all four quadrants. Essential Questions How do you use properties and order of operations to solve problems? How do you use order of operations with fractions, decimals, and percents? How do you use properties to solve problems? Kentucky Core Content Version 4.1 MA-07-1.3.1 Students will add, subtract, multiply and divide whole numbers, fractions and decimals to solve real-world problems and apply order of operations (including positive whole number exponents) to simplify numerical expressions. DOK 2 MA-07-1.5.1 Students will identify and apply prime numbers, composite numbers, prime factorization, factors, multiples and divisibility to solve realworld and mathematical problems (e.g., prime factorization to determine a least common multiple [LCM] or greatest common factor [GCF]). DOK 2 Key Vocabulary 1. Divisibility Rules (2,3,4,5,6,9,10,12) 2. Prime and Composite 3. Exponent 4. Square Root 5. Order of Operations 6. Properties 7. Factor 8. Multiple 9. Prime Factorization 10. Greatest Common Factor 11. Least Common Multiple Activities and Assessments Week Two: Define and apply divisibility rules, identify prime and composite numbers, review exponents and introduce square roots. Week Three: Review order of operations, factors, and multiples. Use the L-Method to complete prime factorization. Week Four: Review GCF and LCM, review for comprehensive unit test. http://www.saab.org/mathdrills/fraction _a.html http://argyll.epsb.ca/jreed/math7/strand1 /1106.htm http://www.mindspring.com/~alanh/frac s.html http://www.bbc.co.uk/skillswise/number s/wholenumbers/multiplication/mental/ http://www.bbc.co.uk/skillswise/number s/wholenumbers/division/mental/ http://mathforum.org/k12/mathtips/divis ion.tips.html http://www.aaamath.com/B/sub39_x2.ht m http://www.aaamath.com/mul.html http://www.skoool.ie/content/skoool_lea rning/junior/lessons/maths/factors_1/int erface.html?id=f1 Essential Questions Kentucky Core Content Version 4.1 Key Vocabulary Activities and Assessments http://library.thinkquest.org/20991/alg/f actoring.html http://www.purplemath.com/modules/fa ctnumb.htm http://sf.factmonster.com/ipka/A093346 9.html http://mathforum.org/dr.math/faq/faq.le arn.factor.html http://amby.com/educate/math/21_GCF.html http://amby.com/educate/math/21_LCM.html http://www.eduplace.com/cgibin/schtemplate.cgi?template=/kids/mw/ help/eh_popup.thtml&grade=6&chapter =3&lesson=3&title=Prime+Factorizatio n&tm=tmfg0303e Essential Questions How do you convert fractions to decimals and percentages and vice versa? Kentucky Core Content Version 4.1 MA-07-1.1.1 Students will provide examples of and describe integers, fractions, decimals, percents, and π. DOK - 1 MA-07-1.1.2 Students will describe and provide examples of representations of numbers (whole numbers, fractions, decimals, percents, integers, square roots and π) and operations in a variety of equivalent forms using models, diagrams and symbols (e.g., number lines, 10 by 10 grids, rectangular arrays, number sentences) based on real-world and mathematical MA-07-1.2.1 MA-07-1.3.1 How do you estimate percentages? MA-07-1.1.1 MA-07-1.1.2 Key Vocabulary 1. 2. 3. 4. 5. 6. 7. 8. Simplest Form Comparing Fractions Ordering Fractions Equivalent Fractions Mixed Numerals Improper Fractions Cancellation Reciprocal Activities and Assessments Week Five: Review reducing fractions and forming equivalent fractions. Review conversions between mixed and improper fractions. Week Six: Review addition and subtraction of fractions, including mixed numbers and renaming. Week Seven: Review multiplying with cross canceling and division of fractions, including mixed numbers. Week Eight: Review all operations and content with fractions to date, prepare for unit assessment. http://www.themathpage.com/ARITH/d ecimals.htm http://www.ricksmath.com/fractions.ht ml http://www.purplemath.com/modules/fr action.htm http://www.mcwdn.org/FRACTIONS/F ractionsMain.html http://www.kidsolr.com/math/fractions. html 1. Fraction Bar (as symbol for division) Week Nine: Review place value and rounding. Introduce conversions Essential Questions Using proportions, how do you solve problems involving percents, ratios, and sales tax? Kentucky Core Content Version 4.1 MA-07-1.2.1 Students will estimate to solve real-world and/or mathematical problems with fractions, decimals, and percents, checking for reasonable and appropriate computational results. DOK - 2 MA-07-1.3.1 Students will add, subtract, multiply and divide whole numbers, fractions and decimals to solve real-world problems and apply order of operations (including positive whole number exponents) to simplify numerical expressions. DOK 2 MA-07-1.4.1 Students will apply ratios and proportional reasoning to solve realworld problems (e.g., percents, sales tax, discounts, rate). DOK - 3 Key Vocabulary 2. Percent 3. “Of” 4. Place Value Activities and Assessments from fractions to decimals and percents. Week Ten: Introduce converting decimals to fractions and percents, as well as percents to fractions and decimals. Week Eleven: Focus on real-world applications of conversions. http://www.saab.org/mathdrills/fraction _a.html http://argyll.epsb.ca/jreed/math7/strand1 /1106.htm http://www.mindspring.com/~alanh/frac s.html http://www.bbc.co.uk/skillswise/number s/wholenumbers/multiplication/mental/ http://www.bbc.co.uk/skillswise/number s/wholenumbers/division/mental/ http://mathforum.org/k12/mathtips/divis ion.tips.html http://www.aaamath.com/B/sub39_x2.ht m http://www.aaamath.com/mul.html Essential Questions How do you use properties to solve problems? Kentucky Core Content Version 4.1 MA-07-1.5.2 Students will identify the use of properties (commutative properties of addition and multiplication, the associative properties of addition and multiplication and the identity properties for addition and multiplication) to justify a given step in solving problems. DOK 1 Key Vocabulary 1. 2. 3. 4. 5. 6. Commutative Associative Additive Identity Multiplicative Identity Zero Property Substitution MA-07-1.5.2 What is an integer? MA-07-1.1.1 MA-07-1.1.2 1. 2. 3. 4. Integer Opposites Positive Negative Activities and Assessments Week Twelve: Introduce KCCT reference guide for properties. Define and identify properties and use to justify steps in a given order of operations problem. http://www.skoool.ie/content/skoool_lea rning/junior/lessons/maths/factors_1/int erface.html?id=f1 http://library.thinkquest.org/20991/alg/f actoring.html http://www.purplemath.com/modules/fa ctnumb.htm http://sf.factmonster.com/ipka/A093346 9.html http://mathforum.org/dr.math/faq/faq.le arn.factor.html http://amby.com/educate/math/21_GCF.html http://amby.com/educate/math/21_LCM.html http://www.eduplace.com/cgibin/schtemplate.cgi?template=/kids/mw/ help/eh_popup.thtml&grade=6&chapter =3&lesson=3&title=Prime+Factorizatio n&tm=tmfg0303e Week Thirteen: Introduce integers and number lines to compare and order. Define all vocabulary terms, discuss applications of integers for the Essential Questions Kentucky Core Content Version 4.1 Key Vocabulary 5. Neutral Number Activities and Assessments real world. Week Fourteen: Introduce adding integers. Week Fifteen: Introduce subtracting integers. Essential Questions How can you use equations and/or formulas to represent real life situations? Does change in one variable affect the change in another, and if so, does it always and why? Are you limited in the numbers of variables you may use to express an everyday situation in an algebraic expression? How do you use inequalities to represent real-life situations? Kentucky Core Content Version 4.1 MA-07-5.1.2 MA-07-5.1.2 Students will represent, analyze and generalize first degree relationships using tables, graphs and words and will apply the relationships to solve real-world and mathematical problems. DOK 2 MA-07-5.1.5 MA-07-5.1.5 Students will explain how the change in one quantity affects the change in another quantity (e.g., in tables or graphs). DOK 2 MA-07-5.2.1 MA-07-5.2.1 Students will substitute values for variables (up to three different variables) and evaluate algebraic expressions. DOK 2 MA-07-5.3.1 Students will model and solve real-world and mathematical problems with one- or two-step single variable, first Key Vocabulary 1. Variable 2. Expression 3. Terms found in translating 4. Equation 5. Inverse Operation 6. Substitution 7. Inequality 8. Inequality Symbols 9. Open Circle 10. Closed Circle Activities and Assessments Week Sixteen: Define variable and expression, practice solving expressions through substitution. Discuss terms used in translating expressions/equations. Week Seventeen: Introduce solving basic equations with addition and subtraction of positive whole numbers. http://www.skoool.ie/content/skoool_lea rning/junior/lessons/maths/addition_sub traction/index.htm http://www.purplemath.com/modules/ex ponent.htm Week Eighteen: Introduce solving basic equation with multiplication and division of whole numbers. Week Nineteen: Begin comprehensive review of Algebraic expressions and equations for midunit test. Week Twenty: Introduce inequalities, symbols, and circles used for graphing. Identify graphs of inequalities. Apply equation rules to solve, translate, and graph positive whole number inequalities. Essential Questions Kentucky Core Content Version 4.1 degree equations or inequalities (e.g., 2x+1 = 9, 3x+3 < 9). (Statements and solutions use only nonnegative numbers.) DOK 2 Key Vocabulary Activities and Assessments Essential Questions Using proportions, how do you solve problems involving percents, rates and sales tax? How do you find percentages using proportions? Name the difference between congruent and similar figures. How do you graph data in a variety of ways? How do you decide which graph to use to display data? When using probability is it beneficial to use counting techniques, tree diagrams, charts, and tables? What is the difference in mean, median, and mode? What is the difference in cluster, gaps, and outliers? Kentucky Core Content Version 4.1 MA-07-1.4.1 MA-07-3.1.4 Students will describe and provide examples of congruent and similar figures and will apply congruent and similar figures to solve real-world and mathematical problems. DOK 2 MA-07-4.1.1 Students will analyze and make inferences from data displays (drawings, tables/charts, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs, stem-and-leaf plots, scatter plots). DOK 3 MA-07-4.1.2 Students will explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related. MA-07-4.2.1 Students will determine Key Vocabulary 1. 2. 3. 4. 5. 6. 7. 8. 9. Ratio Equivalent Ratio Cross Product Rate Unit Rate Proportion “is/of = %/100” Congruent Figures Similar Figures 1. Data 2. Measures of Central Tendency 3. Frequency Chart 4. Bar Graph 5. Histogram 6. Interval 7. Circle Graph 8. Sector 9. Line Graph 10. Key 11. Stem-and-Leaf Plot 12. Line Plot 13. Outlier 14. Cluster 15. Gap 16. Scatterplot 17. Positive Correlation Activities and Assessments Week Twenty-One: Define ratio; write ratios and reduce to lowest terms. Define and discuss rate and unit rate, find unit rates using division. Introduce proportions, practice solving. Week Twenty-Two: Using proportions to set up real-world applications, including basic variables, percents, and similar figures. Week Twenty-Three: Review and create frequency charts and stemand-leaf charts, review measures of central tendency. Review bar graphs, define interval, apply frequency tables to create histograms. Week Twenty-Four: Review circle graph, sectors, make inferences using the circle graph. Review and construct line graphs. Unit Test. Essential Questions Kentucky Core Content Version 4.1 the mean, median, mode and range of a set of data and will identify clusters, gaps and outliers within the data. DOK 2 MA-07-4.1.4 Students will determine and construct appropriate data displays (bar graphs, line plots, Venn diagrams, tables, line graphs, stem-and-leaf plots) and will explain why the type of display is appropriate for the data. DOK 2 Key Vocabulary 18. Negative Correlation 19. No Correlation Activities and Assessments Essential Questions What are the differences in random sampling, stratified sampling, and systematic sampling, and give characteristics of each? What makes theoretical probability different from experimental probability? Using the data that you tabulated, explain how theoretical and experimental probabilities are related? How do you determine the area and perimeter of a rectangle? How do you determine the area and perimeter of a Kentucky Core Content Version 4.1 MA-07-4.4.1 Students will apply counting techniques to determine the size of a sample space for a real-world or mathematical situation. DOK 2 MA-07-4.4.2 Students will: determine theoretical probabilities of simple events; determine probabilities based on the results of an experiment and make inferences from probability data. DOK 3 MA-07-2.1.1 MA-07-2.1.1 Students will measure lengths (to the nearest eighth of an inch or the nearest centimeter) and will determine and use in real-world and Key Vocabulary 1. Probability 2. Experiment 3. Outcome 4. Theoretical Probability 5. Certain 6. Likely 7. Equally Likely 8. Unlikely 9. Impossible 10. Experimental Probability 11. Tree Diagram 12. Fundamental Counting Principle 1. Sides 2. Vertices 3. Angles (Acute, Obtuse, Right) 4. Perpendicular 5. Parallel 6. Intersecting Activities and Assessments Week Twenty-Five: Introduce vocabulary, determine theoretical probabilities and compare results of experiment in class. Week Twenty-Six: Introduce tree diagrams and the fundamental counting principle. Week Twenty-Seven: Begin review of identification of basic geometry elements, describe, and identify their applications to real-world problems. Introduce KCCT Reference sheet. Week Twenty-Eight: Review similar Essential Questions Kentucky Core Content Version 4.1 Key Vocabulary triangle? How do you determine the area and circumference of a circle? What are the characteristic properties of two dimensional figures? What re the differences between and right, acute, and isosceles triangle? What are the differences in congruent and similar figures? mathematical problems: area and perimeter of triangles; area and perimeter of quadrilaterals (rectangles, squares, trapezoids) (using the Pythagorean theorem will not be required as a strategy); area and circumference of circles and area and perimeter of compound figures composed of triangles, quadrilaterals and circles. DOK 2 7. Congruent Parts 8. Two-Dimensional Figures 9. Acute Triangle 10. Obtuse Triangle 11. Scalene Triangle 12. Isosceles Triangle 13. Equilateral Triangle 14. Congruent Figure 15. Similar Figure 16. Formula 17. Transformations MA-07-3.1.2 MA-07-3.1.2 Students will describe and provide examples of the elements (e.g., sides, vertices, angles, Activities and Assessments and congruent figures, use in applications to real-world geometry and measurement. Week Twenty-Nine: Review, identify, and experiment with creating transformations. Week Thirty: Practice finding and transforming figures based on the coordinate plane. Discuss and create tessellations for project grade. Introduce symmetry as time allows. http://www.ucl.ac.uk/Mathematics/geo math/rev/aandv/MHavnb.html http://www.bbc.co.uk/scotland/educatio n/bitesize/standard/mathsI/area/index.sh tml http://www.bbc.co.uk/schools/gcsebitesi ze/maths/shape/arearev1.shtml http://www.bbc.co.uk/schools/gcsebitesi ze/maths/shapeih/areaandvolumerev1.sh tml http://argyll.epsb.ca/jreed/math9/strand3 /3108.htm http://www.aaamath.com/geo.html http://www.mhhe.com/math/devmath/al eks/wtbm/student/olc/graphics/common/media Essential Questions Kentucky Core Content Version 4.1 Key Vocabulary congruent parts) of two-dimensional figures (circles, triangles [acute, right, obtuse, scalene, isosceles, equilateral], quadrilaterals [square, rectangle, rhombus, parallelogram, trapezoid], regular polygons) and will apply these elements and figures to solve real-world and mathematical problems. DOK 2 Activities and Assessments /content/main.htm#0108010129 http://www.mhhe.com/math/devmath/al eks/wtbm/student/olc/graphics/common/media /content/main.htm#0207010131 http://www.bbc.co.uk/schools/gcsebitesi ze/maths/shapeh/circlepropertiesrev1.sh tml http://www.mste.uiuc.edu/dildine/heron/ triarea.html http://www.learningwave.com/chapters/ tools/circle.html MA-07-3.1.4 MA-07-3.1.4 Students will describe and provide examples of congruent and similar figures and will apply congruent and similar figures to solve real-world and mathematical problems. DOK 2 MA-07-3.3.1 REVIEW Weeks Thirty-One through ThirtySix: Review concepts from the year to date as preparation for state assessment. Students will participate in in-depth activities and applications as review.