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Teaching Strategies, Learning Activities, and Differentiation Techniques Mathematical Reasoning and ScienceSkill2014 GED? Assessment TargetRequired Skills*Based upon 2014 GED? Assessment TargetsTeaching StrategiesLearning ActivitiesDifferentiation TechniquesCCR Overarching Standard StatementQuantitative Problem Solvingwith Rational Numbers (25%)2014 GED? Assessment Target Q.1: Apply number sense concepts, including ordering rational numbers, absolute value, multiples, factors, and exponents.4.NF: Extend understanding of fraction equivalence and ordering.6.NS: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.7.NS: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.8.EE: Work with radicals and integer exponents. N.RN: Extend the properties of exponents to rational exponents.Q.1.a: Order fractions and decimals, including on a number line.Q.1.a: Use large group instruction to show a number line on projector – place letters to match locations. Drag & drop, etc.Q.1.b: Will have to teach FOIL pattern to understand distributive property. First demonstrate low numbers and increase difficulty by using letter variables. Show how a larger number expression can be “reduced” or simplified to easier numbers, divide by 10, divide by 100 to decrease numbers. - Reinforce FOIL with a YouTube videoQ.1.c: Share chart of squares compared to multiplication table. Demonstrate square toot to mult. table as well. Demonstrate “chaining” a number to a higher exponent to attach,Q.1.d: Use number lines to refer to thermometers and other real-life number line/negative applications.Make sure that students know their multiplication tables!Talk about how these math problems (and solving them) will help them develop critical thinking skills that will help them on the GED test AND in their everyday life.Students can repeat same using mimio/Students can use worksheets of number lines to match or fill-in decimals/fractions on sheet of paperFind computer instruction on Kahn AcademyFind an interactive numberline on the computer for practice – also uses mouse skillsUse SmartBoard to play Math Jeopardy to identify equivalent fractions/decimalsStudent practice in distributive property with short expressions and increase difficulty. Practice with partners. Try to simplify expression with a white board to erase fastersPrime factor tree worksheet (fill in the blank)Apply the concepts to use in geometry word problems – model real life issues i.e. tiling a floor etc.Students can practice with worksheets that show the solution to an exponent vs numbers multiplied.Find a game online on Multiplication flash cards for those without their basic skillsUse: National Library Virtual Manipulative’s website.Some students may need hands-on manipulatives like a ruler, fraction pieces, or decimal picture cares to place them in order before they can use numeric forms. Advanced students may want to create questions about to do sizes or manufacturing measurementsKeep the acronym in front of the students as pattern – create a worksheet to fill in the missing chain produced in the simplified version.Make a game of “deal or no deal” with exponents and multiplication i.e. I will give you $2.00 a day for 30 days or I will give you $5.00 and increase it exponentially for 4 days. Deal or No Deal?Students may match different flashcards of (hands-on) “2 x 2 with 22 with 4” or “4 x 4 x 4 with 43 with 64” as student gets concept do the 3 matchBalance chemical equationsQ.1.b: Apply number properties involving multiples and factors, such as using the greatest common multiple, greatest common factor, or distributive property to rewrite numeric expressions.Q.1.c: Apply rules of exponents in numerical expressions with rational exponents to write equivalent expressions with rational exponents.Q.1.d: Identify absolute value of a rational number as its distance from 0 on the number line and determine the distance between two rational numbers on the number line, including using the absolute value of their difference.2014 GED? Assessment Target Q.2: Add, subtract, multiply, divide, and use exponents and roots of rational, fraction, and decimal numbers.7.NS: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.7.EE: Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 8.EE: Work with radicals and integer exponents.N.RN: Extend the properties of exponents to rational exponents.N.Q: Reason quantitatively and use units to solve problems.Q.2.a: Perform addition, subtraction, multiplication, and division on rational numbers. Use manipulatives to perform basic functions.ModelingUse real life context to set up practice situations.Explanation of termsUse manipulatives through modelingVideo-Khan Academy,Model thought process used to approach each item type. (Done by following Explicit Instruction Model)Present contextualized real world scenarios and proper application of skills.PEMDASChunking lessons to gradually increase difficulty.“I do, we do, you do” by mapping complex problems into step by step procedures.Vary examples to address sub-topics.Vary examples to link prior knowledge and student interest. Easy way to link to cross-curriculum lesson planning.Whole class instructionSmall group work with students of different levels.Individual practice.Group presentation of problem solving used to accomplish solution.Integrate technology to reinforce the concept via KhanAcademy or other available resources. Provides additional resource outside of the to enrich learning.Scaffolding to meet needs of each individual learner.Engage multiple modalities to address different learning styles. (Manipulatives)Q.2.b: Perform computations and write numerical expressions with squares and square roots of positive, rational numbers.Q.2.c: Perform computations and write numerical expressions with cubes and cube roots of rational numbers.Q.2.d: Determine when a numerical expression is undefined.Q.2.e: Solve one-step or multi-step arithmetic, real world problems involving the four operations with rational numbers, including those involving scientific notation.2014 GED? Assessment Target Q.3: Calculate and use ratios, percents, and scale factors.6.RP: Understand ratio concepts and use ratio reasoning to solve problems.7.RP: Analyze proportional relationships and use them to solve real-world and mathematical problems.7.G: Draw, construct, and describe geometrical figures and describe the relationships between them.N.Q: Reason quantitatively and use units to solve problems.G-MG: Apply geometric concepts in modeling situations.Q.3.a: Compute unit rates. Examples include but are not limited to: unit pricing, constant speed, and persons per square mile, BTUs per cubic foot.Use of Manipulatives, grouping, graphical representations, modeling, Right/Wrong – defend why right and why wrongRecipes – Double, Triple, HalfGraphical representations of D, R, TItem/Price chart – determine if proportional relationshipDetermine proportionality from linear graph to lead to slope.Make trail mix – proportion of fruit to nuts, graph one to the other, find the constantProvide graph/create graphCompare – compare/contrastCompute/explainQ.3.b: Use scale factors to determine the magnitude of a size change. Convert between actual drawing and scale drawings.Q.3.c: Solve multistep, arithmetic, real-world problems using ratios or proportions, including those that require converting units of measure.Q.3.d: Solve multistep, arithmetic, real world problems involving percents. Examples include but are not limited to: simple interest, tax, markups or markdowns, gratuities and commissions, percent increase and decrease.Skill2014 GED? Assessment TargetRequired Skills*Based upon 2014 GED? Assessment TargetsTeaching StrategiesLearning ActivitiesDifferentiation TechniquesCCR Overarching Standard StatementinQuantitative Problem Solvingin Measurement (20%)2014 GED? Assessment Target Q.4: Calculate dimensions, perimeter, circumference, and area of two-dimensional figures.6.EE: Apply and extend previous understandings of arithmetic to algebraic expressions.7.G: Solve real-life and mathematical problems involving angle, measure, area, surface area, and volume. Explain volume formulas and use them to solve problems.8.G: Understand and apply the Pythagorean Theorem. Q.4.a: Compute the area and perimeter of triangles and rectangles. Determine side lengths of triangles and rectangles when given area or perimeter.Give every day examples Wallpaper border is perimeter Paint on the wall is surface area Circle drawn on board to represent circumferenceVocabulary2 dimensionalFacePerimeterCircumferenceRadiusDiameterProvide formulas neededDemonstrate how to solve formulasPresent formula sheet and explain what is supposed to be memorized and how to use each formula using examples.Collect measurements Tools that can be used to measureDivide students into partners.Have e teams solve word problems using formulas.Have students create their own problems where they must find circumference and perimeter of various real world situations.Bring class back together and write out an explanation of the differences between perimeter and circumferenceUse real world topics to show how to use formulas (Ex. Landscaping and building scenarios)Perimeter of fenceArea for grass seedPythagorean theorem for pathwayCircumference of pool/pond/treeYou can use all types of shapes and sizes to illustrate the different types of formulasPartner students so that upper and lower level students work together.All three learning styles are usedCalculator or hand calculationsGroup and individual settingQ.4.b: Compute the area and circumference of circles. Determine the radius or diameter when given area of circumference. Q.4.c: Compute the perimeter of a polygon. Given a geometric formula, compute the area of a polygon. Determine side lengths of the figure when given the perimeter or area. Q.4.d: Compute perimeter and area of 2-D composite geometric figures, which could include circles, given geometric formulas as needed. Q.4.e: Use the Pythagorean theorem to determine unknown side lengths in a right triangle. 2014 GED? Assessment Target Q.5: Calculate dimensions, surface area, and volume of three-dimensional figures.6.EE: Apply and extend previous understandings of arithmetic to algebraic expressions.7.G: Solve real-life and mathematical problems involving angle, measure, area, surface area, and volume.8.G: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.Q.5.a: When given geometric formulas, compute volume and surface area of rectangular prisms. Solve for side lengths or height, when given volume or surface area.L.c.5 Disruption of ecosystems and extinctionResources:TableFormulasTechnology:CalculatorWeb resourcesVocabularyDemonstration with and usage of Manipulatives Websites for modeling volume and surface areaLecture geometric formula for volume and surface area (use demonstration)Word wall or Powepoint or worksheet of vocabulary used in volume and surface areaWeb videos – habitat destruction and deforestation; conservation strategiesDivide class into two groups. 1. Each group is given a problem involving a sample tree and a growth table. Groups will predict the growth of the tree based on the data in the table. 2. Each group then calculates the surface area of the tree to determine the size of tree wrap necessary to protect the tree from winter snow.Physically constructing surface area and volume with cubes and using concrete shapes ie. Kleenex boxWatching videos on YouTube…Introduce vocab. of vol./surf areaEntry ticket of prior knowledge of volume and surface area Practice solving formulas on wkshtsEFL 1-3Focus on vocabulary and determining appropriate formula/operation and basic table reading skillsEFL 4-6Focus on data analysis, making predictions, and deeper exploration of vocabularyAlternative media Partner activities Calculators Level-based progression( use Socrative as deciding tool) Ie. Use Exit ticketQ.5.b: When given geometric formulas, compute volume and surface area of cylinders. Solve for height, radius, or diameter when given volume or surface area.Q.5.c: When given geometric formulas, compute volume and surface area of right prisms. Solve for side lengths or height, when given volume or surface area.Q.5.d: When given geometric formulas, compute volume and surface area of right pyramids and cones. Solve for side lengths, height, radius, or diameter when given volume or surface area. Q.5.e: When given geometric formulas, compute volume and surface area of spheres. Solve for radius or diameter when given the surface area.Q.5.f: Compute surface area and volume of composite 3-D geometric figures, given geometric formulas as needed.2014 GED? Assessment Target Q.6: Interpret and create data displays.3.MD: Represent and interpret data.S.ID: Summarize, represent, and interpret data on a single count or measurable variable.7.RP: Analyze proportional relationships and use them to solve real-world and mathematical problems.8.SP: Investigate patterns of association in bivariate data.Q.6.a: Represent, display, and interpret categorical data in bar graphs or circle graphs.LectureDemonstrationView videosGroup discussionsComputer web searchesHands on science experimentData collection,Data interpretation.Analyze patterns in the data.Model how to make different types of graphs.Students will need to be able to listen for explicit instruction on the formation of the graph creationDisplay the same data in all the different types of graphs given.Internet search: discuss scientific process using websites.Students formulate various hypotheses.Students formulate a classroom science experiment regarding growing tomatoes They must followScientific process. They of course can alter only one variable. Tomatoes are grown in the classroom, data recorded, and students graph data on Excel.Hypothesis is proved or disproved.Poll class and create a graph using info from the class such as…shoe size, hair color, types of clothing, dislikes/likes, track homework over a period time,etc.Use a circle to show percentage of different colors of candy.Scatterplot shoe size to height. Use a line graph to show average salaries from famous people they identify with from year to year.Students are responsible for different activities of the experiment based on their skill levels in a multi-level class.Whole group vs. paired studentsIndividual vs. paired studentsRepresesent numbers vs percentagesLet each individual chose how they represent their data.Add an extension activity to go along with the data informationQ.6.b: Represent, display, and interpret data involving one variable plots on the real number line including dot plots, histograms, and box plots.Q.6.c: Represent, display, and interpret data involving two variables in tables and the coordinate plane including scatter plots and graphs.2014 GED? Assessment Target Q.7: Calculate and use mean, median, mode, and weighted average.6.SP: Develop understanding of statistical variability.S.MD: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.Q.7.a: Calculate the mean, median, mode and range. Calculate a missing data value, given the average and all the missing data values but one, as well as calculating the average, given the frequency counts of all the data values, and calculating a weighted average.Engagement: (I DO) Graph of local temperatures from the previous monthExplain/Model:Define termsShow examples of the different calculations using the temperatures graphTechnology use:Introduce Excel Input data into the spreadsheet and compare answersEngagement: Use scientific results of candy bar samples to find nutritional values (mean, median, mode) Reading candy bar labelsGraph scaffoldingModel/explain: show how to find mean/median/modereading bar graphsinterpreting bar graphsTechUse plotting softwareCollect real-life data: temperature over time, ages of class members, number of family members, etc…Refer to Sport’s Page stats for football, car racing, baseball, etc…Age Activity (WE DO)List the ages of all the studentsUse that data to do the calculations Enter data into Excel and compare results Challenge Question: How would you find a missing age if you were given the average of the ages and the list of ages that had one missing?Write argument which is worst candy bar for body based on fat and sugar Bar graph of different brands candy bar calorie contentDetermine if health claims are valid in advertisingWork backwards to find missing data point when avg. is givenWork with test scores of students to find weighted avg. to determine gradeWhen given median and mode, find missing data pointsCreate” box and whisker” charts.Create graphs/chart using data.Determine fluctuations in statistics depending on games missed due to injury, a bad night at the plate, a blown tire, etc…Discuss how a few ‘high’ or ‘low’ scores can affect the average and how that fluctuation varies ‘depending’ on the number of team members.Assignments (YOU DO)Scaffold data sets of varying complexitySelect individual learning activities to fit student’s ability Include different challenge questions based on student’s abilityUse blocks to model averageScaffold finding mean, median, mode mathematically and pictoriallyModelingChunking informationGroup workUse real-life data2014 GED? Assessment Target Q.8: Utilize counting techniques to determine probabilities.S.CP: Conditional Probability and the Rules of Probability**7.SP: Investigate chance processes and develop, use, and evaluate probability models.Q.8.a: Use counting techniques to solve problems and determine combinations and permutations. Engagement:MarblesTable constructionEquationsVocabulary:RatioProbabilityReducing/lowest termsNumerator/denominatorUse manipulatives to demonstrate probability, combinations, and permutations (different color items, coins, etc,)Discuss factorials (the ! symbol)Group discussionusing marbles to determine probabilityStudents are given instructions for each event through 5 events.students will determine the ratio of striped to black marbles after 5th eventKhan Academy for instruction on combinations and permutationStart with 50% probability, and then make ratios incrementally. Can make more advanced by adding more playersAfter each event, a visual account of the difference in ratios to help determine the final probability at the end of the 5th eventPeer tutoring and reviewsQ.8.b: Determine the probability of simple and compound events. ** Denotes a CCSS STEM standard; not included among the core adult learning standards. Skill2014 GED? Assessment TargetRequired Skills*Based upon 2014 GED? Assessment TargetsTeaching StrategiesLearning ActivitiesDifferentiation TechniquesCCR Overarching Standard StatementAlgebraic Problem Solving withExpressions and Equations (30%)2014 GED? Assessment Target A.1: Write, evaluate, and compute with expressions and polynomials.6.EE: Apply and extend previous understandings of arithmetic to algebraic expressions. Reason about and solve one-variable equations and inequalities. 7.EE: Use properties of operations to generate equivalent expressions.A.APR: Perform arithmetic operations on polynomials.A.SSE: Interpret the structure of expressions. Write expressions in equivalent forms to solve problems. A.1.a: Add, subtract, factor, multiply and expand linear expressions with rational coefficients.Make sure that students know their multiplication tables!Talk about how these math problems (and solving them) will help them develop critical thinking skills that will help them on the GED test AND in their everyday life.A.1.b: Explicit InstructionVocabularyTeach distributive propertiesManipulativesUse: National Library Virtual Manipulative’s website.Hands on Activities – different color M n M candyAlgebra TilesOnline resources – ex: Khan AcademyMultiplication flash cards for those without their basic skills.TutorsSmall GroupSimple and complex expressionsManipulativesA.1.b: Evaluate linear expressions by substituting integers for unknown quantities.A.1.c: Write linear expressions as part of word-to-symbol translations or to represent common settings.A.1.d: Add, subtract, multiply polynomials, including multiplying two binomials, or divide factorable polynomials.A.1.e: Evaluate polynomial expressions by substituting integers for unknown quantities.A.1.f: Factor polynomial expressions.A.1.g: Write polynomial expressions as part of word-to-symbol translations or to represent common settings.A.1.h: Add, subtract, multiply and divide rational expressions.A.1.i: Evaluate rational expressions by substituting integers for unknown quantities.A.1.j: Write rational expressions as part of word-to-symbol translations or to represent common settings.2014 GED? Assessment Target A.2: Write, manipulate, and solve linear equations.6.EE: Reason about and solve one-variable equations and inequalities. 7.EE: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.8.EE: Analyze and solve linear equations and pairs of simultaneous linear equations.A.REI: Solve equations and inequalities in one equation.A.CED: Create equations that describe numbers or relationships.A.2.a: Solve one-variable linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms or equations with coefficients represented by letters. Concept buildingModeling using scales and number blocks to represent equations. Using models, substitute in values for x-guess and test by hands-on movement of pawns and blocks.To increase complexity, increase numbers and steps.Paper pencil algorithm.Introduce equations for a line.Substitute in values for x-guess and test by hands-on movement of pawns and blocks. Using graphing calculatorsBeginning-use pawns and blocksIntermediate- Use Area model for AlgebraPaper/pencil, whiteboard, and dry erase board.For Advanced students-solve for a particular variable in a problem, for example y=mx+b.A.2.b: Solve real-world problems involving linear equations.A.2.c: Write one-variable and multi-variable linear equations to represent context.A.2.d: Solve a system of two simultaneous linear equations by graphing, substitution, or linear combination. Solve real-world problems leading to a system of linear equations.2014 GED? Assessment Target A.3: Write, manipulate, solve, and graph linear inequalities.6.EE: Reason about and solve one-variable equations and inequalities.7.EE: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.A.REI: Solve equations and inequalities in one equation.A.CED: Create equations that describe numbers or relationships.A.3.a: Solve linear inequalities in one variable with rational number coefficients.Algebra vocabularyExplicit instructionExplainModelGuided practiceApplicationManipulatives (real-life items) to represent the values used in the inequalities. Use graphic organizers to add visual component. Gather information (prices) from a store’s website (technology component).Students solve a given problem and use colored pencils to graph the answerConstruct a symbol chart to remember greater than and less thanShopping Spree activity. Students develop/given a list of items to buy. Total spent must be under or less than a certain amount of money. This could be used for a holiday meal, school shopping, etc. The one variable (x) represents dollars. Price of items in terms of x (e.g. $5 item costs 5x, $12 item costs 12x).Assign student activities by complexity levelBudgeting household expenses to not exceed income.Include % discounts to take it to multi-step problems.Buying multiple items in various combinations. (6 times 5x)A.3.b: Identify or graph the solution to a one variable linear inequality on a number line.A.3.c: Solve real-world problems involving inequalities. A.3.d: Write linear inequalities in one variable to represent context.2014 GED? Assessment Target A.4: Write, manipulate, and solve quadratic equations.A.REI: Solve equations and inequalities in one equation.A.CED: Create equations that describe numbers or relationships.A.4.a: Solve quadratic equations in one variable with rational coefficients and real solutions, using appropriate methods. (e.g., quadratic formula, completing the square, factoring, inspection.)Vocabulary including quadratic equationsGraphing various values Provide examplesDrill and PracticeLeveled groups“Write” a quadratic formula by having students memorize and recite it to the class the next day using different tones of voice--as a pregnant women, as a rap, as someone using the restroom, etc. All say some thing but it is entertaining. “Manipulate” with graphing tools to show students how it looks.Teach perfect squareUse story problems to demonstrate real life situations and what it means to solve a quadratic equation.Using graph along side the story problem to demonstrate what the meaning of the points on the graph represent.Generating a graph/chartUse input/output chartAnalysis of an existing chart that is non-linearIdentify relationships between input and outputs. How to read points on a coordinate plane.Story problems to a table to a graphUsing the graphing toolTrial and errorFactoring vs Solving Predicting outcomesDefining Vocabulary related to Quadratics Leveled groupsLower students could plot the points on the graph, input and output table. Higher level students could figure out the units used on the x/y axisCooperative learningA.4.b: Write one-variable quadratic equations to represent context.Skill2014 GED? Assessment TargetRequired Skills*Based upon 2014 GED? Assessment TargetsTeaching StrategiesLearning ActivitiesDifferentiation TechniquesCCR Overarching Standard StatementAlgebraic Problem Solving withGraphs and Functions (25%)2014 GED? Assessment Target A.5: Connect and interpret graphs and functions.6.NS: Apply and extend previous understandings of numbers to the system of rational numbers.8.F: Define, evaluate, and compare functions. Use functions to model relationships between quantities.8.EE: Understand the connections between proportional relationships, lines, and linear equations.A.CED: Create equations that describe numbers or relationships.F.IF: Interpret functions that arise in applications in terms of the context. Analyze functions using different representations.A.5.a: Locate points in the coordinate plane.A.5.aVocabularyCoordinate grids QuadrantsMathematical Reasoning, pg 70-71 (Explicit Instruction and Guided Practice);Use of Technology - Hot Spot PracticeA.5.bVocabularyCoordinate gridsMathematical Reasoning pg 74-75Use of Slope formulaMulti-step Problem-solvingUse of Technology – Fill in blankA.5.b + SP.6.dPlot Points on a graph using real-world relationships from nutrition labelsCompare lines from different productsCompare old/new serving sizesCompare regular vs. liteA.5.dMathematical Reasoning pg Example:Multiple representationsGraph TablesEquationsUse of technologyGraphing calculatorsSpreadsheetsVocabulary developmentProgressions for the Common Core State Standards in Mathematics: FunctionsA.5.aStudents plot, locate and identify points; student whiteboards; Graphit; Workbook pg 98-101Create personal gridA.5.bPlotting points, finding slope of linestudent whiteboards;Workbook pg 106-109Math Can Do project lesson, story to plot points.A.5.b + SP.6.dMake graphsPlot dataIdea of steepnessLook at new graph – determine cal/servingUse graph to create a tableUse a table to create graphIdentify slope (single serving) from just two data pointsA.5.dWorkbook pg Example:Mathematical Models with Applications 2: The Sounds of MusicEgg Launch ContestRiding a Ferris Wheel Has Its Ups and DownsGraphs (2004)Graphs (2007)Sorting FunctionsA.5.aCooperative groups (include multi-level students in each group)“If you do not use you, you lose it. We need a review.”Example:Compare different functionsLinearQuadraticHigher-order functions (e.g., cubic)ExponentialLogarithmicTrigonometricA.5.b + SP.6.dEasier vs. Harder data sets to plotA.5.b: Determine the slope of a line from a graph, equation, or table.A.5.c: Interpret unit rate as the slope in a proportional relationship.A.5.d: Graph two-variable linear equations.A.5.e: For a function that models a linear or nonlinear relationship between two quantities, interpret key features of graphs and tables in terms of quantities, and sketch graphs showing key features of graphs and tables in terms of 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. 2014 GED? Assessment Target A.6: Connect coordinates, lines, and equations.A.CED: Create equations that describe numbers or relationships.G.GPE: Expressing Geometric Properties with Equations**A.6.a: Write the equation of a line with a given slope through a given point.SubstitutionUnderstand coordinate planeVocabulary & DevelopmentPrior knowledge of coordinate plane/slopeSolve equations.Review relationship of equations and graphs.Review vocabulary associated with equations and graphs.Plot an equation together.Graph data based on Science concepts - temperature, mass acceleration, traveling, and distance, miles per hr. Find points on a line, find the slope, determine the y intercept. Use the information to determine the equation of that line.Look at graph line already produced and discuss how to write the appropriate equation.In pairs, have students complete practice problems.Students will present their solutions to the classTranslate to basic algebraic equation. Review prior knowledge. Use a manipulative of a simple roof/slope.This is a higher level math. It would be frustrating to the lower level students and would not be presented to them till they are ready.A.6.b: Write the equation of a line passing through two given distinct points.A.6.c: Use slope to identify parallel and perpendicular lines and to solve geometric problems. 2014 GED? Assessment Target A.7: Compare, represent, and evaluate functions.8.EE: Understand the connections between proportional relationships, lines, and linear equations.8.F: Define, evaluate, and compare functions.F.IF: Understand the concept of a function and use function notation. Analyze functions using different representations.A.7.a: Compare two different proportional relationships represented in different ways. Examples include but are not limited to: compare a distance-time graph to a distance-time equation to determine which of two moving objects has a greater speed.Multiple Representations: GraphTableRuleEquationsTechnology:Graphing calculatorsExcel spreadsheetsComputer delivered instructionVocabulary development Reading1. PowerPoint of variety of graphs2.Vocabulary ( data, x-axis, y-axis, line graph, bar graph, etc.)3. Use technology(PPT, Learning videos)Using the National Weather Service:Students will gather data to develop a table for comparison of average rainfall for a month.Students draw individual graphs and use data from M&M packs using coordinating colored pencils.Use same data and turn into different types of graphsMulti ability groupsPeer TutoringKahn AcademyUse graph paperGive student choice of graph to designA.7.b: Represent or identify a function in a table or graph as having exactly one output (one element in the range) for each input (each element in the domain).A.7.c: Evaluate linear and quadratic functions for values in their domain when represented using function notation.A.7.d: Compare properties of two linear or quadratic functions each represented in a different way (algebraically, numerically in tables, graphically or by verbal descriptions). Examples include but are not limited to: given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.** Denotes a CCSS STEM standard; not included among the core adult learning standards. Skill2014 GED? Science PracticeRequired Skills*Based upon 2014 GED? Science PracticesTeaching StrategiesLearning ActivitiesDifferentiation TechniquesCCR CorrelationsAnalyze Scientific and Technical Arguments, Evidence, and Text-based Information (30%)2014 GED? Science Practice SP.1: Comprehending scientific presentationsCCR Anchor Standards for Reading: R.2, R.4, R.8CCR Anchor Standard for Language: L.4CCR Standards for Mathematical Practice: MP.2, MP.4, MP.6 SP.1.a: Understand and explain textual scientific presentations. Independent reading, sections at a time, highlighting & underlining.Group discussion and student questions followed by teacher inquiry.Examine, discuss, and create graphs & diagrams.Vocabulary developmentScientific TerminologyModelFlow ChartsDemonstrationAn activity which includes individual students collecting data and graphing it.Students present their data and graph to the class.Graphs at different tablesTrack weather-look at pattern of storm-Do regions-Changing seasonsStudents are assigned different levels in the data they collect and the type of graph they generate from that data.Working in a group-Lower level would do the driving-Higher level would explainWork in partners high with low levelSP.1.b: Determine the meaning of symbols, terms and phrases as they are used in scientific presentations. 2014 GED? Science Practice SP.3: Reasoning from dataCCR Anchor Standards for Reading: R.1SP.3.a: Cite specific textual evidence to support a finding or conclusion. Research topic related to collected data.Support a hypothesis with textual evidence.Choose text, talk about big idea “concept”, highlight vocabulary needed, define vocabulary. Include physical and digital resources. Teach main idea AND supporting details. Use text evidence to support findings in data collection.Pose a question for which students will formulate a hypothesis, then find evidence to support.Read article/text as a group, read independently highlighting vocabulary and main ideas/concepts. Independently define vocab./main ideas, and as a group reread article/text and talk about conclusions.Pose questions of different levels.Either provide materials for supporting evidence or have students do their own research.Choose article/text with different EFL’s. Depending on level either give them a conclusion or let them draw their own conclusions.2014 GED? Science Practice SP.5: Working with findings CCR Anchor Standard for Reading: R.9CCR Standards for Mathematical Practice: MP.3, MP.7 SP.5.a: Reconcile multiple findings, conclusions or pare and contrast.Discuss the various theories of global warming: does it really exist?Review data from different studies to analyze and compare and contract findings and determine how scientists use the data to make scientific ‘conclusions’.Students perform experiments and compare findings.Use the internet to research scientific and general public articles on global warmingLevel of experiment.Amount of scaffolding in assigned experiment.ChunkingWork groupsTechnology2014 GED? Science Practice SP.6: Expressing scientific informationCCR Anchor Standard for Reading: R.7CCR Anchor Standard for Writing: W.2CCR Standards for Mathematical Practice: MP.2, MP.6 SP.6.c: Express scientific information or findings verbally.Skill2014 GED? Science PracticeRequired Skills*Based upon 2014 GED? Science PracticesTeaching StrategiesLearning ActivitiesDifferentiation TechniquesCCR CorrelationsApplying Scientific Processes andProcedural Concepts (40%)2014 GED? Science Practice SP.2: Investigation design (experimental and observational)CCR Anchor Standards for Reading: R.2, R.5, R.8, R.9CCR Anchor Standards for Writing: W.5, W.7CCR Standards for Mathematical Practice: MP.3, MP.4, MP.8S.MD: Statistics and Probability: Using Probability to Make DecisionsSP.2.a: Identify possible sources of error and alter the design of an investigation to ameliorate that error.Warm Up: *define terms*Provide example Presentation:*KWL chart *provide explicit instruction*read scientific article*class discussion*form hypothesis*conduct experiment*website dataThe teacher will:prepare the materials for simple investigations that can be done in class.explicitly present the process of a scientific investigation.model vocabulary with contextuse questioning strategies to evaluate the design of the investigationprovide charts to consider strengths and weaknesses Practice:*Textbook/internet reading*Guided practice*small group activity*large group discussionThe student will:prepare and complete a simple investigation (baking soda/vinegar, oil/water, etc)re-form hypotheses based on real-life results and re-perform investigationuse vocabulary within context*reword/re-explain *students explain in their own words*scaffold *reduce number of questions or answers on practice itemsTo provide support for students:lower levels sequence process cards; higher levels create the cards and then sequence processsome see video, some watch a model, some need to do hands-on on own or with othersSP.2.b: Identify and refine hypotheses for scientific investigations.SP.2.c: Identify the strength and weaknesses of one or more scientific investigation (i.e. experimental or observational) designs.SP.2.d: Design a scientific investigation.SP.2.e: Identify and interpret independent and dependent variables in scientific investigations. 2014 GED? Science Practice SP.3: Reasoning from dataCCR Anchor Standards for Reading: R.1, R.2, R.3CCR Standards for Mathematical Practice: MP.3, MP.4, MP.7, MP.8SP.3.b: Reason from data or evidence to a conclusion.SP.3.c: Make a prediction based upon data or evidence.2014 GED? Science Practice SP.4: Evaluating conclusions with evidenceCCR Anchor Standard for Reading: R.8CCR Standards for Mathematical Practice: MP.3, MP.7SP.4.a: Evaluate whether a conclusion or theory is supported or challenged by particular data or evidence. 2014 GED? Science Practice SP.7: Scientific theoriesCCR Anchor Standards for Reading: R.3, R.5CCR Anchor Standards for Language: L.3CCR Standards for Mathematical Practice: MP.2, MP.4SP.7.a: Understand and apply scientific models, theories and processes. Skill2014 GED? Science PracticeRequired Skills*Based upon 2014 GED? Science PracticesTeaching StrategiesLearning ActivitiesDifferentiation TechniquesCCR CorrelationsReasoning Quantitatively and InterpretingData in Scientific Contexts (30%)2014 GED? Science Practice SP.1: Comprehending scientific presentationsCCR Standards for Mathematical Practice: MP.2, MP.4, MP.6S.ID: Statistics and Probability: Interpreting Categorical and Quantitative DataSP: Statistics and ProbabilitySP.1.c: Understand and explain non-textual scientific presentations.2014 GED? Science Practice SP.3: Reasoning from dataCCR Standards for Mathematical Practice: MP.4, MP.7, MP.8S.CP: Statistics and Probability: Conditional Probability and the Rules of ProbabilitySP: Statistics and ProbabilitySP.3.d: Using sampling techniques to answer scientific questions.2014 GED? Science Practice SP.6: Expressing scientific information CCR Anchor Standard for Reading: R.7CCR Anchor Standard for Writing: W.2CCR Standards for Mathematical Practice: MP.2, MP.4, MP.6SP.6.a: Express scientific information or findings visually.SP.6.b: Express scientific information or findings numerically.2014 GED? Science Practice SP.7: Scientific theories CCR Standards for Mathematical Practice: MP.2, MP.4, MP.8SP.7.b: Apply formulas from scientific theories.Multiple:RepresentationsGraphs, Geometric shapes, chartsChemicalsExplosionTechnologyPowerPoint, microscope, videos, SmartBoardPerform chemical explosion/experiment and relate results to Big Bang TheoryShow video discuss facts as presentedCreate evolutionary chartScaffoldingOpen ended questionsStudent demonstration/teachingRole Play (different periods)2014 GED? Science Practice SP.8: Probability and statisticsCCR Standards for Mathematical Practice: MP.4, MP.6S.MD: Statistics and Probability: Using Probability to Make DecisionsS.ID: Statistics and Probability: Interpreting Categorical and Quantitative DataSP: Statistics and ProbabilityS.CP: Statistics and Probability: Conditional Probability and the Rules of ProbabilitySP.8.a: Describe a data set statistically.Survey students as an opening discussionExplicit instruction on calculating probabilityExplainModelGuided practiceApplicationCover relevant vocabulary termsDiscovery, Graphic Organizer, Excel (spreadsheets and creating graphs), presentation of outcomes, analysisSurvey students for favorite fast food, candy bars, etcMake a chart of the results and answer probability questionsUsing M&M’s, Chex Mix, mixed nuts,(don’t use Skittles, they’ve been recalled), do the typical probability experiment. Other data sets can be created using characteristics of people in the room.Scaffolding charts of varying complexityWork in pairs on worksheets of varying complexityIncorporate probability in more complex work problemsLocate statistics on internet and determine the validity of that statistic.Use excel to create spreadsheets.SP.8.b: Use counting and permutations to solve scientific problems.SP.8.c: Determine the probability of events. ................
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