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Grade 8Unit:1.1Unit & Lesson OverviewsRational NumbersMathematicsDays :20Essential QuestionsHow do you write rational numbers as decimals and as fractions?How do you multiply rational numbers?How do you divide rational numbers?How do you add and subtract fractions with unlike denominators?How do you solve equations that contain rational numbers?How do you solve equations that contain multiple operations?Content to be LearnedSkillsWriting rational numbers as decimals and fractions as well as1.1 Rational Numbersmultiplying and dividing rational numbers.1.2 Multiplying Rational NumbersThe sum and difference of fractions with unlike denominators will1.3 Dividing Rational Numbersbe found using a common denominator as well as solving equations1.4 Adding and Subtracting with Unlike Denominatorswith rational numbers.1.5 Solving Equations with Rational NumbersLearn to identify and apply the appropriate property of equality for1.6 Solving Two-Step Equationsa given real world situation.Practice writing and solving two-step equations for real worldsituations.AssessmentsStandards1.1/1.2/1.3 Quiz (9 days)8.NS.11.4/1.5 Quiz (7 days)8.EE.7b1.6 Unit Test (4 days)Sample Instructional ActivitiesResourcesConverting Decimal Representations of Rational Numbers toExplorations in Core MathFraction RepresentationsIllustrative MathematicsConverting Repeating Decimals to FractionsRevised 8/24/2014

Grade 8Unit: 1.1Unit & Lesson OverviewsMultiplying and Dividing Rational NumbersLesson 1 of 2MathematicsDays 9Lesson Focus1. Standards Addressed8.NS.18.EE.7b2. Content to be LearnedWriting rational numbers asdecimals and fractions as well asmultiplying and dividing rationalnumbers.3. Mathematical PracticesStandard 2. Reason abstractlyand quantitatively.Standard 7. Look for and makeuse of structure.4. Essential QuestionsHow do you write rationalnumbers as decimals and asfractions?How do you multiply rationalnumbers?How do you divide rationalnumbers?5. Prerequisite KnowledgeConverting fractions intodecimals.Rational numbersRewriting mixed numbers asimproper fractionsRewriting improper fractions asmixed numbers6. Essential VocabularyRational numberIrrational numberRepeating decimalTerminating decimalReciprocalsInverse7. Possible MisconceptionsThe difference between aterminating and non-terminatingdecimal.Not multiplying by the reciprocalwhen dividing.How many places to move thedecimal point when multiplyingor dividing.Translating from horizontal formto the “division house” form. (notknowing the difference betweenthe dividend and the divisor)8. Teaching MaterialsExplorations in CORE MATHConverting DecimalRepresentations of RationalNumbers to FractionRepresentationsConverting Repeating Decimalsto FractionsRevised 8/24/2014

Grade 8Unit & Lesson OverviewsMathematicsSuggested Learning Practices9. Instruction Practices (What are the teachers doing)Lesson on Rational Numbers Show QR Reader video and then read the Essential question. Askstudents to brainstorm some rational numbers. Direct students to do Example 1. Have the students pay specialattention to whether or not their decimal terminates or repeats. Have students do Example 2. (may want to do a quick mini lessonon repeating decimals and their fraction representation) Have students practice some problems and close with the essentialquestion.10. Learning Practices (What are the students doing) Students will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question;how do you write rational numbers as decimals and as fractions?Student led discussion on the rational numbers they have sharedwith the class.Students will work on Example 1 in their groups and follow with astudent led discussion on the difference between a terminating andrepeating decimal.Students will discuss their results and share them with theirclassmates. Students will work on their practice problems and then discuss theEssential question; how do you write rational numbers as decimalsand as fractions? Students will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question;how do you multiply rational numbers?Students will work on Example 1 in their groups and discusswhether their solutions make sense.Students work on Example 2 as well as discussing how to go frommixed numbers to improper fractions and improper fractions tomixed numbers.Lesson on Multiplying Rational Numbers Show QR Reader video and then read the Essential question.Remind students that whole numbers/integers can be written asfractions with a denominator of 1.Have students do Example 1. Remind students about thereasonableness of their solutions.Instruct students to do Example 2. (You may want to do a quickmini lesson on changing mixed numbers to improper fractions andimproper fractions to mixed numbers). Also remind students aboutrules when multiplying positive and negative numbers.Have students practice some problems and close with the essentialquestion. Students will work on the problems while sharing their solutionsand then discuss the Essential question; how do you multiplyrational numbers?Revised 8/24/2014

Grade 8Unit & Lesson OverviewsLesson on Dividing Rational Numbers Show QR Reader video and then read the Essential question. Have students work on Example 1. Remind students that they needto be careful with decimal placement. Can also remind them thatthey can use multiplication to check their decimal division. Samerules apply when multiplying positive and negative numbers. Instruct students to do Example 2. Remind them when dividingfractions they are actually multiplying by the reciprocal or inverse. Have students practice some problems and close with the essentialquestion. Remind students about moving the decimal point as wellas multiplying by the reciprocal when working with fractions. MathematicsStudents will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question;how do you divide rational numbers?Students will work on Example 1 in their groups and discuss theirresults.Students work on Example 2 as well as discussing how to checktheir results.Students will work on the problems while sharing their solutionsand then discuss the Essential question; how do you divide rationalnumbers?Revised 8/24/2014

Grade 8Unit: 1.1Unit & Lesson OverviewsAdding and Subtracting Fractions and SolvingEquationsLesson 2 of 2MathematicsDays 11Lesson Focus1. Standards Addressed8.EE.7b5. Prerequisite KnowledgeAdding and subtracting with likedenominators.Solving equations with integers.2. Content to be LearnedThe sum and difference offractions with unlikedenominators will be found usinga common denominator as wellas solving equations with rationalnumbers.Learn to identify and apply theappropriate property of equalityfor a given real world situation.Practice writing and solving twostep equations for real worldsituations.6. Essential VocabularyNumeratorDenominatorLinear equationVariableTermCoefficientConstant3. Mathematical PracticesStandard 2. Reason abstractlyand quantitatively.4. Essential QuestionsHow do you add and subtractfractions with unlikedenominators?How do you solve equations thatcontain rational numbers?How do you solve equations thatcontain multiple operations?7. Possible MisconceptionsAdding denominators whenadding/subtracting fractions.Not finding a commondenominator when adding orsubtracting.Not following proper steps whensolving equations. (not using theproperties of equality the correctway)When dividing by a fraction notmultiplying by the inverse.8. Teaching MaterialsExplorations in CORE MATHRevised 8/24/2014

Grade 8Unit & Lesson OverviewsMathematicsSuggested Learning Practices9. Instruction Practices (What are the teachers doing)Lesson on Adding and Subtracting with Unlike Denominators Show QR Reader video and then read the Essential question. Instruct students to do Example 1. Remind them that in order to addand subtract fractions with unlike denominators that they must finda common denominator. Ask some groups to share how theyarrived at their solutions.Instruct students to practice some problems. Let them know youwill be reviewing them one problem at a time as groups completethe task.Close with the Essential question and then ask students for the keypoints.Lesson on Solving Equations with Rational Numbers Show QR Reader video and then read the Essential question. Instruct students to begin Example 1. Emphasize the importance ofdefining a variable. Remind them that they are looking to isolate thevariable to make the equation true, while using the properties ofequality to keep the equation balanced. (Explain that they can checktheir work by plugging in their solution to the original problem)Instruct students to begin Example 2, once again emphasize theimportance of defining a variable. Also give the students a friendlyreminder on needing a common denominator when adding orsubtracting.Have students do Example 3. Remind them that you undomultiplication by using the opposite operation division. Point outthat the word descended indicates a negative amount.Have students do Example 4. Remind them that you undo divisionby using the opposite operation multiplication.Have students practice some problems and close with the essentialquestion. Remind students about the properties of equality when10. Learning Practices (What are the students doing) Students will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question;how do you add and subtract fractions with unlikedenominators? Students will work on Example 1 in their groups and discusswhether their solutions make sense. Some students will presenttheir results to the class explaining their steps. Students will work on their problems in their groups and presenttheir result to the entire class. Students will brainstorm some key points sharing their results withthe class. Students will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question;how do you solve equations that contain rational numbers? Students will work on Example 1. They will share their results.Have a student led discussion on the steps they used to solve theequation. Students will work on Example 2 and share their results with theclass. Students will work on the example and share their solutions withthe class. Students work on Example 4 sharing their solutions. Students will work on the problems while sharing their solutionsRevised 8/24/2014

Grade 8Unit & Lesson Overviewssolving equations.Mathematicsand then discuss the Essential question; how do you solveequations that contain rational numbers?Lesson on Solving Two-Step Equations Show QR Reader video and then read the Essential question.Remind students that when solving a two-step equation that youtypically undo the operations in reverse order. You undo additionand subtraction before you undo multiplication and division. Instruct students to begin Example 1. (Explain that they can checktheir work by plugging in their solution to the original problem) Instruct students to begin Example 2, once again emphasize theimportance of defining a variable.Have students practice some problems and close with the essentialquestion. Remind students about the properties of equality whensolving equations. Students will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question;how do you solve equations that contain multiple operations? Students will work on Example 1. They will share their results.Have a student led discussion on the steps they used to solve theequation.Students will work on Example 2 and share their results with theclass.Students will work on the problems while sharing their solutionsand then discuss the Essential question; how do you solve equationsthat contain multiple operations?Revised 8/24/2014

Grade 8Unit:1.2Unit & Lesson OverviewsGraphs and FunctionsMathematicsDays : 12Essential QuestionsHow do you determine whether an ordered pair is a solution to an equation?How do you locate and name points in the coordinate plane?How can you describe a relationship given a graph and sketch a graph given a description?How do you represent a function with a table or graph?How can you use equations, tables, and graphs to represent relationships between two variables?Content to be LearnedSkillsDetermining whether ordered pairs are solutions to equations as2.1 Ordered Pairswell as locating points on a coordinate plane.2.2 Graphing on a Coordinate PlaneDescribe relationships given a graph while sketching a graph given2.3 Interpreting Graphsa description.2.4 FunctionsRepresent functions with a table or graph as well as using equations,2.5 Equations, Tables, and Graphstables, and graphs to represent relationships between two variables.AssessmentsStandards2.1/2.2 Quiz (3 days)8.EE.82.3/2.4 Quiz (5 days)8.SP.12.1-2.5 Unit Test (4 days)8.F.58.F.18.F.4Sample Instructional ActivitiesResourceshttp://ccssmath.org/?page id 707Explorations in CORE MATHGraphing StoriesRevised 8/24/2014

Grade 8Unit: 1.2Unit & Lesson OverviewsGraphs and FunctionsLesson 1 of 1MathematicsDays 12Lesson Focus1. Standards Addressed8.EE.88.SP.18.F.58.F.18.F.42. Content to be LearnedDetermining whether orderedpairs are solutions to equations aswell as locating points on acoordinate plane.Describe relationships given agraph while sketching a graphgiven a description.Represent functions with a tableor graph as well as usingequations, tables, and graphs torepresent relationships betweentwo variables.3. Mathematical PracticesStandard 2. Reason abstractlyand quantitatively.Standard 6. Attend to Precision.Standard 3. Construct viablearguments and critique thereasoning of others.Standard 4. Model withMathematics.5. Prerequisite KnowledgeSolving one variable equations.SolutionsOrdered pairs6. Essential VocabularyCoordinate planeFunctionLinear functionnonlinear functionRate of changeInput, outputOrdered pairOriginQuadrantx-axis, x-coordinatey-axis, y-coordinate7. Possible MisconceptionsReversing the (x, y) coordinateswhen graphing.Not labeling graphs the properway. (time is always representedas the independent variable)Some students may confuse therate of change (change iny/change in x) and do theopposite.4. Essential QuestionsHow do you determine whetheran ordered pair is a solution to anequation?How do you locate and namepoints in the coordinate plane?How can you describe arelationship given a graph andsketch a graph given adescription?How do you represent a functionwith a table or graph?How can you use equations,tables, and graphs to representrelationships between twovariables?8. Teaching MaterialsExplorations in CORE MATHGraphing StoriesSuggested Learning Practices9. Instruction Practices (What are the teachers doing)Lesson on Ordered Pairs Show QR Reader video and then read the Essential question.10. Learning Practices (What are the students doing) Students will watch the video taking notes. The class will discussRevised 8/24/2014

Grade 8Unit & Lesson OverviewsMathematicsthe video and the students will highlight the Essential question;how do you determine whether an ordered pair is a solution ofan equation? Instruct students to do Example 1. Remind students that whenplugging in the ordered pair (3, 15) (x, y); the value 3 represents thex-value and the value 15 represents the y-value. Thus order in anordered pair is important.Have students practice some problems and close with the Essentialquestion. Students do Example 1 showing their solutions to the class. Students will work on the problems while sharing their solutionsand then discuss the Essential question; how do you determinewhether an ordered pair is a solution of an equation?Lesson on Graphing on a Coordinate Plane: Show QR Reader video and then read the Essential question. Instruct students to do Example 1. Remind them once again that thecoordinate plane is formed by two number lines. The x-axis orhorizontal number line and the y-axis or the vertical number line.These axes intersect at right angles to divide the plane into fourquadrants.The point where the two axes intersect is the origin and labeled bythe ordered pair (0, 0). In an ordered pair (x, y) the first number isthe x-coordinate. It tells how many units to move right or left. They-coordinate tells how many units to move up or down.Have students practice some problems and discuss the Essentialquestion.Lesson on Interpreting Graphs Show QR Reader video and then read the Essential question. how do you locate and name points in the coordinate plane? Students will work on Example 1 and discuss their solutions in astudent led discussion. Students will work on the problems while sharing their solutionsand then discuss the Essential question; how do you locate andname points in the coordinate plane? Instruct students to do Explore 1. Point out that time is alwaysgraphed on the x-axis. Instruct students to do Explore 2 paying special attention to thethree situations in the three graphs.Instruct students to do Explore 3. Students will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question;how can you describe a relationship given a graph and sketcha graph given a description? Students will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question; Students will do Explore 1 as a group and provide their solutions tothe class when done.Students will do Explore 2 and share their solutions to the class.Students will do Explore 3 and share their solutions to the class.Students will work on the problems while sharing their solutionsand then discuss the Essential question; how can you describe aRevised 8/24/2014

Grade 8 Unit & Lesson OverviewsLesson on Functions Show QR Reader video and then read the Essential question.Mathematicsrelationship given a graph and sketch a graph given adescription?Have students practice some problems and close with the Essentialquestion. Students will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question; Students will do Explore 1 as a group and provide their solutions tothe class when done.Students will do Explore 2 and share their solutions to the class. Students will do Explore 3 and share their solutions to the class. Students will work on the problems while sharing their solutionsand then discuss the Essential question; how do you represent ahow do you represent a function with a table or graph? Instruct students to do Explore 1. Instruct students to do Explore 2 reminding them that in a table theleft column or input represents x, while the right column or outputrepresents y.Instruct students to do Explore 3. Have students practice some problems and close with the Essentialquestion.Lesson on Equations, Tables, and Graphs Show QR Reader video and then read the Essential question. Have students do Example 1. Remind the students that they haveused equations to make tables and graphs and will now be movingin the opposite direction to write equations from tables.Have students practice some problems and close with the Essentialquestion.function with a table or graph? Students will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question;how can you use equations, tables, and graphs to representrelationships between two variables?Students will do Example 1 sharing their solutions with theirclassmates.Students will work on the problems while sharing their solutionsand then discuss the Essential question; how can you useequations, tables, and graphs to represent relationshipsbetween two variables?Revised 8/24/2014

Grade 8Unit:2-1Unit & Lesson OverviewsMulti-Step EquationsMathematicsDays :15Essential QuestionsHow do you simplify algebraic expressions?How do you solve equations by collecting like terms and multiplying expressions?How can you give examples of equations with a given number of solutions?How can you solve a system of equations algebraically?Content to be LearnedSkillsSolve one variable equations with variables on both sides of the7.1 Simplify Algebraic Expressionsequal sign and then determine if the equation has one solution,7.2 Solving Multi-Step Equationsinfinitely many solutions, or no solutions.7.3 Solving Equations with Variables on Both SidesUnderstand that the solution to the equation is the value(s) of the7.4 Systems of Equationsvariable, which makes a true equality when substituted back into theequation.Using the Distributive Property and combining like terms.Solve systems of two linear equations in two variables algebraically.Solve real-world and mathematical problems leading to two linearequations in two variables.AssessmentsStandards7.1 Quiz (4 days)8.EE.77.2/7.3 Quiz (6 days)8.EE.7a; 8.EE.7b7.4 Quiz/Unit Test (5 days)8.EE.8b; 8.EE.8cSample Instructional ActivitiesResources8.EE Solving EquationsExplorations in CORE MATH8.EE Cell Phone PlansIllustrative MathematicsRevised 8/24/2014

Grade 8Unit: 2.1Unit & Lesson OverviewsSimplifying Algebraic Expressions and Solving MultiLesson 1 of 2Step Equations with Variables on Both SidesMathematicsDays 10Lesson Focus1. Standards Addressed8.EE.78.EE.7a8.EE.7b5. Prerequisite KnowledgeAlgebraic expressionsIdentifying like termsSolving equations in one variableSolving multi-step equations2. Content to be LearnedWrite, simplify, and evaluatealgebraic expressions.Solve linear equations whosesolutions require expandingexpressions using the distributiveproperty and collecting liketerms.Solve equations in one variablewith one solution, infinitelymany solutions, and no solutions.6. Essential VocabularyLike termsComplementSupplement3. Mathematical PracticesStandard 1. Make sense ofproblems and persevere insolving them.Standard 2. Reason abstractlyand quantitatively.Standard 4. Model withMathematics.Standard 7. Look for and makeuse of structure.4. Essential QuestionsHow do you simplify algebraicexpressions?How do you solve equations bycollecting like terms andmultiplying expressions?How can you give examples ofequations with a given number ofsolutions?7. Possible MisconceptionsStudents turn equations intoexpressions when working withvariables on both sides thusrendering the opposite of thedesired solution.Not distributing to all termsinside of the grouping symbols.8. Teaching MaterialsExplorations in CORE MATHSolving EquationsRevised 8/24/2014

Grade 8Unit & Lesson OverviewsMathematicsSuggested Learning Practices9. Instruction Practices (What are the teachers doing)10. Learning Practices (What are the students doing)Lesson on Simplifying Algebraic Expressions Activate prior knowledge and ask students to give some examplesof algebraic expressions. Could use QR Reader and show video toclass. Ask for a volunteer to read the Essential question. Instruct students to do Example 1 paying special attention to thereflect question and the significance in the context of the problem. Instruct students to do Example 2. Ask students the benefit oradvantages of the simplified expression over the original. Have students practice some problems and close with the essentialquestion. Lesson on Solving Multi-Step equations Show QR Reader video and then read the Essential question.Remind students about the importance of combining like terms orsimplifying before solving. Instruct students to do Example 1 and Try These examples. Askstudents why or if their solution makes sense to Ex. 1.Instruct students to do Explore 2 paying special attention to thekeywords used for each expression.Have students practice some problems and close with the essentialquestion. Remind students to define variables and circle keywordswhen changing verbal phrases to algebraic expressions.Solving Equations with Variables on Both Sides Show QR Reader video and then read the Essential question. Have students do Explore 1. Remind students to use properties ofequality with once again the goal being to isolate the variable.Explain to the students that in the past when solving equations theyfound a single solution and now they will find equations with one Students will give examples of algebraic expressions. After readingthe essential question; how do you simplify algebraic expressions,have a student-led discussion on how they have simplified them inthe past.Students will do Example 1in their groups and then discuss thesignificance of what the variable represents in simplified form.Students will do Example 2 in their groups and then discuss thedifferences of writing a two variable expression to a one variableexpression.Students will work on their practice problems and then discuss as agroup the Essential question; how do you simplify algebraicexpressions?Students will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question;how do you solve equations by collecting like terms andmultiplying expressions?Students will work on Example 1in their groups and discuss theirresults with the class.Students will work on example 2 and discuss their solutions withthe class.Students will work on their practice problems and then discuss theEssential question; how do you solve equations by collecting liketerms and multiplying expressions?Students will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question;how can you give examples of equations with a given number ofsolutions?Students will do Explore 1 in their groups and discuss as theypresent the 3 different possibilities that can occur when solvingRevised 8/24/2014

Grade 8 Unit & Lesson Overviewssolution, an infinite number of solutions, and no solutions.Have students highlight the KEY Concept and discuss as a classwhat the chart shows.Have students do Explore 2.Have students do Explore 3. Remind students to define variablesand circle keywords before writing their equation.Have students practice some problems and then close with theEssential question asking students for the key points from thelesson.Mathematicsequations. Students will highlight the KEY Concept and discuss the chart. Students will discuss their results for Explore 2.Students will discuss their results for Explore 3. Students will work on their practice problems and then discuss theEssential question; how can you give examples of equations with agiven number of solutions?Revised 8/24/2014

Grade 8Unit: 2.1Unit & Lesson OverviewsSystems of EquationsLesson 2 of 2MathematicsDays 5Lesson Focus1. Standards Addressed8.EE.8b8.EE.8c5. Prerequisite KnowledgeSolving systems of equationsgraphicallySlope-intercept form2. Content to be LearnedSolve systems of two linearequations algebraically.Solve real-world mathematicalproblems in two variables.6. Essential VocabularySystems of equations3. Mathematical PracticesStandard 5. Use appropriate toolsstrategically.4. Essential QuestionsHow can you solve a system ofequations algebraically?7. Possible MisconceptionsSubstitution method may beconfusing to some students.Not using properties of equalitythe correct way.8. Teaching MaterialsExplorations in CORE MATHCell Phone PlansSuggested Learning Practices9. Instruction Practices (What are the teachers doing)Lesson on Systems of Equations Show QR Reader video and then read the Essential question.Explain to the students that it may be difficult to solve equationswith very large values or when the solution has non-integercoordinates. In cases like this solving a system algebraically makesmore sense. Have students do Example 1 as well as the reflect question whenthe example is completed.Have students do Example 2 by graphing and then algebraically.Ask the students which way they think is the better method.Omit Example 3.Have students practice some problems and then close with theEssential question asking students for the key points from thelesson.10. Learning Practices (What are the students doing) Students will watch the video taking notes. The class will discussthe video and the students will highlight the Essential question;how can you solve a system of equations algebraically? The classwill then have a student-led discussion on what may happen whenworking with very large numbers or when a solution has noninteger solutions. Students will work on the example in their groups and discuss howthey can check their answer.Students will work on Example 2. They will then have a class-leddiscussion on which way they prefer. Students will work on their practice problems and then discuss theEssential question; how can you solve a system of equationsalgebraically?Revised 8/24/2014

Grade 8Unit:2.2Unit & Lesson OverviewsGraphing LinesMathematicsDays :22Essential QuestionsHow do you find rate of change?How can you show that the slope of a line is the same between any two points on the line?How can you use slopes and intercepts to write and graph linear equations?How can you develop the point-slope form of an equation of a line?How can you identify a direct variation?How can you solve a system of equations by graphing?Content to be LearnedSkillsFind rate of change and show that the slope of a line is the same8.1 Graphing Linear Equationsbetween any two points on the line.8.2 Slope of a LineUse slopes and intercepts to write and graph linear equations.8.3 Using Slopes and InterceptsDevelop the slope-intercept form and the point-slope form of an8.4 Point-Slope Formequation.8.5 Direct VariationIdentify a direct variation.8.6 Solving Systems of Linear Equations by GraphingSolve a system of equations by graphing.AssessmentsStandards8.1/8.2 Quiz (7 days)8.F.48.3 Quiz (4 days)8.EE.68.4/8.5 Quiz (5 days)8.EE.58.6 Quiz followed by a Unit Test (6 days)8

1.1 Rational Numbers 1.2 Multiplying Rational Numbers 1.3 Dividing Rational Numbers 1.4 Adding and Subtracting with Unlike Denominators 1.5 Solving Equations with Rational Numbers 1.6 Solving Two-Step Equations Writing rational numbers as decimals and fractions as well as mu

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