TIPS4Math Grade 8 Whole Number Relationships and Powers of Ten Overall Expectations Students will: • Represent, compare, and order equivalent representations of numbers, including those involving positive exponents (8m8) • Solve problems involving whole numbers, [and] decimal numbers, fractions, and integers, using a variety of computational strategies (8m9) Specific Expectations Students will: • Express repeated multiplication using exponential notation (8m11) • Represent whole numbers in expanded form using powers of ten (8m12) • Determine common factors and common multiples using the prime factorization of numbers (8m15) • Multiply and divide decimal numbers by various powers of ten (8m24) • Estimate, and verify using a calculator, the positive square roots of whole numbers, and distinguish between whole numbers that have whole-number square roots (i.e., perfect square numbers) and those that do not (8m25) Specific Lesson Learning Focus Expectations Factors and Multiples • Determine common factors and multiples using prime factorizing 8m68 • Express repeated multiplication using exponential form 8m75 Squares and Square Roots • Make connections between squares and square roots (e.g. compare side 8m25 lengths and the area of a square) • Estimate and verify square roots and distinguish between whole numbers that have whole number roots and those that do not • Solve real-life context word problems involving squares and square roots Powers of Ten • Express 10, 100, 1000, 10 000, 100 000 and 1 000 000 as powers of ten 8m24 • Make connections between multiplying/ dividing numbers by various powers of ten and place value changes • Multiply and divide decimal numbers by various powers of ten • Apply to real-life context problems involving metric conversions Expanded Form • Express whole numbers as sums in expanded form 8m12 • Represent whole numbers in expanded form using powers of ten (exponential form) Consolidation and Summative Tasks
EduGAINS-Mathematics Page 2 of 10 TIPS4Math Grade 8 Factors and Multiples Specific Expectations: 8m11, 8m15 Learning Focus Blended Learning Other Resources Teacher Guide TIPS4RM Grade 8 Unit 5: Unit 1 Activity 1: Factors, Multiples, and Exponents Fractions and Percents OERB ID: ELO1477240 • Day 11: Connecting to Minds • Review factors, multiples, Unit 1 Activity 1: Action Composites On prime and composite OERB ID: ELO1476860 numbers • Prime Time Homework Help OERB ID: ELO1414870 • Prime Factorization o factors, multiples, prime and composite numbers o prime factorization Gizmos o greatest common factor and lowest common • Factor Trees (Factoring multiple Numbers) • Discussion o prime factor 16, 120, 64 and 625 o strategies to find lowest common multiple of 12 NCTM Illuminations and 16, or 6 and 8 • Factorize Action • Determine common factors Unit 1 Activity 1: Minds On and multiples using prime • Khan Academy Video: Exponents [1:55] GeoGebra factorizing o meaning of power (using base of 6) • Factorization • Express repeated • Discussion multiplication using • Anchor Chart for Exponents exponential form Unit 1 Activity 1: Action • Making Sense of Exponents OERB ID: ELO1414850 o Frayer Model for Powers o powers as repeated multiplication o power representation o practice evaluating powers and representing repeated multiplication as exponents
EduGAINS-Mathematics Page 2 of 10 TIPS4Math Grade 8 Factors and Multiples (Continued) Specific Expectations: 8m11, 8m15 Learning Focus Blended Learning Other Resources Action • Anchor Chart about exponents • Assignment 1 – Finding Factors with Area Models o prime factors using factor tree
• Note: supplementation required for determining common factors and multiples using prime factorizing Consolidation
EduGAINS-Mathematics Page 3 of 10 TIPS4Math Grade 8 Squares and Square Roots Specific Expectations: 8m25 Learning Focus Blended Learning Other Resources Grade 7 Teacher Guide TIPS4RM Grade 7 Unit 4: Composite Figures and Area Unit 1 Activity 5: Squares and of Trapezoids Square Roots • Days 19: Perfect Squares and Their Square Roots OERB ID: ELO1471850 • Day 20: Square Roots of Non-Perfect Squares Minds • Represent perfect squares See Grade 7 Blended Learning On and square roots using a Unit 1 Activity 5 TIPS4RM Grade 8 Unit 3: From Powers to Circles variety of tools OERB ID: ELO1471130 • Day 3: Perfect Square Patterns o geoboards • Day 4: Finding the Root of the Problem o connecting cubes o grid paper Homework Help Action • Make connections between See Grade 7 Blended Learning • Square Roots and Exponents squares and square roots Unit 1 Activity 5 (e.g. compare side lengths Gizmos and the area of a square) • Square Roots • Estimate and verify square • Ordering and Approximating Square Roots roots and distinguish between whole numbers Desmos that have whole number • Square Dance roots and those that do not • Solve real-life context word GeoGebra problems involving squares • Square numbers and square roots • Simplifying Square Roots See Grade 7 Blended Learning Consolidation NCTM Illuminations Unit 1 Activity 5 • Factorize
Gap Closing I/S Student Book: Powers and Roots pp 3 - 16
Gap Closing I/S Facilitator’s Guide: Powers and Roots pp 5 – 6, 8-19
EduGAINS-Mathematics Page 4 of 10 TIPS4Math Grade 8 Powers of Ten Specific Expectations: 8m24 Learning Focus Blended Learning Other Resources Grade 6 Teacher Guide TIPS4RM Grade 8 Unit 3 OERB ID: ELO1474900 • Day 1: Value of the Place Unit 1 Activity 8: Multiplication and • Day 2: Powering Up with Powers of Ten Division of Whole and Decimal Numbers Grade 8 Teacher Guide Homework Help Unit 1 Activity 1: Factors, Multiples, and • Powers Exponents OERB ID: ELO1477240 OERB Minds • Review multiplying and See Grade 6 Blended Learning Unit 1 • Golfing with Whole Numbers and Decimals On dividing decimal numbers Activity 8 OERB ID: ELO1414420 by 10, 100, 1000 and OERB ID: ELO1474830 • Exponents 10 000 using mental OERB ID: ELO1033350 strategies Action • Express 10, 100, 1000, 10 Unit 1 Activity 1: Action mathies 000, 100 000 and • Exponents Part 2 – The Power of 10 • Money Tool • 1 000 000 as powers of OERB ID: ELO1414860 • Decimal Number Rods ten o whole numbers in expanded form • Make connections using powers of ten Geometer’s Sketchpad between multiplying/ • Interactive Area Model dividing numbers by Note: supplementation required for: various powers of ten and • Express 10, 100, 1000, 10 000, Glencoe place value changes 100 000 and 1 000 000 as powers of • Interactive Base Ten Blocks • Multiply and divide ten decimal numbers by • Make connections between Tap Into Teen Minds various powers of ten multiplying/ dividing numbers by • Which would you rather: $1 Million • Apply to real-life context various powers of ten and place value or a Penny a Day, Doubles for a Month? problems involving metric changes conversions • Multiply and divide decimal numbers Gap Closing I/S Student Book: Powers and by various powers of ten Roots • Apply to real-life context problems pp 3 – 16 involving metric conversions Gap Closing I/S Facilitator’s Guide: Powers and Consolidation Roots pp 5 – 19
EduGAINS-Mathematics Page 5 of 10 TIPS4Math Grade 8 Expanded Form Specific Expectations: 8m12 Learning Focus Blended Learning Other Resources Teacher Guide Unit 1 Activity 1: Factors, Multiples, and Exponents OERB ID: ELO1477240 Minds • Review whole number On place values Action • Express whole numbers as sums in expanded form • Represent whole numbers in expanded form using powers of ten (exponential form) Consolidation Unit 1 Activity 1: Consolidation • Assignment 2 – Number Systems (Gizmo) • Assignment 3 – Place Value OERB ID: ELO1476860 o complete chart with standard form, word form, expanded form and expanded form with powers
Consolidation & Summative Tasks Specific Expectations: 8m11, 8m12, 8m15, 8m24, 8m25 Blended Learning Other Resources
EduGAINS-Mathematics Page 6 of 10 TIPS4Math Grade 8 Factors and Multiples Resource URL Teacher Guide: https://download.elearningontario.ca/repository/14/1477240000/GRD8MTHEU06A02/content.html Unit 1 Activity 1: Factors, Multiples, and Exponents Prime Time https://download.elearningontario.ca/repository/14/1476860000/GRD8MTHEU01A01/mme/Gr8_ Math_Num_PrimeTime/Gr8_Math_Num_PrimeTime_OF/Fiore_Gr8NumStoryboard9.html Unit 1 Activity 1: Action https://download.elearningontario.ca/repository/14/1476860000/GRD8MTHEU01A01/content_2. html Khan Academy Video: https://www.khanacademy.org/math/algebra-basics/basic-alg-foundations/alg-basics-exponents/v/ Exponents understanding-exponents Unit 1 Activity 1: Minds On https://download.elearningontario.ca/repository/14/1476860000/GRD8MTHEU01A01/content.html Making Sense of Exponents https://download.elearningontario.ca/repository/14/1476860000/GRD8MTHEU01A01/mme/Gr8_ Math_Num_MakingSenseExponents/Gr8_Math_Num_MakingSenseofExponents_OF/Fiore_Gr- 8ExponentsPt1.html Assignment 1 – Finding Factors https://download.elearningontario.ca/repository/14/1476860000/GRD8MTHEU01A01/assignment. with Area Models html TIPS4RM Grade 8 Unit 5: http://www.edugains.ca/resources/LearningMaterials/TIPS/tips4rm/grade8/Unit5_FractionsPer- Fractions and Percents cents.pdf Homework Help: https://homeworkhelp.ilc.org/chat/chat.php?config=playback&question_id=228224&type=bs#/ques- Prime Factorization tion/228224/type/bs Gizmos: https://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=1033 Factor Trees (Factoring Numbers) NCTM Illuminations: http://illuminations.nctm.org/Activity.aspx?id=3511 Factorize GeoGebra: http://www.geogebra.org/m/146202#material/42380 Factorization
EduGAINS-Mathematics Page 7 of 10 TIPS4Math Grade 8 Squares and Square Roots Resource URL Grade 7 Teacher Guide: https://download.elearningontario.ca/repository/14/1471850000/Gr%207%20Math%20U1%20TG/ Unit 1 Activity 5: Squares and Combined%20Teacher%20Notes%20for%20Activities%201%20-%2010/overview.html Square Roots Grade 7 Blended Learning Unit 1 https://download.elearningontario.ca/repository/14/1471130000/GRD7MTHEU01A05/content.html Activity 5 Minds On Grade 7 Blended Learning Unit 1 https://download.elearningontario.ca/repository/14/1471200000/GRD7MTHEU01/GRD- Activity 5 Action 7MTHEU01A05/content_2.html Grade 7 Blended Learning Unit 1 https://download.elearningontario.ca/repository/14/1471200000/GRD7MTHEU01/GRD- Activity 5 Consolidation 7MTHEU01A05/content_3.html TIPS4RM Grade 7 Unit 4: http://www.edugains.ca/resourcesMath/CE/LessonsSupports/TIPS4RM/Grade7English/Unit4_ Composite Figures and Area of CompositeFigures_AreaOfTrapezoids.pdf Trapezoids TIPS4RM Grade 8 Unit 3: From http://www.edugains.ca/resources/LearningMaterials/TIPS/tips4rm/grade8/Unit3_FromPowersTo- Powers to Circles Circles.pdf Homework Help: https://homeworkhelp.ilc.org/chat/chat.php?config=playback&question_id=242106&type=bs#/ques- Square Roots and Exponents tion/242106/type/bs Gizmos: https://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=103 Square Roots Gizmos: https://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=230&- Ordering and Approximating ClassID=0 Square Roots Desmos: https://teacher.desmos.com/activitybuilder/custom/56c0ee5561d1abbf2f1663ca Square Dance GeoGebra: https://www.geogebra.org/m/EhHajSdq Square numbers GeoGebra: http://www.geogebra.org/m/235951 Simplifying Square Roots NCTM Illuminations: http://illuminations.nctm.org/Activity.aspx?id=3511 Factorize Gap Closing I/S Student Book: http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/5-PowersRoots_SB_ Powers and Roots IS.pdf Gap Closing I/S Facilitator’s http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/5-PowersRoots_FG_ Guide: Powers and Roots IS.pdf EduGAINS-Mathematics Page 8 of 10 TIPS4Math Grade 8 Powers of Ten Resource URL Grade 6 Teacher Guide: https://download.elearningontario.ca/repository/14/1474900000/Combined%20Teacher%20 Unit 1 Activity 8: Multiplication and Notes%20for%20Activities%201%20-%2010/Teacher%20Notes%20-%20Activities%206%20 Division of Whole and Decimal -%2010/content_3.html Numbers Grade 8 Teacher Guide: https://download.elearningontario.ca/repository/14/1477240000/GRD8MTHEU06A02/content. Unit 1 Activity 1: Factors, Multiples, html and Exponents Grade 6 Blended Learning https://download.elearningontario.ca/repository/14/1474830000/GRD6MTHEU01A08/overview. Unit 1 Activity 8 html Exponents Part 2 – The Power of 10 https://download.elearningontario.ca/repository/14/1476860000/GRD8MTHEU01A01/mme/ Gr8_Math_Num_ThePowerofTen/Gr8_Math_Num_ThePowerofTen_OF/Fiore_Gr8Expo- nentsPt2.html TIPS4RM Grade 8 Unit 3 http://www.edugains.ca/resources/LearningMaterials/TIPS/tips4rm/grade8/Unit3_FromPower- sToCircles.pdf Homework Help: https://homeworkhelp.ilc.org/tools/tutorials/details.php?object_id=212 Powers OERB: https://download.elearningontario.ca/repository/14/1414420000/LO1194-Golfing-WholeNum- Golfing with Whole Numbers and bers-Decimals.html Decimals OERB: https://download.elearningontario.ca/repository/1033350000/ProjectFiles/exponents.html Exponents mathies: http://mathies.ca/learningTools.php#Mm0 Money Tool mathies: http://mathies.ca/learningTools.php#Dd0 Decimal Number Rods Geometer’s Sketchpad: http://www.edugains.ca/resourcesMath/CE/LessonsSupports/GSP/Operations/Interactive_ Interactive Area Model Area_Model.gsp Glencoe : http://www.glencoe.com/sites/common_assets/mathematics/ebook_assets/vmf/VMF-Interface. Interactive Base Ten Blocks html Tap Into Teen Minds: https://tapintoteenminds.com/3act-math/penny-a-day/ Which would you rather: $1 Million or a Penny a Day, Doubles for a Month? EduGAINS-Mathematics Page 9 of 10 TIPS4Math Grade 8 Powers of Ten (continued) Resource URL Gap Closing I/S Student Book: http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/5-PowersRoots_SB_ Powers and Roots IS.pdf Gap Closing I/S Facilitator’s Guide: http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade9/5-PowersRoots_FG_ Powers and Roots IS.pdf
Expanded Form Resource URL Teacher Guide: https://download.elearningontario.ca/repository/14/1477240000/GRD8MTHEU06A02/content. Unit 1 Activity 1: Factors, Multiples, html and Exponents Gizmos: https://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=302 Number Systems Assignment 3 – Place Value https://download.elearningontario.ca/repository/14/1476860000/GRD8MTHEU01A01/docs/ A3_Place%20Value%20Assignments.pdf
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