Saginaw Valley State University
Mathematics Pacing Guide
Time Frame: 3 Weeks – September Grade 7
Unit 1: Rational Numbers – Addition and Subtraction
|Standards for Mathematical Practice |Literacy Standards |
|1. Make sense of problems and persevere in solving them |RST. 7.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |
| |are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. |
|5. Use appropriate tools strategically | |
| |RST. 7. 7 Integrate quantitative or technical information expressed in words in a text with a version of |
|6. Attend to precision |that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table). |
| | |
|7. Look for and make use of structure |WHST. 7.4 Produce clear and coherent writing in which the development, organization, and style are |
| |appropriate to task, purpose, and audience. |
| | |
| |WHST.7.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |
| |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|
|Common Core |Essential Questions |Assessment |Vocabulary |Resources |
Mathematics Pacing Guide
Time Frame: 3 Weeks – September/October Grade 7
Unit 2: Rational Numbers – Multiplication and Division
|Standards for Mathematical Practice |Literacy Standards |
|1. Make sense of problems and persevere in solving them |RST. 7.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or |
| |performing technical tasks. |
|5. Use appropriate tools strategically | |
| |RST. 7.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |
|6. Attend to precision |are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. |
| | |
|7. Look for and make use of structure |WHST. 7.4 Produce clear and coherent writing in which the development, organization, and style are |
| |appropriate to task, purpose, and audience. |
| | |
| |WHST.7.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |
| |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|
|Common Core |Essential Questions |Assessment |Vocabulary |Resources |
|Apply and extend previous understandings of |How do you add and subtract fractions |Before: |Absolute value |MAISA curriculum units and resources: |
|operations with fractions to add, subtract, |and decimals? |KWL |Decimals |
|multiply, and divide rational numbers | |Brainstorming |Integers |itCalendar?SourceSiteID=&CurriculumMapID=805&YearID=2013 |
|7. NS.2 Apply and extend previous understandings of |How do you compare the outcomes of |Graphic Organizers |Irrational numbers | |
|multiplication and division and of fractions to |fraction division with the outcomes of|Pretest |Natural numbers |SUPO – Numbers and operations: |
|multiply and divide rational numbers. |decimal division by computing with | |Negative | |
|a. Understand that multiplication is extended from |fraction/decimal equivalents? |During: |Number Line | |
|fractions to rational numbers by requiring that | |KWL |Positive |Basic operations with fractions and a game: |
|operations continue to satisfy the properties of |How do you multiply a positive integer|Quizzes |Rational number |
|operations, particularly the distributive property, |by a negative integer by thinking |Daily Assignments |Real numbers |try/united-states/language/english/?Keywords=rational+numbe|
|leading to products such as (–1)(–1) = 1 and the |about equal groups? |Exit Card |Repeating Decimal |rs+addition+and+subtraction&SortField=DownloadCount30Days_d|
|rules for multiplying signed numbers. Interpret | |Models |Whole number |esc |
|products of rational numbers by describing |How do you multiply a negative integer|Using colored overlays to obtain | | |
|real-world contexts. |by a negative integer by thinking |results from multiplying fractions | | – Common Core: |
|b. Understand that integers can be divided, |about equal groups? |Portfolio | | |
|provided that the divisor is not zero, and every | |Students will create a portfolio | | |
|quotient of integers (with non-zero divisor) is a |How do you rewrite multiplication of |using real world examples | | |
|rational number. If p and q are integers then – |numbers by applying the commutative | | | |
|(p/q) = (–p)/q = p/(–q). Interpret quotients of |property of multiplication? |After: | | |
|rational numbers by describing real-world contexts. | |KWL | |Common Core Initiative: |
|c. Apply properties of operations as strategies to |How do you apply the commutative |Unit Test | |
|multiply and divide rational numbers. |property by rewriting division |Real World Problems | |Map/View/Default?UnitID=15756&YearID=2013&SchoolID=19&TimeP|
| |problems as multiplication? | | |eriodID=14&SourceSiteID=&CurriculumMapID=778& |
| | | | | |
|7. NS.2 Apply and extend previous understandings of |How do you rewrite multiplication | | | |
|multiplication and division and of fractions to |problems with rational numbers by | | | |
|multiply and divide rational numbers. |using the associative property of | | | |
|d. Convert a rational number to a decimal using |multiplication? | | | |
|long division; know that the decimal form of a | | | | |
|rational number terminates in 0s or eventually |How do you rewrite multiplication | | | |
|repeats. |problems with rational numbers by | | | |
| |using the commutative and associative | | | |
| |properties of multiplication? | | | |
| | | | | |
| |How do you rewrite problems with | | | |
| |rational numbers by using different | | | |
| |properties of multiplication and | | | |
| |division? | | | |
| | | | | |
| |How do you rewrite fractions as | | | |
| |decimals or repeating decimals by | | | |
| |using long division? | | | |
| | | | | |
| |How do you rewrite mixed numbers and | | | |
| |improper fractions as decimals by | | | |
| |using long division? | | | |
| | | | | |
| |How do you look at the relationship | | | |
| |between fractions and decimals by | | | |
| |using multiplication? | | | |
| | | | | |
| |How do you determine if a fraction | | | |
| |rewritten as a decimal will repeat or | | | |
| |terminate by using the denominator's | | | |
| |prime factorization? | | | |
|7. NS.3 Solve real-world and mathematical problems |How do you use addition and | | | |
|involving the four operations with rational numbers.|subtraction to solve real-world | | | |
| |problems involving decimals by | | | |
| |analyzing the situation described in | | | |
| |the problem? | | | |
| | | | | |
| |How do you use addition and | | | |
| |subtraction to solve real-world | | | |
| |problems involving fractions or | | | |
| |decimals by analyzing the situation | | | |
| |described in the problem? | | | |
| | | | | |
| |How do you use addition and division | | | |
| |to solve real-world problems with | | | |
| |rational numbers by analyzing the | | | |
| |situation described in the problem? | | | |
Mathematics Pacing Guide
Time Frame: 3 Weeks – November Grade 7
Unit 3: Proportional and Linear Relationships
|Standards for Mathematical Practice |Literacy Standards |
|1. Make sense of problems and persevere in solving them |RST. 7.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |
| |are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. |
|5. Use appropriate tools strategically | |
| |RST. 7. 7 Integrate quantitative or technical information expressed in words in a text with a version of |
|6. Attend to precision |that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table). |
| | |
| |WHST. 7.2 Write informative/explanatory texts, including the narration of historical events, scientific |
| |procedures/experiments, or technical processes. |
| |Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into |
| |broader categories as appropriate to achieving purpose; include formatting (e.g., headings), graphics (e.g.,|
| |charts, tables), and multimedia when useful to aiding comprehension. |
| |Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other |
| |information and examples. |
| |Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and |
| |concepts. |
| |Use precise language and domain-specific vocabulary to inform about or explain the topic. |
| |Establish and maintain a formal style and objective tone. |
| |Provide a concluding statement or section that follows from and supports the information or explanation |
| |presented. |
| | |
| |WHST.7.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |
| |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|
|Common Core |Essential Questions |Assessment |Vocabulary |Resources |
|Analyze proportional relationships and use them to |How do you find unit rate? |Before: |Density |MAISA curriculum units and resources: |
|solve real-world and mathematical problems | |KWL |Derived quantities |
|7. RP.1 Compute unit rates associated with ratios of|How do you approximate unit rates from|Brainstorming |Proportion |itCalendar?SourceSiteID=&CurriculumMapID=805&YearID=2013 |
|fractions, including ratios of lengths, areas and |verbal descriptions and equations by |Graphic Organizers |Proportion equation | |
|other quantities measured in like or different |estimating? |Pretest |Rate |SUPO – Numbers and operations: |
|units. For example, if a person walks 1/2 mile in | | |Rate of change | |
|each 1/4 hour, compute the unit rate as the complex |How do you find unit rates in |During: |Ratio | |
|fraction (1/2)/(1/4) miles per hour, equivalently 2 |situations involving fractions by |KWL |Speed |Promethean planet - A Math Adventure in Unit Rates and |
|miles per hour. |using division? |Quizzes |Unit rate |Price Discounts. |
| | |Daily Assignments |Velocity |
|7. RP.2 Recognize and represent proportional |How do you find the best deal by |Exit Card |Weighted average |stinky-chaz-at-summer-camp-a-math-adventure-in-unit-rates-a|
|relationships between quantities. |comparing unit rates? |Project | |nd-price-discounts#.URu-EB0ZJYA |
|a. Decide whether two quantities are in a | |Picking the better buy | | |
|proportional relationship, e.g., by testing for |How do you apply scale maps and scale |Debate the better car for gas millage| | – Common Core: |
|equivalent ratios in a table or graphing on a |models by using unit rates? |Pictures | | |
|coordinate plane and observing whether the graph is | |Students will graph relationships | | |
|a straight line through the origin. |How do you scale recipes by applying | | | - Ratios |
|b. Identify the constant of proportionality (unit |unit rates? |After: | | |
|rate) in tables, graphs, equations, diagrams, and | |KWL | | |
|verbal descriptions of proportional relationships. |How do you create proportional |Unit Test | |Common Core Initiative: |
|c. Represent proportional relationships by |relationships by expanding ratios? |Real World Problems | |
|equations. For example, if total cost t is | | | |Map/View/Default?UnitID=15755&YearID=2013&SchoolID=19&TimeP|
|proportional to the number n of items purchased at a|How do you determine whether ratios | | |eriodID=14&SourceSiteID=&CurriculumMapID=778& |
|constant price p, the relationship between the total|are proportional by reading tables? | | | |
|cost and the number of items can be expressed as t =| | | | |
|pn. |How do you determine whether ratios | | | |
|d. Explain what a point (x, y) on the graph of a |are proportional by creating tables? | | | |
|proportional relationship means in terms of the | | | | |
|situation, with special attention to the points (0, |How do you determine whether ratios | | | |
|0) and (1, r) where r is the unit rate. |are proportional by reading graphs? | | | |
| | | | | |
|7. RP.3 Use proportional relationships to solve |How do you identify unit rates by | | | |
|multistep ratio and percent problems. Examples: |listening to verbal descriptions? | | | |
|simple interest, tax, markups and markdowns, | | | | |
|gratuities and commissions, fees, percent increase |How do you understand unit rates by | | | |
|and decrease, percent error. |using equations? | | | |
| | | | | |
| |How do you find unit rate in diagrams?| | | |
| | | | | |
| |How do you find unit rates by reading | | | |
| |graphs? | | | |
| | | | | |
| |How do you write an equation that | | | |
| |represents the proportional | | | |
| |relationship between the total cost | | | |
| |and the number of items by finding the| | | |
| |unit price? | | | |
| | | | | |
| |How do you determine the best deal by | | | |
| |comparing equations that represent the| | | |
| |proportional relationship between the | | | |
| |total cost, t and the number of items,| | | |
| |n? | | | |
| |How do you write an equation that | | | |
| |expresses the relationship between the| | | |
| |distance and the time by finding the | | | |
| |unit rate? | | | |
| | | | | |
| |How do you compare rates of speed by | | | |
| |comparing equations that represent the| | | |
| |proportional relationship between the | | | |
| |distance, d and the time, t? | | | |
| | | | | |
| |How do you write equations to | | | |
| |represent the proportional | | | |
| |relationship between the amount change| | | |
| |and the final amount by finding the | | | |
| |percent change? | | | |
| | | | | |
| |How do you calculate simple interest | | | |
| |by using the simple interest equation?| | | |
| | | | | |
| |How do you solve multistep percent | | | |
| |problems by using proportions and | | | |
| |equations? | | | |
| | | | | |
| |How do you compute successive | | | |
| |percentages by using proportions and | | | |
| |equations? | | | |
| | | | | |
| |How do you find the amount of change | | | |
| |and the final amount given the percent| | | |
| |of change and the original amount by | | | |
| |using diagrams, proportions, and | | | |
| |equations? | | | |
| | | | | |
| |How do you find the percent change and| | | |
| |what percent the final amount is of | | | |
| |the original amount by using diagrams,| | | |
| |proportions, and equations? | | | |
| | | | | |
| |How do you find the original amount | | | |
| |and amount of change given the percent| | | |
| |change and final amount by using | | | |
| |proportions and equations? | | | |
Mathematics Pacing Guide
Time Frame: 3 Weeks – November/December Grade 7
Unit 4: Geometric Constructions
|Standards for Mathematical Practice |Literacy Standards |
|1. Make sense of problems and persevere in solving them |RST. 7.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or |
| |performing technical tasks. |
|5. Use appropriate tools strategically | |
| |RST. 7.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |
|6. Attend to precision |are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. |
| | |
|7. Look for and make use of structure |RST. 7.7 Integrate quantitative or technical information expressed in words in a text with a version of that|
| |information expressed visually (e.g., in a flowchart, diagram, model, graph, or table). |
| | |
| |WHST. 7.2 Write informative/explanatory texts, including the narration of historical events, scientific |
| |procedures/ experiments, or technical processes. |
| |Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into |
| |broader categories as appropriate to achieving purpose; include formatting (e.g., headings), graphics (e.g.,|
| |charts, tables), and multimedia when useful to aiding comprehension. |
| |Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other |
| |information and examples. |
| |Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and |
| |concepts. |
| |Use precise language and domain-specific vocabulary to inform about or explain the topic. |
| |Establish and maintain a formal style and objective tone. |
| |Provide a concluding statement or section that follows from and supports the information or explanation |
| |presented. |
| | |
| |WHST. 7.4 Produce clear and coherent writing in which the development, organization, and style are |
| |appropriate to task, purpose, and audience. |
| | |
| |WHST. 7.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |
| |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|
|Common Core |Essential Questions |Assessment |Vocabulary |Resources |
|Draw, construct, and describe geometrical figures and |How do you calculate actual lengths |Before |Acute angle |MAISA curriculum units and resources: |
|describe the relationships between them |from a scale drawing by using ratios |KWL |Angle |
|7. G.1 Solve problems involving scale drawings of |and proportions? |Brainstorming |Angle bisector |nitCalendar?SourceSiteID=&CurriculumMapID=805&YearID=2013 |
|geometric figures, including computing actual lengths and| |Graphic Organizers |Bisector | |
|areas from a scale drawing and reproducing a scale |How do you determine the scale factor|Pretest |Compass |Common Core Initiative: |
|drawing at a different scale. |between two similar figures by | |Congruent |
| |applying ratios? |During |Corresponding angle |tMap/View/Default?UnitID=15755&YearID=2013&SchoolID=19&Tim|
|7. G.2 Draw (freehand, with ruler and protractor, and | |KWL |Corresponding sides |ePeriodID=14&SourceSiteID=&CurriculumMapID=778& |
|with technology) geometric shapes with given conditions. |How do you compute an actual |Quizzes |(parts) | |
|Focus on constructing triangles from three measures of |perimeter from a scale drawing by |Daily Assignments |Equilateral |SUPO –Collection of geometric shapes and activities: |
|angles or sides, noticing when the conditions determine a|using ratios and proportions? |Exit Card |Geometric construction | |
|unique triangle, more than one triangle, or no triangle. | |Project |Obtuse angle | |
| |How do you calculate an actual area |Students determine 5 routs to LA and |Parallel |Promethean planet – What is a scale drawing?: |
| |from a scale drawing by using ratios |discover the better rout to take for |Perpendicular |
| |and proportions? |shortest distance and cost |Protractor |6/what-is-a-scale-drawing#.URvS3R0ZJYA |
| | |Map Centers |Right angle | |
| | |Journal |Ruler | – Common Core: |
| |How do you make a new scale drawing |Students will complete a journal of |Straight edge | |
| |from a given one by using ratios and |the different types of similarity of | | |
| |proportions? |triangles | | – Scale drawing |
| | | | | |
| |How do you draw geometric shapes by |After | | |
| |using a given length of sides? |KWL | | |
| | |Unit Test | | |
| |How do you draw triangles by using |Real World Problems | | |
| |given angles? | | | |
| | | | | |
| |How do you determine if given | | | |
| |measurements will allow you to create| | | |
| |the appropriate shapes by drawing the| | | |
| |triangle? | | | |
| | | | | |
| |How do you draw a shape by using more| | | |
| |than one condition? | | | |
Mathematics Pacing Guide
Time Frame: 3 Weeks – December Grade 7
Unit 5: Geometric Constructions
|Standards for Mathematical Practice |Literacy Standards |
|1. Make sense of problems and persevere in solving them |RST. 7.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |
| |are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. |
|5. Use appropriate tools strategically | |
| |WHST. 7.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |
|6. Attend to precision |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|
| | |
|7. Look for and make use of structure | |
|Common Core |Essential Questions |Assessment |Vocabulary |Resources |
|Draw, construct, and describe geometrical |How do you describe the cross |Before: |Area |MAISA curriculum units and resources: |
|figures and describe the relationships between |sections of a right rectangular |KWL |Circumference |
|them |prism by slicing at different |Brainstorming |Cone |itCalendar?SourceSiteID=&CurriculumMapID=805&YearID=2013 |
|7. G.3 Describe the two-dimensional figures that|angles? |Graphic Organizers |Cross section | |
|result from slicing three-dimensional figures, | |Pretest |Cube |Promethean planet - circumference and area of circles |
|as in plane sections of right rectangular prisms|How do you describe the cross | |Cylinder |
|and right rectangular pyramids. |sections of a right rectangular |During: |Hemisphere |circles-area-circumference#.URvVTx0ZJYA |
| |pyramid by slicing at different |KWL |Lateral area | |
| |angles? |Quizzes |Perimeter | – Common Core: |
| | |Daily Assignments |Prism | |
| | |Exit Card |Pyramid | |
| | |Drawing |Radius | – Cross Sections |
| | |Students will create a drawing of |Rectangular prism | |
| | |planar cross sections |Solid of revolution | |
| | | |Sphere |Common Core Initiative: |
| | |After: |Surface area |
| | |KWL |Volume |Map/View/Default?UnitID=15869&YearID=2013&SchoolID=19&TimeP|
| | |Unit Test | |eriodID=14&SourceSiteID=&CurriculumMapID=778& |
| | |Real World Problems | | |
|Solve real-life and mathematical problems |How do you determine the measures of| | | |
|involving angle measure, area, surface area, and|a circle by exploring the definition| | | |
|volume |of a circle? | | | |
|7. G.4 Know the formulas for the area and | | | | |
|circumference of a circle and use them to solve |How do you find the circumference of| | | |
|problems; give an informal derivation of the |a circle by exploring the ratio of | | | |
|relationship between the circumference and area |the diameter and circumference? | | | |
|of a circle. |How do you find the area of a circle| | | |
| |by exploring the relationship | | | |
| |between a circle and a rectangle? | | | |
| | | | | |
| |How do you find the area of a circle| | | |
| |by using the measure of the | | | |
| |circumference? | | | |
| | | | | |
| |How do you find the circumference of| | | |
| |a circle by using the measure of | | | |
| |area? | | | |
Mathematics Pacing Guide
Time Frame: 3 Weeks – January Grade 7
Unit 6: Geometric Constructions
|Standards for Mathematical Practice |Literacy Standards |
|1. Make sense of problems and persevere in solving them |RST. 7.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |
| |are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. |
|5. Use appropriate tools strategically | |
| |WHST. 7.2 Write informative/explanatory texts, including the narration of historical events, scientific |
|6. Attend to precision |procedures/ experiments, or technical processes. |
| |Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into |
|7. Look for and make use of structure |broader categories as appropriate to achieving purpose; include formatting (e.g., headings), graphics (e.g.,|
| |charts, tables), and multimedia when useful to aiding comprehension. |
| |Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other |
| |information and examples. |
| |Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and |
| |concepts. |
| |Use precise language and domain-specific vocabulary to inform about or explain the topic. |
| |Establish and maintain a formal style and objective tone. |
| |Provide a concluding statement or section that follows from and supports the information or explanation |
| |presented. |
| | |
| |WHST. 7.4 Produce clear and coherent writing in which the development, organization, and style are |
| |appropriate to task, purpose, and audience. |
| | |
| |WHST. 7.5 With some guidance and support from peers and adults, develop and strengthen writing as needed by |
| |planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience |
| |have been addressed. |
| | |
| |WHST. 7.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |
| |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|
|Common Core |Essential Questions |Assessment |Vocabulary |Resources |
|Solve real-life and mathematical problems |How do you find the measure of|Before |AAA similarity |MAISA curriculum units and resources: |
|involving angle measure, area, surface area, and |an unknown angle by using |KWL |Acute angle |
|volume |supplementary, complimentary, |Brainstorming |Angle |alendar?SourceSiteID=&CurriculumMapID=805&YearID=2013 |
|7. G.5 Use facts about supplementary, |vertical, and adjacent angles?|Graphic Organizers |Angle bisector | |
|complementary, vertical, and adjacent angles in a | |Pretest |Bisector |Common Core Initiative: |
|multi-step problem to write and solve simple |How do you find the measure of| |Compass |
|equations for an unknown angle in a figure. |an unknown angle by using |During |Congruent |/View/Default?UnitID=15869&YearID=2013&SchoolID=19&TimePeriodI|
| |supplementary angles? |KWL |Corresponding angle |D=14&SourceSiteID=&CurriculumMapID=778& |
|7. G.6 Solve real-world and mathematical problems | |Quizzes |Corresponding sides (parts) | |
|involving area, volume and surface area of two- |How do you solve for unknown |Daily Assignments |Equilateral |SUPO –Tangram activities: |
|and three-dimensional objects composed of |angle measures by using |Exit Card |Geometric construction | |
|triangles, quadrilaterals, polygons, cubes, and |complementary angles? |Project |Obtuse angle | |
|right prisms. | |Students use pipe cleaners to model |Parallel |Promethean planet – Angle relationships: |
| |How do you solve for unknown |different angles. |Perpendicular |
| |angle measures by using | |Protractor |le-relationships#.URvYTB0ZJYA |
| |vertical and adjacent angles? |After |Right angle | |
| | |KWL |Ruler | – Common Core: |
| |How do you solve for unknown |Unit Test |SAS similarity | |
| |angle measures by using |Real World Problems |Scale factor | |
| |interior and exterior angles? | |SSS similarity | – Complimentary angles |
| | | |Straight edge | |
| |How do you solve for unknown | |Unit | |
| |angle measures by using | |Unit squared | |
| |consecutive interior angles? | | | |
| | | | | |
| |How do you solve for unknown | | | |
| |angle measures by using | | | |
| |measures of interior angles of| | | |
| |triangles? | | | |
Mathematics Pacing Guide
Time Frame: 3 Weeks – January/February Grade 7
Unit 7: Linear Equations
|Standards for Mathematical Practice |Literacy Standards |
|1. Make sense of problems and persevere in solving them |RST. 7.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or |
| |performing technical tasks. |
|5. Use appropriate tools strategically | |
| |RST. 7.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |
|6. Attend to precision |are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. |
| | |
|7. Look for and make use of structure |WHST. 7.6 Use technology, including the Internet, to produce and publish writing and present the |
| |relationships |
| |Between information and ideas clearly and efficiently. |
| | |
| |WHST. 7.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |
| |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|
|Common Core |Essential Questions |Assessment |Vocabulary |Resources |
|Use properties of operations to generate equivalent |How do you reverse the |Before: |Additive identity |MAISA curriculum units and resources: |
|expressions |distributive property? |KWL |Additive inverse |
|7. EE.1 Apply properties of operations as strategies | |Brainstorming |Algebraic equation |ndar?SourceSiteID=&CurriculumMapID=805&YearID=2013 |
|to add, subtract, factor, and expand linear |How do you simplify an |Graphic Organizers |Algebraic expressions | |
|expressions with rational coefficients. |expression? |Pretest |Associative property of addition |Common Core Initiative: |
| | | |Associative property of |
|7. EE.2 Understand that rewriting an expression in |How do you expand linear |During: |multiplication |ew/Default?UnitID=15864&YearID=2013&SchoolID=19&TimePeriodID=14&S|
|different forms in a problem context can shed light |expressions? |KWL |Commutative property of addition |ourceSiteID=&CurriculumMapID=778& |
|on the problem and how the quantities in it are | |Quizzes |Commutative property of | |
|related. For example, a + 0.05a = 1.05a means that |How do you factor linear |Daily Assignments |multiplication |Promethean planet – Intro to linear functions and equations: |
|“increase by 5%” is the same as “multiply by 1.05.” |expressions with rational |Exit Card |Composite |
| |coefficients by using the | |Distributive property |uction-to-functions-and-linear-equations#.URva6R0ZJYA |
|Solve real-life and mathematical problems using |distributive property? |After: |Equation | |
|numerical and algebraic expressions and equations | |KWL |Exponent | – Common Core: |
|7. EE.3 Solve multi-step real-life and mathematical |How do you rewrite an expression?|Unit Test |Expression | |
|problems posed with positive and negative rational | |Real World Problems |Formula | |
|numbers in any form (whole numbers, fractions, and |How do you identify equivalent | |Graph | – Linear equations |
|decimals), using tools strategically. Apply |expressions by using | |Multiplicative identity | |
|properties of operations as strategies to calculate |substitution? | |Multiplicative inverse | |
|with numbers in any form; convert between forms as | | |Reciprocal | |
|appropriate; and assess the reasonableness of answers|How do you solve multi-step | |Solution | |
|using mental computation and estimation strategies. |problems with integers? | |Term | |
|For example: If a woman making $25 an hour gets a 10%| | | | |
|raise, she will make an additional 1/10 of her salary|How do you convert a real world | | | |
|an hour, or $2.50, for a new salary of $27.50. If you|situation into an equation? | | | |
|want to place a towel bar 9 3/4 inches long in the | | | | |
|center of a door that is 27 1/2 inches wide, you will|How do you solve inequalities by | | | |
|need to place the bar about 9 inches from each edge; |using inverse operations? | | | |
|this estimate can be used as a check on the exact | | | | |
|computation. | | | | |
| | | | | |
|7. EE.4 Use variables to represent quantities in a | | | | |
|real-world or mathematical problem, and construct | | | | |
|simple equations and inequalities to solve problems | | | | |
|by reasoning about the quantities. | | | | |
|a. Solve word problems leading to equations of the | | | | |
|form px + q = r and p(x + q) = r, where p, q, and r | | | | |
|are specific rational numbers. Solve equations of | | | | |
|these forms fluently. Compare an algebraic solution | | | | |
|to an arithmetic solution, identifying the sequence | | | | |
|of the operations used in each approach. For example,| | | | |
|The perimeter of a rectangle is 54 cm. Its length is | | | | |
|6 cm. What is its width? | | | | |
|b. Solve word problems leading to inequalities of | | | | |
|the form px + q > r or px + q < r, where p, q, and r | | | | |
|are specific rational numbers. Graph the solution set| | | | |
|of the inequality and interpret it in the context of | | | | |
|the problem. For example: As a salesperson, you are | | | | |
|paid $50 per week plus $3 per sale. This week you | | | | |
|want your pay to be at least $100. Write an | | | | |
|inequality for the number of sales you need to make, | | | | |
|and describe the solutions. | | | | |
Mathematics Pacing Guide
Time Frame: 3 Weeks – April Grade 7
Unit 8: Inferences and Probability
|Standards for Mathematical Practice |Literacy Standards |
|1. Make sense of problems and persevere in solving them |RST. 7.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or |
| |performing technical tasks. |
|5. Use appropriate tools strategically | |
| |RST. 7.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |
|6. Attend to precision |are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. |
| | |
| |RST. 7.7 Integrate quantitative or technical information expressed in words in a text with a version of that|
| |information expressed visually (e.g., in a flowchart, diagram, model, graph, or table). |
| | |
| |WHST. 7.2 Write informative/explanatory texts, including the narration of historical events, scientific |
| |procedures/ experiments, or technical processes. |
| |Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into |
| |broader categories as appropriate to achieving purpose; include formatting (e.g., headings), graphics (e.g.,|
| |charts, tables), and multimedia when useful to aiding comprehension. |
| |Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other |
| |information and examples. |
| |Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and |
| |concepts. |
| |Use precise language and domain-specific vocabulary to inform about or explain the topic. |
| |Establish and maintain a formal style and objective tone. |
| |Provide a concluding statement or section that follows from and supports the information or explanation |
| |presented. |
| | |
| |WHST. 7.6 Use technology, including the Internet, to produce and publish writing and present the |
| |relationships between information and ideas clearly and efficiently. |
| | |
| |WHST. 7.7 Conduct short research projects to answer a question (including a self-generated question), |
| |drawing on several sources and generating additional related, focused questions that allow for multiple |
| |avenues of exploration. |
| | |
| |WHST. 7.9 Draw evidence from informational texts to support analysis reflection, and research. |
| | |
| |WHST. 7.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |
| |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|
|Common Core |Essential Questions |Assessment |Vocabulary |Resources |
|Use random sampling to draw inferences about a population |How do you collect data about a |Before: |Double bar |MAISA curriculum units and resources: |
|7. SP.1 Understand that statistics can be used to gain |population by identifying a |KWL |graph |
|information about a population by examining a sample of the |sample of the population? |Brainstorming |Histogram |iew/UnitCalendar?SourceSiteID=&CurriculumMapID=805&Ye|
|population; generalizations about a population from a sample are | |Graphic Organizers |Interval |arID=2013 |
|valid only if the sample is representative of that population. |How do you identify |Pretest |Line plot | |
|Understand that random sampling tends to produce representative |representative samples by | |Mean |Common Core Initiative: |
|samples and support valid inferences. |differentiating between biased |During: |Median |
| |and unbiased methods of sampling?|KWL |Mode |e/UnitMap/View/Default?UnitID=15874&YearID=2013&Schoo|
|7. SP.2 Use data from a random sample to draw inferences about a | |Quizzes |Range |lID=19&TimePeriodID=14&SourceSiteID=&CurriculumMapID=|
|population with an unknown characteristic of interest. Generate |How do you generate a |Daily Assignments |Ratio |778& |
|multiple samples (or simulated samples) of the same size to gauge|representative sample by |Exit Card |Tables | |
|the variation in estimates or predictions. For example, estimate |identifying types of random | | |Promethean planet – Probability to life!: |
|the mean word length in a book by randomly sampling words from |samples? |After: | |
|the book; predict the winner of a school election based on | |KWL | |30312/fun-with-probability#.URvkth0ZJYA |
|randomly sampled survey data. Gauge how far off the estimate or |How do generate a representative |Unit Test | | |
|prediction might be. |sample by identifying types of |Real World Problems | | – Common Core: |
| |biased samples? | | | |
|Draw informal comparative inferences about two populations | | | | |
|7. SP.3 Informally assess the degree of visual overlap of two |How do you make inferences about | | | – Probability: Independent Events |
|numerical data distributions with similar variabilities, |a population with an unknown | | |
|measuring the difference between the centers by expressing it as |characteristic by analyzing | | |ependent.html |
|a multiple of a measure of variability. For example, the mean |random samples? | | | |
|height of players on the basketball team is 10 cm greater than | | | | |
|the mean height of players on the soccer team, about twice the |How do you make estimates about a| | | |
|variability (mean absolute deviation) on either team; on a dot |population with an unknown | | | |
|plot, the separation between the two distributions of heights is |characteristic by using | | | |
|noticeable. |proportional reasoning? | | | |
| | | | | |
|7. SP.4 Use measures of center and measures of variability for |How do you test whether an | | | |
|numerical data from random samples to draw informal comparative |inference is valid by analyzing | | | |
|inferences about two populations. For example, decide whether the|data from multiple samples? | | | |
|words in a chapter of a seventh-grade science book are generally | | | | |
|longer than the words in a chapter of a fourth-grade science |How do you make estimates about a| | | |
|book. |population with an unknown | | | |
| |characteristic by using the mean | | | |
| |of multiple samples? | | | |
| | | | | |
| | | | | |
| |How do you informally compare two| | | |
| |populations by using the mean? | | | |
| | | | | |
| |How do you informally compare two| | | |
| |populations by using the median? | | | |
| | | | | |
| |How do you informally compare two| | | |
| |populations by using the range | | | |
| |and interquartile range? | | | |
Mathematics Pacing Guide
Time Frame: 3 Weeks – April/May Grade 7
Unit 9: Inferences and Probability
|Standards for Mathematical Practice |Literacy Standards |
|1. Make sense of problems and persevere in solving them |RST. 7.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or |
| |performing technical tasks. |
|2. Reason abstractly and quantitatively | |
| |RST. 7.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |
|3. Construct viable arguments and critique the reasoning of others |are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. |
| | |
|4. Model with mathematics |RST. 7.7 Integrate quantitative or technical information expressed in words in a text with a version of that|
| |information expressed visually (e.g., in a flowchart, diagram, model, graph, or table). |
|5. Use appropriate tools strategically | |
| |WHST. 7.5 With some guidance and support from peers and adults, develop and strengthen writing as needed by |
|6. Attend to precision |planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience |
| |have been addressed. |
|8. Look for and express regularity in repeated reasoning | |
| |WHST. 7.6 Use technology, including the Internet, to produce and publish writing and present the |
| |relationships between information and ideas clearly and efficiently. |
| | |
| |WHST. 7.8 Gather relevant information from multiple print and digital sources, using search terms |
| |effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and |
| |conclusions of others while avoiding plagiarism and following a standard format for citation. |
| | |
| |WHST. 7.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |
| |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|
| | |
| |SL. 7. 2 Interpret information presented in diverse media and formats (e.g., visually, quantitatively, |
| |orally) and explain how it contributes to a topic, text, or issue under study. |
| | |
| |SL. 7. 4 Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, |
| |and details to accentuate main ideas or themes; use appropriate eye contact, adequate volume, and clear |
| |pronunciation. |
| | |
| |SL. 7. 5 Include multimedia components (e.g., graphics, images, music, sound) and visual displays in |
| |presentations to clarify information. |
|Common Core |Essential Questions |Assessment |Vocabulary |Resources |
|Investigate chance processes and develop, use, and |How do you calculate the probability of an |Before |Combinations |MAISA curriculum units and resources: |
|evaluate probability models |event by creating a ratio? |KWL |Dependent events |
|7. SP.5 Understand that the probability of a chance event| |Brainstorming |Empirical |iew/UnitCalendar?SourceSiteID=&CurriculumMapID=805&Ye|
|is a number between 0 and 1 that expresses the likelihood|How do you describe the probability of an |Graphic Organizers |Equally likely events |arID=2013 |
|of the event occurring. Larger numbers indicate greater |event by using a number line? |Pretest |Independent events | |
|likelihood. A probability near 0 indicates an unlikely | | |Iterations |Common Core Initiative: |
|event, a probability around 1/2 indicates an event that |How do you calculate the probability of an |During |Likely |
|is neither unlikely nor likely, and a probability near 1 |event by making a sum of 1? |KWL |Measure of certainty |e/UnitMap/View/Default?UnitID=15874&YearID=2013&Schoo|
|indicates a likely event. | |Quizzes |Networks |lID=19&TimePeriodID=14&SourceSiteID=&CurriculumMapID=|
| |How do you analyze the probability of an |Daily Assignments |Permutations |778& |
|7. SP.7 Develop a probability model and use it to find |event by assigning equal probability to all |Exit Card |Probability | |
|probabilities of events. Compare probabilities from a |outcomes? | |Recurrence |Promethean planet – Probability to life!: |
|model to observed frequencies; if the agreement is not | |After |Sets |
|good, explain possible sources of the discrepancy. |How do you find the probability of events |KWL |Simple event |30312/fun-with-probability#.URvkth0ZJYA |
|a. Develop a uniform probability model by assigning |with multiple possibilities by combining |Unit Test |Theoretical | |
|equal probability to all outcomes, and use the model to |their probabilities? |Real World Problems |Unlikely events | – Common Core: |
|determine probabilities of events. For example, if a | | | | |
|student is selected at random from a class, find the | | | | |
|probability that Jane will be selected and the | | | | – Probability: Independent Events |
|probability that a girl will be selected. | | | |
| | | | |ependent.html |
Mathematics Pacing Guide
Time Frame: 3 Weeks – May/June Grade 7
Unit 10: Probability Models
|Standards for Mathematical Practice |Literacy Standards |
|1. Make sense of problems and persevere in solving them |RST. 7.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or |
| |performing technical tasks. |
|2. Reason abstractly and quantitatively | |
| |RST. 7.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |
|3. Construct viable arguments and critique the reasoning of others |are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. |
| | |
|4. Model with mathematics |RST. 7.7 Integrate quantitative or technical information expressed in words in a text with a version of that|
| |information expressed visually (e.g., in a flowchart, diagram, model, graph, or table). |
|5. Use appropriate tools strategically | |
| |WHST. 7.2 Write informative/explanatory texts, including the narration of historical events, scientific |
|6. Attend to precision |procedures/ experiments, or technical processes. |
| |Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into |
|8. Look for and express regularity in repeated reasoning |broader categories as appropriate to achieving purpose; include formatting (e.g., headings), graphics (e.g.,|
| |charts, tables), and multimedia when useful to aiding comprehension. |
| |Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other |
| |information and examples. |
| |Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and |
| |concepts. |
| |Use precise language and domain-specific vocabulary to inform about or explain the topic. |
| |Establish and maintain a formal style and objective tone. |
| |Provide a concluding statement or section that follows from and supports the information or explanation |
| |presented. |
| | |
| |WHST. 7.4 Produce clear and coherent writing in which the development, organization, and style are |
| |appropriate to task, purpose, and audience. |
| | |
| |WHST. 7.6 Use technology, including the Internet, to produce and publish writing and present the |
| |relationships between information and ideas clearly and efficiently. |
| | |
| |WHST. 7.7 Conduct short research projects to answer a question (including a self-generated question), |
| |drawing on several sources and generating additional related, focused questions that allow for multiple |
| |avenues of exploration. |
| | |
| |WHST. 7.9 Draw evidence from informational texts to support analysis reflection, and research. |
| | |
| |WHST. 7.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |
| |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|
|Common Core |Essential Questions |Assessment |Vocabulary |Resources |
|Investigate chance processes and develop, use,|How do you find the experimental |Before: |Basic counting principal |MAISA curriculum units and resources: |
|and evaluate probability models |probability by creating a ratio? |KWL |Biased sample |
|7. SP.6 Approximate the probability of a | |Brainstorming |Box plots |dar?SourceSiteID=&CurriculumMapID=805&YearID=2013 |
|chance event by collecting data on the chance |How do you interpret a set of data by |Graphic Organizers |Coordinate graph | |
|process that produces it and observing its |comparing experimental and theoretical|Pretest |Counting tree |Common Core Initiative: |
|long-run relative frequency, and predict the |probability? | |Cumulative frequency |
|approximate relative frequency given the | |During: |Dependent event |w/Default?UnitID=15874&YearID=2013&SchoolID=19&TimePeriodID=14&Sou|
|probability. For example, when rolling a |How do you predict the frequency of an|KWL |Experimental probability |rceSiteID=&CurriculumMapID=778& |
|number cube 600 times, predict that a 3 or 6 |event by using the results from |Quizzes |Extrapolations | |
|would be rolled roughly 200 times, but |experiments? |Daily Assignments |Five number summary |Promethean planet – Probability to life!: |
|probably not exactly 200 times. | |Exit Card |Frequency table |
| |How do you predict the frequency of an| |Histogram |h-probability#.URvkth0ZJYA |
|7. SP.7 Develop a probability model and use it|event by using the theoretical |After: |Independent event | |
|to find probabilities of events. Compare |probability? |KWL |Interpolations | – Common Core: |
|probabilities from a model to observed | |Unit Test |Intersection | |
|frequencies; if the agreement is not good, |How do you compare experimental |Real World Problems |IQR (inter-quartile) range | |
|explain possible sources of the discrepancy. |results to the theoretical | |Line graph | – Probability: Independent Events |
|a. Develop a uniform probability model by |probability? | |Line of best fit |
|assigning equal probability to all outcomes, |How do you explain discrepancies in | |Line plot | |
|and use the model to determine probabilities |results from a probability model by | |Lower quartile | |
|of events. For example, if a student is |comparing experimental and theoretical| |Mean | |
|selected at random from a class, find the |probabilities? | |Measures of central tendency | |
|probability that Jane will be selected and the| | |Median | |
|probability that a girl will be selected. |How do you analyze independent and | |Mode | |
|b. Develop a probability model (which may not|dependent events by finding their | |Organized list | |
|be uniform) by observing frequencies in data |probabilities? | |Outcomes | |
|generated from a chance process. For example, | | |Population | |
|find the approximate probability that a |How do you find the probability of | |Probability | |
|spinning penny will land heads up or that a |compound events by creating an | |Proportion | |
|tossed paper cup will land open-end down. Do |organized list? | |Quartile | |
|the outcomes for the spinning penny appear to | | |Random | |
|be equally likely based on the observed |How do you find the probability of | |Range | |
|frequencies? |compound events by creating a tree | |Relative frequency | |
| |diagram? | |Repeated events | |
|7. SP.8 Find probabilities of compound events | | |Sample | |
|using organized lists, tables, tree diagrams, |How do you find the probability of | |Sampling | |
|and simulation. |compound events by creating a table? | |Scatter plot | |
|Understand that, just as with simple events, | | |Stem-and-leaf plot | |
|the probability of a compound event is the |How do you find the total number of | |Theoretical probability | |
|fraction of outcomes in the sample space for |possible combinations by using the | |Trend union | |
|which the compound event occurs. |Fundamental Counting Principle? | |Upper quartile | |
|Represent sample spaces for compound events | | |Venn diagram | |
|using methods such as organized lists, tables | | | | |
|and tree diagrams. For an event described in | | | | |
|everyday language (e.g., “rolling double | | | | |
|sixes”), identify the outcomes in the sample | | | | |
|space which compose the event. | | | | |
|Design and use a simulation to generate | | | | |
|frequencies for compound events. For example,| | | | |
|use random digits as a simulation tool to | | | | |
|approximate the answer to the question: If 40%| | | | |
|of donors have type A blood what is the | | | | |
|probability that it will take at least 4 | | | | |
|donors to find one with type A blood? | | | | |
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