Unit 1: Rational Numbers Addition and Subtraction
Mathematics Pacing Guide
Time Frame: 3 Weeks – September Grade 7
Unit 1: Rational Numbers – Addition and Subtraction
Standards for Mathematical Practice / Literacy Standards1. Make sense of problems and persevere in solving them
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure / 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.
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. 7.4 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 operations with fractions to add, subtract, multiply, and divide rational numbers
7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
d. Apply properties of operations as strategies to add and subtract rational numbers. / How do you add and subtract fractions and decimals?
How do opposite quantities combine to make zero by using a number line?
How do you add integers by using a number line?
How do you add positive and negative numbers by using a number line?
How do you subtract integers by adding the additive inverse?
How do you find the distance between two points by finding the absolute value of their difference?
How do you subtract rational numbers by using real world contexts?
How do you add two positive or two negative integers by using a number line?
How do you add positive and negative integers by using a number line?
How do you demonstrate the commutative property of addition by using a number line?
How do you rethink a subtraction problem as an addition problem by using the additive inverse?
How do you subtract integers by using the “take away” definition of subtraction on a number line?
How do you determine the distance between integers by examining absolute value and number lines?
How do you subtract integers by using the difference definition of subtraction on a number line? / Before:
KWL
Brainstorming
Graphic Organizers
Pretest
During:
KWL
Quizzes
Daily Assignments
Exit Card
Pictures and Drawings
- Using number lines to demonstrate absolute value and opposites
Model
- Students model using a human number line
- Students can use chips (counters)
After:
KWL
Unit Test
Real World Problems / Absolute value
Decimals
Integers
Irrational numbers
Natural numbers
Negative
Number Line
Positive
Rational number
Real numbers
Repeating decimal
Whole number / MAISA curriculum units and resources:
http://gomaisa-public.rubiconatlas.org/Atlas/Browse/View/UnitCalendar?SourceSiteID=&CurriculumMapID=805&YearID=2013
SUPO – Numbers and operations:
http://www.math.com/school/subject2/lessons/S2U3L4GL.html
Basic operations with fractions and a game:
http://www.prometheanplanet.com/en-us/Search/resources/country/united-states/language/english/?Keywords=rational+numbers+addition+and+subtraction&SortField=DownloadCount30Days_desc
Learnzillion.com – Common Core:
http://learnzillion.com/common_core/math/7
Mathisfun.com
http://www.mathsisfun.com/fractions-menu.html
Common Core Initiative:
http://oaklandk12-public.rubiconatlas.org/Atlas/Browse/UnitMap/View/Default?UnitID=15756&YearID=2013&SchoolID=19&TimePeriodID=14&SourceSiteID=&CurriculumMapID=778&
This site has multiple resources for teachers and students.
http://apps.svsu.edu/mathsci-center/uploads/math/MiddleSchool.html
Mathematics Pacing Guide
Time Frame: 3 Weeks – September/October Grade 7
Unit 2: Rational Numbers – Multiplication and Division
Standards for Mathematical Practice / Literacy Standards1. Make sense of problems and persevere in solving them
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure / RST. 7.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.
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.
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 operations with fractions to add, subtract, multiply, and divide rational numbers
7. NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then – (p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.
c. Apply properties of operations as strategies to multiply and divide rational numbers. / How do you add and subtract fractions and decimals?
How do you compare the outcomes of fraction division with the outcomes of decimal division by computing with fraction/decimal equivalents?
How do you multiply a positive integer by a negative integer by thinking about equal groups?
How do you multiply a negative integer by a negative integer by thinking about equal groups?
How do you rewrite multiplication of numbers by applying the commutative property of multiplication?
How do you apply the commutative property by rewriting division problems as multiplication? / Before:
KWL
Brainstorming
Graphic Organizers
Pretest
During:
KWL
Quizzes
Daily Assignments
Exit Card
Models
- Using colored overlays to obtain results from multiplying fractions
Portfolio
- Students will create a portfolio using real world examples
After:
KWL
Unit Test
Real World Problems / Absolute value
Decimals
Integers
Irrational numbers
Natural numbers
Negative
Number Line
Positive
Rational number
Real numbers
Repeating Decimal
Whole number / MAISA curriculum units and resources:
http://gomaisa-public.rubiconatlas.org/Atlas/Browse/View/UnitCalendar?SourceSiteID=&CurriculumMapID=805&YearID=2013
SUPO – Numbers and operations:
http://apps.svsu.edu/mathsci-center/uploads/math/M07N.htm
Basic operations with fractions and a game:
http://www.prometheanplanet.com/en-us/Search/resources/country/united-states/language/english/?Keywords=rational+numbers+addition+and+subtraction&SortField=DownloadCount30Days_desc
Learnzillion.com – Common Core:
http://learnzillion.com/common_core/math/7
Mathisfun.com
http://www.mathsisfun.com/fractions-menu.html
Common Core Initiative:
http://oaklandk12-public.rubiconatlas.org/Atlas/Browse/UnitMap/View/Default?UnitID=15756&YearID=2013&SchoolID=19&TimePeriodID=14&SourceSiteID=&CurriculumMapID=778&
7. NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. / How do you rewrite multiplication problems with rational numbers by using the associative property of multiplication?
How do you rewrite multiplication 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 involving the four operations with rational numbers. / How do you use addition and 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 Standards1. Make sense of problems and persevere in solving them
5. Use appropriate tools strategically
6. Attend to precision / 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.
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.
a. 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.
b. Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples.
c. Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Establish and maintain a formal style and objective tone.
f. 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 solve real-world and mathematical problems
7. RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.
7. RP.2 Recognize and represent proportional relationships between quantities.
a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
7. RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. / How do you find unit rate?
How do you approximate unit rates from verbal descriptions and equations by estimating?
How do you find unit rates in situations involving fractions by using division?
How do you find the best deal by comparing unit rates?
How do you apply scale maps and scale models by using unit rates?
How do you scale recipes by applying unit rates?
How do you create proportional relationships by expanding ratios?
How do you determine whether ratios are proportional by reading tables?
How do you determine whether ratios are proportional by creating tables?
How do you determine whether ratios are proportional by reading graphs?
How do you identify unit rates by listening to verbal descriptions?
How do you understand unit rates by 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? / Before:
KWL
Brainstorming
Graphic Organizers
Pretest
During:
KWL
Quizzes
Daily Assignments
Exit Card
Project
- Picking the better buy
- Debate the better car for gas millage
Pictures
- Students will graph relationships
After:
KWL
Unit Test
Real World Problems / Density
Derived quantities
Proportion
Proportion equation
Rate
Rate of change
Ratio
Speed
Unit rate
Velocity
Weighted average / MAISA curriculum units and resources:
http://gomaisa-public.rubiconatlas.org/Atlas/Browse/View/UnitCalendar?SourceSiteID=&CurriculumMapID=805&YearID=2013
SUPO – Numbers and operations:
http://apps.svsu.edu/mathsci-center/uploads/math/M07N.htm
Promethean planet - A Math Adventure in Unit Rates and Price Discounts. http://www.prometheanplanet.com/en-us/Resources/Item/38096/stinky-chaz-at-summer-camp-a-math-adventure-in-unit-rates-and-price-discounts#.URu-EB0ZJYA
Learnzillion.com – Common Core:
http://learnzillion.com/common_core/math/7
Mathisfun.com - Ratios
http://www.mathsisfun.com/numbers/ratio.html
Common Core Initiative:
http://oaklandk12-public.rubiconatlas.org/Atlas/Browse/UnitMap/View/Default?UnitID=15755&YearID=2013&SchoolID=19&TimePeriodID=14&SourceSiteID=&CurriculumMapID=778&
Mathematics Pacing Guide