7th Grade Math – Unit 4 – Rational Numbers Grade Level: Mathematical Practices Conceptual Overview Common Core Standards Essential Understandings Suggested Unit Pacing (# of days): The Mathematical Practices are P1 Make sense of problems and persevere in solving them. K-12 standards and together with P2 Reason abstractly and quantitatively. the content standards prescribe Construct viable arguments and critique the reasoning of P3 that students experience others. mathematics as a coherent, useful, P4 Model with mathematics. and logical subject. Teachers of P5 Use appropriate tools strategically. mathematics should intentionally P6 Attend to precision. provide daily opportunities for P7 Look for and make use of structure. students to develop these P8 Look for and express regularity in repeated reasoning. mathematical habits of mind. During this unit students will… Apply and extend prior operations with rational numbers. By the end of this unit students will be able to… 7.NS.1 Fluently add, subtract, multiply and divide rational numbers. Solve real-world and mathematical problems rational numbers. 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. 7.NS.1a Describe situations in which opposite quantities combine to make 0. 7.NS.1.bo 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. 7.NS.1c o 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. 7.NS.1d o Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 7.NS.2a o 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 realworld contexts. 7.NS.2b o 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. 7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers 7.NS.2d o 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. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. These suggested learning targets were determined based on the intentions of the CCSS and/or NCES. Teachers will need to add the criteria for success in order to create outcome-based targets. Learning Targets Essential Terminology Literacy Integration Add, subtract, multiply and divide signed fractions and decimals. Convert rational numbers to decimals using long division. Apply operations with signed fractions and decimals to real world problems. rational number, irrational number, terminating and repeating decimal, reciprocal, multiplicative inverse, numerator, denominator, equivalent fractions, improper fractions Integrate quantitative or technical information expressed in words in a text with Literacy a version of that information expressed visually (e.g., in a flowchart, diagram, Standards model, graph, or table). Literature Connections Technology Integration Technology Standards Use appropriate technology tools and other resources to access information. Use appropriate technology tools and other resources to organize information (e.g. graphic organizers, databases, spreadsheets, and desktop publishing). Use appropriate technology tools and other resources to design products to share information with others (e.g. multimedia presentations, Web 2.0 tools, graphics, podcasts, and audio files). Technology Resources Additional Resources Resources with Links: http://www.abss.k12.nc.us/cms/lib02/NC01001905/Centricity/domain/1580/secondary math/7th grade/general/7th Math Unit 4 Resources.docx Cross Curricular Integration Pre-/Postassessment On-going/ Formative Assessment Performance Task http://www.abss.k12.nc.us/cms/lib02/NC01001905/Centricity/domain/1580/sec ondary math/7th grade/general/7th Math Unit 4 PT.docx Assessment Summative Performance Task Rubric http://www.abss.k12.nc.us/cms/lib02/NC01001905/Centricity/domain/1580/sec ondary%20math/7th%20grade/general/7th%20Math%20Unit%204%20PT%20 Rubric.docx Teachers determine the learning plan while reflecting on the range of abilities, styles, interests and needs of students. How will the work be personalized and differentiated in order to achieve the desired learning targets? Considerations for the Learning Plan Re-teaching Enrichment