Unit 2

Integers and Rational Numbers

Unit Description:

Students continue to build an understanding of the number line in Unit 2 from their work in Grade 6. They develop a unified understanding of numbers, recognizing fractions, decimals (that have a finite or repeating decimal representation), and percents as different representations of rational numbers.  Students should apply and extend their understanding of addition, subtraction, multiplication, and division to add, subtract, multiply and divide within the entire set of rational numbers. Students should begin this unit representing addition and subtraction on a horizontal or vertical number line diagram and finish the unit being able to apply properties of operations as strategies to add, subtract, multiply and divide rational numbers. They should also apply their understanding of positive and negative numbers to establish the rules for multiplying signed numbers. Additionally, students should understand that integers can be divided, provided that the divisor is not zero, and develop an understanding that the quotient of integers (with non-zero divisors) is a rational number.  Students should leave this unit with a deeper conceptual understanding of positive and negative rational numbers and be able to use them to solve real-world and mathematical problems including real-world problems where the sum is zero. Although procedural skill and fluency should be improved through this unit, conceptual understanding should be the basis for discovery and instruction.  Unit 2 includes rational numbers as they appear in expressions and equations—work that is continued in Unit 3.  A focus on equivalent expressions is important as student prepare for work with equations and inequalities in Unit 3.

Standards for Mathematical Practice

MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP.3 Construct viable arguments and critique the reasoning of others.

MP.4 Model with mathematics.

MP.5 Use appropriate tools strategically.

MP.6 Attend to precision.

MP.7 Look for and make use of structure.

MP.8 Look for and express regularity in repeated reasoning.

Louisiana Student Standards for Mathematics (LSSM)

Enduring Understandings:

·         Rational numbers use the same properties as whole numbers.

·         Rational numbers can be used to represent and solve real-life situation problems.

·         Rational numbers can be represented with visuals (including distance models), language, and real-life contexts.

·         A number line model can be used to represent the unique placement of any number in relation to other numbers.

·         There are precise terms and sequences to describe operations with rational numbers.

Essential Questions:

·         Why do I need mathematical operations?

·         What is the relationship between properties of operations and types of numbers?

·         How do I know which mathematical operation (+, -, x, ÷, exponents, etc.) to use?

·         How do I know which computational method (mental math, estimation, paper and pencil, and calculator) to use?

·         How do you add rational numbers?

·         How do you subtract rational numbers?

·         How do you multiply rational numbers?

·         How do you divide rational numbers?

·         How is computation with rational numbers similar to and different from whole number computation?

·         How are rational numbers used and applied in real-life and mathematical situations?

·         How does the ongoing use of fractions and decimals apply to real-life situations?