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.
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.
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. Apply properties of operations as strategies to multiply and divide rational numbers.
c. Apply properties of operations as strategies 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 0’s or eventually repeats.
• use a number line or positive/negative chips to show that an integer and its opposite will always have a sum of zero.
• use a number line to show addition as a specific distance from a particular number in one direction or the other, depending on the sign of the value being added.
• interpret the addition of integers by relating the values to real-world situations.
• rewrite a subtraction problem as an addition problem by using the additive inverse.
• show the distance between two integers on a number line is the absolute value of their difference.
• describe real-world situations represented by the subtraction of integers.
• use the properties of operations to add and subtract rational numbers.
• use patterns and properties to explore the multiplication of integers.
• use patterns and properties to develop procedures for multiplying integers.
• describe real-world situations represented by the multiplication of integers.
• use the relationship between multiplication and division to develop procedures for dividing integers.
• explain why the property of closure exists for the division of rational numbers, but not for whole numbers.
• describe real-world situation represented by the division of integers.
• interpret the quotient in relation to the original problem.
• generalize the procedures for multiplying and dividing integers to all rational numbers.
• use long division to convert a rational number to a decimal.
• verify that a number is rational based on its decimal equivalent.
• identify rational numbers as numbers that can be written in ratio form vs non-rational numbers that are non-terminating decimals or undefined fractions.
This week we are beginning our Integer Unit. During this unit, students will learn how to perform the four operations (add, subtract, multiply and divide) using both positive and negative numbers. Students will be completing multiple activities to practice the above standards including structured notes, notebook activities, and practice with MathSpace.
If additional help is needed, students are encouraged to view a lesson regarding a given topic on Khan Academy. This website is free and provides both video instruction as well as practice problems.
Students are able to complete additional practice on both MathSpace and IXL.
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