7NS-Apply+&+extend+previous+understandings+of+operations+with+fractions+to+add,+subtract,+multiply,+&+divide+rational+numbers

7.MP.2. Reason abstractly and quantitatively. 7.MP.4. Model with mathematics. 7.MP.7. Look for and make use of structure. **7NS 2** 7.MP.2. Reason abstractly and quantitatively. 7.MP.4. Model with mathematics. 7.MP.7. Look for and make use of structure. 7.MP.1. Make sense of problems and persevere in solving them. 7.MP.2. Reason abstractly and quantitatively. 7.MP.5. Use appropriate tools strategically. 7.MP.6. Attend to precision. 7.MP.7. Look for and make use of structure. 7.MP.8. Look for and express regularity in repeated reasoning. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**===
 * ===**Common Core Standard**===
 * 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.
 * 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.
 * 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.
 * 7.NS.3.** Solve real-world and mathematical problems involving the four operations with rational numbers.*
 * Computations with rational numbers extend the rules for manipulating fractions to complex fractions. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**===
 * 7NS 1**
 * 7NS 3**
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**=== || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking**=== ||
 * 7.NS.1 Students add and subtract rational numbers using a number line. For example, to add -5 + 7, students would find -5 on the number line and move 7 in a positive direction (to the right). The stopping point of 2 is the sum of this expression. Students also add negative fractions and decimals and interpret solutions in given contexts.**


 * Example 1:** Use a number line to add -5 + 7.

Solution: Students find -5 on the number line and move 7 in a positive direction (to the right). The stopping point of 2 is the sum of this expression. Students also add negative fractions and decimals and interpret solutions in given contexts. In 6th grade, students found the distance of horizontal and vertical segments on the coordinate plane. In 7th grade, students build on this understanding to recognize subtraction is finding the distance between two numbers on a number line. In the example, 7 – 5, the difference is the distance between 7 and 5, or 2, in the direction of 5 to 7 (positive). Therefore the answer would be 2.


 * Example 2:** Use a number line to subtract: -6 – (-4)

Solution: This problem is asking for the distance between -6 and -4. The distance between -6 and -4 is 2 and the direction from -4 to -6 is left or negative


 * Example 3:** Use a number line to illustrate:

• p – q ie. 7 – 4 • p + (-q) ie. 7 + (– 4) • Is this equation true p – q = p + (-q)?

Students explore the above relationship when p is negative and q is positive and when both p and q are negative. Is this relationship always true?


 * Example 4:** Morgan has $4 and she needs to pay a friend $3. How much will Morgan have after paying her friend?

Solution: 4 + (-3) = 1 or (-3) + 4 = 1


 * 7.NS.2 Students recognize that when division of rational numbers is represented with a fraction bar, each number can have a negative sign. Using long division from elementary school, students understand the difference between terminating and repeating decimals. This understanding is foundational for work with rational and irrational numbers in 8th grade. For example, identify which fractions will terminate (the denominator of the fraction in reduced form only has factors of 2 and/or 5)**

a. 4/-5 b. -16/20 c. -4/-5
 * Example 1:** Which of the following fractions is equivalent to -4/5 ? Explain your reasoning.


 * Example 2:** Examine the family of equations in the table below. What patterns are evident? Create a model and context for each of the products. Write and model the family of equations related to 3 x 4 = 12. Using long division from elementary school, students understand the difference between terminating and repeating decimals. This understanding is foundational for the work with rational and irrational numbers in 8th grade.

Identify which fractions will terminate (the denominator of the fraction in reduced form only has factors of 2 and/or 5)
 * Example 3:** Using long division, express the following fractions as decimals. Which of the following fractions will result in terminating decimals; which will result in repeating decimals?


 * 7.NS.3 Students use order of operations from 6th grade to write and solve problem with all rational numbers.**


 * Example 1:** Calculate: [-10(-0.9)] – [(-10) • 0.11]

Solution: 10.1


 * Example 2:** Jim’s cell phone bill is automatically deducting $32 from his bank account every month. How much will the deductions total for the year?

Solution: -32 + (-32) + (-32) + (-32)+ (-32) + (-32) + (-32) + (-32) + (-32) + (-32) + (-32) + (-32) = 12 (-32)


 * Example 3:** It took a submarine 20 seconds to drop to 100 feet below sea level from the surface. What was the rate of the descent?

Solution: __-100 feet__ = - __5 feet__ = -5 ft/sec 20 seconds 1 second


 * Example 4:** A newspaper reports these changes in the price of a stock over four days: -1/8,-5/8 ,3/8 ,-9/8 . What is the average daily change?

Solution: The sum is -12/8; dividing by 4 will give a daily average of -3/8

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can apply and extend my knowledge of operations with fractions to add, subtract, multiply, and divide rational numbers.**===


 * (7NS1) I can add and subtract integers using a number line.**
 * **(7NS1a) I can describe examples of quantities that make 0. (For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.)**
 * **(7NS1b) I can explain why a number and its opposite have a sum of zero; therefore, are called additive inverses.**
 * **(7NS1c) I can** **change a subtraction problem to an equivalent addition problem.**
 * **(7NS1d) I can apply properties of operations to make addition and subtraction integers easier.**


 * (7 NS 2) I can multiply and divide integers.**
 * **(7NS2a) I can apply the rules for multiplying signed integers.**
 * **(7NS2b) I can apply the rules for dividing signed integers.**
 * **(7NS2c) I can apply properties of operations to make multiplication and division of integers easier.**
 * **(7NS1d) I can convert rational numbers to decimals by using long division.**


 * (7 NS 3) I can solve real-world math problems involving the four operations with rational numbers.**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Essential Vocabulary**

 * rational number, integer, number line, additive inverse**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**

 * peer tutoring, guided notes, grouping, blogs, foldables, inquiry based learning to accelerate/remediate, justification of answers, create/post a number line in classroom, post a rule chart for the 4 operations with integers**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**

 * [|DPI math resources]**
 * "I Have, Who Has" Integer Operations**
 * Integer Computation Square Puzzle**
 * Number Tile Integer Operations**
 * Beat Me to the Top-Integers**
 * Integer War Game--using a set of regular playing cards**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Enrichment:**
[|Create an Integer Review Game]

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources**=== [|Activities with Integers] [|More Activities with Integers] http://www.dpi.state.nc.us/curriculum/mathematics/middlegrades/grade07/ http://qta.quantiles.com/qtaxon/goal/29748/ http://qta.quantiles.com/qtaxon/goal/29749/ http://qta.quantiles.com/qtaxon/goal/29750/ http://qta.quantiles.com/qtaxon/goal/29751/ http://qta.quantiles.com/qtaxon/goal/29752/ http://qta.quantiles.com/qtaxon/goal/29753/ http://qta.quantiles.com/qtaxon/goal/29754/ http://qta.quantiles.com/qtaxon/goal/29755/ http://qta.quantiles.com/qtaxon/goal/29756/
 * Math Partners resources,**
 * +/- Number line, poster paper,**

http://kutasoftware.com/freeipa.html

http://www.montgomery.k12.nc.us/18032092913393583/site/default.asp
 * http://www.mathgoodies.com,**

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Informatio n**===