# Unit 2 Multiplying and Dividing Rational Numbers

Unit 2 Multiplying and Dividing Rational Numbers

Days: 1 – 11MathematicsGrade: 7th

Standard: /**Standard: 7.NS.2a 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.**

**7.NS.2b Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.**

**b. Understand that integers can be divided provided that the divisor is not zero and every quotient of integers (with nonzero 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 and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.**

**c. Apply properties of operations as strategies to multiply and divide rational numbers.**

**7.NS.2d Apply and extend previous understandings of multiplication and division 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 zeroes or eventually repeats.**

**7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.1**

**1 Computations with rational numbers extend the rules for manipulating fractions to complex fractions.**

Domain: / The Number System / Cluster: / Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. / Grade: / 7 / Target Type: / K, R

Make sense of problems and persevere in solving them. / Reason abstractly and quantitatively. / Construct viable arguments and critique the reasoning of others. / Model with mathematics. / Use appropriate tools strategically. / Attend to precision. / Look for and make use of structure. / Look for and express regularity in repeated reasoning.

Knowledge Target

(Prerequisite Skill or Underpinning) / Reasoning Target

(Mastery) / Performance Skill Target

(Mastery) / Product Target

Recognize that the process for multiplying fractions can be used to multiply rational numbers including integers.

Know and describe the rules when multiplying signed numbers.

Explain why integers can be divided except when the divisor is 0.

Describe why the quotient is always a rational number.

Know and describe the rules when dividing signed numbers, integers.

Recognize that –(p/q) = -p/q = p/- q.

Identify how properties of operations can be used to multiply and divide rational numbers (such as distributive property, multiplicative inverse property, multiplicative identity, commutative property for multiplication, associative property for multiplication, etc.)

Convert a rational number to a decimal using long division.

Explain that the decimal form of a rational number terminates (stops) in zeroes or repeats.

Add rational numbers.

Subtract rational numbers.

Multiply rational numbers.

Divide rational numbers. / Apply the properties of operations, particularly distributive property, to multiply rational numbers.

Interpret the products of rational numbers by describing real-world contexts.

Interpret the quotient of rational numbers by describing real-world contexts.

Apply properties of operations as strategies to multiply and divide rational numbers.

Solve real-world mathematical problem by adding, subtracting, multiplying, and dividing rational numbers, including complex fractions.

**Formative Pre-assessment**/

**Student Learning Target**/

**Formative Assessment**

Day 1:

I can use the properties of operations to multiply integers. (K)

Day 2:

I can convert improper fractions to mixed numbers and vice versa. (K)

Day 3:

I can use the properties of operations to multiply rational numbers. (K)

Day 4:

I can use the properties of operations to divide integers. (K)

Day 5:

I can use the properties of operations to divide rational numbers including complex fractions. *Fractions (K)

Day 6:

I can use the properties of operations to divide rational numbers.

*Long Division (K)

Day 7:

I can use properties of operations to multiply and divide fractions and decimals in order to solve real world mathematical problems. (R)

Day 8:

I can convert between all forms of rational numbers using various strategies including long division and place value.

*mental math, place value, long division, factors in the denominator (K)

Day 9:

I understand that the decimal form of a rational number will either repeat or terminate. Irrational numbers do neither. (K)

Day 10:

I can identify rational numbers as numbers that can be represented by a fraction. I know that a rational number cannot have a zero as a denominator. (K)

Day 11:

I can use place value to round decimal numbers in order to solve real world and mathematical problems. (R) / Day 1:

Please describe and give two examples of multiplying positive and negative integers.

If the product of two integers is -50 and one of the integers was -5 what is the other integer?

Day 2:

- 7/5 =
- 2½ =

- 1/5 x 4/7=
- 3½ x 2¾ =
- 2.45 x 6.8 =

Please describe and give two examples of dividing positive and negative integers.

Day 5:

- 4/5 / 3/2 =
- 4x2/2x9 =
- The square root of 18 is between which two whole numbers?

12.456 / 4.5 =

Day 7:

- The bill for the dinner was $80.00. One of the diners had a coupon for $25.00 toward the dinner. The five diners then split the remaining bill equally. How much did each diner have to pay?
- A piece of wood that is 9 feet long is cut in half lengthwise. Each half is half is then cut lengthwise into 6 congruent pieces of wood. What is the length of each of the twelve small pieces of wood?

- Change the following decimal to fraction using mental math. 0.8 =
- Change the following fraction to a decimal using factors of 100. 1/5 =
- Change the following fraction to a decimal using long division. 1/8 =

Using the nested Venn diagram explain your understanding of rational and irrational numbers.

Day 10:

- Use long division to convert 1/7 into a decimal and determine how many places the repeating block goes until it begins to repeat.
- Determine if the numbers are rational or irrational.

Day 11:

Before 2000, stocks on the New York stock exchange were listed with fractional values. Now they are listed with a decimal to the nearest penny. In 1999, a stock’s value changed by 10/32. What would its change in value be, using today’s value system, to the nearest penny?

**Critical Content Vocabulary**/

**Suggested Strategies/Activities**/

**Instructional Resources**