UNIT 7: Making relevant connections within the number system
IN THIS UNIT, STUDENTS WILL BUILD UPON THEIR UNDERSTANDING IN GRADE 6:
- Quantities can be shown using + or – and having opposite directions or values
- Points on a number line show distance and direction
- Opposite signs of numbers indicate locations on opposite sides of 0 on the number line,
- The opposite of an opposite is the number itself
- The absolute value of a rational number is its distance from 0 on the number line
- The absolute value is the magnitude of a positive or negative quantity
- Coordinates can be located and compared on a coordinate grid using negative and positive rational numbers
- Order of operations should be applied to operations with rational numbers.
- Quantities can be shown using + or – and having opposite directions or values
- Points on a number line show distance and direction
- Opposite signs of numbers indicate locations on opposite sides of 0 on the number line,
- The opposite of an opposite is the number itself
- The absolute value of a rational number is its distance from 0 on the number line
- The absolute value is the magnitude of a positive or negative quantity
- Coordinates can be located and compared on a coordinate grid using negative and positive rational numbers
- Order of operations should be applied to operations with rational numbers.
LEARNING OBJECTIVES:
7.NR.1. Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers).
7.NR.1.1. Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.
7.NR.1.2. Show and explain 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. Interpret sums of rational numbers by describing applicable situations.
7.NR.1.3. Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve real-life problems.
7.NR.1.4. Show and explain the subtraction of rational numbers by 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 contextual situations.
7.NR.1.5. Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
7.NR.1.6. Make sense of the multiplication of rational numbers using realistic applications.
7.NR.1.7. Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rational number.
7.NR.1.8. Represent the multiplication and division of integers using a variety of strategies and interpret products and quotients of rational numbers by describing them based on the relevant situation.
7.NR.1.9. Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.
7.NR.1.10. Convert rational numbers between forms to include fractions, decimal numbers, and percents, using an understanding of the part divided by the whole. Know that the decimal form of a rational number terminates in 0s or eventually repeats.
7.NR.1.11. Solve multi-step contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.
7.NR.1. Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers).
7.NR.1.1. Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.
7.NR.1.2. Show and explain 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. Interpret sums of rational numbers by describing applicable situations.
7.NR.1.3. Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve real-life problems.
7.NR.1.4. Show and explain the subtraction of rational numbers by 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 contextual situations.
7.NR.1.5. Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
7.NR.1.6. Make sense of the multiplication of rational numbers using realistic applications.
7.NR.1.7. Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rational number.
7.NR.1.8. Represent the multiplication and division of integers using a variety of strategies and interpret products and quotients of rational numbers by describing them based on the relevant situation.
7.NR.1.9. Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.
7.NR.1.10. Convert rational numbers between forms to include fractions, decimal numbers, and percents, using an understanding of the part divided by the whole. Know that the decimal form of a rational number terminates in 0s or eventually repeats.
7.NR.1.11. Solve multi-step contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.
LEARNING TARGETS (I Can Statements):
- I can describe real-world situations where opposites have a sum of 0.
- I can solve problems where two quantities sum to 0.
- I can define additive inverse as a rational number added to its opposite which results in a sum of zero.
- I can describe the absolute value of a rational number as a distance from 0.
- I can represent addition on a horizontal/vertical number line.
- I can solve real-world problems involving adding rational numbers.
- I can solve real-world problems involving adding and subtracting rational numbers.
- I can represent addition on a horizontal/vertical number line.
- I can demonstrate the subtraction of rational numbers by adding the additive inverse.
- I can calculate the distance between two rational numbers by taking the absolute value of their difference.
- I can solve real-world problems involving subtracting rational numbers.
- I can apply commutative, associative, identity, and inverse properties to add and subtract rational numbers.
- I can solve real-world problems involving multiplying rational numbers.
- I can multiply positive and negative rational numbers using properties of operations.
- I can divide integers, provided the divisor is not zero.
- I can explain that a negative symbol can be written in the numerator, denominator, or next to the fraction without changing the value of the fraction.
- I can represent real-world situations with multiplication and division of integers using a variety of strategies.
- I can interpret products and quotients of rational numbers in real-world situations.
- I can apply properties of operations as strategies to multiply and divide rational numbers.
- I can utilize the distributive property to solve multiplication and division problems.
- I can write positive and negative values in fraction, decimal, and percentage forms.
- I can identify decimal values as repeating or terminating.
- I can solve multi-step problems involving rational numbers.
- I can describe real-world situations where opposites have a sum of 0.
- I can solve problems where two quantities sum to 0.
- I can define additive inverse as a rational number added to its opposite which results in a sum of zero.
- I can describe the absolute value of a rational number as a distance from 0.
- I can represent addition on a horizontal/vertical number line.
- I can solve real-world problems involving adding rational numbers.
- I can solve real-world problems involving adding and subtracting rational numbers.
- I can represent addition on a horizontal/vertical number line.
- I can demonstrate the subtraction of rational numbers by adding the additive inverse.
- I can calculate the distance between two rational numbers by taking the absolute value of their difference.
- I can solve real-world problems involving subtracting rational numbers.
- I can apply commutative, associative, identity, and inverse properties to add and subtract rational numbers.
- I can solve real-world problems involving multiplying rational numbers.
- I can multiply positive and negative rational numbers using properties of operations.
- I can divide integers, provided the divisor is not zero.
- I can explain that a negative symbol can be written in the numerator, denominator, or next to the fraction without changing the value of the fraction.
- I can represent real-world situations with multiplication and division of integers using a variety of strategies.
- I can interpret products and quotients of rational numbers in real-world situations.
- I can apply properties of operations as strategies to multiply and divide rational numbers.
- I can utilize the distributive property to solve multiplication and division problems.
- I can write positive and negative values in fraction, decimal, and percentage forms.
- I can identify decimal values as repeating or terminating.
- I can solve multi-step problems involving rational numbers.
TEXTBOOK CONNECTIONS:
(Use Georgia Reveal Math - Course 2 - 7th Grade)
Module 3 – Operations with Integers
Add, subtract, multiply, and divide integers.
Lesson 3-1 Add Integers
Students will solve problems involving adding integers.
Lesson 3-2 Subtract Integers
Students will solve problems involving subtracting integers.
Lesson 3-3 Multiply Integers
Students will solve problems involving multiplying integers.
Lesson 3-4 Dividing Integers
Students will solve problems involving dividing integers.
Lesson 3-5 Apply Integer Operations
Students will solve problems by applying all operations to integers.
Module 4 – Operations with Rational Numbers
Perform addition, subtraction, multiplication, and division of rational numbers.
Lesson 4-1 Rational Numbers
Students will identify terminating and repeating decimals and use long division to convert rational numbers to decimals.
Lesson 4-2 Add Rational Numbers
Students will demonstrate the application of the additive inverse and an understanding of rational numbers.
Lesson 4-3 Subtract Rational Numbers
Students will demonstrate an understanding of the subtraction of rational numbers by adding the additive inverse and applying it to solving real-world problems.
Lesson 4-4 Multiply Rational Numbers
Students will apply their understanding of multiplication to rational numbers and use the order of operations to solve real-world problems.
Lesson 4-5 Divide Rational Numbers
Students will apply their understanding of division to rational numbers and use the order of operations to solve real-world problems.
Lesson 4-6 Apply Rational Number Operations
Students will apply their understanding of the four operations with rational numbers to evaluate mathematical expressions.
(Use Georgia Reveal Math - Course 2 - 7th Grade)
Module 3 – Operations with Integers
Add, subtract, multiply, and divide integers.
Lesson 3-1 Add Integers
Students will solve problems involving adding integers.
Lesson 3-2 Subtract Integers
Students will solve problems involving subtracting integers.
Lesson 3-3 Multiply Integers
Students will solve problems involving multiplying integers.
Lesson 3-4 Dividing Integers
Students will solve problems involving dividing integers.
Lesson 3-5 Apply Integer Operations
Students will solve problems by applying all operations to integers.
Module 4 – Operations with Rational Numbers
Perform addition, subtraction, multiplication, and division of rational numbers.
Lesson 4-1 Rational Numbers
Students will identify terminating and repeating decimals and use long division to convert rational numbers to decimals.
Lesson 4-2 Add Rational Numbers
Students will demonstrate the application of the additive inverse and an understanding of rational numbers.
Lesson 4-3 Subtract Rational Numbers
Students will demonstrate an understanding of the subtraction of rational numbers by adding the additive inverse and applying it to solving real-world problems.
Lesson 4-4 Multiply Rational Numbers
Students will apply their understanding of multiplication to rational numbers and use the order of operations to solve real-world problems.
Lesson 4-5 Divide Rational Numbers
Students will apply their understanding of division to rational numbers and use the order of operations to solve real-world problems.
Lesson 4-6 Apply Rational Number Operations
Students will apply their understanding of the four operations with rational numbers to evaluate mathematical expressions.
IXL SKILLS: