How do adding and subtracting rational numbers help us solve real-world problems?
Critical Thinking: Analyzing and applying the rules of adding and subtracting rational numbers to various situations.
Responsibility: Taking ownership of their learning process by practicing and applying these concepts.
Global Citizenship: Understanding how math skills like these are fundamental in making informed decisions in daily life.
What steps do we follow to add and subtract rational numbers?
How can the addition and subtraction of rational numbers be applied in real-life scenarios?
Why is it important to understand the rules for adding and subtracting negative numbers?
Demonstrate the ability to add and subtract rational numbers accurately.
Apply the concepts of adding and subtracting rational numbers to solve real-world problems.
Understand and explain the mathematical reasoning behind the addition and subtraction of rational numbers.
Skills Demonstrated
Recognize that rational numbers include integers, fractions, and terminating or repeating decimals.
Represent rational numbers on a number line and identify their opposites (e.g., the opposite of –3/4 is 3/4).
Understand that zero is the additive identity (adding zero does not change the value).
Interpret real-world contexts that use positive and negative numbers (e.g., temperatures, elevations, debts, gains/losses).
Use number lines, counters, or models to visualize addition of positive and negative numbers.
Understand addition as combining quantities or moving along a number line.
Apply rules for adding integers:
Same signs → add and keep the sign.
Different signs → subtract and keep the sign of the larger absolute value.
Add fractions and decimals with both positive and negative values.
Apply addition of rational numbers to real-world problems (e.g., changes in temperature, money, or elevation).
Interpret subtraction as adding the additive inverse (e.g., a−b=a+(−b)a - b = a + (-b)a−b=a+(−b)).
Use number lines and models to represent subtraction of rational numbers.
Subtract integers with positive and negative signs correctly.
Subtract fractions and decimals that include negative numbers.
Solve real-world situations involving subtraction (e.g., comparing debts or changes in position).
Reasoning and Connections
Explain why the rules for adding and subtracting rational numbers make sense using models or number line reasoning.
Understand that rational number addition and subtraction are closed operations (the result is always rational).
Justify the distance between two numbers on a number line as the absolute value of their difference.
Use absolute value to describe magnitude and distance in real-world situations.
Solve multi-step problems involving gains/losses, temperature changes, or elevations.
Represent and solve problems using equations that include addition and subtraction of rational numbers.
Use reasoning to determine whether an answer makes sense based on context (e.g., a temperature decrease represented by subtraction).
Mathematical Practices Embedded
MP1: Make sense of problems and persevere in solving them.
MP2: Reason abstractly and quantitatively.
MP4: Model with mathematics (using number lines, diagrams, or equations).
MP6: Attend to precision in calculation and labeling (especially with signs and units).
CCSS.MATH.CONTENT.7.NS.A.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.
CCSS.MATH.CONTENT.7.NS.A.1.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.
CCSS.MATH.CONTENT.7.NS.A.1.D: Apply properties of operations as strategies to add and subtract rational numbers.
[Our Hidden Google Drive Resource link]