7.NS.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.

Hands-on Activities

1. Temperature Changes

Use a thermometer or weather app to track daily temperature changes. If the morning temperature is 15°F and the afternoon temperature is -3°F, find the difference: 15 - (-3) = 15 + 3 = 18°F change. Practice with different temperature scenarios throughout the week.

2. Bank Account Tracking

Create a mock bank account starting with $50. Practice transactions like withdrawing $75 (going to -$25) then depositing $30. Calculate: 50 - 75 = 50 + (-75) = -25, then -25 + 30 = 5. Track how subtracting becomes adding the opposite.

3. Elevator Number Line

Use a building's floors as a number line. Start on floor 4, go down 7 floors: 4 - 7 = 4 + (-7) = -3 (3 floors below ground). Practice finding distances between floors using absolute value: |4 - (-3)| = 7 floors apart.

4. Sports Score Differences

Track team scores during games. If Team A has 24 points and Team B has -8 points (penalty points), find the difference: 24 - (-8) = 24 + 8 = 32 point spread. Use real game scores to practice these calculations.

5. Sea Level Activities

Research locations above and below sea level. Death Valley is -282 feet, Mount Whitney is 14,505 feet. Find the distance: |14,505 - (-282)| = |14,505 + 282| = 14,787 feet difference in elevation.

Strategies When Your Child Struggles

1. Use the "Add the Opposite" Rule

When your child struggles with subtracting negatives, teach them to rewrite subtraction as addition. Show them that 5 - (-3) becomes 5 + 3. Use the phrase "subtracting a negative is like adding a positive."

2. Number Line Visualization

Draw a horizontal number line and have your child physically move along it. Start at the first number, then "subtract" by adding the opposite. This makes abstract concepts concrete and visual.

3. Temperature Analogy

Use temperature changes as a consistent reference. "If it's 10° and the temperature drops 15°, where are we?" helps children understand going below zero naturally.

4. Distance Focus

When finding distance between two points, emphasize that distance is always positive. Show that |a - b| and |b - a| give the same answer because distance doesn't depend on direction.

5. Step-by-Step Breakdown

Break complex problems into smaller steps: identify the operation, rewrite subtraction as addition, perform the calculation, then interpret the result in context.

5-Minute Activities

Activity 1: Daily Temperature Check

Each morning, look up yesterday's high and low temperatures. Calculate the difference and discuss what it means. Practice with different cities or compare morning/evening temperatures.

Activity 2: Floor Elevator Game

Pick two random floors (including basement levels as negatives). Have your child calculate the distance between them. Make it competitive by timing how quickly they can solve it.

Activity 3: Bank Balance Tracker

Create simple transactions with positive and negative numbers. Start with $20, spend $35, deposit $10. Track the balance and discuss what negative balances mean in real life.

Activity 4: Number Line Jumping

Draw a number line on paper or use tape on the floor. Call out subtraction problems and have your child physically jump to show the solution, reinforcing the "add the opposite" concept.

Mid-Year Expectations

By the middle of 7th grade, your child should be able to:

• Subtract positive rational numbers confidently
• Understand that subtracting a negative number means adding its opposite
• Use a number line to visualize subtraction problems
• Calculate simple distances between points on a number line

End-of-Year Expectations

By the end of 7th grade, your child should be able to:

• Fluently subtract any combination of positive and negative rational numbers
• Apply the distance formula using absolute value in various contexts
• Solve real-world problems involving temperature changes, elevations, and account balances
• Explain why the distance between two points is always positive

Mastery Signs

Your child has mastered this standard when they can:

• Quickly convert any subtraction problem into addition of the opposite
• Calculate distances between rational numbers without hesitation
• Explain their reasoning clearly when solving multi-step problems
• Apply these concepts to new, unfamiliar real-world situations

Questions to Ask:

Ask your child to solve these problems and explain their process:

• What is 8 - (-5)? Show me two different ways to solve this.
• If the temperature was -12°F this morning and 7°F this afternoon, what was the temperature change?
• How far apart are -15 and 23 on a number line? Show your work.
• If you have -$40 in your account and withdraw another $25, what's your new balance?
• A submarine is at -150 feet and a plane is at 8,000 feet. What's the distance between them?
• Explain why -6 - (-10) gives the same answer as -6 + 10.