7.NS.2.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.

Hands-on Activities

1. Temperature Changes

Track the daily temperature for a week. Multiply negative numbers to predict temperature changes. For example, if the temperature drops 5 degrees each day from 10 degrees, calculate the temperature for each day.

2. Shopping Discounts

Create a shopping list with prices. Apply different negative discounts (e.g., -20%, -15%) to items and have students calculate the final prices, demonstrating how multiplication of rational numbers works in discounts.

3. Recipe Adjustments

Take a recipe and ask the student to adjust the quantities for more or fewer servings using fractions. Include multiplying fractions by whole numbers, and negative numbers if reducing ingredients.

4. Elevation Gain and Loss

Use maps or hiking apps to find trails with elevation gains and losses. Calculate the total elevation change by multiplying positive and negative integers.

5. Budget Balancing

Give students a budget and list expenses including some debts as negative numbers. They should multiply and add these to see what the final budget balance would be.

Strategies When Your Child Struggles

1. Visual Representations

Use number lines and area models to visually demonstrate how multiplication of negative numbers and fractions works.

2. Interactive Games

Incorporate educational games that focus on multiplying rational numbers. Games can be found online and often make learning these concepts more engaging.

3. Small, Incremental Steps

Break down problems into smaller, more manageable parts, especially when dealing with negative signs and fractions.

4. Relate to Known Quantities

Connect problems to real-life quantities that are familiar to the student, such as money or measurements, to make abstract concepts more relatable.

5-Minute Activities

Activity 1: Flashcard Drills

Create flashcards with various multiplication problems involving rational numbers and use them for quick practice sessions.

Activity 2: Real-Life Applications Discussion

Spend 5 minutes discussing how multiplication of rational numbers appears in different aspects of everyday life, such as cooking or shopping.

Activity 3: Quick Quizzes

Create or find quick quizzes online that test multiplication of rational numbers and have the student complete them under time constraints.

Activity 4: Create a Story Problem

Ask the student to create a story problem that involves multiplying rational numbers, which helps in understanding and applying the concept.

Mid-Year Expectations

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

• Students should be able to multiply positive and negative integers accurately.
• Students should understand and apply the distributive property to simplify expressions involving rational numbers.

End-of-Year Expectations

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

• Students should confidently multiply fractions, decimals, and mixed numbers.
• Students should be able to apply multiplication of rational numbers to solve complex real-world problems.

Mastery Signs

Your child has mastered this standard when they can:

• Able to explain and demonstrate the multiplication of negative numbers and the rationale behind the rules.
• Can solve and create real-world problems involving the multiplication of rational numbers without errors.

Questions to Ask:

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

• Calculate: (-7) x 3
• If the temperature is 0 degrees and it drops 4 degrees each hour for 3 hours, what is the temperature?
• Multiply: 1/2 x (-3/4)
• A store offers a 20% discount and then an additional 10% off the discounted price. If an item originally costs $50, what is the final price after both discounts?