7.NS.2.b: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero 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.

I can explain that integers (with a non-zero divisor) can be divided. I know that the quotient of integers (with a non-zero divisor) is a rational number.

What Your Child Needs to Know

Understanding how integers and their divisions work is crucial for grasping more advanced mathematical concepts. In 7th grade, students will explore the properties of dividing integers, ensuring that they recognize that division by zero is undefined and that the quotient of integers (where the divisor is not zero) always results in a rational number. This foundational knowledge aids in the comprehension of algebra and beyond, and helps students apply math to real-world scenarios effectively. It's important for students to also understand the symmetry in division, such as –(𝘱/𝘲) = (–𝘱)/𝘲 = 𝘱/(–𝘲), which shows how signs affect the outcome of division.

Real World Practice

Visual models and hands-on activities

Hands-on Activities

1. Cooking by the Book

Use recipes to adjust ingredient amounts, dividing the total amount by different integers to create servings for fewer or more people.

2. Budget Planning

Help plan a family budget by determining how much money can be spent on different categories based on total available funds divided by the number of categories.

3. Road Trip Planning

Calculate the number of stops needed on a road trip by dividing the total distance by the average distance a car can travel on a tank of gas.

4. Reading Time Division

Determine how long it will take to finish a book by dividing the total number of pages by the number of pages they can read in an hour.

5. Playtime Scheduler

Divide total playtime over a week into equal parts to allocate time for different activities, ensuring a variety of engagements throughout the week.

Quick Checks

Strategies and quick activities

Strategies When Your Child Struggles

1. Use of Number Line

Encourage the use of a number line to help visualize the division of positive and negative integers.

2. Real-Life Examples

Discuss everyday scenarios like temperature changes or bank transactions where division of integers is applicable.

3. Peer Discussion

Arrange discussions with peers to solve division problems together, which can clarify doubts through collaborative learning.

4. Step-by-Step Guidance

Break down each division problem into smaller, manageable steps to avoid overwhelming the student.

5-Minute Activities

Activity 1: Flashcard Drills

Create flashcards with different division problems involving integers and practice regularly.

Activity 2: Math Apps

Use educational math apps focused on integer operations for quick, interactive learning sessions.

Activity 3: Daily Math Problems

Introduce a daily math problem involving integer division to be solved before dinner or bedtime.

Activity 4: Worksheet Completion

Complete worksheets that focus specifically on dividing integers and identifying rational numbers.

Check Progress

Track improvement

Mid-Year Expectations

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

  • Students should be able to divide integers accurately, understanding the effect of negative signs.
  • Students should begin to apply their knowledge of integer division in simple real-world contexts.

End-of-Year Expectations

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

  • Students should fluently divide integers and explain the concepts behind their calculations.
  • Students should confidently interpret and solve real-world problems involving division of integers.

Mastery Signs

Your child has mastered this standard when they can:

  • Correct and consistent application of integer division rules.
  • Ability to explain why the quotient of integers is always a rational number.
  • Confidence in applying integer division to solve complex real-world problems.
  • Effective use of mathematical vocabulary related to integer division in explanations and problem-solving.

Questions to Ask:

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

  • Divide -45 by 9 and explain the result.
  • If you divide -100 by -4, what is the quotient? Describe why.
  • How would dividing 36 by -6 be different from dividing -36 by 6?
  • Create a real-world problem involving division of integers, solve it, and explain your reasoning.