8.EE.7.b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

I can solve linear equations that have rational number coefficients, including equations that have solutions that need to be expanded by using the distributive property and collecting like terms.

What Your Child Needs to Know

In eighth grade, your child will encounter more complex algebraic concepts, specifically solving linear equations with rational number coefficients. This skill is essential as it lays the groundwork for high school algebra and beyond. Understanding how to distribute, combine like terms, and solve these equations will not only enhance their problem-solving skills but also their ability to think logically and analytically. This standard, coded as 8.EE.7.b, is pivotal in helping students grasp how algebra relates to real-world scenarios and prepares them for more advanced mathematical concepts.

Real World Practice

Visual models and hands-on activities

Hands-on Activities

1. Shopping on a Budget

Give your child a set budget and a list of items to buy with individual prices as simple algebraic expressions. Ask them to calculate the total cost by solving the equations.

2. Recipe Adjustments

Provide a recipe and ask your child to adjust the quantities of ingredients (expressed in fractions or decimals) for more or fewer servings using equations.

3. Distance Time Challenges

Use linear equations to solve problems involving distance, rate, and time. For example, if a car travels at a certain speed for a given amount of time, how far does it go?

4. Budgeting for a School Event

Have your child manage a hypothetical budget for a school event, using equations to allocate funds to different areas like decorations, food, and activities.

5. Mobile Plan Comparisons

Compare different mobile plans using linear equations. Each plan has a fixed monthly cost plus a variable cost depending on usage expressed in equations.

Quick Checks

Strategies and quick activities

Strategies When Your Child Struggles

1. Using Manipulatives

Encourage your child to use algebra tiles or other manipulatives to physically represent and solve equations.

2. Equation Solving Worksheets

Provide additional worksheets focused on expanding expressions and collecting like terms to build proficiency.

3. Step-by-Step Breakdown

Help your child break down each equation into manageable steps, focusing first on distributing, then combining like terms, and finally isolating the variable.

4. Visual Aids

Use visual aids such as flowcharts or diagrams to outline the steps to solve equations, which can be a handy reference for students.

5-Minute Activities

Activity 1: Five-Minute Drills

Practice quick solving of equations with a timer to build speed and accuracy.

Activity 2: Flashcard Review

Use flashcards with different parts of the equation solving process for quick review sessions.

Activity 3: Real-Life Equation Hunt

Spend five minutes finding real-life scenarios at home where equations might be applied (e.g., balancing a checkbook, measuring ingredients).

Activity 4: Algebra Apps

Utilize educational apps designed for solving linear equations to reinforce learning through interactive challenges.

Check Progress

Track improvement

Mid-Year Expectations

By the middle of 8th grade, your child should be able to:

  • Students should be able to solve simple linear equations using basic operations.
  • Students should begin to feel comfortable with expanding expressions and identifying like terms.

End-of-Year Expectations

By the end of 8th grade, your child should be able to:

  • Students can solve complex linear equations involving multiple steps and rational coefficients.
  • Students can apply the distributive property accurately in various contexts.

Mastery Signs

Your child has mastered this standard when they can:

  • Consistently solves linear equations correctly and efficiently.
  • Demonstrates understanding by explaining the process and reasoning behind each step.

Questions to Ask:

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

  • Solve for x: 3/4x + 5 = 2(x - 1/2)
  • Solve the equation and check your solution: 2/3(x + 3) = 1/4x - 7
  • Given the equation 5(x - 2) + 3x = 4 - 2(2x - 3), find the value of x.
  • Solve for x if 2x + 1/3 = 3(x - 1/4) + 1/2