8.EE.7.a: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form 𝘹 = 𝘢, 𝘢 = 𝘢, or 𝘢 = 𝘣 results (where 𝘢 and 𝘣 are different numbers).

Hands-on Activities

1. Shopping Spree Equations

Create a mock shopping list with prices and ask your child to figure out the total cost. Present different scenarios where discounts or taxes apply and let them form and solve the equations.

2. Cooking by Numbers

Involve your child in cooking by asking them to adjust recipes for different numbers of servings. They will need to solve equations to figure out the necessary ingredient amounts.

3. DIY Budget Planning

Help your child create a budget for a small project, such as redecorating their room. They should form equations to manage their spending within budget constraints.

4. Sports Statistics

Use sports statistics (like batting averages or points per game) and ask your child to predict future performances by forming and solving equations based on past data.

5. Weather Predictions

Gather historical temperature data and challenge your child to create an equation to predict future temperatures. Discuss how equations can model real-world phenomena like weather patterns.

Strategies When Your Child Struggles

1. Break It Down

If your child struggles, encourage them to break the equation into smaller parts and simplify step-by-step.

2. Equation Balancing Games

Use online games or apps that focus on balancing equations to help your child visualize and understand the concept of keeping equations balanced.

3. Daily Equation Solving

Integrate equation solving into daily activities, such as calculating time for tasks, to make the concept more tangible.

4. Peer Study Sessions

Arrange study sessions with classmates. Explaining concepts to peers can reinforce your child’s understanding.

5-Minute Activities

Activity 1: Equation of the Day

Each day, give your child a new equation to solve. This regular practice helps reinforce concepts.

Activity 2: Flashcard Fun

Create flashcards with different types of equations. Use these for quick review sessions.

Activity 3: Real-Life Equations

Challenge your child to write equations for different scenarios they observe around the house or while outside.

Activity 4: Equation Story Problems

Write short story problems for your child to translate into equations and solve.

Mid-Year Expectations

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

• Students should be able to identify types of solutions an equation might have.
• Students should be comfortable transforming complex equations into simpler forms.

End-of-Year Expectations

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

• Students should effortlessly solve linear equations in one variable and correctly identify the type of solution.
• Students should be able to apply their equation-solving skills to real-world problems and other subjects.

Mastery Signs

Your child has mastered this standard when they can:

• Your child can explain the difference between equations with one, none, or infinitely many solutions.
• Your child shows confidence in transforming and simplifying equations independently.

Questions to Ask:

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

• Solve 3x + 9 = 12. How many solutions does this equation have?
• Determine if the equation 2(x - 3) + 4 = 2x has one, none, or infinitely many solutions.
• What type of solution would the equation x/2 - x/2 = 0 have?
• Simplify the equation 5(2x + 3) - 10x = 6x + 15 and identify the type of solution.