6.EE.7: Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers.

I can write and solve equations with variables to solve a real-world problem.

What Your Child Needs to Know

Understanding and solving equations is a fundamental skill in mathematics that forms the basis for higher-level math and everyday problem-solving. In 6th grade, students are introduced to equations in the form x + p = q and px = q, where p, q, and x are nonnegative rational numbers. These equations help students grasp the concept of variables and the process of isolating these variables to solve for unknowns. This standard is crucial as it lays the groundwork for algebraic thinking, enhances logical reasoning, and applies math in real-life contexts, such as budgeting, cooking, and planning.

Real World Practice

Visual models and hands-on activities

Hands-on Activities

1. Shopping Budget

Give your child a set budget and a list of items to buy from a store flyer. Ask them to write an equation to figure out how much more money they need or how much they will have left.

2. Recipe Adjustments

Ask your child to adjust a recipe for a different number of servings. They will write equations to find the new amounts of each ingredient needed.

3. Distance Challenges

Present a scenario where a family plans a trip and knows the total distance and the distance covered per day. Your child can solve for the number of days the trip will take using the equation px = q.

4. Saving Up

Have your child plan a savings goal for a desired item. They should set up an equation to determine how many weeks it will take to save enough, given a weekly allowance.

5. Time Planning

Create a schedule with your child for completing various homework assignments. Let them write equations to solve how much time they can spend on each subject based on total available study time.

Quick Checks

Strategies and quick activities

Strategies When Your Child Struggles

1. Using Manipulatives

Use objects like coins or blocks to visually represent equations and solve them, which can make abstract concepts more tangible.

2. Equation Balancing Games

Play games that involve balancing equations, which can be fun and educational, reinforcing the idea that both sides of an equation must be equal.

3. Step-by-Step Breakdown

Break down each step of the equation-solving process, ensuring the child understands why each step is necessary and how it contributes to solving the equation.

4. Real-Life Situations

Apply equations to daily scenarios like shopping or time management, which can help make the relevance of math in everyday life clearer.

5-Minute Activities

Activity 1: Flashcard Drills

Use flashcards with different simple equations, asking your child to solve them quickly. This helps improve speed and accuracy.

Activity 2: Equation Creation

Have your child come up with their own equations based on real-world scenarios they choose, which enhances understanding and creativity.

Activity 3: Reverse Engineering

Present the solution to an equation and ask your child to come up with the original equation, which can be a challenging and educational exercise.

Activity 4: Math Apps

Utilize educational math apps focused on equation solving for short, interactive learning sessions.

Check Progress

Track improvement

Mid-Year Expectations

By the middle of 6th grade, your child should be able to:

  • Students should be able to solve one-step equations using addition and subtraction.
  • Students will begin to understand equations using multiplication and division.

End-of-Year Expectations

By the end of 6th grade, your child should be able to:

  • Students can solve one-step equations of all types confidently.
  • Students can apply their skills to solve real-world problems using equations.

Mastery Signs

Your child has mastered this standard when they can:

  • Consistently solves equations correctly and understands the steps involved.
  • Can explain their thought process and the mathematics behind their solutions.
  • Applies equation-solving skills to new and unfamiliar problems efficiently.

Questions to Ask:

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

  • Solve for x: x + 7 = 15
  • Solve for x: 5x = 20
  • If you have $50 and you spend x dollars, write an equation for how much money you have left.
  • A recipe calls for x grams of flour to make 2 cakes. If you have 150 grams of flour, how many cakes can you make?