Standard: 7.EE.B3 – Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
Grade level: Grade 7
Subject: Mathematics
Domain: Expressions & Equations
Teacher Overview
This standard focuses on solving multi-step real-life and mathematical problems involving positive and negative rational numbers in various forms. It emphasizes strategic use of tools, application of properties of operations, and assessment of answer reasonableness. Mastery of this standard is crucial for developing problem-solving skills and preparing for more advanced algebraic concepts. Before tackling this standard, students should be comfortable with basic arithmetic operations, properties of operations, and handling rational numbers in different forms.
Mastering this standard will prepare students for more complex algebraic expressions and equations, enhancing their problem-solving skills and readiness for higher-level mathematics.
Common Misconception 1
A common misconception is that properties of operations, such as the distributive property, do not apply to fractions and decimals. This is incorrect because these properties are universal and apply to all rational numbers.
Intervention 1
To address this misconception, provide guided practice with examples that demonstrate the application of properties of operations to fractions and decimals. Use visual aids and manipulatives to reinforce understanding.
Common Misconception 2
Another misconception is that checking the reasonableness of answers is unnecessary. This is incorrect because verifying results through estimation and mental math is crucial for ensuring accuracy and understanding.
Intervention 2
Introduce estimation strategies and mental math techniques. Use real-world scenarios where checking the reasonableness of answers is essential, such as budgeting or measuring.
Prerequisite Knowledge
Students should have a solid understanding of basic arithmetic operations (addition, subtraction, multiplication, and division) with whole numbers, fractions, and decimals. They should also be familiar with the properties of operations and basic concepts of rational numbers.
Subsequent Knowledge
After mastering this standard, students will be able to tackle more complex algebraic expressions and equations, including those involving variables. They will also develop stronger problem-solving skills that can be applied in higher-level mathematics and real-world scenarios.
Instructional Activities
- Solve multi-step word problems involving shopping discounts and taxes.
- Adjust recipes based on serving sizes and ingredient ratios.
- Calculate travel distances and times using different forms of rational numbers.
- Create and manage a simple budget involving income and expenses.
- Design a small construction project, such as building a bookshelf, using measurements and calculations.
