Standard: 4.NBT.B6 – Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Grade level: Grade 4
Subject: Mathematics
Domain: Number & Operations in Base Ten
Teacher Overview
This standard focuses on teaching students to find whole-number quotients and remainders when dividing up to four-digit dividends by one-digit divisors. It is important because it builds on their understanding of place value, properties of operations, and the relationship between multiplication and division, which are crucial for more advanced mathematical concepts. Students should already know basic multiplication and division facts and understand place value up to four digits. They should also be comfortable with the concept of remainders in simple division problems.
After mastering this standard, students will be able to tackle more complex division problems, including those with multi-digit divisors, and will have a deeper understanding of the relationship between multiplication and division.
Common Misconception 1
Some students might think that the remainder can be larger than the divisor. This is incorrect because the remainder represents what is left after the division process, and it must be smaller than the divisor for the division to be complete.
Intervention 1
Use visual aids such as area models or rectangular arrays to demonstrate that the remainder must be less than the divisor. Hands-on activities with physical objects can also help solidify this understanding.
Common Misconception 2
Another common misconception is that the quotient is always a whole number. This is not true, as division often results in a quotient with a remainder, representing the ‘leftover’ part of the division.
Intervention 2
Provide examples and practice problems where the quotient includes a remainder. Use real-world scenarios to illustrate the concept of ‘leftover’ in division, such as dividing a set number of items among a group of people and having some items left over.
Prerequisite Knowledge
Students should have a solid understanding of basic multiplication and division facts, as well as familiarity with place value up to four digits.
Subsequent Knowledge
Students will develop the ability to solve more complex division problems, including those involving multi-digit divisors, and will also strengthen their understanding of the relationship between multiplication and division.
Instructional Activities
- Use base-ten blocks to model division problems.
- Practice division problems using area models and rectangular arrays.
- Solve real-world word problems involving division with remainders.
- Create and solve division equations and explain the process using diagrams.
