What we like about this task
- Addresses standards: 4.OA.A, 4.NBT.B, 4.OA.A.3, 4.NBT.B.6, MP.1, and MP.6
- Requires students to understand the meaning of the quotient and remainder in order to solve problems in a real-world context
- Addresses content across two major clusters (4.OA.A and 4.NBT.B) within the grade, specifically 4.OA.A.3 and 4.NBT.B.6
- Requires students to interpret what is being asked and perform extensive calculations (MP.1) accurately and efficiently (MP.6)
In the classroom:
- Offers opportunities for students to use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to solve division problems
- Provides repeated practice of multi-digit division and can be easily altered to allow for repeated use throughout the year
- Allows for small group, partner, or individual work
This task was designed to include specific features that support access for all students and align to best practice for English Language Learner (ELL) instruction. Go here to learn more about the research behind these supports. This lesson aligns to ELL best practice in the following ways:
- Provides opportunities for students to practice and refine their use of mathematical language.
- Allows for whole class, small group, and paired discussion for the purpose of practicing with mathematical concepts and language.
- Elicits evidence of thinking both verbally and in written form.
- Includes a mathematical routine that reflects best practices to supporting ELLs in accessing mathematical concepts.
- Provides students with support in negotiating written word problems through multiple reads and/or multi-modal interactions with the problem.
Making the Shifts
How does this task exemplify the instructional Shifts required by CCSSM?
Focus Belongs to the major work of fourth grade Coherence Builds on grade 3 understanding of division as an unknown factor problem; Continues trajectory toward operational fluency with rational numbers Rigor
Conceptual Understanding: not targeted in this task
Procedural Skill and Fluency: primary in this task
Application: primary in this task
In eastern North Carolina there are 3,277 fourth graders signed up for basketball. In western North Carolina there are 2,981 fourth graders signed up for basketball. In the Piedmont region there are 1,512 players signed up. Every player will get placed on a team in their region of the state.
The league wants to place 9 players on each team. Leftover players will be added to teams, so some teams will have ten players. How many teams will have 9 players? How many teams will have 10 players? Explain your reasoning.
In order to maximize playing time, the league decides to only place 7 players on each team. If there are extra players, some teams will have 8 players. How many teams will have 7 players? How many teams will have 8 players? Explain your reasoning.
This task offers students an opportunity to practice division with whole numbers, including problems that have remainders. The required computation is intensive and occurs through non-routine problems. The task includes two parts which are nearly identical, so teachers may choose to use only one part, or have the class work on different parts in groups. Students in grade four should have practice finding whole number quotients and remainders throughout the year, and teachers may assign part 2 at a later time: for additional practice or for homework.
Depending on students' ability to work with four-digit dividends and when this task is presented in a unit, the number of players in each region can easily be modified to three- or even two-digit numbers. Alternative dividends are: 327, 298, and 151. These numbers are chosen so that students interpret remainders, as in the original problem. Using alternate numbers for each dividend may be appropriate for the whole class or for a small group of students. Using modified numbers still allows all students to work with and practice grade-level problems.
To extend this task, the teacher might ask students to investigate whether there is a team size where no regions would have any leftover players. The teacher might suggest the numbers to investigate to the students or leave it up to the students to determine.
It is important to note that this task does not address the second or third parts of the standard, representing problems using equations with a letter standing for the unknown and assessing the reasonableness of the answers using mental computation and estimation strategies including rounding. A teacher may modify this task to more fully address the standard by asking students to round or use compatible numbers to estimate the quotient before completing the computation.