Embedded Files
Thirty years ago, the president of the Mathematical Association of America predicted that “when computers and calculators truly come of age in the schools, paper and pencil long division will probably be ‘as dead as a dodo bird’. Unfortunately, three decades later, schools spend at least two years of instructional time teaching procedures students find hard to follow; as a result, they tend to make a multitude of mistakes. Sadly, the meaning of division gets lost in the shuffle.
Teaching Student−Centered Mathematics presents division in two ways:
The Measurement Interpretation
The Partitive Interpretation
The measurement interpretation of division may be thought of as repeated subtraction or equal groups. For example, 15 ÷ 3 means, ‘How many groups of 3 are in 15?’ In this situation, equal groups of 3 can be subtracted repeatedly from 15 (5 times).
The partitive interpretation of division may be thought of as partitioning the whole group. Partition problems include sharing problems and rate problems. For example, 15 ÷ 3 means, ‘How many per one group?’ In this situation, 15 is partitioned into 3 groups with 5 items in one group (or in each group)?
Module Five explores efficient strategies using different examples because specific strategies work more efficiently with different types of division problems. When solving division problems, students may choose to keep track of their thinking with paper and pencil. Keeping track this way helps students use methods they understand to solve problems that may be too big or too complex to do in their heads.
Module Five concludes with attention to normalizing mistakes and the questions we ask.
Step One
Step One
Click here to work through the Google Slides outlining four different division strategies that work efficiently across the continuum of rational numbers.
Click here to work through the Google Slides outlining four different division strategies that work efficiently across the continuum of rational numbers.
Rational Numbers: Click here to work through Google Slides outlining three strategies that work specifically with decimals.
Step Two
Step Two
Read Making Number Talks Matter, Chapter 7 Division Across the Grades, pages 93−106.
Read Making Number Talks Matter, Chapter 7 Division Across the Grades, pages 93−106.
Reflection Question:
Reflection Question:
What does division mean?
When will students choose to keep track of their thinking with pencil and paper when dividing?
Step Three
Step Three
Click here to watch a teacher facilitate a division Number Talks. Focus on mistakes made and teacher questioning.
Click here to watch a teacher facilitate a division Number Talks. Focus on mistakes made and teacher questioning.
Step Four
Step Four
Optional Reading:
Optional Reading:
Digging Deeper, Making Number Talks Matter Even More, Chapter 2: Mistakes, pages 19−32, to learn more about managing mistakes.
Digging Deeper, Making Number Talks Matter Even More, Chapter 2: Mistakes, pages 19−32, to learn more about managing mistakes.
Reflection Questions:
Reflection Questions:
How can you normalize mistakes?
Click here to watch Hailey ‘press’ Danni to explain her thinking about decomposing a number when subtracting.
Click here to watch Hailey ‘press’ Danni to explain her thinking about decomposing a number when subtracting.
Optional Reading:
Optional Reading:
Read Digging Deeper, Making Number Talks Matter Even More, Chapter 4: The Questions We Ask: What? Why? When?, pages 45−56, to learn more about asking authentic questions (See Appendix A, page 98).
Read Digging Deeper, Making Number Talks Matter Even More, Chapter 4: The Questions We Ask: What? Why? When?, pages 45−56, to learn more about asking authentic questions (See Appendix A, page 98).
Reflection Questions:
Reflection Questions:
What is meant by authentic questions?
Step Five
Step Five
Rational Numbers: Click here to review Division Problems (decimals) for two strategies.
Click here to complete the Module Five Survey by March 9, 2025.
Facilitate Division Number Talks, two to three times per week, in one class, for about five weeks.
Page updated
Report abuse