# Good Questions: Great Ways to Differentiate Mathematics Instruction, Second Edition (0)

## Marian Small

Language: English

Pages: 216

ISBN: 0807753130

Format: PDF / Kindle (mobi) / ePub

*Praise for the First Edition!*

''A must for any educator who is serious about reaching more students more often and achieving more positive results.''

--*Resources for the Mathematics Educator*

''This is a valuable book for mathematics teachers, teacher educators, and faculty involved in differentiated instruction.''

--*Choice*

''This book is a great resource, with realistic applications to current instruction and tips for creating solid math discourse with your students.''

--*Mathematics: Teaching in the Middle School*

''The glossary is a great resource for math language, and the index of big ideas provides a snapshot of focus points. . .I highly recommend this user-friendly resource for all mathematics teachers.''

--*Teaching Children Mathematics*

''User-friendly teaching examples of questions and tasks will enable teachers to empower learners on all levels, and the tasks are presented with real-world scenarios that students will relate to as intriguing challenges.''

--**Carolyn Chapman**, Creative Learning Connections, Inc., and **Rita King**, King Learning Associates

Expanded to include connections to Common Core State Standards, as well as National Council of Teachers of Mathematics (NCTM) standards, this critically acclaimed book will help every teacher and coach to meet the challenges of differentiating mathematics instruction in the K-8 classroom. In this bestseller, math education expert Marian Small explains two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks. Showing teachers how to get started and become expert with these strategies, Small also demonstrates more inclusive learning conversations that promote broader student participation and mathematical thinking required by CCSS. Specific strategies and examples for each grade band are organized around NCTM content strands: Number and Operations, Geometry, Measurement, Algebra, and Data Analysis and Probability.

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interest to them, for example, the arts or the environment. The intention of the question is to help students see how commonplace the use of ratios is. There are many possible solutions, and many students will be very happy to talk about them. These include, for example: Baseball: batting averages Football: fumbles per 300 touches Basketball: assist to turnover ratio * * * Two integers are on opposite sides of the number line, but one is just a bit closer to 0 than the other. They

Choice 3: Make an isosceles triangle with these corners. * * * CCSS: Geometry: 3.G, 4.G Mathematical Practices: 1, 2, 5, 6 Some students will favor Choice 3 because they only need to place one more point. The fact that the triangle must be isosceles makes the task appropriately challenging, however. Some students who choose Choice 1 will choose to make the dots the endpoints of a diagonal so that the sides can be horizontal and vertical. Others will realize that the square can be

writes 5 + 5 + 5 = 15, then adds again, writing 15 + 15 + 15 = 45. Rebecca uses a combination of multiplication and addition and writes 3 × 5 = 15, then 15 + 15 + 15 = 45. The Teacher’s Response What do all these different student approaches mean for the teacher? They demonstrate that quite different forms of feedback from the teacher are needed to support the individual students. For example, the teacher might wish to: Follow up with Tara and Dejohn by introducing the benefits of using

Only after a teacher has determined a student’s level of mathematical sophistication, can he or she even begin to attempt to address that student’s needs. PRINCIPLES AND APPROACHES TO DIFFERENTIATING INSTRUCTION Differentiating instruction is not a new idea, but the issue has been gaining an ever higher profile for mathematics teachers in recent years. More and more, educational systems and parents are expecting the teacher to be aware of what each individual student needs and to plan

that the remainder must be 1 when a square number is divided by the number of letters in the animal’s name. So, for example, if the name has 5 letters, a 4 by 4 grid would work, as would a 6 by 6 grid. Both have 1 more square than a multiple of 5. Both groups could be asked questions such as: What animal name did you use? Why does the number of letters in your animal’s name matter? How did you predict the size of the grid that would work? How would your answer change if the number of rows