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Estimation and Questioning Skills

Teaching Questioning Skills

Can the questions you are asking in the Maths classroom be answered with a simple "Yes" or "No" or do they invite students to deepen their understanding?
100 suggestions on how to improve your questioning in the classroom divided according to what you are hoping to achieve - see diagram right - Click here  Whole file can be downloaded via a link at the bottom of the linked page.

Effective Questioning Prompt Sheet - Click here

Questioning Prompts while withholding the answer - Click here

What do you notice and What are you wondering? -  Video Clip

This document seeks:
To identify and explore a range of questioning techniques for individuals and groups.
To identify appropriate questioning techniques in teaching situations.
To evaluate questioning techniques for individuals and groups.  Click here

Duncan entered a second grade classroom and the regular teachers turned the class over to him. He told the students that their task would be to identify the number he had in mind

The children were obviously familiar with this kind of game and immediately began waving their hands to be called on. "Is it even?" one student asked. "Is it a number (as opposed to a symbol)?" asked another. "Does it have more than three digits?" "Is it black?" "Is it in a row marked with a vowel?"  Click here to read or download the full document.

Deepening Understanding

This set of growing resources poses questions with the aim of deepening the pupils understanding of the topic and encouraging discussion, the site is the brainchild of Ben @DUMaths and is aimed at Year 2 and Year 6 Primary students but all of the Year 6 resources are equally useful in KS3 and often in KS4, not only that but they encourage the teacher to think differently when posing questions rather than the repetitive, uninspiring questions that is the experience of many students - Click here

Fermi Type Estimation Questions

Two "typical" Fermi questions are posed and solved in this section.

  • How many piano tuners are there in New York City ?
  • How many jelly beans fill a one-litre jar?

WARNING: Fermi questions are not really typical and Fermi questions do not have single solutions.
Click here to read or download the full document.

Pasta Pass for $100 - Click here

Over 200 Estimation Problems - Click here

MEI PowerPoint on Modelling in Maths and Estimating Solutions - Click here

Taboo Cards

These can be used to encourage students to convey mathematical words in more imaginative ways by preventing them from using some "taboo" words

All GCSE Topics Taboo Cards                  Shape Taboo Cards

Higher Order Questioning

Several types of questions have the capacity to increase the cognitive level of student responses and shift the environment from one of "show and tell" to one of inquiry and discussion:

- Reasoning questions require students to construct logically organized information, e.g., "How do you know?", "What would happen if...?"
- Open questions allow for more than one acceptable answer, e.g., "Tell us everything you notice about...."
- Interpretive questions focus on applications, relationships, connections, or evaluations and lead students to analyze facts, e.g., "How would this be different if..."
Click here to read or download the full document.

Advice sheet on types of questions click here
A document on effective teaching strategies click here


Exemplars of probing questions produced by the DfES

Probing questions Level 4  
Probing questions Level 5
Probing questions Level 6  
Probing questions Level 7
Probing questions Level 8

Exploring boundaries

The following extract is taken from the excellent book Questions and Prompts for Mathematical Thinking produced by the Association of Teachers of Mathematics (ATM) Tel 01332 346599  
ISBN 1 898611 05 X

Quadrilaterals

Draw a quadrilateral
Draw a quadrilateral with one pair of opposite sides parallel
Draw a quadrilateral with one pair of opposite sides parallel, and one pair of opposite angles equal
Draw a quadrilateral with one pair of opposite sides parallel, and one pair of opposite angles equal and diagonals intersecting at right angles

Now go back and make sure that each example is different
Now go back and make sure that your example at stage k does not satisfy condition k+1
Now go back and describe what all xamples at stage k which do not satisfy condition condition k+1 look like.

Integers

Write down number which leaves 1 on division by 7
Write down number which leaves 1 on division by 7, and is a perfect square
Write down number which leaves 1 on division by 7, and is a perfect square, and is a perfect cube

Now go back and make sure that each example is different
Now go back and make sure that your example at stage k does not satisfy condition k+1
Now go back and write down other specific examples, and a general expression for all numbers satisfying condition k but not condition k+1

Decimals

Write down a number
Write down a number, lying between 3 and 4
Write down a number, lying between 3 and 4, which has a rational square root
Write down a number, lying between 3 and 4, which has a rational square root, whose numerator differs from its denominator by a multiple of 3

Now go back and make sure that each example is different
Now go back and make sure that your example at stage k does not satisfy condition k+1
Now go back and write down other specific examples, and a general expression for all numbers satisfying condition k but not condition k+1

Effective Questioning in the ClassroomA PowerPoint presentation using concepts taken from the Questioning unit from the Pedagogy and Practice materials.

Teaching Mental Maths from level 5 These resources provide rich questions to use in the classroom.