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#### Bounds of Error: Probing Questions

Whether you are looking for a question to stimulate discussion in lesson, or a challenge at the end of a homework, then hopefully you will find these useful.

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#### Convince Me That... *keyboard_arrow_up*
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I use Convince Me That questions lots in my lessons and homeworks. Providing students with a statement and challenging them to come up with as many different ways of convincing you as possible can lead to some fascinating discussions. The different ways of seeing the same thing can also help improve the depth of students’ understanding. Thanks so much to the Thornleigh Maths Department, in particular Erica Richards, Anton Lewis and Gareth Fairclough for helping me put these together, and we will endeavour to keep adding more!

4.5 is the smallest number which when rounded to the nearest whole will give 5

A number n is rounded to 2 decimal places giving 4.49. Convince me that the bounds of error are given by 4.485 ≤ n < 4.495 and that use of the symbol < is essential.

If something is rounded to the nearest 10, the width of the bound of error is also 10

When you want the lower bound of a subtraction or division, you do not use the lower bounds of the numbers involved

#### VI3 Treatment *keyboard_arrow_up*
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We devised VI3 Treatment as a versatile way of giving students meaningful follow-up work at once we have marked their homework. The idea is that students are challenged to come up with 3 things with certain constraints. These are ideal to use as an extension for students who have got everything correct, and also as further purposeful practise for students who have got a particular question wrong. Use the ideas below and adapt them accordingly, using different numbers where appropriate. Either mark them yourself or better still, get other students to do it. Thanks so much to the Thornleigh Maths Department, in particular Erica Richards, Anton Lewis and Gareth Fairclough for helping me put these together, and we will endeavour to keep adding more!

Write 3 different questions where the width of the bound of error is equal to 100

Write 3 different bounds of error questions which will have an answer of 3.35 ≤ n < 3.45.

Invent 3 questions, each involving different operations, and show how you calculate the upper bound in each case