Introduction

About Daily Workouts

Daily Workouts is a primary mathematics resource offering a comprehensive range of daily activities fostering mental computation and the development of mathematical skills, thinking and understandings. It is aligned with the Australian Curriculum: Mathematics, Number and Algebra strand and incorporates the proficiencies of understanding, fluency, problem-solving and reasoning.

What is mental computation?

Mental computation is a cognitive process used to produce an exact answer by mental methods, without the need for external devices such as pencil and paper or the electronic calculator – although pencils, paper and calculators can be and are used in this book to help develop mental skills. Mental computation requires the use of different strategies and instant recall of basic facts from memory in solving problems. The effect of manipulating numbers ‘in the head’ promotes the development of number sense, or a ‘feel’ for how numbers work.

Why use mental computation?

Mental mathematics is crucial for everyday living. It has been established that 80% of calculations made by adults are made mentally. Often estimation is needed to determine whether an answer obtained electronically is reasonable or not, for example, during shopping. Daily Workouts aids in the development of these necessary estimation skills.

How do I use Daily Workouts to teach mental computation?

Each activity in Daily Workouts has been designed as a teacher-led discussion to promote verbal communication among students, enhancing their thinking and reasoning. Activities have been designed primarily as lesson warm-ups, in which the teacher and students discuss and develop mathematical ideas. The activities may be also used flexibly during lesson breaks or for revision of previous concepts.

The activities in Daily Workouts are laid out in inquiry style with scripts of possible teacher questions and student responses/answers provided so that teachers can extend discussion and develop different ideas about the problem. Instead of drilling a fixed mental strategy in isolation, the teacher needs to explore a range of strategies suggested by the students, according to the type of activity given. In each case, the students are given a short time to investigate the problem concerned, before considering a variety of solution methods in classroom discussion with the teacher. The strategies that are most efficient are thus investigated and highlighted.

How do teachers assess students’ mental computation strategies?

By allowing students enough time to discuss their mathematical thinking and not intervening too soon, the teacher can observe and note their responses, which provide a window to their thoughts. Requesting students to justify their strategies by asking questions such as ‘Why?’, ‘How do you know that?’ or ‘Can you prove that?’ can elicit further responses.

Skills in mental computation are thus best developed by students constructing their own knowledge from physical and mental activities in problem-solving contexts. The classroom emphasis should be on students’ investigation, discussion and implementation of various mental methods, as their strategy of first choice when solving number problems, but answers are also provided for some problems.