Working with Number Lines
This resource from ILEA Learning Resources explains that before students can form abstract mathematical ideas they invariably need experience in the physical world, and they also need to talk and think about this experience. Making and using number lines allows opportunities for students to develop an understanding of the structure of the denary system.
Although this book is mostly about number lines, it does contain brief suggestions as to when, and how, children should do complementary work with sets of objects, including base ten materials.
[b]Becoming confident with the number sequence 0 - 1000[/b] - this work will help students become confident with the names, symbols and order of numbers up to 1000 and develops the basic ideas of place value.
[b]Jumping along a number line[/b] - provides a basis for doing calculations on a number line.
[b]Operations with whole numbers[/b] - by modelling and solving problems, involving all four operators, on a physical number line students develop a mental image of the number system.
[b]Fractional numbers[/b] - using a model of the denary system can help students to understand that number is continuous and between any two whole numbers lie an infinite number of fractional numbers, which can be ordered.
[b]Negative numbers[/b] - a number line can also be extended in the opposite direction to show negative numbers where, for example, the result of subtracting seven from four can be shown clearly.
[b]Rounding off[/b] - the ability to round off numbers is also important when students want to make a rough estimate of what sort of answer they expect to get from a calculation, or to check whether a calculation they have carried out provides a reasonable answer.
[b]Working with measures[/b] - if a line is used to make a model of units of measurement it can help students develop a feel for the relative sizes of various quantities.
Each chapter contains a section with ideas for activities and discussion.
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