LEARNING OUTCOMES
By the end of this chapter, you will:
• recognise the difference between additive and multiplicative thinking
• be able to plan for appropriate use of drill and practice activities
• choose appropriate representations to illustrate different ways of thinking about multiplication and division
• use technology effectively to develop understanding of whole number computation.
KEY TERMS
• Algorithm: A step-by-step procedure for undertaking a computation
• Computation: All operations on numbers that are used to calculate a result or answer
• Distributive property: When multiplying one number by another number, the result is the same as multiplying its addends and summing the products. It can be expressed as a(b + c) = ab + ac (e.g. 5 x 17 = 5 x 10 + 5 x 7 = 50 + 35 = 85).
• Factor: A whole number that divides exactly into another number or a whole number that multiplies with another whole number to make a third number (e.g. 3 and 4 are both factors of 12)
• Multiplicative thinking: Thinking and reasoning about more than one quantity or value at once (e.g. doubling the side length of a square means that the area quadruples)
• Place value: The value of a digit depends on its place in the number. For example, in the number 361, the 3 has the value of 300 or three hundreds, 6 has a value of 60, or six tens, and there is one unit.
• Whole number: A number that has no fractional parts; an integer (e.g. 71 is a whole number but 71.5 is not)
Developing computational skills and the concepts that underpin proportional reasoning is a large component of the primary mathematics curriculum. Moving children's thinking towards proportional reasoning will be covered in more detail in Chapter 6. There is a very large research base about the development of these aspects of number and algebra. In this chapter, the focus is on the effective use of technology to enhance learning: developing computational skills, the relationships between different operations and moving from additive to multiplicative thinking.
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