Working with Sums and Products
Develops technical and reasoning skills in algebra, fractions, decimals and integers
Key Stage suitability • Explanation
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Working with Sums and Products
The Working with Sums and Products CD-ROM contains eight programs: four of them are for use with an interactive whiteboard or multi-media projector; the other four are for use by pupils, either individually or in small groups. Many detailed ideas for using the programs in the classroom are also provided.
The four programs for whole-class use are about: integers; decimals; fractions and algebraic expressions. For each program the user can choose to have either two or three inputs. The screen displays these inputs, together with their sum and product. Thus, there are either four or five boxes on the screen containing either numbers (integers, decimals, fractions) or algebraic expressions. The numbers (or algebraic expressions) in the five boxes are updated by the click of a button: the computer selects these numbers randomly within certain constraints, which can be varied by the user. The user can choose to hide the contents of any of these boxes by clicking on it. This provides the means for asking questions about the addition, subtraction, multiplication and division of two or three integers, decimals, fractions or algebraic expressions. When all the inputs are hidden and only the sum and product are displayed the programs provide problems to be solved.
We are particularly pleased that the DfES has included a selection from Sums and Products in their KS3 Pack ‘Embedding ICT @ Secondary’.
Each of the four pupil programs corresponds to one of the four whole-class programs. The boxes on the screen containing numbers or algebraic expressions correspond exactly with those in the whole-class programs. Instead of being able to turn these boxes on and off, the pupil is given empty boxes to fill by typing in numbers or algebraic expressions. The constraints used by the computer, when generating the box entries, can be varied in exactly the same way as in the whole-class programs. The user can also choose which boxes have entries displayed and which boxes are left to be filled. When these choices have been made the user can begin an ‘exercise’ and receive a set of questions to answer. Each question has to be answered correctly before the user can move on to the next question. At the end of the exercise the user can choose to have the answered questions printed out.
You need Excel 2000 or later to run it.
The range of the numbers selected by the computer to fill the input boxes can be varied. The range can also include negative integers.
In addition to the four or five boxes containing integers there are boxes providing information about each of the integers: whether it is even or odd, whether it is prime, whether it is a square. This information can be hidden or revealed.
There are also optional ‘hold’ facilities. The user can at any time choose to ‘hold’ a particular sum or product. When the computer randomly generates subsequent numbers to fill the boxes it will ensure that the value of a sum or product that is ‘held’ remains unchanged, until the user decides to ‘release’ the sum or product.
The user chooses the maximum number of decimal places and the maximum number of significant figures for the two or three input numbers. (The maximum number of decimal places can be set at zero. This makes it possible to lead in to the use of decimals by working first with whole numbers.)
In addition to the four or five boxes containing decimals there are boxes providing information about which of the decimals is largest and which is smallest. This information can be hidden or revealed.
Some of the fractions can be mixed numbers. The user chooses the maximum size of the fraction. The user also chooses the maximum value of the denominator. For some choices of maximum value of denominator, the set of denominators is restricted, thus making it possible to work with ‘fraction families’. Here are the restrictions:
It is also possible to choose to have the computer select an integer for one of the two, or three, input numbers.
In addition to the four or five boxes containing fractions there are boxes providing information about which of the fractions is largest and which is smallest. This information can be hidden or revealed.
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