Wooden Projects

The millimetre is a common unit of measurement for woodworking and building. The students need to understand that there are 1 000 millimetres in 1 metre. Thus, all the fractions in this activity have to be treated as fractions of 1 000.
As with the activity on page 15 of the students’ book, there are different ways in which the fractions of a metre can be converted to millimetres. One way is to use a double number line, for example:

Another way is by using ratios, for example, 3/4 =  /1 000. Whatever the 4 has to be multiplied by to get 1 000, the 3 at the top has to be multiplied by too, that is, 3/4 x (250/250 ) = 750/1 000. Astute students will probably see that this is simply another application of the identity principle.
Alternatively, and still using ratios, the students could reason that whatever the 4 has to be divided by to get 3, the same should be done to the 1 000. Using a calculator, they could soon find that 4 divided by 3 is 1.3333 recurring and dividing 1 000 by the same number gives 750.
Perhaps the easiest way to convert the fractions of metres to millimetres is to use the calculator in a different way. The students could turn each fraction into a decimal (for example, 3/4 is 3 divided by 4, which gives 0.75) and then multiply this by 1 000 (0.75 x 1 000 = 750) because it is a decimal fraction of 1 000, and “of”
in this context means multiplied by.
Finally, you may wish to use question iii to challenge the students to work out:
• the area of the chessboard (400 mm x 400 mm = 160 000 mm²)
• the area of each small square (50 mm x 50 mm = 2 500 mm²).
An additional challenge would be to work out the area in square metres of the chessboard (0.4 m x 0.4 m = 0.16 m² ) and then of each small square (0.05 m x 0.05 m = 0.0025 m² ). As a check, the students could see if 0.0025 m² x 64 (the total number of small squares) gives 0.16 m².

Answers to Activity

i. 3/4 m= 750 mm
1/2 m= 500 mm
1/4 m= 250 mm
ii. 3/8 m= 375 mm
3/5 m= 600 mm
1/8 m= 125 mm
iii. 2/5 m= 400 mm
Each small square is 50 mm x 50 mm.
iv. 9/10 m = 900 mm
1/5 m= 200 mm
11/4 m = 1 250 mm