history of mathematics - National STEM Centre

13 Hints
Activity 7.3, page 89
1 Write MP and MO in the forms MP = MN - NL and MO = MN + NL .
Activity 9.8, page 120
3 What is the size of the difference between the areas?
Activity 10.1, page 125
2 b Remember that 2 x 3 is the same as 0 + 3 + 3 . Think about -3 + (-3) . How
can you can write this in multiplication notation? Does this help you extend further
your number line model? You might have difficulty extending this model to include
examples such as -4x2 and -4 x -2 . If your model can interpret these types of
examples, discuss it with a friend or your teacher.
Activity 10.2, page 125
1 You are much more likely to come across subtracted numbers, as opposed to free
standing negative numbers, in the modelling of practical problems. Can you see how
these might have made them more acceptable? Can you think of some examples
where subtracted numbers arise in problems relating to everyday situations? Would
free standing negative numbers arise in the same situations in a meaningful way?
Activity 10.3, page 126
1 Set out the problem as
-5x + 6y + 8z = 290
where x, y and z are the prices of cows, sheep and pigs respectively. Solve these
equations for x, y and z.
Activity 10.5, page 127
1 The area of the rectangle with sides (a - b) and (c - d) is the same as the area of
the large rectangle with sides a and c, provided that you subtract off the area of the
L-shaped border. Write this statement as an equation.
Activity 10.6, page 128
1 a The first part of the extract explains about the construction of the geometrical
figure shown in the diagram. The result of the proposition is actually described in
the section of the extract entitled Demonstration. You should concentrate on this
part. Try to identify the squares and rectangles referred to in this section and then
describe in your own words the relationship between them. Note that the extract
refers to squares and rectangles by just two points, those at opposite ends of one of
the diagonals of the square or rectangle.
Introduce letters to represent the lengths of the sides of the squares, then you should
be able to write down an algebraic formula which is equivalent to the result.