Q1.
Discuss the answers with your classmates. Give reasons why you think your answer is right.
Answer
A reason is not the same as an answer. Say why each step is allowed, not just what the number is. Here is the kind of reasoning to bring to the discussion.
- Why the top number splits in half: the sample pictures show a scale marked 4 carrying 2 and 2 hanging level, and a scale marked 7 carrying 4 and 3 tilting. So the circled number is the total, and a level beam means the two sides are equal. Equal parts of 16 are 8 and 8.
- Why a level beam gives an equation: "the left side weighs the same as the right side" is exactly what the sign '=' means.
- Why removing the same weight from both sides is safe: if two things were equal and you take away the same amount from each, what is left must still be equal. That is how the star was cancelled in Fig. 7.7 and the orange in Fig. 7.8.
- Why the answer must be the only one: in Fig. 7.4, once 4c = 4, no number other than 1 can work for c, because 4 × 1 is the only product of 4 and a single value that gives 4.
Try this in class: two friends may have used different routes — one may have started from the left string, another from the right. Compare them. Different methods that reach the same answer are a good sign that the answer is right.