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Published 2011
Many students | Highly attaining students |
work randomly | work systematically |
notice obvious patterns $\quad \quad$ | conjecture and generalise |
make statements | offer explanations and proofs |
$2$ | $3$ | $4$ |
$1=0+1$ $\quad \quad$ | ||
$2=$ | ||
$3=1+2$ | $0+1+2$ $\quad \quad$ | |
$4=$ | ||
$5=2+3$ | ||
$6=$ | $1+2+3$ | $0+1+2+3$ |
$7=3+4$ | ||
$8=$ | ||
$9=4+5$ | $2+3+4$ | |
$10=$ | $1+2+3+4$ |
Find the area and perimeter of a $3cm \times 8cm$ rectangleask:
If the area of a rectangle is $24$ cm ² and the perimeter is $22$ cm, what are its dimensions?
Find the area and perimeter of a $3cm \times 8cm$ rectangleask:
What if the area of a rectangle (in cm ²) is equal to the perimeter (in cm), what could its dimensions be?
Find the perimeter of a $3cm \times 8cm$ rectangle
Find a rectangle which has unit sides and a perimeter of $100$ .
How many answers are there and how do you know you've got them all?
Find the area and perimeter of a $3cm \times 8cm$ rectangle.
If the area of a rectangle is $24$cm ² and the perimeter is $22$cm, what are its dimensions? How did you work this out?
"A teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking."
"I don't expect, and I don't want, all children to find mathematics an engrossing study, or one that they want to devote themselves to either in school or in their lives. Only a few will find mathematics seductive enough to sustain a long term engagement. But I would hope that all children could experience at a few moments in their careers...the power and excitement of mathematics...so that at the end of their formal education they at least know what it is like and whether it is an activity that has a place in their future."