No questions found
(a) Use the grid to complete each window and find the opposite difference.
$34 \times \text{...........} = \text{..........}$
$14 \times 36 = \text{..........}$
$\text{..........} - \text{..........} = \text{..........}$
Opposite difference = ................................................
...........................................................
........................................................... [4]
(b) What do you notice about the opposite difference for each of these windows on this grid?
................................................................................................................................. [1]
561
588
595
A 3 by 3 window moves on the same grid.
(a) Complete the corner squares in the first window.
[1]
(b) Complete the opposite difference calculations for this window.
$\text{..........} \times 6 = \text{..........}$
$2 \times \text{..........} = \text{..........} \quad \text{..........} - \text{..........} = \text{..........}$
[2]
(c) Complete the corner squares for each window and find the opposite difference.
.............................................
.............................................
.............................................
[4]
506
599
567
A 4 by 4 window moves on the grid on page 2.
(a) Complete the corner squares in the first window.
[Image_1: Grid with numbers 2 and 8 in the first row of the window]
(b) Complete the opposite difference calculations for this window.
.......... \times 8 = ..........
2 \times .......... = .......... .......... - .......... = ..........
(c) Complete the corner squares for each window and find the opposite difference.
[Image_2: A grid with number 64]
[Image_3: A grid with number 20]
588
528
546
(a) Copy the opposite differences that you have found and complete the table.
[Table_1]
Size of window | Opposite difference
2 by 2 | $(2-1)^2 = 1$
3 by 3 | $(3-1)^2 = 4$
4 by 4 | $(4-1)^2 = 9$
5 by 5 |
|
$w \text{ by } w$ | 40( )
[4]
(b) Find the greatest possible opposite difference for a square window on the grid on page 2.
................................................
[3]
(c) Can a square window on this grid have an opposite difference of 1400? Show how you decide.
[2]
547
507
566
Another grid of consecutive even numbers has width 5. The diagram shows the start of the grid.
The diagram shows a 2 by 2 window on the grid. $n$ is the first number in the window.
(a) Complete the window using expressions in terms of $n$.
(b) Use your expressions to show that the opposite difference for a 2 by 2 window is 20.
545
536
560
A square window moves on the grid of width 5 with squares numbered 2, 4, 6, ... .
The opposite difference for this window is 180.
Find the size of the window.
538
533
532
