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(a) Complete this Number Wall.
(b) In part (a), the number 3 is on the middle brick of the bottom row. In the example, the number 3 is on the end brick of the bottom row.
Explain why putting the number 3 on the middle brick of the bottom row increases the total.
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544
568
552
(a) Complete this Number Wall.
Total =
1 2 3 4
(b) Put the numbers 1, 2, 3 and 4 on the bottom row and complete this Number Wall so that the total is bigger than the total in part (a).
Total =
(c) Complete this Number Wall.
You may use negative numbers.
Total = 31
4 10
7 4
527
565
571
This Number Wall is 3 bricks high.
(a) Complete each brick using expressions in terms of $a$, $b$ and $c$. Write each expression in its simplest form.
(b) Use the expression for the total you found in part (a) to find the value of $b$.
594
523
560
(a) This \textit{Number Wall} is 4 bricks high.
Complete each brick using expressions in terms of $a, b, c,$ and $d$.
Write each expression in its simplest form.
[Image_1: Number Wall Diagram]
(b) In another wall that is 4 bricks high, the total is 34 and the values of $a, b, c,$ and $d$ are all the same.
Use the expression for the total you found in \textit{part (a)} to show that the value of $a$ cannot be an integer.
(c) In this \textit{Number Wall} that is 5 bricks high, only integers greater than 0 are used.
Find one set of possible values for $a, b, c, d,$ and $e$.
[Image_2: Number Wall Diagram with 5 bricks high]
$a = \text{..................}$ $b = \text{..................}$ $c = \text{..................}$ $d = \text{..................}$ $e = \text{..................}$
566
508
585
In 1653 a French mathematician, Blaise Pascal, wrote about a triangle of numbers similar to the one shown below.
It is made in the same way as Number Walls but
* the number on a brick is the sum of the numbers on the two bricks above
and
* the number on the first and last brick in each row is always 1.
(a) The wall in question 4(a) is 4 bricks high.
Show clearly how your expression for the total in question 4(a) connects to the numbers in one row of this triangle. Write down which row this is.
Row \text{...........................................}
(b) A wall that is 5 bricks high has $a$, $b$, $c$, $d$ and $e$, in that order, along the bottom row.
Write down an expression in terms of $a$, $b$, $c$, $d$ and $e$ for the total.
\text{..................................................................................}
(c) Use your expression from part (b) to check that the set of values you found for $a$, $b$, $c$, $d$ and $e$ in question 4(c) gives a total of 43.
(d) A wall that is 5 bricks high has the number 2017 on each brick of the bottom row.
Find the total.
509
567
525
