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(a) Complete the tables to show the Number Stems for these multiples of 3, 12, 21 and 30.
| Multiple of 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 |
|---------------|---|---|---|----|----|----|----|----|----|----|
| Number Stem | 3 | 6 | 9 | 3 | 6 | 9 | 3 | 6 | 9 | 3 |
| Multiple of 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 |
|----------------|----|----|----|----|----|----|----|----|-----|-----|
| Number Stem | 3 | 6 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 3 |
| Multiple of 21 | 21 | 42 | 63 | 84 | 105 | 126 | 147 | 168 | 189 | 210 |
|----------------|----|----|----|----|-----|-----|-----|-----|-----|-----|
| Number Stem | 3 | 9 | 3 | 6 | 9 | 3 | 6 | 9 | 3 | 3 |
| Multiple of 30 | 30 | 60 | 90 | 120 | 150 | 180 | 210 | 240 | 270 | 300 |
|----------------|----|----|----|-----|-----|-----|-----|-----|-----|-----|
| Number Stem | 3 | 3 | 9 | 3 | 6 | 9 | 3 | 6 | 9 | 3 |
(b) Complete this statement.
The numbers in the table that have a Number Stem of 9 are all ................................... of 9.
(c) Complete this table.
| 3 ÷ 9 = 0 remainder 3 |
| 12 ÷ 9 = 1 remainder 3 |
| 21 ÷ .......... = 2 remainder 3 |
| .......... ÷ 9 = 3 remainder 3 |
| 39 ÷ 9 = .......... remainder .......... |
(d) Complete the statement.
A number that has a ............................... of 3 when divided by 9 has a Number Stem of ................ .
(e) The only one-digit number with a Number Stem of 3 is 3.
This sequence shows the first four numbers greater than 3 with a Number Stem of 3.
12, 21, 30, 39, ...
(i) Write down the rule for continuing this sequence.
....................................................................
(ii) Find the nth term of this sequence.
....................................................................
(iii) Find the 87th number greater than 3 that has a Number Stem of 3.
....................................................................
510
559
517
(a) Complete the tables to show the Number Stems for different multiples of 2 and 11.
[Table: Multiple of 2, Number Stem 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24; Number Stem 2, 4, 6, 8]
[Table: Multiple of 11, Number Stem 11, 22, 33, 44, 55, 66, 77, 88, 99; Number Stem 2, 4, 6, 8]
(b) The sequence shows the first three numbers greater than 2 with a Number Stem of 2.
11, 20, 29, ...
(i) Write down the next two numbers of the sequence.
..., ...
(ii) Find the $n^{th}$ term of this sequence.
...
(iii) Show that 1352 is the 150th number greater than 2 that has a Number Stem of 2.
524
552
593
(a) Write down the first four numbers greater than 8 with a \textit{Number Stem} of 8.
\text{....................... , ........................ , ........................ , .......................}
(b) Find the $n^{th}$ term of this sequence.
.....................................................
(c) Using your answer to \textbf{part (b)}, find the number closest to 10000 that has a \textit{Number Stem} of 8.
.....................................................
537
582
600
The integer $k$ is a \textit{Number Stem}.
(a) Write down, in terms of $k$, expressions for the first four numbers \textbf{greater than} $k$ with a \textit{Number Stem} of $k$.
\text{.................... , .................... , .................... , ....................}
(b) Write down, in terms of $n$ and $k$, the $n$th term for the sequence of numbers \textbf{greater than} $k$ with a \textit{Number Stem} of $k$.
\text{........................................................}
535
508
506
