1. Trial & Improvement Activity
What number to 1 d.p. must be multiplied to the number on your sticky note to reach 100?
Take a sticky note
Find your group
Write your thinking process together

2. 32
TRIALS
ANSWER
TOO BIG/TOO SMALL 3
3 x 32 = 96
TOO SMALL 4
4 x 32 = 128
TOO BIG
3.5 x 32 = 112
TOO BIG
3.5
3.2 x 32 = 102.4
TOO BIG
3.2
3.1
3.1 x 32 = 99.2
TOO SMALL
3.15 x 32 = 100.8
3.15
100.8
3.1
3.15
3.2
closer 3.1 to 1 d.p.

3. 48
TRIALS
ANSWER
TOO BIG/TOO SMALL 2 .0
2 x 48 = 96
TOO SMALL 3
3 x 48 = 144
TOO BIG
2.5
2.5 x 48 = 120
TOO BIG
2.1
2.1 x 48 = 100.8
TOO BIG
2.05
2.05 x 48 = 98.4
98.4
2.0
2.05
2.1
2.1 TO 1 D.P.

4. 11
TRIALS
ANSWER
TOO BIG/TOO SMALL 9 .0
9 x 11 = 99
TOO SMALL 10
10 x 11 = 110
TOO BIG
9.5 x 11 = 104.5
TOO BIG
9.5
9.1 x 11 = 100.1
TOO BIG
9.1
9.05 x 11 = 99.55
9.05
99.55
9.0
9.05
9.1
9.1 TO 1 D.P.

5. 22
TRIALS
ANSWER
TOO BIG/TOO SMALL 4
4 x 22 = 88
TOO SMALL 5
5 x 22 = 110
TOO BIG
4.5 x 22 = 99
TOO SMALL
4.5
4.6 x 22 = 101.2
TOO BIG
4.6
4.55
4.55 x 22 = 100.1
100.1
4.5
4.55
4.6
4.5 TO 1 D.P.

6. 45
TRIALS
ANSWER
TOO BIG/TOO SMALL 2
2 x 45 = 90
TOO SMALL 3
3 x 45 = 135
TOO BIG
2.5 x 45 = 112.5
TOO BIG
2.5
2.2 x 45 = 99
TOO SMALL
2.2
2.3
2.3 x 45 = 103.5
TOO BIG
2.25 x 45 =
2.25
101.25
2.2
2.25
2.3
2.2 TO 1 D.P.

7. Substitution Activity

8. Let’s do it! Solve x2 + x = 53 correct to 1 decimal place
First find the two whole number values of 𝑥 that will give the closest answers to 53: one will be a bit too small, the other will be a bit too big
Then ZOOM in between these two numbers to find the two numbers with one decimal place that give the closest answers to 53: again one will be a bit too small, the other will be a bit too big
To work out which one of those two numbers is the BEST answer you need to ZOOM in again to HALFWAY between them, then you will be able to see which one was closest to 53 – and sometimes you may be surprised
This last step is the most commonly missed out part because sometimes it seems unnecessary.
This means we need to find a number with one decimal place which gives the closest answer to 53
Let’s do it!

9. Solve x2 + x = 53 correct to 1 decimal place
First find the two whole number values of 𝑥 that will give the closest answers to 53 x
x2+x 6 42
too small 7 56
too big 6 7 10 42 56

10. Solve x2 + x = 53 correct to 1 decimal place
ZOOM in between these two numbers to find the two numbers with one decimal place that give the closest answers to 53 x
x2+x 6 42
too small 7 56
too big 6 7 42 56
Let’s zoom in!

11. The best answer to 1dp will be either 6.7 or 6.8, but which one?
Solve x2 + x = correct to 1 decimal place
Now we try sensible values to find the two best values of x with one decimal place. x
x2+x 6 42
too small 7 56
too big
6.5
48.75
6.8
53.04
6.7
51.59 6
6.5 7
6.7
6.8 42
48.75
51.59
53.04 56
The best answer to 1dp will be either 6.7 or 6.8, but which one?
Let’s try halfway for starters
Let’s try a bit higher but still just one decimal place

12. Solve x2 + x = 53 correct to 1 decimal place
ZOOM in between these two numbers to HALFWAY – then we’ll be able to see which side the true answer lies x
x2+x 6 42
too small 7 56
too big
6.5
48.75
6.8
53.04
6.7
51.59
6.75
6.75
6.7
6.8
51.59
53.04
We write:
𝑥 = 6.8 to 1dp
Let’s zoom in!
53 is this
side of
half way
It may seem like 6.8 was obviously the closest answer, but without this final checking stage you won’t know for sure

13. So In Summary… You write this: x x2+x 6 42 too small 7 56 too big 6.5
48.75
6.8
53.04
6.7
51.59
6.75
Find the best two whole number solutions
Zoom in to find the best two solutions to 1dp
Zoom in halfway to find which one of them was the closest overall
Answer: x = 6.8 to 1dp

14. Solve x2 - x = 17 correct to 1 decimal place
First find the two whole number values of 𝑥 that will give the closest answers to 17 x
x2 - x 5 20
too big 4 12
too small 5 4 10 20 12

15. The best answer to 1dp will be either 4.6 or 4.7, but which one?
Solve x2 - x = correct to 1 decimal place
Now we try sensible values to find the two best values of x with one decimal place. x
x2 - x 5 20
too big 4 12
too small
4.5
15.75
4.7
17.39
4.6
16.56 4
4.5 5
4.6
4.7 12
15.75 20
The best answer to 1dp will be either 4.6 or 4.7, but which one?
Let’s try halfway for starters
Let’s try a bit higher but still just one decimal place

16. Solve x2 - x = 17 correct to 1 decimal place
ZOOM in between these two numbers to HALFWAY – then we’ll be able to see which side the true answer lies x
x2 - x 5 20
too big 4 12
too small
4.5
15.75
4.7
17.39
4.6
16.56
4.65
16.97
4.65
4.6
4.7
16.56
17.39
16.97
Let’s zoom in!
17 is this
side of
half way
We write:
𝑥 = 4.7 to 1d.p.

17. Classwork Worksheet

18. 3
= 13
too big
2.5
= 10.25
too big
2.3
= 9.29
too big
too small
2.2
= 8.84
2.25 =
2.2
2.25
2.3
2.2
9.0625

19. 2 23 + 2 = 10 too small 3 33 + 3 = 30 too big 2.5 too small 2.6=
too small
2.6 =
too big
2.55 =
2.5
2.55
2.6
2.5
19.13

20. 3 32 + 4(3) = 21 too small 4 42 + 4(4) = 32 too big 3.5 too small 3.7
(3.5) = 26.25
too small
3.7
(3.7) = 28.49
too small
3.8
(3.8) = 29.64
too big
3.75
(3.75) =
3.7
3.75
3.8
3.7

21. 6 too small 7 too big 6.5 too big 6.2 too small 6.3 too big 6.25 6.2
63 + 3(6) = 234
too small 7
73 + 3(7) = 364
too big
6.5
(6.5) =
too big
6.2
(6.2) =
too small
6.3
(6.3) =
too big
6.25
(6.25) =
6.2
6.25
6.3
6.2