Unit 2
Lesson 1
Master:
Round to a given number of
decimal places
Experience:Square roots
Do Now
Each of these numbers round to 30.
Work out what each number is and what it has been rounded to (nearest integer, nearest
10).
I am the square root of 1156
My third digit is 6 less than the sum of my
first two
I am a multiple of 7
I am a factor of 162
I am a perfect square
I am half of a perfect square
My four digits are all the same
The sum of my three digits is 7
I am the average of two square
numbers
What numbers can you find that round to 30?
Write a clue to uniquely identify them.
1
Answers - Rounding to 30
How can all of these numbers be rounded to 30?
29.5
34
27
28
32
36
33.33
30.4
26
How can we show this on a number line?
2
Estimating square roots
25
30
36
30 is about halfway between 25 and 36.
I think the square root is 5.5.
Why has he picked 5.5?
3
Estimating square roots
25
30
36
30 is closer to 25 than 36.
I think the square root is 5.4.
How could we check which estimate
is closer?
4
Estimating square roots
31
30
29
29.16
30.25
5.42 = 5.4 x 5.4
= 29.16
5.52 = 5.5 x 5.5
= 30.25
Who has the closest answer?
How do you know?
5
Rounding roots
Take it in turns to pick a card from the board.
Each player estimates the size of the square root. (The player who picks the card makes
the first estimate.)
Whoever has the closest answer gets to mark their card with their initials
5
8
10
12
18
23
27
35
38
40
44
51
56
59
66
73
79
84
92
97
101
121
125
130
Who has the most cards?
What strategies did you use? Would the result be the same if you had rounded your
answers to the nearest integer?
6
Estimating square roots
30
29
31
30.25
29.16
5.42 = 5.4 x 5.4
= 29.16
29.1
5.52 = 5.5 x 5.5
= 30.25
29.2
30.2
30.3
Where would these numbers be placed on the number lines?
Why?
7
Rounding to integer values
√12 = 3.464106153.......
√12
Which two integer values does this number lie between?
8
Rounding to decimal places
√12 = 3.464106153.......
√12
What would the values at the end of the number line be if we were rounding to
the nearest tenth, hundredth or thousandth?
9
Final three
How many places would you need to round each of these numbers to for the
last digit to be a 3?
√8
√10
√12
√18
√23
√40
√44
√51
√56
√125
What is the value of this 3 in the number?
Is there more than one possible answer?
How could you use this number line to represent each of the numbers?
10
True or false?
The square root of 14 is 3.741 (to 3 d.p.).
The square root of 5 is 2.24 (to 1 d.p.).
The square root of 35 is 9.91 (to 2 d.p.).
The square root of 121 is 11.0 (to 1 d.p.).
11