DAILY MATH for Session 1 Week 3
TUES 9/6/11
Order the following numbers on
1
MON 9/6/10
1
2,1, , 0.75
2
the number line:
-0.5
0
answer
2
WED 9/7/11
0.5
1
, 0.75, 1,
Simplify: 2 
2
1.5
2.5 x
THURS 9/8/11
Which two whole numbers
Order from greatest
does
to least:
46 lie between on
the real number line?
answer 6 and 7
1 3 1
, ,
16 8 2
FRI 9/9/11
Which two whole
numbers does
lie
between on the real
number line?
Answer
Answer 8 and 9
(≈1.41)
1
2
answer 4
Classify each as rational
Simplify:
or irrational:
20  32  2(4  3)
2
, 0.33,
3
4, 
answer (R),
Answer 13
Classify each as rational
or irrational:
Answer R, R, I, I
(R),
(R), π (I)
3
Simplify: 3  (2  1)  4
answer 4
What is 65% of 200?
Answer 130
Write
1
as a decimal.
5
Answer 0.2
4
Find the seventh term in
the following pattern:
1, 1.5, 2, 2.5, 3 …
Solve for x: x – 3 = 7
answer x = 10
answer 4
5
Compare: 1  3 ____
Compare:
30% _____ 0.33
1
3
Answer 30% < 0.33
Answer
What two whole
numbers does 12 lie
between on the real
number line?
Find the next two
numbers in the pattern:
9, 18, 27, 36, ____,
____
answer 3 and 4
answer
45, 54
Classify each as
rational or irrational:
Simplify:
5
4,
9,

2
,
answer 4 (R),
(I),
(I)
6
What is 50% of 106?
answer 53
If we start with 3 pennies
in a jar, but add 5 pennies
each day, how many
pennies would be in the
jar at the end of day 1?
____ at the end of day
2?____ 3?_____
Answer Day 1: 8;
Day 2: 13; Day 3: 18
If a shirt is on sale for
15% off the regular
price of $20, how much
is the sale price?
Answer $20(100%-15%)
=
$20(85%) = $20(0.85) =
$17
1
5
5
Answer 25
(R),
Solve for x: 2x = 10
Answer x = 5
Compare:
2
_____
3
0.6
answer
7
What percent of 30 is 3?
answer
What percent of 38 is 15?
Answer
What is 60% of 14 m?
Answer: 14m (0.60) =
8.4 m
16 inches is 40% of
what?
Answer:
EXPLANATORY NOTES
Every integer can be “squared”—that is, multiplied by itself to get another integer. For example, 5
“squared” is 5 x 5 = 25. For integers, this process can be visualized as taking 25 objects and arranging
them in a square—with 5 rows of 5 objects each. The number of objects is the square (25 in this example)
and the number of rows and number of objects in each row is the square root (5 in this example).
Only certain numbers of objects can be arranged in a square. These are the perfect squares. For
example, we can put 16 objects into a square (4 rows of 4 each) and we can put 25 objects into a square
(5 rows of 5 each). But we can’t put 20 objects into a square (at least, we can’t without cutting the
objects into pieces). We say that 20 does not have a rational square root.
But does 20 have an irrational square root?
If we shift our perspective away from squares of counted objects towards squares with measured sides, the
idea of squares and square roots expands. In this new context, it is perfectly conceivable to have a
square with sides 4.5 inches each, with an area of 4.5 in. x 4.5 in. = 20.25 in2. In this new context, the area is
the square and the length of each side is the square root.
Is it possible to have a square with an area of exactly 20 in2?
Of course, each side would have to be a smidge less than 4.5 inches long. (We know that 4.5 x 4.5 =
20.25—a smidge more than 20 exactly). Thus, the square root of 20 exists, but isn’t a neat clean
terminating decimal. Irrational square roots (those not associated with perfect squares) can be
approximated to however many decimal places you wish, but can never be exactly written down
completely. Their decimal representations never terminate and never repeat.
Finally, remember that many fractions and decimals are also perfect squares. For example, we just saw
that 20.25 is a perfect square because it is exactly equal to 4.52. Similarly, is a perfect square because it
is exactly equal to
. Thus,
are all rational numbers, but
is an irrational number
(whose decimal approximation begins 4.472135955 . . .).
The only way to write an irrational number exactly is to write its symbolic form, such as
or π. This often
means that
is a better answer than 4.472135955. However, at other times, such as for graphing,
plotting, measuring, and estimating, you will prefer to use the approximate decimal form of an irrational
number.