Transcript Relationship between #s

ASSESSMENT ANCHOR
M4.A.1 Demonstrate an
understanding of numbers, ways of
representing numbers,
relationships among numbers and
number systems.
M4.A.1.2 Compare quantities and
magnitudes of numbers.
M4.A.1.2 Eligible Content
• M4.A.1.2.1 Locate/identify fractions or
decimals on a number line (decimals and
fractions through the tenths – do not mix
fractions and decimals).
• M4.A.1.2.2 Compare and/or order whole
numbers through 6 digits and amounts of
money to $100 (limit sets for ordering, to
no more than 4 numbers).
M4.A.1.2.1 Locate/identify
fractions or decimals on a
number line (decimals and
fractions through the tenths – do
not mix fractions and decimals).
PSSA Sample Item
• Representation of Decimals on a Number
Line
• To represent a decimal on a number line,
divide each segment of the number line into
ten equal parts. E.g. To represent 8.4 on a
number line, divide the segment between 8
and 9 into ten equal parts.
•
• The arrow is four parts to the right of 8
where it points at 8.4.
• "Decimal" comes from the Latin root decem, which means
ten. To understand decimal numbers you need to understand
how ten forms the basis of our number system.
• Let's first explore decimals on the number line. Draw little
lines between 0 and 1 so that it is divided into ten tiny parts tenths!
•
• Now let's zoom in between 0 and 1. See how the number line
between 0 and 1 is divided into ten increments or parts. Each
of these ten parts is a tenth.
•
• The first digit after the decimal point tells how many tenth
parts or tenths are in the number.
•
0.4 means four tenths - the same as
•
2
1.2 is the same as 1
10
4
10
How to Find a Fraction on a
Number line
A number line and a ruler are very
much alike.
0
1
2
On a ruler, each inch is considered
one whole inch
Nine whole inches
One Inch
Two Inches
Three Inches
The marks in between the whole
inches are fractions of an inch
½ Inch
2 ¾ Inches
7 ¼ inches
Number lines are read the same
way.
• The Numbers are read as whole numbers.
• The marks in between are read as
fractions.
0
1
2
There are three steps to reading
fractions on a number line
Step One-Count the spaces in between the zero
and the one on the number line. That is your
denominator.
0
1
4
2
Step Two- Count the sticks, starting at the first
stick after zero. Stop at the point you are naming.
This is the Numerator.
0
1
3
4
There is only a step three if the
fraction is past a whole number.
If the fraction is past a whole number, steps one
and two are the same except that you count the
spaces and marks in between the whole
numbers closest to the fraction.
0
1
2
Mixed number fractions
Step One-Count the spaces in
between the whole numbers
where the fraction is placed. That
is your denominator.
0
1
2
4
Mixed number fractions
Step Two- Count the sticks, starting at the first
stick after the whole number. Stop at the point
you are naming. This is the Numerator.
2
0
1
2
4
Mixed number fractions
Step Three- Write the whole number as a whole
number beside the fraction.
0
1
2
1
2
4
Practice Finding
Decimals and Fractions on a
Number Line
• Which decimal on this number line
corresponds to the fraction 1/2?
• Put these decimals in the proper place on
the number line
• What number is at the arrow?
•
• Answer. The unit has been cut five times
-- into six equal pieces.
• That number is 5
6
Write the decimal number that the arrow
points at in the following diagrams:
24.3
M4.A.1.2.2 Compare and/or
order whole numbers through 6
digits and amounts of money to
$100 (limit sets for ordering, to no
more than 4 numbers).
PSSA Sample Item
Comparing and Ordering Whole
Numbers
Example 1: Compare 76 and 67
Write:
67 < 76
76 > 67
Say:
67 is less than 76
76 is greater than 67
Remember, the mouth of the symbol (> or <)
always opens to the greater number.
Example 2: Blanca Peak is 14,345 feet above sea
level. Crestone Peak is 14,294 feet above sea
level. Which peak is taller?
1. Line Up the place
values by lining up the
ones.
14,345
14,294
2. Begin at the left. Find 3. Compare the value of
the first place where the the digits.
digits are different
14,345
14,294
different
same
300 > 200
So
14,345 > 14,294
Caution!!!!!
Be sure to line up digits with the same place value when comparing or
computing.
Example: You score 108,464 points. Your friend scores 97,996. The higher
score wins. Who wins?
Lined Up Incorrectly
108,464
97,996
Lined Up Correctly (at the ones place)
108,464
97,996
Note: When one whole number has
more digits than the other, it is greater.
Write: 108,464 > 97,996 or 97,996 < 108,464
Let’s Try!
Compare using <,>, or =.
• 534 __ 509
• 45,943 __ 45,494
• 109,015 __ 109,005
• 845,182 __ 846,182
Order the following numbers from greatest to least.
61,565; 71,649; 75,367
1. Line up the numbers
at the ones place.
61,565
71,649
75,367
2. Begin to compare at
the left.
61,565
71,649
75,367
70,000 > 60,000
So 61,565 is the least.
3. Continue. Find the
first place where the
digits are different.
71,649
75,367
5,000 > 1,000
So 75,367 > 71,649
75,367 ; 71,649; 61,565 (greatest to least)
Let’s Try!!
• Order from least to greatest…
• 756,833; 756,820; 756,338
• 756,338; 756,820; 756,833
• Order from greatest to least…
• 90,654; 87,223; 87,954; 90,556
• 90,654; 90,556; 87,954; 87,223