Transcript Problem of the Day 2.1

PROBLEM OF THE DAY 2.1
The number on Holly’s house is a 3-digit
number. The digit in the hundreds
place is twice the value of the digit in
the tens place. The tens digit is three
more than the ones digit. The sum of
the digits is 13. What is the number on
Holly’s house?
The number on Holly’s house is 841.
PROPERTIES OF ADDITION
• Commutative Property- the
order of the addends can
change without affecting the
sum.
• Proof:
2 + 3 = 5 and 3 + 2 = 5
6 + 4 = 10 and 4 + 6 = 10
PROPERTIES OF ADDITION
• Associative Property – in an addition
problem using more than two
addends, the groupings of the
numbers and the order these groups
are added will not change the sum.
• Proof:
(2 + 3) + 7 = 12 and 2 + (3 + 7) =
12
(6 + 4) + 3 = 13 and 6 + (4 + 3) = 13
PROPERTIES OF ADDITION
• Associative Property – in an addition
problem using more than two addends,
the groupings of the numbers and the
order these groups are added will not
change the sum.
• Proof:
(2 + 3) + 7 = ?
2 + (3 + 7) = ?
Which of these problems is easier to
compute?
PROPERTIES OF ADDITION
• Associative Property – in an addition
problem using more than two
addends, the groupings of the
numbers and the order these groups
are added will not change the sum.
• Proof:
(6 + 4) + 3 = ?
6 + (4 + 3) = ?
Which of these problems is easier to
compute?
COMPENSATION (ISHY-OSHY-ATION)
• Compensation allows you to change
numbers in the problem as long as you
make adjustments in the answer.
• Example:
4.25- 3.08 change the problem to
4.25-3.10 (you subtracted .02 more than the problem)
4.25-3.10 = 1.15 (now add the .02 back)
4.25-3.08=1.17
COMPENSATION (ISHY-OSHY-ATION)
• Compensation allows you to change
numbers in the problem as long as you
make adjustments in the answer.
• Example:
$3.47 + $4.35 = compensate the
problem to:
$3.50 + $4.35 = $7.85
$7.85- (the extra $0.03)=$7.82
PARTIAL-SUMS METHOD:
*Addition is performed form left to right, column by column
*The sum for each column is recorded on a separate line.
*The partial sums are added either at each step or at the
end.
348 + 177 = ?
400 + 110 + 15
525
3
4
8
+ 1
7
7
PARTIAL-SUMS METHOD:
.
4.65 + 3.25 = ?
7 + 0.8+ 0.1
7.9
4.
6
5
+3.
2
5
EQUAL ADDITION
PROPERTY
• Open your textbook to page 32.
• Look at problem 27. Explain the Equal
Additions Property to a partner.
• How is the Equal Addition Property
different from Compensation?
• Using Equal Addition Property, solve A
and B
EQUAL ADDITION
PROPERTY
• Open your textbook to page 32.
• Look at problem 28.
• What strategies can you use to solve 28
mentally?
• Use one strategy to find the answer.
EQUAL ADDITION
PROPERTY
• Open your textbook to page 32.
• Read problem 29. How can you
reorganize the numbers to add the sum
mentally?
• Explain the strategy you will use to
subtract $100.00 from the total.
EQUAL ADDITION
PROPERTY
• Open your textbook to page 32.
• Read problem 30.
• Find the answer using a mental math
strategy.
• Share your answer with a partner.
• Explain the strategy you used and how
it helped you.
LET’S TALK…
• About problems 31 and 32
• Think about problem 33. How can
partial sums help you find the answer?
WHAT ABOUT DECIMALS?
• How do these strategies apply to
decimals?
• What are the possible problems you
will have with these methods and
decimals?
• Try some on your own
66 + 1.8 +2.2 (what two numbers
make sense to add?)
9.7 + 3 + 6.3
22 + 4.6 + 4.4
23.7 + 1.95 + 2.3
3.99 + 3.11 + 6.3
MENTAL MATH ROCKS
• Try some with a partner
• Textbook page 31
• Work your way through 1-6
• Mental math only
• Write your answers down in your
math spiral
• Label your answers –Textbook p. 31