Ch. 12 Developing Strategies for Addition and Subtraction Computation
Kelsey Lorenz
Big Ideas:
1. Flexible methods of addition and subtraction computation involve taking apart (decomposing) and
combining (composing) numbers in a wide variety of ways.
2. “Invented” strategies are flexible methods of computing that vary with the numbers and the situation.
3. Flexible methods for computation require a strong understanding of the operations and properties of
the operations, especially the commutative property and the associative property.
4. The standard algorithms are elegant strategies for computing that have been developed over time.
5. Multidigit numbers can be built up or taken apart in a variety of ways.
6. Nearly all computational estimations involve using easier-to-handle parts of numbers or substituting
difficult-to-handle numbers with close “compatible” numbers so that the resulting computations can be
done mentally.
Direct Modeling
Direct Modeling:
The use of manipulatives or drawing along with counting to represent directly the
meaning of an operation or story problem.
EX: Base- ten models, snap cubes, or number lines.
Adding and Subtracting Single-Digit Numbers
Up Over 10:
Use known facts that equal 10 and then add the rest of the number onto 10.
Ex: 8+8=
8+(2+6)=
(8+2)+6=
10+6=16
Ch. 12 Developing Strategies for Addition and Subtraction Computation
Kelsey Lorenz
Adding Two-Digit Numbers
EX: 46+38
Add Tens, Add Ones, Then
Combine:
Add the tens together. Add the ones
together. Then combine them.
EX: 40+30=70
6+8=14
70+14=84
Add on Tens, Then Add Ones:
46 and 30 more is 76. Then add on the
other 8. 76 and 4 is 80 and 4 is 84.
EX: 46+30=76
76+4=80
80+4=84
Move Some to Make Tens:
Take 2 from the 46 and put it with the
38 to make 40. Now you have 44 and 40
is 84.
EX: 46-2=44
38+2=40
44+40=84
Use a Nice Number and
Compensate:
Round up one of the numbers to make
it nice. Then add the numbers together.
Take away the extra amount to get the
number you need.
EX: 46+40=86
86-2=84
Subtracting by Counting Up
EX: 73-46
Add Tens to Get Close, Then Ones: Add Ones to Make a Ten, Then
46 and 20 is 66. (30 is too much.) Then Tens and Ones:
4 more is 70 and 3 more is 73. That’s 20
and 7 or 27.
EX: 46+20=66
66+4=70
70+3=73
46 and 4 is 50. 50 and 20 is 70 and 3
more is 73. The 4 and 3 is 7 and 20 is
27.
EX: 46+4=50
50+20=70
Ch. 12 Developing Strategies for Addition and Subtraction Computation
20+4+3=27
Kelsey Lorenz
70+3=73
4+20+3=27
Add Tens to Overshoot, Then
Come Back:
Add Ones to Make a Ten, Then
Tens and Ones:
46 and 30 is 76. That’s 3 too much, so
it’s 27.
EX: 46+30=76
76-3=70
30-3=27
Similarly, 46 and 4 is 50. 50 and 23 is
73. 23 and 4 is 27.
EX: 46+4=50
50+23=73
23+4=27
Take-Away Subtractions
EX: 73-46
Take Tens from the Tens, Then
Subtract Ones:
70 minus 40 is 30. Take away 6 more is
24. Now add in the 3 ones -> 27.
EX: 70-40=30
30-6=24
24+3=27
Take Tens from the Tens, Then
Subtract Ones: (cont.)
70 minus 40 is 30. I can take those 3
away, but I need to take away 3 more
from the 30 to make 27.
EX: 70-40=30
(73-3=70)
30-3=27.
Add to the Whole If Necessary:
Give 3 to 73 to make 76. 76 take away
46 is 30. Now give 3 back is 27.
EX: 73+3=76
76-46=30
30-3=27
Take Away Tens, Then Ones:
73 minus 40 is 33. Then take away 6: 3
makes 30 and 3 more is 27.
EX: 73-40=33
33-3=30
30-3=27.
Take Extra Tens, Then Add Back:
73 take away 50 is 23. That’s 4 too
many. 23 and 4 is 27.
EX: 73-50=23
23+4=27
Ch. 12 Developing Strategies for Addition and Subtraction Computation
Kelsey Lorenz
Estimation
Estimation: A number that is a suitable approximation for an exact number
given the particular context.
Measurement Estimation: Determining an approximate measure without
making an exact measurement. Length and weight.
EX: About how much will the watermelon weigh? 3 pounds.
Quantity Estimation: approximating the number of items in a collection.
EX: Estimate about how many jellybeans are in the jar. 250 jellybeans.
Computational Estimation: Determining a number that is an approximation
of a computation that we cannot or do not wish to determine exactly.
EX: Will $50 cover the amount of a pair of Nikes ($45) and socks ($10)? Yes or No?
Language of Estimation: Words and phrases such as about, close, just about,
a little more (or less) than, and between.