Strategies for Whole Number Computation
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Transcript of Strategies for Whole Number Computation
STRATEGIES FOR WHOLE NUMBER COMPUTATION
February 2013 Coaches Meeting
CCSS
Fluently add and subtract within ____ using strategies and algorithms (3rd and 4th grade) based on place value, properties of operations, and/or relationship between addition and subtraction.
Solve 7 + 52 +186 without paper and pencil. Private think time
Share with your shoulder partner how you arrived at your answer.
Comparison of three 2nd grade classes
Algorithms Some algorithms taught at home
No algorithms
17 students 19 students 20 students
12% correct 26 % correct 45% correct
Range of answers9308-29
Range of answers989-114
Range of answers617-139
Research from Constance Kamii. Young Children Reinvent Arithmetic: Implications of Piaget’s Theory, Columbia University, 2000
Big Ideas
Flexible methods of computation involve taking apart and combining numbers in a variety of ways.
Invented strategies are flexible methods of computing that vary with the numbers and the situation.
Flexible methods for computation require a good understanding of the operations and the properties of operations.
The traditional algorithms are clever strategies for computing that have been developed over time. They work for all numbers but are often far from the most efficient or useful method of computing.
Three Types of Computational Strategies
• Counts by ones• Use of base-ten models
Direct Modeling
• Supported by written recordings
• Mental methods
Invented Strategies
• Usually requires guided development
Traditional Algorithm
s
Benefits of Student Invented Strategies
Students make fewer errors. Less re-teaching is required. Students develop number sense. Invented strategies are the basis for
mental computation and estimation. Flexible methods are often faster than
the traditional algorithms. Algorithms invention is itself a
significantly important process of “doing mathematics.”
Invented Strategies vs Traditional
Invented strategies are number oriented rather than digit oriented. 45 + 32 think of 40 + 30 rather than 4 +3
Invented strategies are left-handed rather than right handed.
Invented strategies are flexible rather than rigid. Try each mentally 465 + 230 and 526 + 98 Did you use the same method?
Algorithms
Students will not invent the traditional methods because they are right-handed methods and are simply not natural. This means that the teacher must introduce and explain each algorithm.
Students will sense that they are the “right way” or “real way” to compute and will abandon any flexible method they have been developing.
They will happen.
Invented Strategies for Addition
Add Tens, Add Ones and Combine
46 + 3840 + 30 is 706 and 8 is 14
70 and 14 is 84
Move Some to Make Tens
46 + 38Take 2 from the 46 and
put it with the 38 to make a 40. Now you have 44 and 40 more
is 84.
Invented Strategies for Subtraction
Take Tens from Tens, Then Subtract
Ones73-46
70 minus 40 is 30Take away 6 more is
24Now add in the 3 ones
27
Take Away Tens, Then Ones
73 – 4673 minus 40 is 33Then take way 6
3 makes 30 and 3 more is 27
Mental Strategies
Developing Fluency
Strategies
Strategies
Strategies
Strategies using Place Value
Yesterday there were 57 penguins sitting on the iceberg. Later 34 penguins joined them. How many penguins are now on the iceberg?
There were 72 penguins sitting on the iceberg. 49 penguins jumped into the icy water. How many penguins are still on the iceberg?