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Making Sense of Making Sense of Place Value and Place Value and
Multidigit Addition Multidigit Addition and Subtractionand Subtraction
Juli K. Dixon, Ph.D.Juli K. Dixon, Ph.D.
University of Central University of Central FloridaFlorida
Solve this – aloud…
Empowering Young Empowering Young LearnersLearners
Solve this – aloud…
Was the language you used in talking through the solution “precise”?
Empowering Young Empowering Young LearnersLearners
Solve this – aloud…
Does our math talk sound more like this?
http://video.google.com/videoplay?docid=7106559846794044495
Empowering Young Empowering Young LearnersLearners
The 8 Standards for Mathematical Practice:
Making Sense of the Making Sense of the Mathematical Mathematical PracticesPractices
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the
reasoning of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated
reasoning
Counting on the Open Counting on the Open Number LineNumber Line
48 58 68 70 73
+10 +10 +2 +3
A solution for 48 + 25
Counting on the Open Counting on the Open Number LineNumber Line
48 58 68 70
48 50 70
+20+2
73
+10 +10 +2 +3
73
+3
Consider Subtraction Consider Subtraction on the Open Number on the Open Number LineLineSolve 53 – 37 with an open number line.
Consider Subtraction Consider Subtraction on the Open Number on the Open Number LineLineSolve 53 – 37 with an open number line.
Compare your solution with someone near you.
Consider Subtraction Consider Subtraction on the Open Number on the Open Number LineLineSolve 53 – 37 with an open number line.
Compare your solution with someone near you.
What did you do? Did you:
- Count Up?- Count Back? Or- Take Away?
37 47 50 53
+ 10 + 3 + 3
16 43 53
- 10- 7 - 10
33
- 10
23
A
C
37 40 43 53
- 10- 3 - 3
B
Solve this – aloud…Solve this – aloud…
Empowering Young Empowering Young LearnersLearners
It is unlikely you used counting strategies to solve this – you probably used place value concepts.
Add this – aloud…Add this – aloud…
1 4 9+ 2 8 5
It is unlikely you used counting strategies to solve this – you probably used place value concepts.
Making Sense of Place Making Sense of Place Value to 1,000Value to 1,000 The 10-to-1 relationship
– Issues with base ten blocks– Pennies and string– Candy Shop
Exploring algorithms– Candy Shop– Invented Algorithms– Standard Algorithms
Grouping StrategiesGrouping Strategies
Making sense of Place Value with the Candy Shop.
Grouping StrategiesGrouping Strategies
Making sense of Place Value with the Candy Shop.
How will you package your candy?
Grouping StrategiesGrouping Strategies
Boxes Rolls Pieces
Grouping StrategiesGrouping Strategies
How else can you package this candy?
Grouping StrategiesGrouping Strategies
Base-ten Blocks
1 4 9+ 2 8 5
Grouping StrategiesGrouping Strategies
Base-ten BlocksPartial Sums
1 4 9+ 2 8 5
Grouping StrategiesGrouping Strategies
Base-ten BlocksPartial SumsColumn Addition
1 4 9+ 2 8 5
Grouping StrategiesGrouping Strategies
Base-ten BlocksPartial SumsColumn AdditionTraditional Algorithm
1 4 9+ 2 8 5
Grouping StrategiesGrouping Strategies
4 3 6 - 8 2
Grouping StrategiesGrouping Strategies
4 3 6 - 8 2
Base-ten Blocks
Grouping StrategiesGrouping Strategies
4 3 6 - 8 2
Base-ten BlocksFlexible Grouping
Solve this…Solve this…
2 0 3 - 6 8
Grouping StrategiesGrouping Strategies
4 3 6 - 8 2
Base-ten BlocksFlexible GroupingTrade First Subtraction
Grouping StrategiesGrouping Strategies
4 3 6 - 8 2
Base-ten BlocksFlexible GroupingTrade First SubtractionTraditional Algorithm
Making Sense of Making Sense of Computation with Whole Computation with Whole NumbersNumbers Conceptual understanding MUST
precede memorization and procedural algorithms.
Quick recall is still important, it is when this is the focus that must change.
Students should be expected to explain their mathematical moves.