Making Sense of Place Value and Multidigit Addition and Subtraction Juli K. Dixon, Ph.D. University...

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


Was the language you used in talking through the solution “precise”?



Does our math talk sound more like this?

http://video.google.com/videoplay?docid=7106559846794044495


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.


Compare your solution with someone near you.


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…


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.


Making sense of Place Value with the Candy Shop.

How will you package your candy?


Boxes Rolls Pieces


How else can you package this candy?


Base-ten Blocks

1 4 9+ 2 8 5


Base-ten BlocksPartial Sums

1 4 9+ 2 8 5


Base-ten BlocksPartial SumsColumn Addition

1 4 9+ 2 8 5


Base-ten BlocksPartial SumsColumn AdditionTraditional Algorithm

1 4 9+ 2 8 5


4 3 6 - 8 2


4 3 6 - 8 2

Base-ten Blocks


4 3 6 - 8 2

Base-ten BlocksFlexible Grouping

Solve this…Solve this…

2 0 3 - 6 8


4 3 6 - 8 2

Base-ten BlocksFlexible GroupingTrade First Subtraction


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.

Making Sense of Place Value and Multidigit Addition and Subtraction Juli K. Dixon, Ph.D. University...

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