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

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Presentation transcript:

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

Solve this – aloud… Empowering Young Learners

Solve this – aloud… Was the language you used in talking through the solution “precise”? Empowering Young Learners

Solve this – aloud… Does our math talk sound more like this? Empowering Young Learners

The 8 Standards for Mathematical Practice: Making Sense of the Mathematical Practices 1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look for and make use of structure 8Look for and express regularity in repeated reasoning

Counting on the Open Number Line A solution for

Counting on the Open Number Line

Consider Subtraction on the Open Number Line Solve 53 – 37 with an open number line.

Consider Subtraction on the Open Number Line Solve 53 – 37 with an open number line. Compare your solution with someone near you.

Consider Subtraction on the Open Number Line Solve 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?

A C B

Solve this – aloud… Empowering Young Learners It is unlikely you used counting strategies to solve this – you probably used place value concepts.

Add this – aloud… It is unlikely you used counting strategies to solve this – you probably used place value concepts.

Making Sense of Place Value 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 Strategies Making sense of Place Value with the Candy Shop.

Grouping Strategies Making sense of Place Value with the Candy Shop. How will you package your candy?

Grouping Strategies BoxesRollsPieces

Grouping Strategies How else can you package this candy?

Grouping Strategies Base-ten Blocks

Grouping Strategies Base-ten Blocks Partial Sums

Grouping Strategies Base-ten Blocks Partial Sums Column Addition

Grouping Strategies Base-ten Blocks Partial Sums Column Addition Traditional Algorithm

Grouping Strategies

Grouping Strategies Base-ten Blocks

Grouping Strategies Base-ten Blocks Flexible Grouping

Solve this…

Grouping Strategies Base-ten Blocks Flexible Grouping Trade First Subtraction

Grouping Strategies Base-ten Blocks Flexible Grouping Trade First Subtraction Traditional Algorithm

Making Sense of Computation with Whole Numbers 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.