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Composing and Decomposing Numbers

Composing and Decomposing Numbers. Important Pre-Requisite Math Skills based on presentation by Dinah Chancellor, Math Consultant CAMT 2012. Research suggests…. Between the ages of 9-12, the brain matures enough to take things apart and put them together in new ways.

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Composing and Decomposing Numbers

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  1. Composing and Decomposing Numbers Important Pre-Requisite Math Skills based on presentation by Dinah Chancellor, Math Consultant CAMT 2012

  2. Research suggests… • Between the ages of 9-12, the brain matures enough to take things apart and put them together in new ways. “Well! That explains why my second graders just don’t get REGROUPING!”

  3. But Texas expects 2nd graders to… • Add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations WHAT?!?!?!? • Solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value including algorithms AND…

  4. In April 2012, Texas revised the TEKS in Mathematics… Kinder-2ndKnowledge Statement: The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system.

  5. K.2 Number and operations. The student is expected to : (I) compose and decompose numbers up to 10 with objects and pictures. • 1.2 Number and operations. The student is expected to: (B) use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones.

  6. 2.2 Number and operations. The student is expected to : (A)use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones.

  7. Composing and decomposing numbers requires… FLEXIBLE THINKING

  8. To Compose and Decompose Numbers… • Children must be able to name numbers FLEXIBLYin order to have what is called number sense. • For example: 35 can be… • 30 + 5 • 20 + 15 • 25 + 10 • 32 + 3

  9. It’s all about the power of … TEN!

  10. Kinder and 1st Benchmark Numbers • FIVEand TEN are important anchor numbers. Other numbers can be thought of in relation to them. • For example: 7can bethought of as five and 2 more or ten and 3 less

  11. 1st and 2nd • MAKE TENas an ADDITIONSTRATEGY • For example: 7 + 5 = ? Because I know that 5 is 3 and 2, I can “make 10” : 7 + 3 + 2 = ? 10 + 2 = 12

  12. 2nd Decompose to Add36 + 7 = ? Make the nearest TEN 36 + 7 = ? 36 + 4 + 3 = ? 40 + 3 = 43 Add the TENS then add the ONES 27 + 35 = ? 20 + 7 + 30 + 5 = ? 20 + 30 + 7 + 5 = ? 50 + 12 = 62

  13. 2nd Regroup to Subtract 34 - 6 = ? 2 tens 8 ones HUGE IDEA: 2 tens and 14 ones means the same as 3 tens and 4 ones.

  14. So What Can We Do? Teach students to conceptualize numbers by composing and decomposing!

  15. How many different ways can you make 5 with the fingers on both hands?

  16. ORGANIZE YOUR WORK How do you know you found all the ways?

  17. Composing/Decomposing Tasks:Building Flexible Thinking About Numbers • Make FIVE with counters.

  18. Making 5 With Counters

  19. Making 5 With Counters • Spill 5 counters. • Draw your spill on a recording slip: • or • Put your recording slip where it belongs on our graph.

  20. Composing/Decomposing Tasks:Building Flexible Thinking About Numbers • Make FIVE with counters • Workjobs and other work mats • Make FIVE with counters

  21. Workjobs and Other Work Mats

  22. Workjobs and Other Work Mats

  23. Composing/Decomposing Tasks:Building Flexible Thinking About Numbers • Make FIVE with counters • Workjobs and other work mats • Trains • Make FIVE with counters • Workjobs and other work mats

  24. Trains

  25. Composing/Decomposing Tasks:Building Flexible Thinking About Numbers • Make FIVE with counters • Workjobs and other work mats • Trains • Literature • Make FIVE with counters • Workjobs and other work mats • Trains

  26. Literature

  27. Literature

  28. Literature

  29. Literature

  30. Literature

  31. Importance of Composing/Decomposing Numbers • Conceptualize numbers • Fosters good number sense • Pre-requisite for developing mental math strategies • Pre-requisite for developing algorithms for finding sums and differences when regrouping is necessary.

  32. A Numerically Powerful Child: • develops meaning for numbers, • makes sense of numerical and quantitative situations, • looks for relationships among numbers and operations, • understands computational strategies and uses them appropriately and efficiently ~ Randy Charles and Joanne Lobato

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