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Coherence in Mathematics Instructional Shifts

Explore instructional shifts in mathematics focusing on coherence and the use of models, strategies, and reasoning to solve problems. Includes examples and guidance for making a ten, multi-digit multiplication, and more.

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Coherence in Mathematics Instructional Shifts

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  1. 10/26/16 K-2 Coherence in Mathematics

  2. Instructional Shifts

  3. Focus

  4. Instructional Shifts

  5. Coherence K.CA.1: Use objects, drawings, mental images, sounds, etc., to represent addition and subtraction within 10. 1.CA.5: Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; describe the strategy and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and that sometimes it is necessary to compose a ten. 2.CA.4: Add and subtract within 1000, using models or drawings and strategies … 3.C.1: Add and subtract whole numbers fluently within 1000.

  6. Shifts

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

  8. Instructional and Assessment Guidance

  9. Making a Ten 8 + 5 2 3

  10. Making a Ten 58 + 5 2 3 60 + 3

  11. Flexibility with Numbers

  12. Place Value • Use the base ten blocks to show the number 23. • Can you show 23 in a different way? 1.NS.6: Show equivalent forms of whole numbers as groups of tens and ones, and understand that the individual digits of a two - digit number represent amounts of tens and ones.

  13. Subtraction 23 – 15 1 13

  14. Multi-digit Multiplication • Use your base ten blocks to show 1 x 14. then 2 x 14 then 9 x 14 • Use your base ten blocks to show 23 x 14.

  15. 20 + 3 23 x 14 10 x 3 = 30 10 x 20 = 200 + 4 4 x 3 = 12 4 x 20 = 80

  16. Area Model revisited Multiply (2x + 3) (x + 4)

  17. Multiply (2x + 3) (x + 4) 2x + 3 x x x2 3x x2 x x + 8x 12 4

  18. Questions? Nick Meyer meyern@myips.org Kathy Jones jonesk@myips.org

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