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The Most Powerful Tool You've Probably Never Heard Of

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  1. The Most Powerful Tool You've Probably Never Heard Of To download this presentation go to www.mathematicallyminded.com

  2. What is Fluency? • What is something you are fluent at? • Fluency has three components: • Accuracy - when speaking another language • Flexibility - when cooking and you don't have a needed ingredient, do you know an alternative? • Efficiency - when driving we want the most efficient route

  3. In This Session • Progression of how children solve addition problems. • What understandings children need before they can progress. • Activities using the MathRack (a.k.a Rekenrek)

  4. Early Numeracy • Four interrelated aspects of early numeracy: • Counting - learning the list of number words in correct order • Enumerating - knowing the number words are said in correspondence with objects • Cardinality - understanding that the last number said tells how many in the set • Subitizing - instantly recognizing and naming how many in a set

  5. How the MathRack Can Help


  6. How the MathRack Can Help

  7. How the MathRack Can Help • What do you notice?let the children explore the tool and learn the built-in structure before you have them use the tool. • builds Counting, Enumerating, Cardinality • Show me On one row, "Show me __." Have them show a certain number. Some may count one-by-one but the structure of the tool allows for more advanced strategies. • builds Counting, Enumerating, Cardinality, and possibly Subitizing • Flash Forward Once children become more confident with the tool, show a certain number on the MathRack for a few seconds and have them determine which number was flashed. • builds Subitizing, but some kids may still be working on Enumerating & Cardinality

  8. What if I can't remember 7+8? • 7+7+1 • 8+8-1 • 7+3+5 • 5+2+8 • 2+5+5+3

  9. Essential Number Relationships • Spatial Relationship - recognizing how many without counting by seeing a visual pattern • One/Two More or Less - knowing which numbers are one/two more or less than any given number • Benchmarks of 5 & 10 - how any given number relates to 5 and 10 • Part-Part-Whole - ability to conceptualize a number as being made up of two or more parts Van De Walle, 2006

  10. How the MathRack Can Help • Show me and Flash Forward • builds Spatial and Benchmarks of 5 & 10 • Just One More show a certain number on the MathRack and have the kids build theirs to show "one more" or "two less." • builds One/Two More or Less • Show Me using two rows, "Show me ___." • builds Part-Part-Whole • Peek-a-Boo cover the right side of the MathRack, push some beads over so kids can see them and ask how many beads are hiding. • builds Part-Part-Whole (is a Missing Part activity) and Benchmarks of 5 & 10

  11. Using The MathRack to Add • Show 8 + 7 on your MathRack • Write down a number sentence that represents how you determine the total number of beads shown • What relationships did you use? • Model what you did on your Number Path • Show 9 + 8 on your MathRack • Write down a number sentence that represents how you determine the total number of beads shown • What relationships did you use? • Model what you did on your Number Path

  12. Using The MathRack to Subtract • Show 15 - 9 on your MathRack • Write down a number sentence that represents how you determine the total number of beads left • What relationships did you use? • Model what you did on your Number Path • Show 16 - 7 on your MathRack • Write down a number sentence that represents how you determine the total number of beads left • What relationships did you use? • Model what you did on your Number Path

  13. Story Problems • There are 7 people on the double-decker bus. At the next stop, 8 people got on the bus. How many people are on the bus now? • There are 7 people on the double-decker bus. At the next stop, some people got on the bus. Now there are 15 people on the bus. How many people got on the bus? • At Sierra's slumber party some of the girls were playing on her bunk bed. There were 6 girls sitting on the top bunk and 8 girls on the bottom bunk. How many girls were on the bunk bed? • There are 15 people on the double-decker bus. At the first stop, 7 people got off the bus. How many people are still on the bus? • At Sierra's slumber party 14 girls were playing on her bunk bed. There were 6 girls sitting on the top bunk. How many girls were on the bottom bunk?

  14. Algebraic Reasoning • True/False Number Sentences - use your MathRack to prove if these are true or false: • 7 + 8 = 8 + 7 • 3 + 3 = 4 + 2 • 6 = 5 + 2 • Understanding Equality - use your MathRack to determine what number goes in the box to make the number sentence true: • 3 + 4 = + 5 • 1 + = 3 + 6

  15. MathRack 100

  16. MathRack 100 Activities • Show me - have students show a number on the MathRack. Challenge them to see who can show the number in the least amount of "pushes." • Flash Forward - cover the MathRack and briefly flash numbers (from 1-100). • Hidden Numbers - show a number on the MathRack, have them make that number using the place value cards. • True/False Number Sentences - separate the Add-a-Row into two sets of 5 rows of 10. Show each side of the equation on a 5 rows of 10and have them determine if the number sentence is true or false. 13 + 24 = 10 + 28 • Make My Array - bring in objects that have a built-in array (egg cartons, muffin tin, etc). Have the kids model the array on the MathRack 100 and use that to determine the total.

  17. Resources • www.mathematicallyminded.com • www.MathRack.com • Teaching Student Centered Mathematics by John Van de Walle • Mastering the MathRack by Christina Tondevold • Contexts for Learning Mathematics by Catherine Fosnot