Create Presentation
Download Presentation

Download Presentation
## Balanced Math Framework

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Balanced Math Framework**Mental Math MNPS 2012-2013**What’s In?**• Student Centered • Conceptual Understanding • Problem Solving • What’s Out? • Traditional , textbook driven • Teacher Centered • Rote Learning without Meaning**Conceptual Understanding**Anatomy of a Lesson Skill Acquistion**How do I use my math time**60 minute of math daily !**CCSS Required Fluencies**• K Add/subtract within 5 • 1 Add/subtract within 10 • 2 Add/subtract within 20. Add/subtract within 100 (pencil and paper) . By end of year, know from memory all sums of two one‐digit numbers • 3 Multiply/divide within 100. Add/subtract within 1000. By end of year, know from memory all products of two one‐digit numbers • 4 Add/subtract within 1,000,000**Memorization vs Automaticity**• Memorization of basic facts usually refers to committing the results of unrelated operations to memory so that thinking through a computation is unnecessary. • Isolated additions and subtractions are practiced one after another as if there were no relationships among them; the emphasis is on recalling the answers. • Teaching facts for automaticity, in contrast, relies on thinking. Answers to facts must be automatic, produced in only a few seconds; counting each time to obtain an answer is not acceptable. But thinking about the relationships among the facts is critical. • The issue here is not whether facts should eventually be memorized but how this memorization is achieved: by drill and practice, or by focusing on relationships.**Memorization vs Automaticity**• Isn’t memorization faster? Interestingly, no! • When relationships are the focus, there are far fewer facts to remember, and big ideas like compensation and part-whole relationships come into play. Also, a child who forgets an answer has a quick way to calculate it. • Children who commit the facts to memory easily are able to do so because they have constructed relationships among the facts.**Memorization vs Automaticity**• Double plus or minus—for example, 6 + 7= 6 +6 + 1 (or 7 +7 – 1) =13. • Working with the structure of five—for example, 6 + 7 = 5 + 1 + 5 + 2 =10 + 3 =13. • Making ten—for example, 9 + 7 =10 + 6 =16. • Using compensation—for example, 6 + 8 = 7 + 7 = 14. • Using known facts—for example, 6 + 8 = 14, so 7 + 8 must be 14 + 1 =15.**Number Wars**• Ace = 1; Face cards= 10 • Put a card down and first to call out answer. Put card down before looking at it; Think Mentally; Penalty is 5 cards • Partner A and Partner B • (Partner A) + (Partner B) • Write down the 5 most difficult facts and use as a reference sheet • (Partner A) x (Partner B) • (Double Partner A) + (Partner B)**Vocabulary beyond the Word Wall**• First even whole number • First prime number • First 2-digit prime number • How do you cube a number • Faces on a cube • Degrees in a right angle • Minutes in an hour**Mental String**• Start with number of faces on a cube • Multiply by the first even prime number • Add the digits • Cube the results • Round to the nearest 10 • Add the number of degrees in a right angle • Divide your answer by the number of minutes in an hour**Mental String**• Start with number of faces on a cube- 6 • Multiply by the first even prime number- 6 x 2=12 • Add the digits- 1+2=3 • Cube the results- 3x3x3=27 • Round to the nearest 10 - 30 • Add the number of degrees in a right angle- 30 + 90=120 • Divide your answer by the number of minutes in an hour- 120/60= 2**Mental Strings**• Create strings for grade level • Preview vocabulary • Congratulate success • Allow one student to model • Invite students to write their own**Mental Strings**• Sides on a triangle • First even number • First odd number • Quarts in a gallon • Double a number**Mental Strings**• Start with two more than a number of sides on a triangle • Multiply by itself • Add the first odd whole number • Add the digits of your answer together • Add the number of quarts in a gallon • Double your number**Mental Strings**• Start with two more than a number of sides on a triangle------5 • Multiply by itself ------5 x5=25 • Add the first odd whole number------25 + 1=26 • Add the digits of your answer together----2 +6=8 • Add the number of quarts in a gallon----8 +4=12 • Double your number 12 x 2= 24**Mental Math String – 3rd Grade**• Start with number of sides in a triangle • Double your answer • Add the number of diagonals that can be drawn on a square • Multiply by the number of sides on a pentagon