Balanced Math Framework

Mental Math

MNPS 2012-2013

Elements of Balanced Math

Makes Balanced Math a Reality

Problem Solving

Conceptual Understanding

Fluency-computation

and procedures

Common Coreand

Balanced Math

Coherence Focused

Rigor

The What-CCSS

The How- Balanced

Math

What’s In?Student CenteredConceptual UnderstandingProblem Solving

What’s Out?Traditional , textbook drivenTeacher CenteredRote Learning without Meaning

Anatomy of a Lesson

Math with

Meaning

Problem Solving

Small Groups/Centers

Vocabulary

Use of Manipulatives

Math Review

Mental Math

Conceptual Understanding

Skill Acquistion

How do I use my math time

Review

Mental Math

Closure

LessonTime

60 minute of

math daily !

Mental Math

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.

Have you practiced making combinations of five and ten?

You are getting faster at this! Keep practicing!

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 WarsAce = 1; Face cards= 10Put a card down and first to call out answer. Put card down before looking at it; Think Mentally; Penalty is 5 cardsPartner 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

WallFirst even whole numberFirst prime numberFirst 2-digit prime numberHow do you cube a numberFaces on a cubeDegrees in a right angleMinutes in an hour

Mental String

Start with number of faces on a cubeMultiply by the first even prime numberAdd the digitsCube the resultsRound to the nearest 10Add the number of degrees in a right angleDivide your answer by the number of minutes in an hour

Mental String

Start with number of faces on a cube- 6Multiply by the first even prime number- 6 x 2=12Add the digits- 1+2=3Cube the results- 3x3x3=27Round to the nearest 10 - 30Add the number of degrees in a right angle- 30 + 90=120Divide your answer by the number of minutes in an hour- 120/60= 2

Mental Strings

Create strings for grade levelPreview vocabularyCongratulate successAllow one student to modelInvite students to write their own

Mental Strings

Sides on a triangleFirst even numberFirst odd numberQuarts in a gallonDouble a number

Mental Strings

Start with two more than a number of sides on a triangleMultiply by itselfAdd the first odd whole numberAdd the digits of your answer togetherAdd the number of quarts in a gallonDouble your number

Mental Strings

Start with two more than a number of sides on a triangle------5Multiply by itself ------5 x5=25Add the first odd whole number------25 + 1=26Add the digits of your answer together----2 +6=8Add the number of quarts in a gallon----8 +4=12Double your number 12 x 2= 24

Mental Math String – 3rd Grade

Start with number of sides in a triangleDouble your answerAdd the number of diagonals that can be drawn on a squareMultiply by the number of sides on a pentagon

QUESTIONS?