Problem Solving with Fractions

UCLA

CGI

CMC

Shernice Lazare Rosangela Viera October 24, 2014

AGENDA

•  Warm-up & Goals

•  Brief Overview of CGI

•  Common Core Fractions

•  Problem Solving w/ Fractions

•  Q & A, Next Steps

•  Evaluation

GOALS

•  Brief Intro/Overview of CGI

•  Highlight CCSS Fractions Domain

•  Experience Problem Solving w/ Fractions

•  Answer Questions

•  Provide Resources

 

WARM UP: SKIP COUNTING

•  Start at 0 and skip count by quarters

•  Place 4 numbers in each row

•  We’ll tell you when to stop

•  Extensions: What are some different ways you could use skip counting in relation to fractions?

WHAT IS CGI? •  Cognitively Guided Instruction •  Philosophy not a curriculum •  Instructional decisions based on student

thinking •  Student articulation of thinking •  Thinking like a mathematician

PROBLEM SOLVING TRAJECTORY

•  Direct Modeling

•  Counting

•  Derived Facts / Invented Algorithm

•  Recall / Standard Algorithm

 

DIRECT MODELING

Coun%ng  COUNTING

DERIVED FACTS & INVENTED ALGORITHMS

RECALL & STANDARD ALGORITHM

CCSS: FRACTIONS •  K: No mention

•  1st: Time (half hour) & Geometry (halves, fourths & quarters)

•  2nd: Time & Money & Geometry

•  3rd: First Time Fraction Domain is mentioned: •  Parts of a Whole, On a Number Line & Equivalence

•  4th: Ordering & Comparing, Adding, Subtracting & Multiplying w/ like denominators, Express as decimal w/ denominators of 10 or 100

•  5th: Adding, Subtracting, Multiplying & Dividing with unlike denominators

LET’S SOLVE SOME PROBLEMS!

•  Four children are sharing ___ large cookies so each child gets the same amount. How many cookies does each child get?

•  Solve the problem as your students might solve the problem.

FAIR SHARING VIDEOS

•  Lexi: 2 years old •  Jeremy: 5 years old •  Ella: 8 years old

MORE PROBLEM SOVLING!

•  Angela has ____ cup(s) of rabbit food. Her rabbit needs ____ cup(s) of food for each meal. How many meals can Angela make for her rabbit?

•  Solve as your students might solve.

OUR ADVICE

•  Start young •  Context matters •  Authentic fair sharing opportunities (start

with wholes then move to fractions) •  Look for misconceptions •  Highlight fractions in the real world

FRACTION RESOURCES

Q & A, CONTACT INFO

What questions do you have about the information presented today?

Shernice Lazare: slazare@labschool.ucla.edu Rosangela Viera: rviera@labschool.ucla.edu Please fill out the evaluation and return it.

Thanks for coming! Our evaluation code: 44366

!""""""""""""""""""#""""""""""""""""""$""""""""""""""""""%"

&'()"*+,-".'/."0'1123'".+".451"64+('"7,08'-9""%:;!:"

!"#$%&'())*+,-&#..)

&.-+(3<*""=3-''"

>5123-''" =3-''"

&?'2@'-"A21"A'<<B?-'?2-')"2()"

@(+A<')3'28<'"C!B%D"

&?'2@'-"A21"'(3235(3"2()"2("'E'FGH'"?-'1'(.'-"C!B%D"

&'115+("02.F4')"G.<'"2()")'1F-5?G+("5("?-+3-20"8++@"C!B%D"

I.4'-"F+00'(.1J"1,33'1G+(1J"+-"K'')82F@"CA+-)1D"

"""""""""""""""""""""""""""LLL"LLL"LLL"""""""""""""LLLLLLLLLLL""LLLLLLL""""""""

!"#$%&'9"""""MM%;;"%$%"""N-'2."1'115+(O"

P")535.""?+<<"F+)'""

K+-".451"1'115+("

()*+,%#-',.+

/*)0!"#$%&'9"""""MM%;;"%""$""%"""N-'2."1'115+(O"

(1+,%#-'.+ (1+,%#-'.+

/*)0!"#$%&'9"""""MM%;;%B$B%N-'2."1'115+(O"

44366

!""""""""""""""""""#""""""""""""""""""$""""""""""""""""""%"

&'()"*+,-".'/."0'1123'".+".451"64+('"7,08'-9""%:;!:"

!"#$%&'())*+,-&#..)

&.-+(3<*""=3-''"

>5123-''" =3-''"

&?'2@'-"A21"A'<<B?-'?2-')"2()"

@(+A<')3'28<'"C!B%D"

&?'2@'-"A21"'(3235(3"2()"2("'E'FGH'"?-'1'(.'-"C!B%D"

&'115+("02.F4')"G.<'"2()")'1F-5?G+("5("?-+3-20"8++@"C!B%D"

I.4'-"F+00'(.1J"1,33'1G+(1J"+-"K'')82F@"CA+-)1D"

"""""""""""""""""""""""""""LLL"LLL"LLL"""""""""""""LLLLLLLLLLL""LLLLLLL""""""""

!"#$%&'9"""""%M#!$"""%$%"""N-'2."1'115+(O"

P")535.""?+<<"F+)'""

K+-".451"1'115+("

()*+,%#-',.+

/*)0!"#$%&'9"""""%M#!$"""%""$""%"""N-'2."1'115+(O"

(1+,%#-'.+ (1+,%#-'.+

/*)0!"#$%&'9"""""%M#!$%B$B%N-'2."1'115+(O"