Step By Step Model DrawingDiscover the Ah Ha Moments
Dawn Sparks
Donald Bender
What do you do when you really wantsomething?
Making the Case…Focus on number sense!
Research indicates that early number sensepredicts school success more than othermeasures of cognition like verbal, spatial ormemory skills or reading ability.
Jordoan, Kaplan, Locuniak, and Ramineni, 2007
Washington State Report Card5th Grade Migrant Math Data
Migrant Math Data 5th Grade Math
Understand the specific needs of migrant math students
Use model drawing to develop academic language
Use model drawing as a way to provide migrant studentsmodifications that support math learning withoutlessoning the rigor of math problems
Sample Problem: Try It
The sum of two numbers is 36. The small number is one-third of the larger number. Find the two numbers.
Sharing Strategies…
How did you solve the problem
Share your ideas with a partner
Ideas from the group-what were some of the strategiesyou used?
Instructional Principles for Diverse Learners
All students learn mathematics in essentiallythe same way.
Learning is based on..
big conceptual ideas
what students already know
informal knowledge of mathematics
Accommodations and Modifications
How could we provide accommodations ormodifications to help our migrant students?
With a partner share some of your ideas
Write an idea on a sheet of paper
Share ideas with the group
Write and State Content and LanguageObjectives
Math: Students will be able to answer a story problem withmore than two steps.
Language: Students will be able to explain how theysolved their math problem using sentences.
Build Background
Give Real Experiences
Make Tasks Non Threatening
Build up the strengths of the Migrant Lifestyle
Build Background-Hiccups???
The names of teen numbers in English don’t correspondto place value.
Teen and Decade Number Confusion
Measurement~ What’s a pint? A Quart??
What do you mean by foot? Yard?
Different algorithms-notations
Home envirionment
Vocabulary
Helping students who are EnglishLanguage Learners…
Social Language
Add
Subtract
Less
More
Foot
Yard
Plus
Sum
Combine
Left
Whole
Even
Odd
Helping students who are EnglishLanguage Learners…
Social Language
Academic Language: Mean, Median, Mode?Ratio?
Compare
Explain
Predict
Conjecture
Explore
Represent
Construct
Formulate
Solve
Describe
Investigate
Use
Develop
Justify
Verify
How Can We Explicitly Teach Vocabulary
Concept maps
Word walls
CCD’s
Picture representations
Grammar and Syntax
Consider the implications for a second languagelearner…
Samuel bought 2 bags of oranges with 7 oranges ineach bag. How many oranges did he buy?
Lisa gave a total of 12 treats to her cats. She gave herlarge cat 2 more treats than she gave her small cat.How many treats did she give each cat?
How might these question be a problem for ELL students?
Use Comprehensible Input: Making themeaning clear and understandable…
Shorten sentences
Remove confusing words
Use gestures
Use wait time
But do not lower the complexity of themath!!!
Use Comprehensible Input
Use a variety of tools to help students visual andunderstand what is being verbalized.
Pictures
Diagrams
Real objects
A Tale of Three Story ProblemsScaffolding the Language of a problem
A.The sum of two numbers is 36. The small number isone-third of the larger number. Find the two numbers.
B.Jerry and Tom had 36 marbles altogether. Jerry hadone-third as many marbles as Tom. How many marblesdid each boy have?
C.Jerry and Tom were going out to the playground to playmarbles. When they reached into their pockets theypulled out all of their marbles and counted them.Together they had 36 marbles. Jerry had one-third asmany marbles as Tom. How many marbles did each boyhave?
Honor Use of Home Language
Discuss problem in small groups using their dominatelanguage
Present answers after practice in English
Present answers after practice with a translator
Use cognates when available
Honor Use of Home Language
Allow Code-Switching, moving between two languages
Assess students in their primary language
Validate the minority language
Use Discourse that Reflects Language Needs
Revoicing-hearing the same concept in more than oneway
Pressing for details- number heads together, come back toanswer question, don’t let them off the hook .
Plan Cooperative/Interdependent Groups toSupport Language
Think about how you group students
Use pairs that are mutually beneficial to each other’slanguage development
Numbered heads together -Project GLAD
Helping our students…
Create a “Math Movie”
Visualize the problem then draw using the GLAD “Listenand Sketch” strategy
Use “Model Drawing” to practice the Singapore problem-solving method
Gather ideas for supporting Migrant Student’s academiclanguage in Mathematics
Model Drawing Let’s Get Started-Moving from the Abstract to the Comprehensible
Learn the process or how to use model drawings tosolve word problems
Apply the process independently when solving wordproblems
STEPS for Model Drawing…
1.Teacher reads real world problem
2.Students listen and visualize the problem.
3.Students write down the key facts
a)who, what, how
4.Students write a mmm statement
5.Teacher rereads and students sketch a diagram or barmodel
6.Students solve problem and show work
7.Students write equations and rewrite statement
STEPS for Model Drawing…
Listen and Sketch- Project GLAD
1.Fold paper into four sections
Understand the Problem:
Plan/Sketch:
Solve:
Check:
Equation
Answer Statement
Sample Problem: Try IT!
Adrian, Ben and Christy put theirmoney together to buy a birthdaypresent for their mother. They had$78.75 altogether. Ben had half asmuch as Christy and Adrian had 4times as much as Ben. How muchmoney did Christy contribute?
Jose collected ____ sports cards. He had___ more baseball cards than footballcards. How many baseball cards did Josehave?
Mmm Statement:
Jose collected 425 sports cards. He had75 more baseball cards than footballcards. How many baseball cards did Josehave?
Mmm Statement:
Listen and Sketch- Project GLADBaseball Problem
Understand the Problem:
Plan/Sketch:
Solve:
Check
Equation:
Answer Statement
Listen and Sketch- Project GLADBaseball Problem
Understand the Problem:
Jose
Baseball Cards- 75 more
Football Cards
Plan/Sketch:
Jose’s Football Cards
Jose’s Baseball Cards
Solve:
Check:
Equation
Answer Statement
Jose had ____ baseball cards.
425
?
Primary Question-Discrete
Janet picked 3 daisies and 2 sunflowers from her garden.How many total flowers did Janet pick from her garden?
Use real object first before the model
Janet’sFlowers
D
D
D
S
S
?
3 + 2 = 5
Janet picked 5 flowers.
Addition- Continuous
One bag of lettuce weighed 14 ounces. Another bagweighed 12 ounces. What was the total weight of the 2bags of lettuce?
Subtraction
After selling ____ books, Michael had ___books left. How many books did he have atfirst?
After selling ____ books, Michael had ___ booksleft. How many books did he have at first?
Michael had ___ books at first.
Michaels Books
46
27
?
Multiplication
Itty and Bitty each did jumping jacks. Itty did 8 jumpingjacks. Bitty did 4 times as many jumping jacks as Itty.How many jumping jacks did Itty and Bitty do altogether?
Multiplication
Itty and Bitty each did jumping jacks. Itty did 8 jumpingjacks. Bitty did 4 times as many jumping jacks as Itty.How many jumping jacks did Itty and Bitty do altogether?
Draw the unit bars/make the sketch:
Itty’s JumpingJacks
8
Bitty’s JumpingJacks
8
8
8
8
Multiplication
Itty’s JumpingJacks
8
Bitty’s JumpingJacks
8
8
8
8
?
8 x 5 = 40
Itty and Bitty did 40 jumping jacks altogether.
Division:
Mr. Rodriguez is finding drivers to take 17 of his studentson a field trip. If only 4 students can ride in each car, howmany cars will Mr. Rodriquez need?
Division:
Mr. Rodriguez is finding drivers to take 17 of his studentson a field trip. If only 4 students can ride in each car, howmany cars will Mr. Rodriquez need?
Studentsin cars
17
? # of Cars
Fractions
There is ½ of a candy bar that needs to be divided evenlyamong 3 children. What fraction of the total candy barwill each child receive?
Fractions (Mixed Operations)
Terra’s monthly allowance is $48. she puts ½ of herallowance into savings and gives ¾ of the remainingmoney to a local charity. How much money does Terrahave left for herself each month.
Ratios
The ratio of children to adults at the football game was2:3. If there were 140 children at the football game, howmany adults were there?
Bridge to Algebra
Together Jasmine and Laura earned a total of $64babysitting. If Jasmine earned $14 more than Laura, howmuch money did each girl earn?
Sample Problem: Try It Again…
The sum of two numbers is 36. The small number is one-third of the larger number. Find the two numbers.
Opportunities for Further PD
September 20th- ESD 8:30-3:30
District In-service As Needed
Professional Learning Communities: Video Series
Additional Resources:
Step By Step Model Drawing
Model Drawing for Challenging Word Problems
Seminar on CD ROM
Word Problems for Model Drawing Practice
Grades 1-5
Revisit Goals-
Understand the specific needs of migrant math students
Use model drawing to develop academic language
Use model drawing as a way to provide migrant studentsmodifications that support math learning withoutlessoning the rigor of math problems