Step By Step Model Drawing
Discover the Ah Ha Moments
Dawn Sparks
Donald Bender
What do you do when you really want
something?
Making the Case…
Focus on number sense!

Research indicates that early number sense
predicts school success more than other
measures of cognition like verbal, spatial or
memory skills or reading ability.
Jordoan, Kaplan, Locuniak, and Ramineni, 2007
Washington State Report Card
5th 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 students
modifications that support math learning without
lessoning the rigor of math problems
Sample Problem: Try It

The sum of two numbers is 36. The small number is onethird 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 strategies
you used?
Instructional Principles for Diverse Learners

All students learn mathematics in essentially
the 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 or
modifications 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 Language
Objectives
Math: Students will be able to answer a story problem with
more than two steps.
Language: Students will be able to explain how they
solved 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 correspond
to 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 English
Language Learners…

Social Language
Add
Subtract
Less
More
Foot
Yard
Plus
Sum
Combine
Left
Whole
Even
Odd
Helping students who are English
Language 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 language
learner…

Samuel bought 2 bags of oranges with 7 oranges in
each bag. How many oranges did he buy?
Lisa gave a total of 12 treats to her cats. She gave her
large 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 the
meaning clear and understandable…

Shorten sentences

Remove confusing words

Use gestures

Use wait time
 But
do not lower the complexity of the
math!!!
Use Comprehensible Input

Use a variety of tools to help students visual and
understand what is being verbalized.

Pictures

Diagrams

Real objects
A Tale of Three Story Problems
Scaffolding the Language of a problem
A.
B.
C.
The sum of two numbers is 36. The small number is
one-third of the larger number. Find the two numbers.
Jerry and Tom had 36 marbles altogether. Jerry had
one-third as many marbles as Tom. How many marbles
did each boy have?
Jerry and Tom were going out to the playground to play
marbles. When they reached into their pockets they
pulled out all of their marbles and counted them.
Together they had 36 marbles. Jerry had one-third as
many marbles as Tom. How many marbles did each boy
have?
Honor Use of Home Language

Discuss problem in small groups using their dominate
language

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 one
way

Pressing for details- number heads together, come back to
answer question, don’t let them off the hook .
Plan Cooperative/Interdependent Groups to
Support Language

Think about how you group students

Use pairs that are mutually beneficial to each other’s
language development

Numbered heads together -Project GLAD
Helping our students…

Create a “Math Movie”

Visualize the problem then draw using the GLAD “Listen
and Sketch” strategy

Use “Model Drawing” to practice the Singapore problemsolving method

Gather ideas for supporting Migrant Student’s academic
language in Mathematics
Model Drawing Let’s Get StartedMoving from the Abstract to the Comprehensible

Learn the process or how to use model drawings to
solve word problems

Apply the process independently when solving word
problems
STEPS for Model Drawing…
1.
2.
3.
Teacher reads real world problem
Students listen and visualize the problem.
Students write down the key facts
a)
4.
5.
6.
7.
who, what, how
Students write a mmm statement
Teacher rereads and students sketch a diagram or bar
model
Students solve problem and show work
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 their
money together to buy a birthday
present for their mother. They had
$78.75 altogether. Ben had half as
much as Christy and Adrian had 4
times as much as Ben. How much
money did Christy contribute?
 Jose
collected ____ sports cards. He had
___ more baseball cards than football
cards. How many baseball cards did Jose
have?
 Mmm
Statement:
 Jose
collected 425 sports cards. He had
75 more baseball cards than football
cards. How many baseball cards did Jose
have?
 Mmm
Statement:
Listen and Sketch- Project GLAD
Baseball Problem
Understand the Problem:
Plan/Sketch:
Solve:
Check
Equation:
Answer Statement
Listen and Sketch- Project GLAD
Baseball Problem
Understand the Problem:
Jose
Plan/Sketch:
Jose’s Football Cards
Baseball Cards- 75 more
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’s
Flowers
D
3
D
D
S
+
Janet picked 5 flowers.
S
2 =
?
5
Addition- Continuous

One bag of lettuce weighed 14 ounces. Another bag
weighed 12 ounces. What was the total weight of the 2
bags of lettuce?
Subtraction

After selling ____ books, Michael had ___
books left. How many books did he have at
first?
After selling ____ books, Michael had ___ books
left. 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 jumping
jacks. 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 jumping
jacks. 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 Jumping
Jacks
8
Bitty’s Jumping 8
Jacks
8
8
8
Multiplication
Itty’s Jumping
Jacks
8
Bitty’s Jumping 8
Jacks
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 students
on a field trip. If only 4 students can ride in each car, how
many cars will Mr. Rodriquez need?
Division:

Mr. Rodriguez is finding drivers to take 17 of his students
on a field trip. If only 4 students can ride in each car, how
many cars will Mr. Rodriquez need?
Students
in cars
17
? # of Cars
Fractions

There is ½ of a candy bar that needs to be divided evenly
among 3 children. What fraction of the total candy bar
will each child receive?
Fractions (Mixed Operations)

Terra’s monthly allowance is $48. she puts ½ of her
allowance into savings and gives ¾ of the remaining
money to a local charity. How much money does Terra
have left for herself each month.
Ratios

The ratio of children to adults at the football game was
2:3. If there were 140 children at the football game, how
many adults were there?
Bridge to Algebra

Together Jasmine and Laura earned a total of $64
babysitting. If Jasmine earned $14 more than Laura, how
much money did each girl earn?
Sample Problem: Try It Again…

The sum of two numbers is 36. The small number is onethird 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 students
modifications that support math learning without
lessoning the rigor of math problems