Step By Step Model DrawingDiscover 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 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 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 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 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 ProblemsScaffolding the Language of a problem

A. The sum of two numbers is 36. The small number is one-third of the larger number. Find the two numbers.

B. Jerry and Tom had 36 marbles altogether. Jerry had one-third as many marbles as Tom. How many marbles did each boy have?

C. 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 problem-solving method

Gather ideas for supporting Migrant Student’s academic language in Mathematics

Model Drawing Let’s Get Started-Moving 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. Teacher reads real world problem2. Students listen and visualize the problem. 3. Students write down the key facts

a) who, what, how

4. Students write a mmm statement5. Teacher rereads and students sketch a

diagram or bar model6. Students solve problem and show work7. Students write equations and rewrite

statement

STEPS for Model Drawing…Listen and Sketch- Project GLAD1. 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 GLADBaseball Problem

Understand the Problem: Plan/Sketch:

Solve: CheckEquation:

Answer Statement

Listen and Sketch- Project GLADBaseball Problem

Understand the Problem:Jose

Baseball Cards- 75 moreFootball 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’s Flowers

D D D S S ?

3 + 2 = 5

Janet picked 5 flowers.

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 Jacks

8 8 8 8

Multiplication

Itty’s Jumping Jacks

8

Bitty’s Jumping Jacks

8 8 8 8

?

8 x 5 = 40Itty 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 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 students modifications that support math learning without lessoning the rigor of math problems