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 5 th Grade Migrant Math Data

Migrant Math Data 5 th 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 AddSubtractLess MoreFootYard PlusSumCombine LeftWholeEven Odd

Helping students who are English Language Learners…  Social Language  Academic Language: Mean, Median, Mode? Ratio? CompareExplainPredict ConjectureExploreRepresent ConstructFormulateSolve DescribeInvestigateUse DevelopJustifyVerify

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. 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 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 bar model 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 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 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’s Flowers DDDSS ? = 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 4627 ?

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 8888

Multiplication Itty’s Jumping Jacks 8 Bitty’s Jumping Jacks 8888 ? 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 one- third of the larger number. Find the two numbers.

Opportunities for Further PD  September 20 th - 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