Stretch your Mind Activity Model Drawing Schedule 8:30am -11:30am Break: 9:45am- 10:00am 1. Make a Name plate from the note card in front of you. Fold.

Stretch your Mind

Activity

Model DrawingSchedule

8:30am -11:30am

Break: 9:45am- 10:00am 1. Make a Name plate from the note card in front of you. Fold in half and write your name.

2.Work on the FRONT side only and solve the problems any way you choose. Show your work!!!

A PICTURE IS WORTH A

THOUSAND WORDS

Model DrawingAshlie Lord and Natalie Schwartz

Agenda

IntroductionWhy Before HowLearning to Model DrawClosing Assignment

Introduction

Purse/Wallet Activity:Something that reminds you of someone

important to you?Something that you cannot live without?Something that you got recently?

Why Before How

Write two strategies you use to teach word problems in your classroom on a post it note.

• Students struggle with word problems.• Many don’t even attempt them.• Abstract is hard for the students to see.

Lets Ta

lk

Strategies for Solving Word Problems

Guess and Check Look for a pattern Solve a simpler

problem Make a table, chart,

or list Use a picture,

diagram, or model

Act it out Work backwards Eliminate possibilities Use an equation or

formula

-MathMatters: an integrated approach

Concrete It’s of utmost importance for students

to have concrete experiences when solving word problems. At any level you can have your students act out word problems either using manipulatives or using students in the classroom.

We need 16 volunteers.(come up to the front)

At a Springfield Cardinals game, 15 people from the seats get to participate in the games between innings. One fifth of the people play musical chairs. One third of the remaining people participate in the tricycle race. How many people didn’t get to play those two games?

Those of you at your seats can use

the blocks to “act it out”

Concrete—Acting it Out

There are 16 tiles. ½ of the tiles are red. ¼ of the tiles are blue. The rest of the tiles are yellow. How many tiles are yellow?

Concrete—Using Manipulatives

In your classroom, milk the problems for all they are worth? How many tiles are blue? How do you know? What about red?

After you have organized your tiles to represent the problem, DRAW a model on your paper that represents the problem.

What is Model Drawing?

Model Drawing is the pictorial

representation in the concrete-

pictorial-abstract approach to

learning.

“Model drawing is a process of synthesis that a student goes through as they construct the model based on the information given in the problem, then he or she analyzes the model to develop a sequence of logical steps for the solution.”

- The Singapore Model Method

Advantages of Model Drawing

Helps students to:1. Develop proficiency in mathematics2. Understand fundamental mathematical concepts

such as fractions, ratios, and percentages3. Develop problem-solving skills4. Participate in conversation, debates, “math talk”5. Solve challenging word problems using the

student’s higher-level thinking skills.6. Develop visual thinking capabilities and algebraic

thinking.7. Write equations based on the models.

Lilly picked 3 apples in the morning and 2 apples in the afternoon. How many apples did Lilly pick altogether?

Pre Model Drawing

Stage 1

3 + 2 = 5Lilly picked ___ apples altogether.

Lilly’s Apples

5

Pre Model DrawingStage

2

__ + __ = __

Lilly picked ___ apples altogether.

Lilly’s Apples

3 2 5

5

Pre Model DrawingStage

3

__ + __ = __

Lilly picked ___ apples altogether.

Lilly’s Apples

3 2 5

5

Discrete Model—uses one-to-one correspondence (small #’s) 1 or 2 variables

Pre Model Drawing

morning

afternoon Still using just apples…one

variableLilly’s Apples

Lilly picked ___ apples altogether.

5

__ + __ = __3 2 5

Pre Model Drawing

Lilly ate 2 apples and 1 orange. What was the total number of pieces of fruit that Lilly ate? (2 variables)

Lilly’s Fruit

a o

3

__ + __ = __2 1 3

3Lilly picked ___ pieces of fruit.

Step-by-Step Model Drawing

1. Read the entire problem.2. Rewrite the question in sentence form,

leaving a space for the answer.3. Determine who and/or what is involved in

the problem.4. Draw the unit bar(s).5. Chunk the problem, adjust the unit bars,

and fill in the question mark.6. Correctly compute and solve the

problem.7. Write the answer in the sentence, and

make sure the answer makes sense.

Model Drawing—We do 4 Basic Problems

Mrs. Felton bought 11 feet of cloth for her front bulletin board, 8 feet of cloth for her side bulletin board and 22 feet for her back bulletin board. How many yards of cloth did Mrs. Felton buy? (addition, whole # continuous model)

Model Drawing—We do 4 Basic Problems

Jennifer has $54. Stephanie has $35. How much more money does Jennifer have than Stephanie? (subtraction, whole #, comparison model)

Model Drawing—We do 4 Basic Problems

Teachers at Glendale High School assign nine problems every school night in September. There are 21 school nights in September. How many total problems did the students work on during their evenings? (multiplication w/whole #’s)

Model Drawing—We do 4 Basic Problems

There are 23 students in a Drivers Ed classroom. If only three students can ride in each car, how many cars does the school need? (Division w/remainders)

Let’s Have YOU try ONE Work with your partner on ONE of the

problems and then take a break! Joey had 4 times as many

baseball cards in his collection as Bobby did. If they had 345 baseball cards altogether, how many more cards did Joey have than Bobby?

After selling 24 books, Miles had 53 books left. How many books did he have at first?

Fractions—I do/We do

The football coach gave Logan A BIG BOX of candy bars to sell. Logan sold 5/12 of his candy bars last week and 1/4 of his candy bars this week. He has 20 left to sell. How many did he start with?

Fractions—YOU do

Mary sold 1/4 of the raffle tickets last week and 2/3 of the raffle tickets this week. If she sold 24 raffle tickets this week, how many did she sell last week? How many does she have left to sell?

Fractions—I do/We do

Mary found ¼ of the fraction problems on her homework assignment have like denominators. 2/5 of the remainder have unlike denominators and the rest are problems using mixed numbers. There are 18 problems that use mixed numbers. How many problems are there altogether?

Fractions—YOU do

I traveled from Integer Park to Fraction Falls last week. I completed 4/5 of the distance in the morning and 3/4 of the remaining distance in the afternoon. I still had 3 miles to travel. What is the distance from Integer Park to Fraction Falls?

Fractions—I do/We do

If ¾ of a sum of money is $80.25, then how much would 2/5 of the same sum of money be?

Fractions—You do

Three-fifths of a sum of money is $861.30. What is 2/3 of that sum of money?

Fractions—I do/We do

Sara had 2/3 as much money as Caylee at first. After Caylee gave ½ of her money to Sara, Sara had $280. How much did Sara start with?

Fractions—You do

At first, Fiona had 2/5 as many books as Adam. After Adam gave Fiona 1/3 of his books, Fiona had 44. How many books did Adam have to begin with?

Brain Break!!!

Ratios—I do/We do

The ratio of the length of Taylor's banner to the length of Emily's banner is 5:8. Emily's banner is 36 inches longer than Taylor's banner. How long is Taylor's banner?

Ratios—You do

A group of eighth grade students voted for their favorite sport. 5 out of 11 students voted for football. The other students voted for hockey. There were a total of 66 votes. How many students voted for hockey?

Ratios—I do/We do

Larry and Antonio each have an mp3 player. The ratio of Larry's songs to Antonio's songs was 9:2. When Larry accidentally erased 32 songs from his mp3 player, Antonio had twice as many songs as his friend. How many songs did Larry have at first?

Ratios—You do

The ratio of Devin's money to Justin's money was 7:4 before Devin went to the store. After Devin spent $55 on DVDs, the ratio became 1:2. How much money did Devin have at first? (Assume every DVD is the same price.)

Percents—I do/We do

The Calculators and the Super Solvers have solved a total of 110 math puzzles. The Calculators solved 75% more puzzles than the Super Solvers. How many math puzzles has Calculators solved?

Percents—You do

My friend and I have 208 lollipops altogether. I have 60% more lollipops than my friend. How many lollipops do I have?

Percents—I do/We do

The Pet Emporium had 140 pets in its store. 60% of the pets were parrots. The rest were hamsters. When more parrots arrived later that day, the percentage of hamsters decreased to 25%. How many parrots were delivered to the pet shop?

Percents—You do

Get a Pet had 20 pets in its store. 70% of the pets were gerbils. The rest were guinea pigs. When more gerbils arrived later that day, the percentage of guinea pigs decreased to 10%. How many gerbils were delivered to the pet shop?

Web Resources

www.mathplayground.comwww.thinkingblocks.comhttp://www.teach-kids-math-by-model-

method.com/the-best-model-drawing-website.html

http://www.thesingaporemaths.com/

Closing Problem

Preview for December….

There are 73 children at the playground. 1/3 of the boys and 2/7 of the girls are swimming in the pool. If there are 22 kids in the pool in all, how many boys are there at the playground? How many girls are there at the playground? (Two Unknowns)

Closing Assignment

Please try these Model Drawing problems with your students….

There are Option 1/Option 2 worksheets for you to take home.

There are extra problems in the workbooks provided.

Bring student work (using Model Drawing) back in December to discuss.