Model Drawing Examples

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Model Drawing Examples

• Grade 1

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Model Drawing Procedure

• Developed in Singapore
• Visual representation of details and actions
  which assists children with problem solving
• Helps children logically think using visual
  models to determine their computations

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Model Drawing Procedure

• Teaches the importance of language within math
  problems
• Provides foundation for algebraic understanding
• Provides for differentiated instruction

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Model Drawing Procedure

• Fosters quantitative reasoning (number sense)
  when teachers question
• Empowers students to think systematically and
  master more difficult problems
• Makes multi-step and multi-concept problems easy
  to work

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Model Drawing does NOT

• Work on every problem
• Specify ONE RIGHT model
• Specify ONE RIGHT operation

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Areas for Use of Model Drawing Procedure in Grade
1

• Whole Number Operations
• Addition
• Subtraction
• Multi-operations

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Use Model Drawing in Four-Step Process
Step 2
Step 1

• Main Idea of Question

Step 4
Step 3

• Describe how the problem was solved.

• Work the computation (s).

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Four Step Process

• Main Idea
• Read the problem.
• Write the main idea in the question.
• Details
• Write who the problem is about (related to main
  idea.)
• Write what the problem is about (related to main
  idea.)
• Draw unit bars of equal length.
• Re-read the problem one sentence at a time
  adjusting the unit bars to match the story and
  identify the question on the model.
• Strategy
• Work the computation (s).
• How
• Describe how the problem was solved.

Model Drawing
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Put Together
Addition
10
Ann has 2 toys. Jeff has 3 toys. How many toys
do they have together?
Ann has 2 toys.
Jeff has 3 toys.
How many toys do they have together?
Step 1
Step 2
2

Ann Jeff
toys toys
1
1
Toys together
?
3
1
1
1
Step 4
Step 3
2 3
Add 2 and 3.
5
First Grade
11
Andy and Henry went to the zoo.
Andy saw 4 .
Henry saw 5 .
How many animals did the 2 boys see?
Details
Main Idea
4

Andy Henry
1
1
1
1
Animals seen
?
5
1
1
1
1
1
Strategy
How
4 5
Put together 4 and 5 to get a sum of 9.
9
First Grade
12
Take Away
Subtraction
13
Ann has 4 toys. She gave away 1 toy. How many
toys are left?
She gave away 1 toy.
Ann has 4 toys.
How many toys are left?

Step 1
Step 2
4
X
Ann
toys
1
1
1
1
Toys left
?
Step 4
Step 3
4 - 1
Subtract 1 from 4.
3
First Grade
14
(No Transcript)
15
Ann has 4 toys. Jeff has 1 toy. How many more
toys does Ann have than Jeff?
Jeff has 1 toy.
Ann has 4 toys.
How many more toys does Ann have than Jeff?
Step 1
Step 2

4
Ann Jeff
toys toys
1
1
1
1
More toys Ann than Jeff
?
1
1
Step 4
Step 3
4 - 1
Subtract 1 from 4.
3
First Grade
16
Anabel bought 3 at the carnival.
Leo bought 4 at the carnival.
How many more were bought than ?
Main Idea
Details
3
1
1
Anabel Leo
1
more ice cream than apples

?
4
1
1
1
1
How
Strategy
4 - 3
Compared 3 to 4 to get 1.
1
First Grade
17
Ann has 2 toys. Jeff has 4 toys. How many more
toys does Jeff have than Ann?
Ann has 2 toys.
Jeff has 4 toys.
How many more toys does Jeff have than Ann?
Step 1
Step 2
2
Ann Jeff
toys toys
1
1
More toys Jeff than Ann
4
1
1
1
1

?
Step 4
Step 3
4 - 2
Subtract 2 from 4.
2
First Grade
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(No Transcript)
19
Ann has 5 balls. Three are baseballs. The rest
are footballs. How many are footballs?
The rest are
Ann has 5 balls.
Three are baseballs.
How many are footballs?
footballs.

Step 1
Step 2
5
Ann
balls
1
1
1
1
1

footballs
?
3 BB
FB
Step 4
Step 3
5 - 3
Subtract 3 from 5.
2
First Grade
20
Carlos had 11 coins in his pocket. Eight coins
were quarters and the rest were dimes. How many
coins were dimes?
Carlos had 11 coins in his pocket.
Eight coins were quarters and
the rest were dimes.
How many coins were dimes?

Main Idea
Details
11

Carlos
coins
1
1
1
1
1
1
1
1
1
1
1
coins dimes
D
Q
?
Strategy
How
Found the difference of 11 and 8.
11 - 8
3
First Grade
21
Put Together and Take Away
Addition and Subtraction
22
Lisa had 8 marbles. On Monday, she gave 3 away
and on Tuesday she gave away 2 more. How many
marbles does she have left?
On Monday, she gave 3 away
Lisa had 8 marbles.
and on Tuesday she
How many marbles does she have left?
gave away 2 more.
Step 2
8
Step 1
marbles
X
Lisa
1
1
1
1
1
1
X
X
1
1
X
X

marbles left
?
Step 4
Step 3
3 2
8 - 5
Add 3 and 2. Subtract 5 from 8.
3
5
First Grade
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Extra Information

• If a child understands that the details are what
  is needed to answer the main idea of the
  question, he will NOT include the extra
  information in the details.
• Try to keep students focused on what the question
  is asking them to find.
• However, if the child includes the extra
  information in the drawing, placing the ? in the
  model will help them understand that the extra
  information is NOT needed.

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Hold These Thoughts

• In first grade, be sure all the unit bars for
  each variable are touching each other so
  comparisons are clearer.
• At the beginning of first grade, show one unit
  for each item. Modeling each part of the model
  drawing with unifix cubes concretely represents
  the picture that is being drawn.
• In the drawing, list the variables in the order
  they appear in the problem.
• To show take away, mark off the appropriate unit
  bar segments and draw a X.
• Including labels helps clarify drawings.

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Hold These Thoughts

• Unit bars need to be proportional. Make sure
  that the bar of 25 is not larger than the bar of
  30.
• Continuously asking students to describe how the
  unit bars should be adjusted, connecting the
  adjustment to the vocabulary in the sentence
  improves students number sense and reasoning.
• You can always adjust the size of a unit bar as
  you learn more information. When you lengthen
  the bar, it means the number is larger, and when
  you shorten the bar, it means the number is
  smaller.
• If there is more than one number given in a
  sentence, adjust the model one number at a time.
  Break long sentences into partsand or commas.
• Too often, students rush through a problem and
  answer the wrong question. Placing the question
  mark helps to prevent that.

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Hold These Thoughts

• The computation is the differentiated part of the
  lesson. The model looks the same for all
  students, but the way they achieve success with
  computation is differentiated. No matter how you
  calculate it, the answer is the same! This is
  very important for students to see.
• Draw a dotted line between unit bars to point out
  segments of equal value.
• Dont get distracted looking for extraneous
  information. Focus on what the question is
  asking you to find.
• When a problem says, three times as many add
  one unit bar at a time. Otherwise, many students
  will add three MORE unit bars instead of adding
  just two.

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Model Math Art
_______________ Is certified as a Model Math
Artist.
__________Teacher Name
__________ Date