Transcript 9 Steps to Model Drawing

Why Bar Models?
- Makes an abstract word problem or equation pictorial. (Concrete → Pictorial → Abstract)
- Allows for deeper analysis and understanding of the problem by teaching students to:
Identify all information given and its relationship to other pieces of
information
Identify missing information that needs to be found
Understand what mathematical operation needs to take place
- Bar modeling is a very versatile strategy! It can be used for problems involving:
Addition, subtraction, multiplication, division, fractions, decimals, percentages, ratios
- Bar modeling trains students to think algebraically.
“develops students’ visual thinking capabilities and algebraic thinking and reinforces
higher level thinking.”
9 Steps to Model Drawing
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READ the entire problem.
REPHRASE the question into a statement.
WHO is involved in the problem?
WHAT is involved in the problem?
Draw BAR(s).
Read each sentence ONE at a time.
LABEL bar(s) and write a question mark for the unknown.
Write an EQUATION and a NUMBER BOND.
Write the answer in the blank to complete the statement.
Try a problem!
One number is 1/3 of another number. If the
difference between the numbers is 26, find
the two numbers.
1st Grade
Mike had 8 big blocks and 6 small blocks in a basket. How many blocks are there in the basket?
14 blocks in the basket.
There are ________
8+6=14
9 Steps to Model Drawing
Mike’s
Blocks
8
Big
6
Small
?
1. READ the entire problem.
2. REPHRASE the question into a statement.
3. WHO is involved in the problem?
4. WHAT is involved in the problem?
5. Draw BAR(s).
6. Read each sentence ONE at a time.
7. LABEL bar(s) and write a question mark for
the unknown.
8. Write an EQUATION and a NUMBER BOND.
9. Write the answer in the blank to complete
the statement.
1st Grade
John has 15 marbles. 4 of them are outside the bag. How many marbles are there in the
bag?
11
There are ________ marbles in the bag.
15-4=11
9 Steps to Model Drawing
John’s
marbles
?
in
4
out
15
1. READ the entire problem.
2. REPHRASE the question into a statement.
3. WHO is involved in the problem?
4. WHAT is involved in the problem?
5. Draw BAR(s).
6. Read each sentence ONE at a time.
7. LABEL bar(s) and write a question mark for
the unknown.
8. Write an EQUATION and a NUMBER BOND.
9. Write the answer in the blank to complete
the statement.
1st Grade
Mary has 11 storybooks. She has 2 more storybooks than Sally. How many storybooks does
Sally have?
9
Sally has ________ storybooks.
11
11-2=9
9 Steps to Model Drawing
Mary’s
storybooks
Sally’s
storybooks
2
?
?
1. READ the entire problem.
2. REPHRASE the question into a statement.
3. WHO is involved in the problem?
4. WHAT is involved in the problem?
5. Draw BAR(s).
6. Read each sentence ONE at a time.
7. LABEL bar(s) and write a question mark for
the unknown.
8. Write an EQUATION and a NUMBER BOND.
9. Write the answer in the blank to complete
the statement.
3rd Grade
Pam has 4 times as much money as Kurt. If Pam has $30 more than Kurt, how much money
do they have in all?
$50
They have ________
money in all.
a) 1 unit, 30 ÷ 3=10
Pam’s
money
10
10
10
$30
Kurt’s
money
10
b) Pam+ Kurt,
40 + 10 = 50
10
?
9 Steps to Model Drawing
1. READ the entire problem.
2. REPHRASE the question into a statement.
3. WHO is involved in the problem?
4. WHAT is involved in the problem?
5. Draw BAR(s).
6. Read each sentence ONE at a time.
7. LABEL bar(s) and write a question mark for
the unknown.
8. Write an EQUATION and a NUMBER BOND.
9. Write the answer in the blank to complete
the statement.
5th Grade
Peter has twice as many stickers as Joe. Joe has 20 less stickers than Emily. They have 300
stickers altogether. How many stickers does Peter have?
Peter has ________ stickers.
a) 300 – 20 = 280
Peter’s
stickers
70
Joe’s
stickers
70
Emily’s
stickers
70
70
b) 280 ÷ 4 = 70 (1 unit)
?
9 Steps to Model Drawing
C) Peter 70 x 2 = 140
300
20
1. READ the entire problem.
2. REPHRASE the question into a statement.
3. WHO is involved in the problem?
4. WHAT is involved in the problem?
5. Draw BAR(s).
6. Read each sentence ONE at a time.
7. LABEL bar(s) and write a question mark for the
unknown.
8. Write an EQUATION and a NUMBER BOND.
9. Write the answer in the blank to complete the
statement.
5th Grade
There are 3 pieces of rope. Rope A is 3 times as long as Rope B. Rope C is 10.4 cm longer
than Rope A. The total length of all 3 ropes is 116.1 cm. How long is Rope C?
55.7
Rope C is ________cm
long.
a) 116.1 - 10.4 = 105.7
b) 105.7 ÷ 7 = 15.1 (1 unit)
Rope A
15.1
Rope B
15.1
Rope C
15.1
15.1
15.1
c) Rope c =
(15.1x3) + 10.4 = 55.7
116.1
15.1
15.1
10.4
?
9 Steps to Model Drawing
1. READ the entire problem.
2. REPHRASE the question into a statement.
3. WHO is involved in the problem?
4. WHAT is involved in the problem?
5. Draw BAR(s).
6. Read each sentence ONE at a time.
7. LABEL bar(s) and write a question mark for
the unknown.
8. Write an EQUATION and a NUMBER BOND.
9. Write the answer in the blank to complete
the statement.
5th Grade
Betsy made cupcakes for the class party. 1/3 of the cupcakes were chocolate. 2/5 of the
remaining were vanilla and the remaining 12 cupcakes were strawberry. How many cupcakes
did Betsy make in all?
30
Betsy made ________cupcakes
in all.
20
Betsy’s
cupcakes
a) 12 ÷ 3 = 4
b) 5 x 4 = 20
10
chocolate
10
4 4
4
Vanilla
?
10
4
4
Strawberry
4
c) 10 x 3 = 30
9 Steps to Model Drawing
1. READ the entire problem.
2. REPHRASE the question into a statement.
3. WHO is involved in the problem?
4. WHAT is involved in the problem?
5. Draw BAR(s).
6. Read each sentence ONE at a time.
7. LABEL bar(s) and write a question mark for the
unknown.
8. Write an EQUATION and a NUMBER BOND.
9. Write the answer in the blank to complete the
statement.
5th Grade
The ratio of Carla’s postcards to Juan’s postcards was 2:5. If together they had a total of 35
postcards, how many more postcards did Juan have than Carla?
15 more postcards than Carla.
Juan had ________
a) 35 ÷ 7 = 5 (1 unit)
Carla’s
postcards
5
b) 5 x 3 = 15
?
5
9 Steps to Model Drawing
35
Juan’s
postcards
5
5
5
5
5
1. READ the entire problem.
2. REPHRASE the question into a statement.
3. WHO is involved in the problem?
4. WHAT is involved in the problem?
5. Draw BAR(s).
6. Read each sentence ONE at a time.
7. LABEL bar(s) and write a question mark for the
unknown.
8. Write an EQUATION and a NUMBER BOND.
9. Write the answer in the blank to complete the
statement.
One number is 1/3 of another number. If the difference between the numbers is 26, find the two
numbers.
13
39
The two numbers are ________
and _________.
a) 26 ÷ 2 = 13 (1 unit)
b) Num. 1 = 13
Num . 2 (13x3 =39)
Number 1
13
9 Steps to Model Drawing
26
Number 2
13
13
13
1. READ the entire problem.
2. REPHRASE the question into a statement.
3. WHO is involved in the problem?
4. WHAT is involved in the problem?
5. Draw BAR(s).
6. Read each sentence ONE at a time.
7. LABEL bar(s) and write a question mark for the
unknown.
8. Write an EQUATION and a NUMBER BOND.
9. Write the answer in the blank to complete the
statement.