201 NCSM & NCTM Presentation with Lauri Susi of ConceptuaMath. Description: These visual components sit at the intersection of Common Core, Singapore Math, and now technology! Learn why this visual model for word problems is so powerful, try some problems from the simple to the complex, and investigate web-based programs and iPad apps that will help anyone incorporate this effective strategy into their classrooms.

1. Strip Models, Tape Diagrams,
Bar Models, Oh My!
Cassy Turner
Lauri Susi
SingaporeMathSource.com

2. What is a Tape Diagram?
“A drawing that looks like a segment of
tape, used to illustrate number
relationships. Also known as a strip
diagram, bar model, fraction strip, or
length model.”
-CCSS Glossary

3. Like this?
Progression statements

4. How about C-P-A Sequence?
Concrete
?
Abstract
Pictorial
7 + 3 =

5. How about C-R-A Sequence?

6. Forms of Bar Models
Part-Whole
Comparison
10
6 ?
106
?

7. Addition & Subtraction Situations
10
6 ?

8. Models for Add To:
Two bunnies sat on the grass. Three more bunnies
hopped there. How many bunnies are on the
grass now?
Results Unknown

9. Models for Add To:
Two bunnies sat on the grass. Some more bunnies
hopped there. Then there were five bunnies. How
many bunnies hopped over to the first two?
Change Unknown

10. Models for Add To: Start Unknown
Some bunnies sat on the grass. Three more bunnies
hopped there. Then there were five bunnies. How
many bunnies were on the grass at first?

11. Models for Take From:
Five apples were on the table. I ate two apples.
How many apples are on the table now?
Results Unknown

12. Models for Take From:
Five apples were on the table. I ate some apples.
Then there were 3 apples. How many apples are
on the table now?
Change Unknown

13. Models for Take From: Start Unknown
There were some apples were on the table. I ate
2 apples. Then there were 3 apples on the table.
How many apples were on the table at first?

15. PARCC Grade 3
Patricia needs to read for 120 minutes each week.
• She read for 26 minutes on Monday
• She read for 39 minutes on Tuesday
• She read for 38 minutes on Thursday
How many more minutes does Patricia need to read this week?

16. PARCC Grade 3
Patricia needs to read for 120 minutes each week.
• She read for 26 minutes on Monday
• She read for 39 minutes on Tuesday
• She read for 38 minutes on Thursday
How many more minutes does Patricia need to read this week?
Monday
150 minutes in all
Minutes left?
?26
Tuesday Thursday
39 38

17. Fractions
There were 48 chocolates in a box. After eating
some of them, Tara found that she had
5
8
of the
chocolates left. How many chocolates did she eat?

19. Addition & Subtraction Situations10
6
?

20. Models for Compare

21. Models for Compare: Difference Unknown
Lucy has two apples. Julie has five apples. How
many more apples does Julie have than Lucy?
How many fewer?

23. Models for Compare: Bigger Unknown
Lucy has 3 fewer apples
than Julie. Lucy has 2
apples. How many apples
does Lucy have?
Julie has 3 more apples
than Lucy. Lucy has 2
apples. How many apples
does Julie have?
2
?
3
Julie
Lucy
2
?
3
Julie
Lucy

24. Models for Compare: Smaller Unknown
Lucy has 3 fewer apples
than Julie. Julie has 5
apples. How many apples
does Lucy have?
Julie has 3 more apples
than Lucy. Julie has 5
apples. How many apples
does Lucy have?
?
5
3
Julie
Lucy
?
5
3
Julie
Lucy

25. SBAC Grade 3
A pencil has a mass of 25 grams. An apple has a
mass that is 75 grams more than the pencil. What is
the mass of the apple?
apple
?
75 g
25 g
pencil 25g

27. Multiplication & Division Situations
10
5 ?

28. Models for Multiplication & Division: Equal groups
There are 3 bags with 6
plums in each bag. How
many plums are there in
all?
You need 3 lengths of
string, each 6 inches long.
How much string will you
need altogether?
? in all
6 in
each bag

29. Multiplication & Division: How many in a group?
If 18 plums are shared
equally into 3 bags,
then how many plums
will be in each bag?
You have 18 inches of
string, which you will cut
into 3 equal pieces. How
long will each piece of
string be?
18
?
plums

30. Multiplication & Division:How many groups?
If 18 plums are to be
packed 6 to a bag,
then how many bags
are needed?
You have 18 inches of
string, which you will cut
into pieces that are 6
inches long. How many
pieces of string will you
have?

31. Adding Fractions
James bought a bag of sourballs.
1
4
of the sourballs
were cherry,
1
8
were apple and
1
5
of the remainder
were blueberry. If there were 24 blueberry
sourballs, how many sourballs did he buy?

32. Multiplication & Division Situations15
?

33. Multiplication & Division Comparison: Equal groups
A blue hat costs $6. A
red hat costs 3 times as
much as the blue hat.
How much does the red
hat cost?
A rubber band is 6 cm
long. How long will the
rubber band be when it is
stretched to be 3 times as
long?
$6
?
red hat
blue hat

34. Multiplication & Division Comparison: Equal groups
A blue hat costs $6. A
red hat costs 3 times as
much as the blue hat.
How much does the red
hat cost?
A rubber band is 6 cm
long. How long will the
rubber band be when it is
stretched to be 3 times as
long?
?
At first
In the end
6cm

37. Comparison:
A red hat costs $18 and
that is 3 times as much as
a blue hat costs. How
much does a blue hat
cost?
A rubber band is stretched
to be 18 cm long and that
is 3 times as long as it was
at first. How long was the
rubber band at first?
?
$18
red hat
blue hat
How many in a group?

38. Comparison:
A red hat costs $18 and
that is 3 times as much as
a blue hat costs. How
much does a blue hat
cost?
A rubber band is stretched
to be 18 cm long and that
is 3 times as long as it was
at first. How long was the
rubber band at first?
?
How many in a group?
At first
In the end
18 cm

39. Comparison:
A red hat costs $18 and
a blue hat costs $6. How
many times as much does
the red hat cost as the
blue hat?
A rubber band was 6 cm
long at first. Now it is
stretched to be 18 cm long.
How many times as long is
the rubber band now as it
was at first?
How many in a group?

40. Mixed Operations
40

41. Multi-step fraction models
A wading pool is half filled with water. When
12 more gallons of water are added, the pool
is
7
8
full. How many gallons of water can the
wading pool hold?

42. ?
12 gallons
The wading pool can
hold 32 gallons.
3 ⃞ = 12 gal
1 ⃞ = 12 gal ÷ 3
= 4 gal
8 ⃞ = 4 gal x 8 units
= 32 gal
A wading pool is half filled with water. When 12
more gallons of water are added, the pool is
7
8
full.
How many gallons of water can the wading pool
hold?

43. On a shopping trip, Joonha spends
1
3
of his money at the Sports Plus. He
then spends
1
3
of the money he has left at Target. Finally, he spends his
remaining $40 on a video game. How much money did Joonha have at
first?
Sports Plus
Target $40 video game
?
$60
Joonha had $90 at first.
2 ⃞ → $40
1 ⃞ → $40÷2=$20
3 ⃞ → $20x3=$60
2 ⃞ → $60
1 ⃞ → $60÷2=30
3 ⃞ → $30x3=90

46. Questions?
Bit.Ly/barmodeltool

47. Cassy Turner
Cassy@SingaporeMathSource.com
Handout:
singaporemathsource.com/resources/handouts
Lauri Susi
lsusi@conceptuamath.com
ConceptuaMath.com