For any strategy instruction, students need to learn:
 What the strategy is
 How to use the strategy
 Why use the strategy
 When and where to use the strategy
Singapore Bar Model Intervention
Materials:
- Picture of the 4 models: part-whole for addition and subtraction, comparison for addition and
subtraction, part-whole for multiplication and division, comparison for multiplication and
division.
- Supply of one-step problems for addition, subtraction, multiplication and division.
Intervention:
1. Model several examples of part-whole bar model - talk aloud as you decide which part goes in the bar
model
2. Guide the student through several problems using the part-whole model
3. Provide the student with problems to complete independently, but monitor their work and if they do not
use the model correctly, then stop and model using the picture and thinking aloud, then guide the student
through at least one problem, then try independent practice again.
a. If the student still cannot do the model correctly, then:
i. Teacher models 3 problems
ii. Guide student through 3 problems
iii. Try independent practice again
b. If the student still cannot do the independent practice with 90% accuracy, then continue with
daily models and guided practice until the student can do the guided practice largely on their
own. Then try independent practice again.
4. When student can use the model correctly in independent practice with 90% accuracy, it is time to
introduce the Comparison Model for Add & Sub. Repeat steps 1-3 with the Comparison Model for
Addition and Subtraction.
5. When the student is 90% accurate in the Comparison model, introduce practice work that has both partwhole for add & sub and comparison for add & sub problems mixed. Guide student in distinguishing
when to use each model.
6. When student is 90% accurate in determining which model to use in mixed practice, then it is time to
introduce Part-Whole for Multiplication and Division. Repeat steps 1 through 3 with the part-whole for
mult and div.
7. When the student can complete the part-whole for mult and div with 90% accuracy it is time to
introduce mixed practice using all three models (part-whole for add & sub, comparison for add & sub,
and part-whole for mult and div). Pay special attention to when to use part-whole for add and sub versus
part-whole for mult and div – when we are talking about many groups of equal size it’s part-whole for
mult and div.
8. When the student can do independent practice of the 3 models mixed, then it is time to introduce the last
model - comparison for mult and div. Follow steps 1 through 3 for the comparison model for mult and
div.
9. When the student is 90% accurate at using the comparison model for mult and div, then introduce mixed
practice of all 4 models.
Englard, L. (2010). Raising the Bar on Problem Solving, Teaching Children Mathematics, Vol. 17 (3), 156-163.
166
10. When the student can complete mixed practice of all four models on one-step problems, introduce how
to use the models in multi-step problems.
Student:
Teacher:
Date:
School Year:
Observer:
The observer may not see all the parts outlined below, however, these are the key ingredients to the
effectiveness of this intervention. Observer should check the parts that apply to the date they observe and mark
the other parts as NO – not observed on this date. The person implementing the intervention needs to ensure that
all of the below parts are followed.
Singapore Bar Model Intervention – Integrity Checklist
Yes
No
Teacher modeled at least 3 examples for student.
Teacher did thinking aloud as worked through examples.
Teacher referred to picture of model.
Teacher stated:
 what the strategy is,
 how to use it,
 why student should use it,
 when the strategy should be used – when do I use the part-whole add &
sub versus the comparison for add & sub; when do I use the part-whole for
add& sub versus the part-whole for mult & div; when do I use the
comparison for add & sub versus the comparison for mult & div.
Teacher did guided practice with the student.
Teacher asked student questions through guided practice to encourage student to
take over process such as – what do we do next; where does that value fit in the
model; which part is going to be the bigger part, smaller part; what operation do
we need to do?
Student completed independent practice with 90% accuracy.
Teacher monitored student independent practice.
If student did not complete independent practice with 90% accuracy teacher
followed up with more modeling and guided practice.
If student did not complete independent practice with 90% accuracy teacher
continued modeling and guided practice over several days.
Teacher provided mixed practice after student learned models 2, 3, and 4.
Student achieved 90% accuracy in using a model before moving to mixed
practice.
Student achieved 90% accuracy in mixed practice before learning new model.
Englard, L. (2010). Raising the Bar on Problem Solving, Teaching Children Mathematics, Vol. 17 (3), 156-163.
167
Part-Whole Model (Add & Sub)


To find a whole, add the parts.
To find a missing part, subtract the
known part from the whole.
Englard, L. (2010). Raising the Bar on Problem Solving, Teaching Children Mathematics, Vol. 17 (3), 156-163. 168
Comparison Model (Add & Sub)



To find the larger quantity, add the smaller quantity and the
difference.
To find the difference, subtract the smaller quantity from the
larger quantity.
To find the smaller quantity, subtract the difference from the
larger quantity.
Englard, L. (2010). Raising the Bar on Problem Solving, Teaching Children Mathematics, Vol. 17 (3), 156-163. 169
Part-Whole Model (Mult & Div)


To find the whole, multiply the part by the number of
equal partitions in the whole.
To find the part, divide the whole by the number of
equal partitions it contains.
Englard, L. (2010). Raising the Bar on Problem Solving, Teaching Children Mathematics, Vol. 17 (3), 156-163. 170
Comparison Model (Mult & Div)


To find x, multiply y by three.
To find y, divide x by three.
Englard, L. (2010). Raising the Bar on Problem Solving, Teaching Children Mathematics, Vol. 17 (3), 156-163. 171