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Bar Diagrams and Equations for Problem Solving

Grade 2
Aug 22, 2023


Models to Solve Problems: 

Here are some models we use or make to represent/show problems:

  1. Arrays
  2. Bar diagram
  3. Drawing
  4. Equations

Then we use any strategy to find the sum.

Bar Diagram:

It shows parts and a whole.

Find the Sum

Here 28 & 29 are the parts.

And 57 is the whole.



An equation uses numbers and symbols.

28 + 29 = 57

Model to solve the problem: 

Example 1:

Betty had 18 shells in her pail. Jug gave her 27 more. How many shells did she have in her pail now?

solve the problem

Solution 1:


Bar diagram to model the problem.

Bar diagram
model the problem

Example 2:

19 books are in the blue bin and 27 books are in the green bin. The red bin has 18 more books than the blue bin. The yellow bin has 14 more books than the green bin.

  1. How many books were in the red bin?
  2. How many books are in the yellow bin?
Example 2

Solution 2 (a):

Number of books in the blue bin = 19

Let’s represent the total number of books in the red bin by an equation:

19 + 18 = ?

Use partial sums to solve the model 

Partial Sums

19 + 18 = 37

So, there are 37 books in the red bin.

Solution 2 (b):

Number of books in the green bin = 27

Let’s represent the total number of books in the yellow bin by an equation:

27 + 14 = ?

Use partial sums to solve the model 

solve the model

27 + 14 = 41

So, there are 41 books in the yellow bin.


  1. Jose has 28 chickens and 18 ducks. How many fowls does he have? Draw the bar diagram to model the question.
  2. Lino picked up 29 shells at the seashore in the morning and 24 shells in the afternoon. How many shells did he pick up in all? Draw the bar diagram to model the question.
  3. The food bank expected to recruit 60 volunteers. 34 men and 45 women signed up. How many volunteers were recruited? Write an equation to model the question.
  4. The bank opens 18 days in January and 21 days in February. If it will be open for 15 days in March, how many days is it open in these three months? Write an equation to model the question.
  5. A store had 40 boxes of pasta sauce in storage and received 47 more boxes last month. How many boxes of pasta sauce are there?
  6. A new movie theatre just opened downtown. In the theatre, the first cashier sold 28 tickets and the second cashier sold 13 tickets. Together with the 41 tickets sold online, how many tickets were sold?
  7. There are 32 candy bars. There are two boxes of candy bars in the storage room. If each box contains 24 candy bars, how many candy bars are there in total?
  8. On a bus, There were 23 girls and 18 boys on the bus. Together with the 2 teachers and the bus driver, how many people were on the bus?
  9. The store is open every day. Last week, 31 customers came in on Saturday, 28 customers came in on Sunday, and 41 customers came in on Monday. How many customers came in on the weekend?
  10. On a flight, there are three compartments for luggage and each compartment has a capacity of 25 pieces of luggage. The first two compartments are full and the last one contains 8 pieces of luggage. How many pieces of luggage are there?

Concept Map:

Model with Math
Bar Diagrams and Equations for Problem Solving


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