Solve One-step and Two-step Problems With Bar Diagrams

Introduction:

In the previous session, we used different strategies to find the sum of 2-digit numbers. In this session, we solve one-step and two-step problems by representing them as bar diagrams and equations.

Let’s understand bar diagrams in brief:

Bar Diagram:

It represents the problem in visual form in which it is easy to identify the whole and the parts.

We know that the sum of 35 and 15 is 50. 

Let’s represent the sum by a bar diagram.

Here 35 and 15 are parts of the bar diagram.

And 50 is the whole of the bar diagram.

Bar Diagram or Equation:

Let’s represent the situation in the form of a bar diagram or an equation.

Example:

Amy has 24 apples in her basket. Emerson has 19 apples in her basket. In all, they have 43 apples in the basket. Represent this situation in the form of a bar diagram or an equation.

Solution:

Number of apples with Amy = 24

Number of apples with Emerson = 19

The total number of apples with both Amy and Emerson = 43.

Bar Diagram:

Equation:

24 + 19 = 43.  

One-step Problem:

Let’s solve the one-step problem.

Example:

Carrie has 34 more crayons than Hannah. Hannah has 48 crayons. How many crayons are there with Carrie?

Solution:

Number of crayons with Hannah = 48

Carrie has 34 more crayons than Hannah.

The total number of crayons with Carrie = the sum of 48 and 34.

Let’s represent the problem with a bar diagram:

Equation:

48 + 34 =?

Break apart 34 into tens and ones. Then add.

48 + 30 = 78

78 + 2 = 80

80 + 2 = 82

48 + 34 = 82.

So, Carrie has 82 crayons.

Two-step Problem:

Let’s solve a two-step problem.

Example:

Drew read 23 books in the library. Franco read 6 fewer books than Drew. Lee read 9 more books than Drew. How many books did each person read?

Solution:

Step 1:

23 – 6 = 17

So, Franco read 17 books.

Step 2:

23 + 9 = 32

So, Lee read 32 books.

Books read by Drew = 23

Books read by Franco = 17

Books read by Lee = 32

Exercise:

1. A cookie jar is sitting on the high shelf. Francesca stands on a pile of 10 couch pillows and 13-bed pillows to reach it. Francesca used a total of 23 pillows to reach the cookie jar. Represent the given statement with an equation.
2. The green team has 16 more points than the red team. The red team has 14 points, and the green team has 30 points. Represent the given statement by using a bar diagram.
3. Steve sees 26 birds in a tree. Hailey sees 23 birds in a tree. Steve and Hailey see 49 birds in all. Represent the given statement by using a bar diagram.
4. Linda’s mother made 17 ham sandwiches and 23 jelly sandwiches. She made 40 sandwiches in all. Represent the given statement with an equation.
5. Shawn catches 14 fish. Then he catches 18 more fish. How many fish does Shawn have now?
6. Stacy drew 23 stars with crayons. Then she drew 13 more stars. Tara drew 40 stars. How many more stars did Tara draw than Stacy?  
7. Austin has 38 Pokémon cards. Bryan gave him 25 Pokémon cards. How many Pokémon cards does Austin have now?
8. There are 23 chickens in the yard. There are 19 chickens in the barn. How many chickens are there in all?
9. Scott has 18 pens. He bought 11 new pens. Then he finds 15 more pens. How many pens does Scott have now?
10. Toby walks 13 miles. Wilson walks 7 fewer miles than Toby. Nick walks 5 more miles than Wilson. How many miles did each person walk?

Concept Map:

What We Have Learned

• Use drawings and equations to represent problems.
• Solve one-step and two-step problems.