Solve Two-step Problems Using Equations

Introduction:

For any problem, these steps need to be performed:

1. Model the problem using an equation or bar diagram.
2. Solve the problem with any strategy.

Model Two-Step Problem:

Example:

There are 27 butterflies in the garden. After some time, 12 butterflies fly away. 15 more butterflies joined the group. How many butterflies are there in the garden? Model the problem using a bar diagram and equation.

Solution:

Model the first step of the problem by using a bar diagram.

Model the first step of the problem by using an equation.

Model the second step of the problem by using a bar diagram.

Model the second step of the problem by using an equation.

Solve the Two-Step Problem:

Example:

Larry has 27 red bows and 15 green bows in a box. He used 24 bows for presents. How many bows are left in the box?

Solution:

Step 1:

Red bows = 27

Green bows = 15

Total number of bows in a box = The sum of 27 & 15

Let’s represent the word problem by an equation:

27 + 15 = ?

By using partial sums:

27 + 15 = 42

There are 42 bows in the box.

Step 2:

Total bows in a box = 42

Bows used for present = 24

Remaining bows in a box = The difference of 42 & 24

Let’s represent the word problem by an equation:

42 – 24 = ?

Let’s subtract to find the answer.

42 – 24 = ?

Since 24 = 22 + 2, we can subtract 22 first and then 2.

42 – 22 = 20

20 – 2 = 18

So, there are 18 bows left in the box.

Exercise

1. Identify the equation that has a sum.

a. 34 – 19 = 15

b. 91 – 23 = 68

c. 33 + 28 = 61

d. 67 – 29 = 38

2. Identify the equation that has a difference.

a. 54 + 11 = 65

b. 85 – 35 = 50

c. 43 + 31 = 74

d. 21 + 12 = 33

3. Write an equation that has a sum.

4. Write an equation that has a difference.

5. Bella picked 23 oranges and then 15 more. She gave 12 oranges to Callie. How many oranges does Bella have now?

6. Write the equation: “Lee caught 32 fish and threw back 13 fish back. How many fish does Lee have now?”

7. Clark found 35 shells on Thursday and 26 more shells on Friday. He found 12 more shells on Saturday. How many shells did he have in all?

8. Luke buys 23 color pens and then 25 more. He gives 17 color pens to Neil. How many color pens does Luke have now?

9. Raina has 43 photos in her album. She adds 38 photos. Then Raina takes out some photos in the album. Now she has 62 photos. How many photos did Raina take out?

10. The elves made 44 toys last night and 37 toys today. They were wrapping the toys up and a box fell, and 15 toys got broken. How many toys are left?

Concept Map:

What We Have Learned

• Model two-step problems using equations.
• Solve two-step problems.