How to Solve Two-step Mixed Operation Word Problems?如何解兩步混合運(yùn)算應(yīng)用題？

It is easy for students in Grade Three to do mixed operation， as long as they have mastered the calculating orders of doing mixed operation. For example，

53-28 ÷4 + 36

= 53-7 + 36

= 46 + 36

=82

However， it is not so easy for some students in Grade Three to do mixed operation of word problems. Why? Because many of them have not mastered the strategies and skills of solving word problems. But it is quite important for students to master the strategies and skills of solving word problems.

Firstly， the most important is to read word problems very carefully， underline the key words and get clear what you need to find out.

Secondly， as for solving two-step mixed operation word problems， the following strategies and skills are practical and helpful for primary school students.

1. Listing tables

Let's take the word problem below as an example.

Zhang Hua buys a toy monkey and 3 bottles of mineral water. The toy monkey costs 12 yuan and each bottle of the mineral water costs 2 yuan. How much does Zhang Hua spend in total?

What does this word problem tell us? It mainly tells the information below:

a. Zhang Hua buys a toy monkey and 3 bottles of mineral water.

b. The toy monkey costs 12 yuan.

c. Each bottle of the mineral water costs 2 yuan.

d. The question is that how much Zhang Hua spends in total.

If you are clear about the above， you can find the answer easily.

As Zhang Hua buys “a toy monkey”， that's to say， Zhang Hua buys only one toy monkey. And the toy monkey costs 12 yuan. Now you can underline the key words in the word problem like this:

Zhang Hua buys a toy monkey and 3 bottles of mineral water. The toy monkey costs 12 yuan and each bottle of the mineral water costs 2 yuan. How much does Zhang Hua spend in total?

After that， you may write the information on your draft paper like this:

1 toy monkey: 12 yuan

Zhang Hua also buys “3 bottles of mineral water”and “each bottle of the mineral water costs 2 yuan”. Here， “each bottle of the mineral water costs 2 yuan”means “any one of the three bottles of mineral water costs 2 yuan”. You may write the information on your draft paper like this:

1 bottle of mineral water: 2 yuan

3 bottles of mineral water: ? yuan

There are several strategies to solve word problems， and listing tables is one of them and most common.

As for the problem above， it asks you how much Zhang Hua spend in total. You need to find out how much he spends on the toy monkey and how much he spends on the three bottles of mineral water first. Then， add up the two expenses. The sum is the final answer.

How much does Zhang Hua spend on the toy monkey? In fact， the problem tells you directly. That is 12 yuan， as he only buys one toy monkey.

How much does he spend on the three bottles of mineral water? How can you find the answer? You can list a table， as listing tables is a very common and helpful strategy. You may list a table as the below:

Now you can see 3 bottles of mineral water cost 6 yuan. So you may write the equation sentence as the below:

3×2 = 6 yuan

As one toy monkey costs 12 yuan and 3 bottles of mineral water cost 6 yuan， now you can just add up the two expenses. You can write the equation sentence as the below:

12 + 3 ×2

= 12 + 6

=18 yuan

2. Drawing pictures

Drawing pictures is another useful strategy to solve word problems. By drawing pictures， you can find the relationships between the numbers in the word problems easily.

Let's take the word problem below as an example.

Uncle Sam bought 4 boxes of pencils， and in each of the boxes there were 6pencils. At home， he divided the pencils among his 3 children equally. How many pencils did each of his children get?

After reading the word problem carefully， you can focus the key information below.

a. Uncle Sam bought 4 boxes of pencils.

b. In each of the boxes there were 6 pencils.

c. Uncle Sam divided the pencils among his 3 children equally.

d. The question is how many pencils each of his children got.

Now you can underline the key words in the word problem as the below.

Uncle Sam bought 4 boxes of pencils， and in each of the boxes there were 6pencils. At home， he divided the pencils among his 3 children equally. How many pencils did each of his children get?

According to the key information above， you can see that the first thing you need to do is to find how many pencils Uncle Sam bought. As the word problem tells you “Uncle Sam bought 4 boxes of pencils”and “in each of the boxes there were 6 pencils”， you can list a table to find how many pencils Uncle Sam bought totally.

Now you can write an equation sentence of multiplication as the below:

4×6 = 24 pencils

This is the first step. And the second step is to find out how many pencils each of his children got when the 24 pencils are divided among the 3 children. Now you can draw a picture on your draft paper as the below(1 circle represents 1 pencil):

As you know the whole， which is 24 pencils and the whole was divided into 3 parts equally， you can be sure that division must be used here. So you can write the equation sentence below: 24 ÷3 = 8 pencils

Now you need to combine the two equation sentences， and the word problems is solved.

4×6÷3

= 24 ÷3

=8 pencils

3. Drawing number patterns

Drawing number patterns is easy and popular to solve word problems. Drawing number patterns is absolutely a great strategy， as the number patterns can show us the relationship between factors clearly.

Let's take the word problem below as an example.

Kate rode her bike 3 km to school. She rode home a different way that was 4 km long. This week， Kate rode to school and back 5 times. How many kilometres did Kate ride her bike this week?

What information does this word problem tell us? It tells us the information below:

a. Kate rode her bike 3 km to school.

b. Kate rode her bike home 4 km.

c. Kate rode to school and back 5 times this week.

d. The question is how many kilometres Kate rode her bike this week.

Now try to underline the key information first as the below.

Kate rode her bike 3 km to school. She rode home a different way that was 4 km long. This week， Kate rode to school and back 5 times. How many kilometres did Kate ride her bike this week?

Now you can draw a number pattern on your draft paper as the below.

By drawing the number pattern， you can find easily that Kate rode to school and home 7 km 1 time， as 3 + 4 = 7. So you can write the equation sentence of addition below:

3 + 4 = 7 km

However， the question is that how many kilometres Kate rode her bike this week. 7 km was only the distance Kate rode 1 time. The word problems tells us that Kate rode to school and back 5 times this week. What about 5 times， then? Ybu can list a table as the below.

Also， you can find that the answer is 35 km by multiplying 7 and 5. Now you can write the equation sentence of multiplication as the below.

7 ×5 = 35 km

Now， combine the two steps into one equation sentence as the below:

(3+4)×5

=7×5

=35km

Actually， more strategies and skills can be used in solving two-step operation of word problems. To master them well， you need to do more practice， as practice makes perfect.

Here are some word problems of two-step operation for you to practice after reading.

1. Aunt Smith divided 12 apples among her 3 children， Jack， Jim， and Bill. Jack ate 2 apples right away. How many apples did Jack have left?

2. Haley is getting on an airplane for the first time. The airplane has 10 rows of seats with a path in the middle. Haley sees that there 2 seats on the left side of the path and 2 on the right side. How many seats does she see in all?

3. The students in Mr. Bishop's class have written 28 poems. They are putting their poems together to make a poetry book. They put 4 poems on each page. So far， the students have made 5 pages. How many pages do they still need to make?

4. Li Ling bought a skirt that cost 25 yuan. She paid with three ￥10 bills. How much money did she get back in change?

Keys to How to Solve Two-step Mixed Operation Word Problems?

1. one apple""" 2. 40 seats""" 3. 2 pages""" 4. 5 yuan