What are Multi-step Problems?
Some math problems can be solved in a single step and these problems are usually direct and easy. There are also certain math problems that can only be solved in multiple steps. We need to apply a different strategy while dealing with such problems.
Here is an example of a single step multiplication problem:
There are 20 students in a classroom. Each student owns two pens. Find the total number of pens brought by the students to the classroom.
We can find the solution to this problem in a single multiplication step.
Here is an example of a multi-step multiplication problem:
There are 20 students in a classroom. Each student brings 3 notebooks to the classroom. If all notebooks have 200 pages and weigh 2 ounces, find the total weight of all the notebooks that the students bring to the classroom.
This math problem cannot be solved in a single step easily. We usually break down such problems into multiple steps.
Solving a Multi-step Multiplication Problem
We need to use special strategies while solving multi-step problems. In general, the steps involved in solving multi-step problems are as follows:
- Step 1: Understand the problem.
The first thing to do is to read the problem thoroughly to analyze the little details. Here, we get to pick out the information provided to us and what we need to find with the provided information.
- Step 2: Make a plan.
After having a clear idea about the information we have in hand and what we need to do with it, we need to decide how we are going to solve the problem. We take in the necessary information and discard the rest.
- Step 3: Solve
The problem is solved in multiple steps.
Let’s solve the problem mentioned above using this strategy.
Question: There are 20 students in a classroom. Each student brings 3 notebooks to the classroom. If all notebooks have 200 pages and weigh 2 ounces, find the total weight of all the notebooks that the students bring to the classroom.
Solution:
Step 1: Understand the problem.
Step 2: Make a plan.
Step 3: Solve
We always start by analyzing the information provided in the question. To solve such problems, we need to find the relationship between the known values and the unknown values and form an equation. The goal is always to find the unknown value in the equation with the help of the provided information.
Solved Examples
Example 1: Which expression can be used to solve the following problem?
In a basketball match, all five players of Team A scored a 2-pointer. All five players of Team B scored a 3-pointer. Find the number of points scored in the basketball match.
- (5 + 5)\(\times\)(2 + 3)
- (5 + 2)\(\times\)(5 + 3)
- (5\(\times\)2) + (5\(\times\)3)
Solution:
We use the expression (5\(\times\)2) + (5\(\times\)3) to solve this math problem as this gives the right relationship between the values provided in the question. Since 5 players of Team A scored 2 pointers and the other 5 players of Team B scored 3 pointers, the total number of points scored is the sum of the points scored by each team.
Points scored by Team A = 5\(\times\)2
Points scored by Team B = 5\(\times\)3
So, the correct expression is (5\(\times\)2) + (5\(\times\)3)
Example 2: Jan drinks 2 cups of coffee every day. If a cup of coffee costs $5, how much money did she spend on coffee in April 2022?
Solution:
Step 1: Understand the problem.
Step 2: Make a plan.
Step 3: Solve
Example 3: Ryan kept 5 full decks of playing cards on a table. Each deck has 52 cards. Two of these decks are kept face up, and the rest of the decks are kept face down. How many cards have their face down?
Solution:
Step 1: Understand the problem.
Step 2: Make a plan.
Step 3: Solve
Example 4: A donut shop sells donuts in boxes of dozens and each donut costs $2. The shop serves 20 customers every day, and each customer buys two boxes of donuts. Find the total money earned by the shopkeeper on a Monday.
Solution:
Step 1: Understand the problem.
Step 2: Make a plan.
Step 3: Solve
A multi-step word problem can be solved easily by analyzing the information provided in the question. We always use the useful information to form an equation to relate the known values with the unknown values. Then, we solve the equation to find the unknown value.
Multi-step problems are often word problems. In some cases, we might be provided with information that is not relevant to the question. We need to filter out the irrelevant information and use only the relevant information to solve problems.