Why are math word problems so hard? They are, after all, just stories. In fact, there are 8 different types of math word problems. Teaching our students these types of problems will make solving math word problems more successful for our students. So what are the 8 types of word problems, and how do we solve them?
What follows is a summary of the 8 different types of problems. I also included their associated schematic (thinking map/graphic organizer) to model solving each problem type, and to help students organize and understand relationships in the word problem. It is important to model out loud how to solve each problem type, and use each schematic regularly.
Add To Word Problems:
Add to word problems include situations in which someone has something, they get some more, and now they have a greater amount than when they started.
Example:
Maria had 24 stickers. She earned 14 more at school. How many stickers does she have now?
You can use two different schematics for this type of problem. Remember, CONSISTENTLY use whichever schematic you choose.
When teaching this problem type, or any for that matter, it is important to use consistent language as you discuss the problem. Add to problems come in three types:
1) Start unknown
2) Change unknown
3) Result unknown
You can help your students with solving math word problems of this type by reading more about them HERE.
Take From Word Problems
Solving these math word problems requires a schematic that is very similar to the add to problem schematic.
In these problems, someone starts with a greater amount, part of it is taken away, and they are left with a lesser amount.
An example of this problem type is:
Davy had some flour. He used 3 and 1/2 cups to make a loaf of bread. Now he has 2 and 1/3 cup of flour left. How many cups of flour did he have to begin with?
Remember that these problems, just like add to problems have a start, change, and result that can be unknown. Helping your students focus on what each number represents in the problem will help in solving these math word problem types.
Using the schematics, or thinking maps, will also help your students decide how to best solve the equation. This is why it is important that we NOT focus on KEY WORD identification when solving word problems.
In the above example, the start is unknown. We do know the change and the result, but the word LEFT when taught in isolation encourages students to subtract. The schematic and focusing on the situation of the problem tells us that we in fact need to add to find the solution.
Solving math word problems is more successful for our students when we build their experience with problem types, as well as the situations that accompany them. The schematics help our students identify relationships in the numbers from the problem and increase their success in choosing the correct operation.
Put Together/Take Apart Problems
In these word problem types, different types of materials are being combined. Solving these math word problem types focuses on determining if the amounts given in the problem are one of the two addends (or ingredients) being combined, or the total amount of the combined materials.
For example, Manuel mixed 1 and 1/4 cup of water with 2 and 2/3 cup of clay to make an adobe brick. How much water and clay were used to make the brick?
Using a math mountain drawing, your students would see that they had the two addends, since the clay and water are combined to make the brick. The total combined materials is unknown. Had one of the addends been missing, your students would have had to subtract, or take the materials apart to find how much the missing material was.
Additive Comparison Problems
These word problems have a greater amount, a lesser amount, and the difference between the two. Because these problems often use language that can trick those students that rely on keyword identification, using the schematic is especially important.
Here is an example:
Dawn needs 1 and 1/2 yards of fabric. This is 1 and 1/4 yards more than she has. How much fabric does Dawn have?
Some students see the word MORE and automatically think that they need to add to solve this problem. However, if you focused on word relationships by asking your students which amount was more and which was less, your students would be able to label the schematic correctly.
Drawing our students attention to the numbers and what they represent is crucial to improving their success with word problems.
Equal Groups Problems
One strategy I have found especially effective with my students is asking them if one of the numbers they have in their word problem is a total. If they are able to find a total, or think they have a total, then they have a 50% chance of choosing the operation. Why? Because having a total means they should either subtract or divide.
In equal groups problems, the language I use with my students is the number of groups, group size, and product (total).
Here’s an example:
Jazmin had 12 boxes of erasers. There were the same number of erasers in each box. If she had 144 erasers, how many came in a box?
In this problem, we know that there is the same number of eraser in a box. It is not uncommon that the word each is used in these problem types, but I always remind my students that words like this are more evidence to support their claim regarding how to solve a problem. Just like in other subjects, having MORE than one piece of evidence is more convincing.
The second piece of evidence they often use is the schematic drawing. For this type of problem, we return back to the math mountain diagrams, only now they have factors rather than addends since there are groups with the SAME number in each group.
Problems with Arrays
Array problems are mostly word problems about someone setting up rows of chairs or something similar. They can also be about planting, but what is clear in these problems is that someone has rows in which there are the same number of an object in each row.
Take this example:
The PE teacher arranged the students so they were spaced out for warm ups. There are 24 students in the class. If the PE teacher made four rows, how many students would be in a given row?
We use the area model to organize the information, focusing student attention on number of rows and how many there are in each row.
Area Problems
Area problems are those than include length, width, area, and square units. We use all these as evidence that the type of problem we are working with is in fact an area problem.
We also use the area schematic, labeling what we know, either the length, width, or area from the problem as further evidence that we have the right type of problem.
Again, focusing on whether we are given the total area, in units squared (another piece of evidence to support their claim), helps students decide if they should multiply or divide. If both factors (length and width) are given, you simply multiply. If you have the total area, but are missing either the length or width, you will need to divide.
Multiplicative Comparison Word Problems
Like additive comparison word problems, multiplicative comparison word problems are comparing a greater amount to a lesser amount. What makes them different is that they will often times include the phrase “n times as much” or “n times as many”.
These problems use comparison bars, where one bar is a fraction of the size of the other. In these instances, the greater bar should be divided into pieces equivalent to the value of the lesser comparison bar.
When teaching these types of problems, it is important to use the term multiplier to describe how many the lesser amount should be multiplied in order to equal the greater amount.
Solving math word problems doesn’t have to a challenge. Helping children understand that word problems come in a variety of different types will improve their accuracy when solving. Using the associated schematic drawings will also help students make sense of information and relationships between the numbers in the word problem.
What word problems do your students or children find the most difficult? Share in the comments below or head on over to Instagram to share your thoughts there. I look forward to hearing from you!
Build student word problem confidence with Word Problem Sorts
Word problem sorts are wonderful for building student background of word problem types. They allow for math discussion, collaboration, critical thinking, and problem solving skills.
Need resources to use with your child or classroom?
Take a look at these word problem resources below.
