There are several different types of word problem that students may encounter. For each of the different types there can be further differences. For example, in word problems involving the change in amounts, the starting amount, or the final amount, or the amount of change itself can be unknown.
It is important that students learn to solve all these different types of problem as this will demonstrate a full understanding of the meaning of the addition and subtraction operations. Practice with lots of examples is needed but this should be done after starting with plenty of hands-on activities with concrete materials.
The table below shows examples of these different types of addition and subtraction problems. Note: The table is based on The Common Addition and Subtraction Situations in the Common Core Standards For Mathematics (P.88)
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Different Types of Addition and Subtraction Situations
|Add To||Three ducks are on a pond. Four more ducks land on the pond. How many ducks are there now?||3 + 4 = 7|
|Three ducks are floating on a pond. Some more ducks fly in and land beside them and now there are five ducks. How many ducks flew in?||3 + _ = 7|
|Some ducks are floating on a pond. Four more ducks land beside them and there are now seven ducks. How many ducks were on the pond before the four landed?||_ + 4 = 7|
|Take From||Seven candles were burning on a cake. Jake blew three of them out. How many were left burning?||7 - 3 = 4|
|Seven candles were burning on a cake. Jake blew some of them out to leave four burning. How many did he blow out?||7 - _ = 4|
|There were some candles on a cake. Jake blew four of them out to leave three of them burning. How many candles were burning at the start?||_ - 4 = 3|
|There are four red grapes and three white grapes in a bowl. How many grapes are in the bowl?||4 + 3 = _|
|Seven grapes are in a bowl. Four are red and the rest are white. How many white grapes are in the bowl?||4 + _ = 7
7 - 4 = _
|Compare||Sam has three games and Jack has seven games. How many more games does Jack have?ORSam has three games and Jack has seven games. How many fewer games does Sam have?||3 + _ = 7
7 - 3 = _
|Jack has four more games than Sam. Sam has three games. How many games does Jack have?ORSam has four fewer games than Jack. Sam has three games. How many games does Jack have?||3 + 4 = _
4 + 3 = _
|Jack has four more games than Sam. Jack has seven games. How many games does Sam have?ORSam has four fewer games than Jack. Jack has seven games. How many games does Jack have?||7 - 4 = _
_ + 4 = 7
Addition and Subtraction Vocabulary and Language
Being able to solve each type of problem described above requires students to master the vocabulary of addition and subtraction. e.g. how many in total, altogether, combined, more than, difference, how many are needed.
Solving word problems both relies on and develops reading and language skills. Be aware of your children's reading level and use the opportunity to build these skills as you work and discuss the problems. Help your children to identify and comprehend the key words and terms within a problem. The table below contains just a few examples.
Key words and terms for adding and subtracting
|how many||how much||left over|
|still to go||together||combined|
Allow your children as much time and give support and encouragement to help them interpret the problem. Work with them to understand the problem and determine the arithmetic operation required so that it can be translated into an addition or subtraction equation.
Be precise when discussing problems and look out for problems that are poorly worded. For example, “Jack has 7 console games and Sam has 4 console games. How many do they have altogether?” would be better worded as “Jack has 7 console games and Sam has 4 console games. How many console games do they have altogether?”
When more does not mean add
Students look for verbal clues when solving word problems. “More” usually (but not always) suggests addition and “less” usually (but not always) suggests subtraction. Look out for problems where these words suggest the opposite of what they usually do. For example, “The Green Team had 14 players which was 2 more than the Red Team. How many players were on the Red Team.” Students who can interpret this as 14 - 2 = 12 are well on their way to understanding addition and subtraction.
Errors made with word problems
The following is based on work by Anne Newman1 .
Errors that students make in word problems can be categorized under one of five types:
- Reading – key words or symbols are read incorrectly
- Comprehension – failure to understand either the whole problem or specific parts of it
- Transformation – incorrect identification of the operations required to solve the problem
- Procedural or fact - incorrect calculation
- Encoding - solution is found but not correctly or fully stated
Asking students to do, or answer, the following helps identify which type of error they are making:
- Read the question.
- What was the question asking you to do?
- How did you plan to find the answer?
- Show me how you found the answer.
- What was your answer?
1. Newman, A 1977, ‘An analysis of sixth-grade pupils’ errors on written mathematical tasks’, Bulletin of the Victorian Institute of Educational Research, vol 39, pp 31–43.
Addition/ Subtraction Word Problem Worksheets
The two worksheets below have lots of word problems. Work through them with your children and provide help with vocabulary when needed.