Extending the meaning of addition and subtraction

Teaching Pre K-8, Oct 1994 by May, Lola

In the primary grades, children learn the meaning of both the addition and subtraction of numbers by using concrete models. In the upper grades, they often discover many different methods of learning the computation of numbers.

Children of all grade levels can extend their understanding of the computation of numbers in several ways. They can use a calculator; tackle problems that require strategy for their solution; and make use of discussion topics that encourage them to communicate with each other. Here are some examples of all three approaches.

Primary Grades Calculator explorations

1. What number should replace each question mark in the following problems to make the computation correct? Is there a shortcut you can use that will help you avoid trial and error?

64 - ? = 81 ? 18 = 72 ? 32 - ? = 32

2. Can you tell whether the solution in each of the following four problems is true or false? If you think that the answer is false, can you tell where the error was made? (examples omitted)

Problem solving

1. Imagine a target with three circles. The outer circle has a value of 6; the in-between circle has a value of 8; and the bulls eye has a value of 10. If you shoot 5 arrows at this target, how many ways can you get a score of between 38 and 42?

2. On the calculator, using only the 5, 3, -, = keys, see if you can get the number 20. Each key can be used more than once. How did you find the answer?

Discussion topics

1. Here is a way one child used to add numbers. Can you discover the method the child used? Give some examples of addition using the child's method. (examples omitted)

2. Here is a way a child used to subtract numbers. Can you discover the method? Give some examples of this method of subtraction. (examples omitted)

Upper Grades Calculator explorations

1. What three consecutive numbers have a sum of 204? Explain how you approached working on the problem.

2. What number should replace the question mark to make the following computation correct? Is there a shortcut you can use that will help you avoid trial and error?

341- ? = a number between 115 and 120

Problem solving

1. There are five possible scoring plays in a National Football League game: touchdown = 6 points, 2-point conversion = 2 points, point after touchdown = 1 point, field goal = 3 points and safety = 2 points. What final scores between 1 and 30 are not possible for a team? Explain.

2. Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 so that they make two three-digit addends and one three-digit sum. There are over 300 solutions and 32 different sums. Can you find 20 solutions? Here is one solution: (examples omitted)

(Tip: It helps to have numbered chips or pieces of paper to move around.)

Discussion topics

1. In many other countries people subtract differently than the method taught in our country. Look at the following and see if you can discover the method used. (examples omitted)

(Tip: The above method always starts with the ones.)

2. What is an estimate? Are estimates more than just guesses? Give some examples of when estimates are useful, as well as some examples of where you will need exact information.

You'll find these three approaches use ful when making assessments of your students' knowledge (or lack of knowledge) of addition and subtraction.

While your students are involved in calculator explorations, problem-solving and discussions of addition and subtraction topics, you can assess the depth of their understanding of these two basic math operations.