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Operation Target
The goal is to use four digits and the operations +, −, x, and ÷ to make as many different whole numbers as you can. This is a cooperative contest for two or three people.
Materials
- One or two pieces of paper for each player
- Pencil for each player
- Calculator that uses order of operations
Directions
- You must use each of the four digits 9, 5, 2, and 1 exactly once.
- You can use the operations +, −, , and ÷ once, more than once, or not at all.
- Parentheses are allowed.
- Make as many whole numbers as you can. For example, 9 + 5 2 − 1 = 18.
- All division operations must give whole numbers. For example, 9 ÷ 2 = 4.5 is not allowed.
- List the numbers you make and show how you made them.
Variations
- Play with different digits. For example, play with 3, 4, 5, and 9.
- Allow the digits to be arranged to make fractions and decimals.
- Allow the digits to be arranged into 2-digit numbers. For example, using the digits 9, 5, 2, and 1, the following is permitted: 12 95 = 1140.
- Use 9, 5, 2, and 1 and the directions for Operation Target to answer the following questions.
- What is the largest whole number you can make?
- What is the smallest whole number you can make?
- How many whole numbers less than 10 can you make?
- What whole numbers can you make in more than one way? Show at least two number sentences for each.
- Pick four different digits. Make as many whole numbers as you can using your four new digits and +, −, , and ÷. List the numbers you make and show how you made them.
- Use 1, 2, 3, and 4 to make 10. Can you think of another way?
- Luis used 1, 2, 3, and 4 to make 24. How could he have done it?
- Romesh used 1, 3, 5, and 7 to make 8. How could he have done it?
- Make up your own problem like those in Questions 7, 8, and 9.