Use the properties of operations, and the relationships between multiplication and division, to solve problems and check calculations.

Use the properties of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and whole number percents, including those requiring multiple steps or multiple operations.

- Students will use their knowledge of order of operations to create equations using the digits 2, 0, 2, and 3. Answer results must range from one to 100.
- This activity can be performed with any four-digit number! After students have completed 2023, ask whether they would like to attempt another number.

- 2023 Worksheet (Appendix A)
- Calculators
- Pencil and Eraser
- GOOS Paper

Introduction:

- Facilitate a class discussion and introductory activity around order of operations.
- To ensure students consider all operations while conducting this activity, consider asking students to think of as many mathematical operations as possible. Write them on the board.
- Some possibilities: addition, subtraction, multiplication, division, fractions, exponents, decimals, factorials, etc.

- Introduce the activity to the whole class.

Lesson:

- Tell the class they will create unique equations that result in each number between one and 100. The challenge is that only the numbers of the new year (2, 0, 2, and 3) can be used.
- In each equation, each number (2, 0, 2, and 3) must be used and may only be used once.

- Students may combine numbers to make larger ones (e.g., combine 2 and 0 to form 20).
- Students may use any combination of operations.
- Students may use parentheses to create more complex equations (e.g., (20)(3+2) = 100, (20)(3-2) = 20)
- Suggestions:
- Students work through equations on rough paper and place their final equation in the appropriate box in Appendix A.
- Students work in small groups to help compile the large number of equations.
- If students struggle, remind them of mathematical rules, such as anything multiplied by 0 is 0, which will help to eliminate some terms (or anything to the exponent of 0 is 1, etc.)
- Encourage students to work through equations with pencil and paper before verifying with a calculator.
- Manipulatives, such as number lines, hundreds charts, base ten blocks, etc., may also benefit students.

Conclusion:

- As a class, share the different equations used to get to each number and discuss any patterns they may see.

Modifications:

- Teachers may also choose to modify the “use-a-digit-only-once” or “all-digits-must-be-used” rules to make it easier for younger grades. For example, allow students repeated use of digits.
- This activity can be conducted over several days. For instance, work on equations with answers ranging from one to 10 on Day 1, 11 to 20 on Day 2, etc.

- Are students using order of operations correctly?
- Which operations are students using most often?
- Are students able to come up with multiple equations to get to the same answer?
- What mathematical language are students using to communicate their work?
- What observations and comments do students make when trying to create unique equations?

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