January 2023 Funday: Expressions with 2, 0, 2, & 3

Posted by Angie Seltzer on 12/23/2022 to K-5 Algebraic Thinking

Create Expressions with 2, 0, 2, and 3

Start the new year with a versatile activity that can be modified easily! Have elementary or middle school students write expressions using 2, 0, 2, and 3. Click below to download a FREE worksheet with instructions and a table for values up to 23. This activity can help students review 5 key concepts, explained below.

1. Adding or Multiplying with Zero
2. Order of Operations
3. Using Exponents
4. Expressions with Parentheses
5. Making Organized Lists

1. Adding or Multiplying with Zero

What properties can you apply?

Multiplying any number by 0 gives a result of 0. This is called the Zero Property of Multiplication.
Adding 0 to any number does not change the number. This is called the Zero Property of Addition.

Try these:

Have students write other examples that include multiplication or addition with 0. If you are using the worksheet, have students use the digits 2, 0, 2, and 3 exactly once. See how many different expressions they can write with these restrictions and without using parentheses.

More examples: 23 × 2 × 0 [0], 22 × 3 × 0 [0], 3 × 0 + 22 [22], 2 × 0 + 23 [23]

2. Order of Operations

In expressions without parentheses or exponents, what is the correct order operations?

Do multiplication and division from left to right.
Then do addition and subtraction from left to right.

Try these:

You may want to encourage students to underline the multiplication and division expressions to do first.

3. Using Exponents

How do you evaluate expressions with exponents?

An exponent tells how many times to use the base number as a factor.
Any number with a zero exponent has a value of 1.
When exponents appear along with other operations, evaluate the exponents first.

Try these:

When an expression has several parts, encourage students to copy each simplified expression below the previous expression, and not to leave out any parts. Here is a way to show the work:

4. Expressions with Parentheses

How can parentheses impact the order of operations?

Do the parts within parentheses first.
If there are nested parentheses, do the innermost ones first.
Inserting parentheses can cause the expression to have a different value.

Try these pairs of expressions:

Discuss why the parentheses in the first expression of each pair are not necessary. [The expressions inside parentheses would be computed first due to the rules for order of operations.]

5. Making Organized Lists

How do you organize the ways to find expressions?

Organize the possible numbers made of the digits 2, 0, 2, and 3.
Organize operations to put between the numbers in expressions.

Examples for organizing numbers:

Examples for organizing operations:

By trying the possibilities in an organized way, students should be able to find dozens of expressions using the digits 2, 0, 2, and 3. If you are using the worksheet, you may want to have them limit their answers to expressions that equal whole numbers up to 23.

Summary and Variations

As you can see, students can review many concepts while evaluating expressions. The free download includes an answer key with at least one expression for each value from 1 to 23.

Here are some ideas for creating variations.

For lower grades, have students use only addition and subtraction with 1-digit and 2-digit numbers. Perhaps allow students to include expressions that use two of three of the digits rather than all four digits.
For more challenge, have students find expressions with values up to 100. Some may not be possible. Have teams compete for finding the most expressions.

Happy Holidays!

Angie