How to Explain Fifth Grade Math Variables & Expressions in Florida

Students will learn more if they can manipulate math objects with their hands.

Florida state math standards dictate that fourth grade students understand and use variables in math expressions, equations, and visual representations. This understanding of variables can come quite slowly to some students because it requires abstract thinking that could be above their current level of thought. However, teaching variables and expressions to fourth grade students can become moderately easy with the implementation of hands on instruction through the use of the correct math manipulatives.

Things You'll Need

• Tag board
• Post-it notes
• Variable worksheet

Instructions

Creating the Manipulatives

1. Write five different variables on five different Post-it notes. For example, the five variables could be a, b, c, d, and e. One letter should be written in large under-case writing on each Post-it note.

2. Write one number using the digits zero through 10 on 11 different post-it notes. Write both the addition symbol (+) and the subtraction symbol (-) on two more Post-it notes.

3. Create at least five expressions by sticking the numbered Post-it-notes and the addition and subtraction notes on a large piece of tag board. For example, you can make expressions such as 2 + 3 and 8 - 1 using the notes. Be sure to make more numbered Post-it-notes as needed. Turn the expressions into equations by adding equal signs and answers using new notes. For example, the expressions will now be 2 + 3 = 5 and 8 - 1 = 7.

4. Stick a variable Post-it-note over one of the numbers in each equation. For example, the equation 2 + 3 = 5 would now appear as 2 + a = 5 with the variable covering the note with the 3 on it.

Teaching with the Manipulatives

1. Divide the class into groups of three to four students each. Small groups allow each student to physically manipulate the variable tag board. Meet with each group for five to 10 minutes of instruction.

2. Explain that a variable is any letter that acts like a hiding place for a number. It represents the number, but it is up to them to figure out which number is hidden by the variable. Explain to each group that finding this number is like trying to find buried treasure, which is the hidden number.

3. Model how to discover what each variable stands for by working with one equation. For example, using the expression 2 + a = 5, you can say "two plus what number will equal five? I know that two plus three equals five so that means that variable a must be hiding the number three. The variable a is the same thing as three." Remove the a variable to reveal the number three under it.

4. Allow each student to practice discovering the hidden number under a different variable by following the teacher model. If more practice is needed for certain students, allow them to stay with you and watch additional groups work with the variables.

5. Provide a variable work sheet for each student to practice with independently as they leave the small group instruction. This will help with long-term retention. Continue giving formative assessments using variables in expressions and equations over the next few weeks. Provide opportunities using the variable tag board for those students who do not show mastery on the formative assessments.

Tips & Warnings

• As students progress forward with the addition and subtraction equations, make multiplication and division equations on the tag board, and allow them to work through the new equations.

• Do not use the letter x as a variable. Students often confuse this letter as a multiplication symbol.

References

• "Math at Hand"; Sandra P. Alley; 1999
• Florida State math standards