Mathematics Awareness Month - Fifth Grade

The mathematics awareness blogs have introduced the concept of algebraic thinking and shown how important it is to develop this thinking as children move from one grade to the next. So far, these posts have focused on a first grade and a third grade standard. This week, we will spotlight algebraic thinking in fifth grade. Students in fifth grade must use algebraic thinking to express calculations as expressions and extend their knowledge of operations of whole numbers to apply them to fractions and decimals. This post will feature a focus standard, as well as examples and resources to deepen your child’s procedural skill and application of algebraic thinking.

Focus Standard

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.


Brayden’s Video Game


Brayden is playing a video game. He resumed his game from a previous day, where he had 795 points. Today, while playing the following events occurred:

  • He lost 195 points when he made a wrong turn.

  • He earned 250 points during the bonus round.

  • At the end of the game, his final score was tripled.


Show your child the problem above. Ask your child to write an expression that represents the total number of points Brayden has at the end of the game. Your child may write one of the following expressions: (795 - 195 + 250) x 3 or 3 x [(795 - 195) + 250].


If your child struggles to write an expression, you could ask

  • Can you repeat the problem in your own words?
  • What is happening in this problem?
  • What is the first thing we should do? How do you know?

If your child struggles to complete the expression, you could ask

  • How can we use the order of operations to help write the expression?
  • What should be the last step?
  • How could using parentheses help you write the expression?

When your child correctly writes an expression, you could ask

  • Are your parentheses in the correct places? How do you know?
  • Is there another expression you could write for this problem?
  • What if Brayden started with zero points? How would your expression change?


Asking questions when students are solving a mathematical problem causes them to explain and justify their thinking. The questions you ask should encourage students to formulate hypotheses, make connections or provide reasons for their solution, like the examples above. Using a variety of questions helps students to expand their algebraic thinking.


Have your child write an expression based on a mathematical scenario or story problem they create. Don’t forget to ask questions throughout the process. Use #FLMathAware to post your child’s problem and expression on Twitter.


CPALMS is the State of Florida’s official site for standards and course descriptions, as well as vetted instructional resources. There are over 12,000 free resources on CPALMS. Each of these resources is aligned to a specific Florida Standard. One type of resource available on CPALMS is the Mathematics Formative Assessment System (MFAS), like Brayden’s Video Game, the example from above. The MFAS tasks are designed to provide feedback on how well a student understands a particular standard. The tasks provide a problem for students to solve, possible misconceptions, examples of student work and questions to elicit thinking. There are multiple MFAS tasks for each standard in mathematics.


There are only two more blogs in the mathematics awareness series! Next week will feature algebraic thinking in seventh grade, which will be followed by algebra.