Mathematics Awareness Month - Third Grade

Last week we began a series on mathematics awareness to bring attention to the importance of mathematics in today’s technology-driven world and highlight the progression of algebraic thinking in the Florida Standards. Algebraic thinking encourages students to not only solve problems, but also to understand the relationships between numbers, operational symbols and letters. In third grade, students develop their algebraic thinking skills by representing and solving problems involving the four operations. This post will feature a focus standard for third grade, as well as examples and resources to develop your child’s procedural skill and application of algebraic thinking.

Focus Standard

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation.



Multiple Representations, Two-Step Word Problems

Some third grade students are playing a basketball game. Alexis scored 12 points and Joshua scored 8 points. If their team scored 35 points, how many points did their teammates score?  


Show your child the problem above. Have your child identify what the problem is asking. Then have your child solve the problem by manipulating objects. Ask your child to explain how they used the manipulatives. Below are two examples that show how your child may have used objects to solve the problem and the possible explanations. 


Alexis has 12 points. Joshua has 8 points. It takes 15 more points to make it to 35 points.

The team scored 35 points. Alexis scored 12 and Joshua scored 8. Together they made 20. Their teammates had to score 15 points to get to 35.

Alexis has 12, one ten and 2 ones. Joshua has 8 ones. It takes 1 ten and 5 ones or 15 to get to the total points of 35.

There were 35 points. Alexis scored 12, so take away 12 from the total. Joshua scored 8. Take that away. 15 is left.


Then, have your child write an equation to represent the problem. Encourage them to use a letter to stand for the unknown value. Their equation may look like one of the examples below.


When children solve problems in multiple ways or use at least two representations to show their thinking, they make greater sense of the mathematics and can apply their learning to more complex problems. Have your child solve the problem below using multiple representations like manipulatives, pictures and equations.

Jackson has 6 pieces of rope that each measure 7 inches long. Robin gives Jackson another piece of rope. Jackson now has a total of 63 inches of rope. How long was the piece of rope that Robin gives Jackson?

Could your child solve the problem with manipulatives, by drawing a picture, and through an equation? Post pictures of your child’s solutions using multiple representations on Twitter using #FLMathAware.



Using multiple representations like in the examples above is a great way to develop algebraic thinking. Multiple representations help students communicate their understanding and create connections between different concepts. In the examples provided, students incorporated their knowledge of place value with their algebraic thinking to solve a two-step problem. More information about using multiple representations can be found on the Florida Department of Education website.


Check back next week as the mathematics awareness series continues with a fifth grade algebraic thinking standard.