## What is a True/False Routine?

In this routine, the teacher poses an equation with two expressions on either side. The students need to determine whether the equation is true or false. Students are expected to reason and justify their conjecture. The teachers asks guiding questions to elicit students' thinking and understanding.

## 2 + 7 = 5 + 2 + 2

5 x 24 = 6 X 23

## What is the learning?

The True/False Equations routine has the potential to engage students in reasoning and analyzing. When teachers design specific sets of problems they can encourage students to explore properties of numbers and operations. Furthermore these flexible routines engage students in considering the meaning of equality and developing relational thinking. True/False routines provide a context in which students develop understanding of the equal sign to mean “the same as.” By providing opportunities for students to develop understanding of equality and strategies for thinking relationally, we can support their development of algebraic reasoning from an early age.

True/false equations provide opportunities for students to conjecture and generalize. Cathy Humphreys and Ruth Parker (2015) discuss the importance of students considering questions such as "Will it always work? Why?" in their book

Students can explore properties, such as:

True/false equations provide opportunities for students to conjecture and generalize. Cathy Humphreys and Ruth Parker (2015) discuss the importance of students considering questions such as "Will it always work? Why?" in their book

*Making Number Talks Matter*.Students can explore properties, such as:

## How do I engage my students in the learning?

In this activity, the teacher poses an equation, with two expressions and asks students to decide whether the equation is true or false, and facilitates a discussion around how they might prove whether it is true or false. Typically I begin with small numbers because my focus is not on computational fluency, but instead about focusing students' attention on equality and how operations work. Initially students will want to compute both sides to determine whether the question is true or false. Our intention is to move them past this, to considering generalizations and the properties of the operations. Before posing the questions, you will want to anticipate how your students will respond and how you will represent their thinking for the class.

When determining which equation I will pose, I ask myself what key idea(s) do I want my students to understand about equality or operations and then carefully select equations based on this.

When determining which equation I will pose, I ask myself what key idea(s) do I want my students to understand about equality or operations and then carefully select equations based on this.

## Supporting websites/videos/blog posts:

The great place to learn more about True/False Routines is on the Tedd.org site. There are amazing videos that show real classrooms using Counting Collections at different grades, as well as informational sheets. You will need to register with your email but they will not send you spam.

Video Examples:

Kindergarten class www.teachingchannel.org/videos/true-false-problem-string-kindergarten

Grade Three class https://www.teachingchannel.org/videos/true-false-equation-routine

Grade Four class www.youtube.com/watch?v=hCxjKTJ9xxQ

**Kristen Gray,**author of MathMinds website, and a math educator in Delware, has written some blog posts about how she has used this routine to highlight mathematical concepts with different grades.Video Examples:

Kindergarten class www.teachingchannel.org/videos/true-false-problem-string-kindergarten

Grade Three class https://www.teachingchannel.org/videos/true-false-equation-routine

Grade Four class www.youtube.com/watch?v=hCxjKTJ9xxQ