**Math Lesson - Balance and Equality **

## Core Decisions

**What:**

Students will build on their knowledge of quantity to compare different quantities and learn how to use symbols to communicate the relationship between them and how they compare to one another. The focus is on building a useable, working knowledge of certain relational symbols (=,>,<). As stated in

*Math Matters,*“Relational or relation symbols establish a relationship between two numbers, two number sentences, or two variable expressions” (Chapin and Johnson, 2006, p. 195). By embedding the equal sign (=) within the context of relational symbols, I hope to emphasize a more accurate interpretation of the equal sign. It indicates a relationship and does not just separate out an “answer”. This is a misconception many students construct early on in school and I hope this lesson addresses it.

The concept of “equality” is a fundamental skill for eventually progressing toward balancing inequalities and other algebraic thinking and reasoning in later grades. To encourage students to have a rich understanding of the concept of equality, I am as suggested in

*Math Matters,*allowing equality to be

*“*modeled by thinking of a balance scale”(Chapin and Johnson, 2006, p. 195).

**How:**

Students will start the lesson with the introduction of a shared problem. The problem is presented by the teacher within a real world context. The problem is one about inequality and how that inequality can be balanced. This task was chosen because it is slightly more challenging and requires more cognitive demand than what will eventually be required of them in their independent work. I will be careful to explain the situation, the materials, and the reason for wanting a solution to the problem. However, I will not yet introduce the mathematical concepts, symbols, or reasoning behind the problem type. I will encourage students to remember that there are different strategies and tools for solving problems. I will also encourage them to think about which of those is most helpful to them for solving the problem. The students will begin the task of working on that same problem but not in groups. Each individual student will be responsible for finding their own way of understanding, making sense of and finding a solution for the problem. They will have certain tools available (manipulatives, pencils and paper, and crayons). After some wait time, the different approaches will be shared as a whole group. I will have students stand up and share their approach/strategy and explain how/why they chose to do it that way. I will explicitly direct students to respond to each others thinking by saying “Who also solved the problem that way?, Can anyone explain what ___ did in your own words?, What do you think about how ___ solved the problem? How is your solution or strategy different from ____'s”.

Students will then be introduced to the math concepts through whole class instruction and guided practice. The teacher will explain to the whole group that these types of problems require us to compare numbers, quantities or amounts. The teacher will also use this whole class time to introduce the mathematical symbols related to these comparisons. Students will be engaged in guided practice of how they can model these comparisons with their bodies (pretending they are like a balance scale) and will have some guided practice for assigning the appropriate symbol for each practice problem.

Then students will receive their own individual worksheet to independently solve quantity comparison problems in the form of a pictorial balance scale. They will be encouraged to use whatever strategies/tools they feel comfortable using to find the solutions. The lesson will close with the development of a class list of examples of encounters with these types of inequality problems in our lives.

**Why:**

I chose to focus my lesson on teaching the concept of inequality and comparing number quantity because I believe it will positively increase my students number sense for numbers that they are beginning to feel very comfortable with and use almost every day in their math lessons through computation tasks.

Also, by embedding the equal sign (=) within the context of relational symbols, I hope to emphasize a more accurate interpretation of the equal sign. It indicates a relationship and does not just separate out an “answer”. This is a

**misconception many students construct early on in school**and I hope this lesson can address it. Although this lesson is focused on naming the relationship between the quantities, it will also set the stage for students to eventually think about balancing inequalities which is a very important foundational skill.

I wanted to start the lesson with a contextualized problem. I believe that having students engage with an authentic problem and making sense of it themselves first leads to them becoming more invested in the related math skills to be taught. This kind of initial personal investment in a problem will help students recognize their own strengths and weaknesses when dealing with that particular type of problem. This also allows me to get a formative assessment right away about where the students thinking and comfort level is with this type of mathematical reasoning and problem solving. The hope is that by watching the way students approach this problem without instruction will then deeply inform what I really need to concentrate on during the direct instruction later in the lesson.

I wanted to provide multiple entry points for students understanding about comparing quantity. This is why I insist on encouraging multiple strategies and use of a variety of tools. I also make a point to introduce them to the idea of thinking about quantities in terms of a balance scale. I believe the students in my class who may be more visual or kinesthetic learners will benefit from conceptualizing the notion of equality this way. I also believe that by using kinesthetic activities like pretending our bodies are a scale, students are forced to stay energized and active throughout instruction and the lesson will be more engaging to all students.

Lastly, sharing ideas and discourse is often a struggle for my students. They are often not willing to actively listen to one another. So I need to try to structure the conversation after the initial problem solving so that they are required to build off of each others' ideas and knowledge. I believe although this a struggle for this class, they need to have structured practice in discourse so that they can learn from each other and not just the teacher.

Scale image retrieved from: http://www.eduplace.com/math/mw/background/5/02/te_5_02_overview.html