# Expressions Everywhere

## Lesson Goals

Essential Questions: What can affect the relationship between numbers? How can we interpret expressions without evaluating them?

Vertical Alignment:
• In 3rd grade, students are introduced to the use of parentheses with the distributive property.
• Students first encounter other grouping symbols (braces and brackets) in 5th grade. Their work in working through the order of operations will build foundational understanding for later algebra work.
• 5th grade is the first time students will work with expressions. The work they will do is limited to writing expressions, not solving them.
• Expressions are a large area of focus in grade 6 and a foundational algebra skill that will build to the understanding of equations in later grades.

How is this resource appropriate for AIG learners?
This task requires students to extend their understanding of developing and interpreting numerical expressions to reasoning through the validity of equations. This task should be completed using relational thinking – not by students solving the equations and comparing, but by explain their thinking using precise mathematical terms.

Rather than rushing to immediately solve math expressions, student exploration of the concept demands deeper understanding. This lesson for 5th grade AIG Math students explores the concept of mathematical expressions through visual art by creating valid math expressions using examples from the North Carolina Museum of Art modern collection, and by creating two-dimensional visual art to represent a given expression.

## Materials

Projector and images from NCMA modern collection may include, but are not limited to:
http://ncartmuseum.org/art/detail/wall_of_light_peru
http://ncartmuseum.org/art/detail/raqqa_ii
http://ncartmuseum.org/art/detail/jan_iii
http://ncartmuseum.org/art/detail/no._265
http://ncartmuseum.org/art/detail/oriole
http://ncartmuseum.org/art/detail/image_iii
http://ncartmuseum.org/art/detail/red_shift
http://ncartmuseum.org/art/detail/tide
http://ncartmuseum.org/art/detail/ion
Blank paper, graph paper, construction paper
Rulers, protractors (or, tools for creating straight and curved lines)
Markers, colored pencils, crayons
Scissors, glue sticks

## Activities

1. What is an expression? How many different definitions for the word expression can we identify?
expression definition
– the look on someone’s face that conveys a particular emotion
– a word or phrase, especially an idiomatic one, used to convey an idea
– the process of making known one’s thoughts or feelings
– the conveying of feeling in the face or voice, in a work of art, or in the performance of a piece of music
– Mathematics: a collection of symbols that jointly express a quantity

2. Using http://ncartmuseum.org/art/detail/wall_of_light_peru as the model for whole class exploration, generate multiple ways that the shapes and colors can be expressed numerically and conceptually with math operations and properties. Expressions that represent the same value should be grouped together, so that students can see that different expressions can be used to represent the same numerical value.

3. Print out (in color) or display on individual devices additional works (see resources) from the NCMA. In pairs, students select one piece of art to explore. Pairs collaborate to analyze the paintings components (line, shape/form, space/perspective) in order to create one mathematical expression. Pairs should have the opportunity to share their artwork and justify their choices and mathematical reasoning with other pairs or the whole group.
3. Select one of the expressions below. These expressions come from the WCPSS cmapp assessment for this unit. If homeroom teachers will be using this assessment in their classrooms, then similar expressions using different numbers should be offered to students for this exploration.
• “Add three and two, then multiply by four”
• “Divide one hundred forty four by twelve, and then subtract seven”
• “Four more than three doubled”
• “The sum of four and eight, subtracted by two”
Write the correct mathematical expression using numbers and math symbols. Choose the necessary tools to accurately represent your selected expression visually and artistically. Ready individual art for display, and create an object label, explaining how the art is a valid reflection of the corresponding expression.

## Differentiation Approaches

1. This lesson is appropriate for AIG enrichment and as extension for highly able learners.
2. Challenge – students can create the math expression, rather than being given an expression to follow.
3. Challenge – students can be asked to visually interpret a more complex expression using multiple properties and order of operations grouping symbols including parentheses, braces, and brackets.
4. Challenge – what will student(s) do to interpret this piece of art mathematically? http://ncartmuseum.org/art/detail/zero

## Assessment

Students will understand that expressions are used to symbolize the relationship between numbers:
Can students identify the math expression used to create the visual art? If the correct math expression can be paired with the art by peer or teacher, then students have successfully completed the task with level 4 thinking. If the correct math expression cannot be paired with the art through visual observation only, students should have the opportunity to consult with the teacher and verbally explain their thinking as to how their selected expression is represented in their art. If explanation is based on solid mathematical reasoning, this should also be considered level 4 mastery.

## Follow Up and Extension Ideas

Each student will create multiple pieces of art. Individually or in groups, write the didactic text, wall panels, brochures and/or gallery guides for a Math Museum Special Exhibition. Invite guests so that students act as the curators for their art and for their mathematical thinking.