Using Symbols to Model and Write Algebraic Expressions Unit of Study: 16 Global Concept Guide: 1 of 2

Content Development Students need to understand the difference between an expression and an equation and recognize the difference between a numerical expression (utilized in unit 2)and an algebraic expression. An expression is a part of a number sentence that has numbers and operation signs and may have one or more variables, but does not have an equal sign. An equation is a statement that uses an equal sign to show that two quantities are equal. A numerical expression uses only numbers and operation signs. An algebraic expression includes one or more unknowns represented by letters or symbols.

Day 1 The focus of Day 1 is choosing the correct operation when writing an algebraic expression to describe a problem. This GCG requires students to decontextualize scenarios into expressions. It is imperative that the teacher supports students discovery of the action of the scenario, rather than looking for key words. It might be a good idea to create an anchor chart like the one below with your students as you identify situations where different operations are appropriate. It is also important for students to understand that some actions can be represented by multiple operations, depending on the context of the scenario.

Day 1 Sample Task 1: Provide students with the following scenario: Kylie buys a ticket to the water park. She spends $6 for lunch. How much money does Kylie spend for a ticket and lunch? Provide students the opportunity to directly model the expression using manipulatives. Then have them generate an algebraic expression. Students may struggle finding: What operation matches the scenario. How to represent an unknown amount in an equation. (Students may suggest using a question mark, a box, a letter, or a symbol. Complete the expression using one of these suggestions.) Examples: t + 6, + 6, ? + 6,  + 6 Once students are comfortable with the operation used within the expression, introduce the term variable. A Variable is a letter or symbol that stands for a number or numbers.

Day 2 The focus of Day 2 is contextualizing and decontextualizing. Decontextualizing: Taking a concrete representation (story problem) and making it abstract (expression). Contextualizing: Taking an abstract representation (expression) and making it concrete (story problem). Sample Task: Write a story problem to match the expression below. 45÷n

Day 3 Third grade students can use parentheses to tell what part of the expression was done first, but should not be concerned with the order of operations at this time. The focus of Day 3 is contextualizing and decontextualizing multistep story problems and expressions. Sample Task: Expressions Café Pgs. 155-156 Students take turns being the customer and the waitperson. Have one partner of each pair read the orders while the other writes the order (expressions), using the code on Expression’s Café TR1.

Day 3 Sample Task: Speaking Math P. 76 Students write expressions to match multistep scenarios. Note: Also provide students ample opportunities to contextualize. (Write story problems based on given expressions.)

Enrich/Reteach Reteach: Enrich: Students should continue to use manipulatives to physically act out problem scenarios, recording each action performed. After, make the connection to recording as a numerical or algebraic expression. “Mix-Freeze-Pair-Share” Numerical Expressions Activity Enrich: