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

Content Development Understanding equality is a key underlying concept for writing and solving equations. Research shows that many students do not understand the equal sign. They often think that it is just a symbol that is written before they write the answer. One way to reinforce the idea of equality is to use a balance scale to model equations. Students must realize that for the scale to balance, the quantities on both sides must be equal. For the model below the triangle on the left side represents the unknown. Each block represents one. Students learn to represent the models on this scale as y + 2 = 5.

Day 1  The focus of Day 1 is choosing the correct operation when writing an algebraic equation to describe a problem.  This standard requires students to estimate to check for the reasonableness of their answers. Embed estimation in the beginning of each task presented to students. Begin by asking: What could our answer be close to? Why do you think this?  This GCG requires students to decontextualize scenarios into equations. 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 with your students as you identify situations where different operations are appropriate/applicable.  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 the opportunity to model the scenario and then write an algebraic equation to match their model: Ajavius was collecting snap cubes for Ms. Meade at the end of her lesson. She passed out 125 total, but he has only collected 98 so far. How many snap cubes does he still need to collect?  Possible Sample Equations:  98 + C = 125 C = 27 OR  125 – C = 98 C = 27  Sample Task 2: Equation Mix-Freeze-pair-ShareEquation Mix-Freeze-pair-Share  Students are given an story problem or equation and asked to make a match. (A match consists of a story problem and equation).

Day 2  The focus of Day 2 is contextualizing and decontextualizing.  Decontextualizing: Taking a concrete representation (story problem) and making it abstract (equation).  Contextualizing: Taking an abstract representation (equation) and making it concrete (story problem).

Day 3  The focus of Day 3 is contextualizing and decontextualizing multistep story problems and equations.  Sample Task 1: Provide students the opportunity to model the scenario and then write an algebraic equation to match their model: Mike runs 2 miles a day. His goal is to run 25 miles. After 5 days, how many miles does Mike have left to run in order to meet his goal?  Possible Sample Equations:  m = 5 x 2 m = 10 L + 10 = 25 L = 15 OR  (5 x 2) + m = m = 25 m = 15 Here students write two equations, the first solves for m, or miles run after 5 days. The second solves for L, the number of miles left to run after 5 days. Here students write one equation to solve for m, or miles left using parentheses to show what they did first.

Day 3  Sample Task 2: Provide students the opportunity to model the scenario and then write an algebraic equation to match their model : There are 5 cars in the garage. Each car has 4 tires. Three of the tires are flat. How many tires are not flat?  Possible Sample Equations:  (5 x 4) – 3 = m = m 17 = m OR  5 x 4 = t t= = n n= 17 t= total tires n= non-flat tires Here students write one equation to solve for m, or miles left using parentheses to show what they did first.

Enrich/Reteach  Reteach:  Students should continue to use manipulatives to physically act out single- step problem scenarios, recording each action performed. After, make the connection to recording as a numerical or algebraic equation.  Enrich: