In collaborative groups of four, students will act out a dinner party where four dinner guests will attend. The students must act out the different ways to arrange four dinner guests.
This is a College- and Career-Ready Standards showcase lesson plan.
In this activity, students will be writing equations using variables that represent different food items. They will develop the foundational understanding of variables being used as a symbol to represent a number. They will also write expressions using variables and then evaluate the expressions at specific values for the variables.
This activity was created as a result of the ALEX Resource Development Summit.
In Module 4, Topic G, students are introduced to the fact that equations have a structure similar to some grammatical sentences. Some sentences are true: “George Washington was the first president of the United States.” or “2 + 3 = 5.” Some are clearly false: “Benjamin Franklin was a president of the United States.” or “7 + 3 = 5.” Sentences that are always true or always false are called closed sentences. Some sentences need additional information to determine whether they are true or false. The sentence “She is 42 years old” can be true or false depending on who “she” is. Similarly, the sentence “x + 3 = 5” can be true or false depending on the value of x. Such sentences are called open sentences. An equation with one or more variables is an open sentence. The beauty of an open sentence with one variable is that if the variable is replaced with a number, then the new sentence is no longer open: it is either clearly true or clearly false. For example, for the open sentence x + 3 = 5:
If x is replaced by 7, the new closed sentence, 7 +3 = 5 is false because 10 ≠ 5.
If x is replaced by 2, the new closed sentence, 2 + 3 = 5 is true because 5 = 5.
From here, students conclude that solving an equation is the process of determining the number(s) that, when substituted for the variable, result in a true sentence (6.EE.B.5). In the previous example, the solution for x + 3 = 5 is obviously 2. The extensive use of bar diagrams in Grades K–5 makes solving equations in Topic G a fun and exciting adventure for students. Students solve many equations twice, once with a bar diagram and once using algebra. They use identities and properties of equality that were introduced earlier in the module to solve one-step, two-step, and multistep equations. Students solve problems finding the measurements of missing angles represented by letters (4.MD.C.7) using what they learned in Grade 4 about the four operations and what they now know about equations.
In Module 4, Topic H, students use their prior knowledge from Module 1 to construct tables of independent and dependent values in order to analyze equations with two variables from real-life contexts. They represent equations by plotting the values from the table on a coordinate grid (5.G.A.1, 5.G.A.2, 6.RP.A.3a, 6.RP.A.3b, 6.EE.C.9). The module concludes with students referring to true and false number sentences in order to move from solving equations to writing inequalities that represent a constraint or condition in real-life or mathematical problems (6.EE.B.5, 6.EE.B.8). Students understand that inequalities have infinitely many solutions and represent those solutions on number line diagrams.