Overview: |
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. |
Content Standard(s): |
Mathematics MA2015 (2016) Grade: 6 | 17 ) Use variables to represent numbers, and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6-EE6]
NAEP Framework
Alabama Alternate Achievement Standards
| Mathematics MA2019 (2019) Grade: 6 | 18. Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true. Unpacked Content
Alabama Alternate Achievement Standards
| Mathematics MA2019 (2019) Grade: 6 | 19. Write and solve an equation in the form of x+p=q or px=q for cases in which p, q, and x are all non-negative rational numbers to solve real-world and mathematical problems.
a. Interpret the solution of an equation in the context of the problem. Unpacked Content
Alabama Alternate Achievement Standards
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