ALEX Classroom Resources

ALEX Classroom Resources  
   View Standards     Standard(s): [MA2019] (6) 15 :
15. Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.

a. Interpret a variable as an unknown value for any number in a specified set, depending on the context.

b. Write expressions to represent verbal statements and real-world scenarios.

c. Identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient, and coefficient.

d. Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.
[MA2019] (6) 18 :
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.
Subject: Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic F: Writing and Evaluating Expressions and Formulas
URL: https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-f-overview
Description:

Students write and evaluate expressions and formulas in Module 4, Topic F. They use variables to write expressions and evaluate those expressions when given the value of the variable (6.EE.A.2). From there, students create formulas by setting expressions equal to another variable. For example, if there are 4 bags containing c colored cubes in each bag with 3 additional cubes, students use this information to express the total number of cubes as 4c + 3.  From this expression, students develop the formula t = 4c + 3, where t is the total number of cubes. Once provided with a value for the amount of cubes in each bag (c = 12 cubes), students can evaluate the formula for t:  t = 4(12) = 3, t = 48 + 3, t = 51. Students continue to evaluate given formulas such as the volume of a cube, V = s3 given the side length, or the volume of a rectangular prism, V = lwh given those dimensions (6.EE.A.2c).



   View Standards     Standard(s): [MA2015] (6) 17 :
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]

[MA2019] (6) 18 :
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.
[MA2019] (6) 19 :
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.
Subject: Mathematics (6), Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic G: Solving Equations
URL: https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-g-overview
Description:

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 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. 



   View Standards     Standard(s): [MA2015] (6) 17 :
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]

[MA2019] (6) 18 :
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.
[MA2019] (6) 19 :
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.
[MA2019] (6) 21 :
21. Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations.

a. Use tables, graphs, and equations to represent the relationship between independent and dependent variables.
Subject: Mathematics (6), Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic H: Applications of Equations
URL: https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-h-overview
Description:

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. 



ALEX Classroom Resources: 3

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