C2. Equations and Inequalities:
demonstrate an understanding of variables, expressions, equalities, and inequalities, and apply this understanding in various contexts
identify and use symbols as variables in expressions and equations
Number of Cars (🚗)
Number of Wheels (N)
Have students dedicate a section of their “learning log” to variables and symbols. Throughout the year, have them enter situations they encounter where variables or symbols are used in equations to represent quantities that are unknown or in expressions to represent quantities that vary. Examples may include a missing element in a pattern that is represented with a symbol, an unknown value needed to make a statement true, the use of letters to label the sides of shapes that can have any value, or their use in formulas such as A = bh.
Throughout the year, as opportunities arise, discuss the ways symbols are used as variables. For example, a symbol in a pattern might be used to represent a missing element. Another example is when a symbol is used to represent a specific unknown, such as 3 × 7 = 30 − □.
solve equations that involve whole numbers up to 50 in various contexts, and verify solutions
25 + 5a = 50
25 + 5a = 25 + 25
5a = 25
a = 5
Provide students with relevant contexts that require them to determine the unknown value that makes the two expressions on either side of the equal sign equivalent. For example, there are 2 boxes of muffins, each containing the same number of muffins. One box contains 12 carrot muffins and 8 blueberry muffins. The other box contains oatmeal muffins and 4 bran muffins. How many oatmeal muffins are there? [12 + 8 = n + 4]
Students can use various strategies to find the unknown. If they use a guess-and-check strategy, encourage them to be strategic in their choices and continue to adapt their choices as they check their answer.
They may also use a balance model, in which they represent each expression and manipulate the expressions until they isolate the variable (see the example that highlights this process). This process helps to build understanding of algebraic manipulations, which is the eventual goal. Ensure that students make a statement about what the variable represents, for example, n = 16.
Provide students with opportunities to solve a range of equations that have the variable in different locations, for example, m + 4 = 17, 4 + m = 17, 17 = 4 + m.
solve inequalities that involve addition and subtraction of whole numbers up to 20, and verify and graph the solutions
Provide each student with a portable whiteboard or large paper. Present a variety of scenarios where there might be more than one answer, such as those below. Ask students to record their solutions on their whiteboards.
As you work through each scenario with the class, invite students to come to the front of the class and show their answers. Support students in recognizing that there is more than one right answer for each of these scenarios.
Have students solve a variety of problems that involve inequalities. For example:
Ask students to create their own problems that involve solving an inequality. Have them exchange their problems with a partner or a group, or do this as a whole-class activity.