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Let’s see how tape diagrams can help us answer questions about unknown amounts in stories.
Let’s think about which way is better when we solve equations with parentheses.
Let’s figure out missing angles using equations.
In this section, students investigate situations that can be represented by tape diagrams and equations in the form and .
Students begin by recognizing that new structures are needed to represent situations that are not proportional (not in the form ). They then examine correspondences between descriptions of such situations and the tape diagrams that represent them. This examination is...
In this section, students build fluency with solving equations of the forms and . They begin by using balanced hanger diagrams to represent equations. They see that doing the same operation on each side keeps the hanger balanced and keeps the equation true. For example, an efficient process for solving an equation of the form involves subtracting from each side,...
Let’s see how a balanced hanger is like an equation and how moving its weights is like solving the equation.
Let’s use hangers to understand two different ways of solving equations with parentheses.
Let’s show that doing the same to each side works for negative numbers too.
Let’s think about which way is better when we solve equations with parentheses.
Let’s use tape diagrams, equations, and reasoning to solve problems.
Let’s use tape diagrams, equations, and reasoning to solve problems with negatives and percents.
In this section, students solve inequalities of the forms and including any of the four inequality symbols, , , , or . First, students consider inequalities of the form or and determine which values make the inequality true. Next, they compare equations and inequalities that represent the same situation. They see that solving the related equation gives the boundary point...