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7.6 Expressions, Equations, and Inequalities

I can think of ways to solve some more complicated word problems.

I can explain how a tape diagram represents parts of a situation and relationships between them.
I can use a tape diagram to find an unknown amount in a situation.

I can match equations and tape diagrams that represent the same situation.
If I have an equation, I can draw a tape diagram that shows the same relationship.

I can draw a tape diagram to represent a situation where there is a known amount and several copies of an unknown amount and explain what the parts of the diagram represent.
I can find a solution to an equation by reasoning about a tape diagram or about what value would make the equation true.

I can draw a tape diagram to represent a situation where there is more than one copy of the same sum and explain what the parts of the diagram represent.
I can find a solution to an equation by reasoning about a tape diagram or about what value would make the equation true.

I understand the similarities and differences between the two main types of equations we are studying in this unit.
When I have a situation or a tape diagram, I can represent it with an equation.

I can explain how a balanced hanger and an equation represent the same situation.
I can find an unknown weight on a hanger diagram and solve an equation that represents the diagram.
I can write an equation that describes the weights on a balanced hanger.

I can explain how a balanced hanger and an equation represent the same situation.
I can explain why some balanced hangers can be described by two different equations, one with parentheses and one without.
I can find an unknown weight on a hanger diagram and solve an equation that represents the diagram.
I can write an equation that describes the weights on a balanced hanger.

I can use the idea of doing the same to each side to solve equations that have negative numbers or solutions.

For an equation like $3(x+2)=15$, I can solve it in two different ways: by first dividing each side by 3, or by first rewriting $3(x+2)$ using the distributive property.
For equations with more than one way to solve, I can choose the easier way depending on the numbers in the equation.

I can solve story problems by drawing and reasoning about a tape diagram or by writing and solving an equation.

I can solve story problems about percent increase or decrease by drawing and reasoning about a tape diagram or by writing and solving an equation.

I can explain what the symbols $\le$ and $\ge$ mean.
I can represent an inequality on a number line.
I understand what it means for a number to make an inequality true.

I can describe the solutions to an inequality by solving a related equation and then reasoning about values that make the inequality true.
I can write an inequality to represent a situation.

I can graph the solutions to an inequality on a number line.
I can solve inequalities by solving a related equation and then checking which values are solutions to the original inequality.

I can match an inequality to a situation it represents, solve it, and then explain what the solution means in the situation.
If I have a situation and an inequality that represents it, I can explain what the parts of the inequality mean in the situation.

I can use what I know about inequalities to solve real-world problems.

I can organize my work when I use the distributive property.
I can re-write subtraction as adding the opposite and then rearrange terms in an expression.

I can organize my work when I use the distributive property.
I can use the distributive property to rewrite expressions with positive and negative numbers.
I understand that factoring and expanding are words used to describe using the distributive property to write equivalent expressions.

I can figure out whether two expressions are equivalent to each other.
When possible, I can write an equivalent expression that has fewer terms.

I am aware of some common pitfalls when writing equivalent expressions, and I can avoid them.
When possible, I can write an equivalent expression that has fewer terms.

Given an expression, I can use various strategies to write an equivalent expression.
When I look at an expression, I can notice if some parts have common factors and make the expression shorter by combining those parts.

I can write algebraic expressions to understand and justify a choice between two options.