EE.2.3

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

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Formative Assessments
Formative Assessments
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CPALMS: Students are asked to assess the reasonableness of an answer using mental computation and estimation strategies.

Alexa’s Account

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CPALMS: Students are asked to solve a multi-step problem involving rational numbers.

Reeling in Expressions

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CPALMS: Students are asked to solve a multi-step problem involving percent.

Discount and Tax

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CPALMS: Students are asked to assess the reasonableness of answers using estimation strategies.

Using Estimation

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CPALMS: Students are asked to solve a multi-step problem involving percent.

Gas Station Equations

Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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This two-player game is designed to help students develop an intuition about comparing signed numbers and to add and subtract signed integers using different notations for the same concept.

“Flipping for Integers” by NCTM Illuminations

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Assessment Questions
Assessment Questions
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Equation Editor 1
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Equation Editor 4
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Equation Editor 2
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Equation Editor 5
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Equation Editor 3
Videos of Expert Instruction
Videos of Expert Instruction
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In this fun and non-intimidating Math Antics video (approx. 11:00 min) Rob goes over a number of examples of solving one-step equations with addition and subtraction. He models and explains the reasons behind each step, as well as goes over what to be careful about.

“Solving Basic Equations – Part 1” by Math Antics

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In this fun Math Antics video (approx. 10:15 min) Rob talks about how to solve two-step equations, and explains how to use the order of operations rules in reverse to help know what order to undo the operations in to solve for the variable in the equation.

“Solving Two-Step Equations” by Math Antics

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This Khan Academy video tutorial introduces averages and algebra problems involving averages.
Averages
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In this fun Math Antics video (approx. 9:30 min) Rob goes over a number of examples of solving one-step equations with multiplication and division. He models and explains the reasons behind each step, as well as goes over what to be careful about.

“Solving Basic Equations – Part 2” by Math Antics

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Hook/Performance Tasks
Hook/Performance Tasks
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Illustrative Mathematics:The purpose here is to give students an opportunity to solve a multi-step percentage problem that can be approached in many ways. Multiple standards can be addressed depending on the tools students have developed and their approach to solving.

Anna in D.C.

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Illustrative Mathematics: In this task, there is a significant amount of rounding in the final answer because heights are almost never reported more precisely than the closet half-inch. Assuming the reported stem heights are rounded this way, students should be precise in giving the solution.

Shrinking

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Illustrative Mathematics:This purpos is to help students see two different ways to look at percentages, both as a decrease and an increase of an original amount. Students will be converting simple % to decimals, as well as identifying equivalent expressions without variables.

Discounted Books

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Illustrative Mathematics: The purpose of this task is for students to find the area and perimeter of geometric figures whose boundaries are segments and fractions of circles and to combine that information to calculate the cost of a project.

Stained Glass

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Illustrative Mathematics: The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways, such as making a table, calculating unit rate. This task could be used to help see the value of algebraic representations.

Gotham City Taxis

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Illustrative Mathematics:The purpose of this task is to give students a real-world context for comparing fractions where it is natural to convert the fractions to decimals or describe the situation in terms of percents.This task also gives a concrete example, with real data.

Who is the Better Batter?