MidSchoolMath 1

Identifying equivalent expressions is twofold: transforming one expression into another by applying the properties of operations (commutative, associative and distributive) and also understanding that equivalent expressions will result in the same value. During ...And a Tin of Rice, Professor Picklebottom is at the General Store gathering provisions for his next excursion with Caterina Fenn. He verbally lists for the clerk the many items he needs one by one, over and over, but the clerk can’t get it exactly right. The Professor has the idea to shorten the list by combining like items. The data provided are Caterina’s shopping list and the Profes-sor’s diary page containing two expressions representing the order: an expanded expression and a shortened one.

LESSON: ...AND A TIN OF RICEAre the two expressions equivalent?

...And a Tin of Rice

Identify when two expressions are equivalent (i.e. when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

The Math SimulatorTM

ImmersionPlay ...And a Tin of Rice Immersion video, whole-class. Restate the question: Are the two expressions equivalent?Facilitate classroom discussion; ask students: "What are your ideas about how to help the professor?"

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2 Data & ComputationPrint the Data Artifact, cut into halves, and distribute to students. Allow students work time. Ask students: "Does your answer make sense?"Consider using a sharing protocol leading to mathematical insights and/or highlighting misconceptions. Allow students to revise their work.

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3 ResolutionPlay ...And a Tin of Rice Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).

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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

+ Simulation TrainerAssign the Simulation Trainer.Use protocols that encourage students to help each other.Use Progress Monitoring to access real-time data for the classroom.Provide individual help for students who are not making progress.

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(Use student headphones.)

6.EE.A.4Expressions & Equations

MidSchoolMath 2...And a Tin of Rice

Clicker QuizLaunch the Clicker Quiz, whole-class.

6.EE.A.4Expressions & Equations

Gladys: Encourage students to use "•" or pa-rentheses to indicate multiplication so as not to confuse it with the variable x.

Kevin: Discourage your students from worry-ing about which letter to use as a variable but remind them it is important to used assigned variables consistently within equations and expressions.

Megan: Guide student thinking to understand that evaluating two expressions for an arbitrary value to see if they are equivalent may be help-ful, but it's impossible to check every possible value. Thus, the properties of operations can always be used to verify equivalence.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #6Standard Math Procedures

Instruction at a Glance

1 Fully simplify each answer option.

A: 3ab – 3ab + 4b = 4b

C: 5b – 3b + 2b + 1 = 1D: 2b + 8b – 6b = 4b

B: 4b + 4 – 4 = 4b

C: 5b – 3b + 1 + 2b2 Choose the option that didn't simplify to 4b.

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...AND A TIN OF RICEAre the two expressions equivalent?

Caterina Fenn and Professor Picklebottom are once again planning another adventure. She has sent the professor to Mr. Slater’s general store with a long list to order the necessary provisions. The list includes fl our, coff ee, rice, and, this time, beans.

Having learned from their last experience, both Mr. Slater and the professor have attempted to rewrite the order into an expression.

Is Mr. Slater’s expression equivalent to Professor Picklebottom’s expression?

Mr. Slater’s Notepad:

Professor Picklebottom’s Diary:

6.EE.A.4

Identify when two expressions are equivalent (i.e. when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

About this standard

Date PeriodName

MidSchoolMath ...And a Tin of Rice 1 of 2

APPLYING THE STANDARD

Decide whether or not the expressions in each pair are equivalent. Explain how you know.1)

MidSchoolMath ...And a Tin of Rice 2 of 2

Date PeriodName

How might this standard appear on a test?

Given the two expressions x2 + 6 and 2x + 6:

7n – 1 and 6n 17h and 14h + 3h 6x + 2y and 8xy

Simplify each expression. Place an “X” in the box next to expressions that are equivalent.2)

12 + 24n + 6 12(1 + n) + 6(1 + 2n)

6(4n + 3) 6(4n + 3) + 12

42n 18n + 24

Simplify each expression. Place an “X” in the box next to expressions that are equivalent.3)

5x + 7y + 3x – y 4(4x + 2y)

2(4x + 3y) 4(2x + 3) + 6y – 12

6y + 8x 14xy

4)

Evaluate each expression for x = 2 and for x = 5.

a) Are the two expressions equivalent?Explain how you know.

b)

Check out my worked example #1 (last pair)

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