Sunday, April 29, 2012

Brainstorm: Intro to Equations/Properties of Equality

Goal: To help students understand the addition and subtraction* properties of equality.

Common Core Standard: 6.EE.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).

ACOS Standard: 7.6.B.3 (2003); 6.15 (2010)

Materials and Other Requirements: 1 deck of playing cards, 3-ring binder to serve as a partition, desk or table, two student volunteers

Time Requirement: 5-10 minutes

Procedure: Stand the 3-ring binder up on a table to serve as a partition. Position Student A and Student B on opposite sides of the partition. Give Student A a 3, a 5, and a 2 card. Give student B an 8 and a 2 card. Have them hold their cards so that the class can see them. Ask the class to state the sum of the cards Student A holds and then the sum of the cards Student B holds (10). Ask the class if the students are holding the same cards (NO). Ask the class if the (values of the cards on the) two sides (of the partition) are equal (YES). Tell students that for the remainder of the activity, the partition will stand in for an equal sign. Be sure that students recognize that the whole set-up (Student A, Student B, and the partition) is really an equation. Narrate as you hand Student A a 7 card. Ask the class if the two sides are equal now (NO). Have the class explain why/how they know this (Student A's hand now adds up to 17 while Student B's hand is still 10). Narrate as you hand Student B a 7 card. Ask if the two sides are equal now (YES). Ask students to explain WHY the two sides are now equal (They both add up to 17). If necessary, guide students towards the appropriate wording(If the sides start out equal, and we add the same number to both sides, the sides remain equal or similar). Repeat three or more times with different cards and different students.

Closure: Instruct the students to use inductive reasoning to write a rule about adding the same value to both sides of an equation. (If your students are not familiar with inductive reasoning, give a brief overview and then model using induction to write a rule.)

* Can easily be modified to show the subtraction property of equality, and with a little tweaking can be used to model the multiplication and division properties of equality.

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