The purpose of this activity is for students to sort addition expressions by their value. Students find the value of each sum on their own and share their method with a partner, moving students towards fluency. This sorting task gives students opportunities to analyze equivalent expressions closely and make connections (MP2, MP7).

During the Synthesis, the teacher introduces an equation with addition expressions on both sides of the equal sign.

• “What sums have a value of 7?” (, , , , , , , )
• Display .
• “What do you notice about this equation?” (Each side has a 3 and a 4, but in a different order. Each side equals 7.)

The purpose of this activity is for students to determine whether equations are true or false. Students may use a combination of computation and reasoning about the commutative property to determine whether each equation is true or false. The Synthesis focuses on how students can use the structure of the expressions to decide whether they are true or false, without finding the value of both sums (MP7).

• “How did you decide this equation is true?”
• “How can you use two-color counters to represent both sides of the equation? Can you use these counters to decide if the equation is true?”

• “Which equations could you tell were true or false without finding the value of both sums?” (Problem 1 because both sides add the same 2 numbers. Problem 2 because you can see that the number you are adding to 6 is different on each side of the equal sign. Problem 5 because  is 9 and the other side of the expression is 9 and some more.)