The purpose of this True or False? is to elicit insights students have about how the commutative property applies to addition and to multiplication, but does not apply to subtraction. The reasoning of students here helps to deepen their understanding of the properties of operations and how they apply to subtracting within 1,000. It also will be helpful later when students recognize the need to decompose a hundred or a ten to get more tens or ones.

This is the first time students experience the True or False? routine in grade 3. Students are familiar with this routine from a previous grade, however, they may benefit from a brief review of the steps involved.

• “¿En qué se diferencia esta última ecuación?” // “What is different about the last equation?” (If we switch the order in subtraction, then both sides of the equal side aren't the same. If we switch the order when we subtract, we don't get the same number.)
• Consider asking:
  • “¿Alguien puede expresar el razonamiento de _____ de otra forma?” // “Who can restate _____'s reasoning in a different way?”
  • “¿Alguien quiere agregar algo al razonamiento de _____?” // “Does anyone want to add on to _____'s reasoning?”
  • “¿Podemos hacer generalizaciones basándonos en las afirmaciones?” // “Can we make any generalizations based on the statements?”

The purpose of this activity is for students to examine an error in an algorithm in which a larger digit is subtracted from a smaller digit in the same place-value position. In such a case, it is common for students to subtract the smaller digit from the larger digit instead, not realizing that subtraction is not commutative. The given algorithm here shows the numbers in expanded form to help students see that it is necessary to first decompose a hundred into tens before the 50 can be subtracted from 20.

When students make sense of and correct Lin’s mistake, they construct viable arguments and critique the reasoning of others (MP3).

The purpose of this activity is for students to practice using the subtraction algorithm introduced in a previous lesson. Provide base-ten blocks for students who choose to use them to support their reasoning about the algorithm.