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).

• “¿Qué error cometió Lin cuando restó?” // “What mistake did Lin make when subtracting?”
• “¿Cómo podríamos usar bloques en base diez para ayudarle a Lin a ajustar su trabajo?” // “How could we use base-ten blocks to help Lin revise her work?”

• “¿Cómo describirían el error de Lin?” // “How would you describe Lin’s mistake?” (She tried to subtract 20 from 50 when subtracting 50 from 20. She needed to decompose a hundred to get more tens.)
• Select previously identified students to share what they would tell or show Lin to help her revise her work.
• If no students suggest the following revision to Lin's work, display the algorithm and ask students to explain the revision:

• “Tengan presente el error de Lin mientras practicamos este algoritmo de resta en la próxima actividad” // “Keep Lin’s mistake in mind as we practice using this subtraction algorithm in the next activity.”

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.

• “¿Qué unidades en base diez tuviste que descomponer en este problema?” // “What units did you need to decompose in this problem?”
• “¿En dónde tendría más sentido para ti registrar cómo descompusiste una centena en más decenas? ¿Y una decena en más unidades?” // “Where would it make the most sense to you to record how you decomposed a hundred into more tens? A ten into more ones?”

• Select students to share their reasoning for 2 or 3 problems. Choose problems to focus on based on common questions that came up. Be sure to discuss the last problem, which requires decompositions of both a ten and a hundred.
• For the last problem, ask: “¿Cómo registraron la decena y la centena que se necesitaba descomponer?” // “How did you record the ten and the hundred that needed to be decomposed?” (I started subtracting the ones by decomposing a ten into 10 ones, so I crossed off the 30 and wrote 20. When I decomposed the hundred into tens, I decided to write the 120 on top of the 20, like I wrote the 20 on top of the 30.)
• Record the completed algorithm, showing the decompositions of tens and hundreds.
• Consider asking:
  • “¿En cuáles expresiones no había suficientes decenas o centenas para restar?” // “In which expressions were there not enough tens or ones to subtract?”
  • “¿Qué unidades se descompusieron y cómo se registraron?” // “What units were decomposed, and how were they recorded?”
  • “¿Identificaron lugares en los que podrían haber cometido el error que vimos en el trabajo de Lin?” // “Did you notice any places where you might have made the error we saw in Lin's work?"