Lesson 4

The purpose of this Number Talk is to elicit strategies and understandings students have for counting back by place as a strategy for subtraction. These understandings help students develop fluency with subtracting multiples of 10 and 100 from three-digit numbers. As students share, represent their thinking on an open number line.

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy on an open number line.
• Keep expressions and work displayed.
• Repeat with each expression.

• Display \(457 - 230\).
• “¿Cómo nos ayudan las últimas 2 expresiones a pensar sobre este problema?” // “How can the last 2 expressions help us think about this problem?” (Even though it is 230 being taken away, we can still subtract the hundreds and then the tens.)
• “Hoy veremos cómo podemos usar métodos para contar que nos ayuden a restar números más grandes” // “Today we will see how we can use counting methods to help us subtract bigger numbers.”

The purpose of this activity is for students to use the relationship between addition and subtraction to make sense of different counting methods for subtracting three-digit numbers. Students analyze 2 different methods for a given problem where a number is being subtracted from a multiple of 100. They consider how thinking about a subtraction expression as an unknown addend equation can be helpful and discuss how counting on can be a useful method for subtraction. The number line can support this method, so they have the opportunity to make connections between counting on a number line and adding on or subtracting by place using equations.

• Groups of 2
• Give students access to base-ten blocks.
• “A Mai y a Lin les pidieron que encontraran el valor de \(500 - 387\). Este es su trabajo” // “Mai and Lin were asked to find the value of \(500 - 387\). Here is their work.”
• Display the images of Mai and Lin’s work.
• “¿En qué se parecen y en qué son diferentes los métodos que usaron para encontrar la diferencia?” // “What is the same and different about the methods they used to find the difference?” (They both represented it with equations, but Mai also used a number line. Mai showed it as addition with a missing addend. They both broke apart the second number. They both got 113 as the answer.)
• 30 seconds: quiet think time
• “Discutan con un compañero” // “Discuss with a partner.”
• 2 minutes: partner discussion
• If it doesn’t come up, ask, “¿En qué parte de la representación de Mai ven la respuesta?” // “Where do you see the answer in Mai’s representation?” (How far she jumped shows the difference.)
• “¿Por qué creen que Lin empezó con \(387 = 300 + 80 + 7\)?” // “Why do you think Lin started with \(387 = 300 + 80 + 7\)?” (That way she could see each part that she needed to take away.)

• “Intenten encontrar estas diferencias de las formas en las que Mai y Lin restaron” // “Now try Mai’s way and Lin’s way.”
• 10 minutes: independent work time

• “¿Cuál método prefieren? Expliquen” // “Which method do you prefer? Explain.” (I prefer counting on because you count until you get to the number. When you count on, you can do it in parts so you can make each part something that is easy for you and get to a ten. The number line helped me. I prefer the equations because it helps me see the parts as they are taken away.)

The purpose of this activity is for students to use their understanding of expanded form, place value, and properties of operations to reason about adding and subtracting by place (MP7). Students analyze different methods and representations that show adding hundreds and hundreds, tens and tens, and ones and ones. Students notice that hundreds, tens, and ones can be added in any order. In the next section, the focus will be on strategies based on place value and will include composing and decomposing tens and hundreds. In the synthesis, there are discussions that honor all methods while connecting each strategy to place value in preparation for the work of the upcoming lessons.

• Groups of 2
• Give students access to base-ten blocks.

• “Hemos usado bloques en base diez, diagramas y ecuaciones para sumar y restar números usando lo que sabemos sobre el valor posicional” // “We have used base-ten blocks, diagrams, and equations to add and subtract numbers using what we know about place value.”
• “Andre y Diego mostraron cómo pensaron de diferentes formas. ¿En qué se parece y en qué es diferente su trabajo?” // “Andre and Diego showed their thinking in different ways. What is the same and what is different about their work?” (They both grouped the same places together. Andre used a different equation to show adding each place. Diego put each number in expanded form and put the places on top of one another.)
• 1 minute: quiet think time
• 3 minutes: partner discussion
• Record responses.
• “¿En qué parte de su trabajo ven cada número?” // “Where do you see each number in their work?” (Diego shows the place value in expanded form, but Andre adds 1 place at a time. In Andre’s I see the numbers up and down, but in Diego’s I see the numbers across.)
• 30 seconds: quiet think time
• Share responses
• “Intenten encontrar el valor de las expresiones de la forma en la que Andre y Diego lo hicieron” // “Try Andre’s way and Diego’s way.”
• 8 minutes: independent work time
• “Comparen con un compañero” // “Compare with a partner”
• 2 minutes: partner discussion
• Monitor for students who use Andre’s way, but add by place value in different orders.

• Invite 1–2 students to share how they used each way.
• “¿Cuál forma prefirieron? ¿Por qué?” // “Which way did you prefer? Why?” (I prefer Diego’s way because I can see how things are grouped and I write fewer equations OR I prefer Andre’s way because it helps me remember to add ones and ones, tens and tens, and hundreds and hundreds.)
• “¿En qué se parecen encontrar la suma y encontrar la diferencia? ¿En qué son diferentes?” // “How was it the same or different when finding the sum versus finding the difference?” (It worked either way. I liked Diego’s way of finding the difference because it was lined up by place, so the answer is across the bottom when you are done.)