Lesson 18

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information.

The expression allows students to preview the work of this lesson and give teachers insight into how students think about subtraction.

• Groups of 2
• Display the expression.
• “¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high?” “Too low?” “About right?”
• 1 minute: quiet think time

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

• “¿Alguien hizo una estimación menor que 30,000?” // “Is anyone’s estimate less than 30,000?”
• “¿Alguien hizo una estimación mayor que 40,000?” // “Is anyone’s estimate greater than 40,000?”
• “Teniendo en cuenta esta discusión, ¿alguien quiere ajustar su estimación?” // “Based on this discussion, does anyone want to revise their estimate?”
• “Averigüemos cómo sumar y restar números como estos” // “Let’s find out how to add and subtract numbers like these.”

The purpose of this activity is for students to add and subtract numbers through the thousands place in a way that makes sense to them. The numbers here do not require regrouping when subtracting. Throughout the activity, teachers have the opportunity to learn what students know about addition and subtraction through the hundreds place and how they apply that prior knowledge to work with four-digit numbers. Working with larger numbers sets the stage for students to think about the standard algorithm as an efficient way to add and subtract.

Students may need an orientation to the context. To give students an idea of what the number of steps means, share that it takes about 1,700 steps to walk a mile.

• Groups of 2
• Display the image in the task.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• “Basándose en los datos, ¿qué día de esa semana estuvo más activa la profesora?, ¿menos activa?” // “Based on the data, when was the teacher most active that week? Least active?”

• 5 minutes: independent work time
• 3 minutes: partner work time

If students consider the one-digit sums and lose track of the place value each digit represents, consider asking: “Si escribes todos los números en forma desarrollada, ¿cómo podría ayudarte eso a llevar la cuenta de los valores?” // “How might writing each number in expanded form help you keep track of the values?” Offer students grid paper to support them in aligning the digits by place value.

• Ask students to share responses and strategies for finding sums and differences. Record strategies.
• “¿Hubo algunas estrategias que se hayan usado bastante en esta actividad? ¿Podemos describirlas?” // “Were there certain strategies that showed up a lot in this activity? Can we describe them?” (Yes, a lot of us added and subtracted by place value.)

The purpose of this activity is for students to analyze strategies for adding and subtracting numbers to the ten-thousands place. Students look at addition problems that require composing new units, when the sum of the digits in a particular place value exceeds 10. The subtraction problems do not require students to decompose a unit, as this will be addressed in future lessons. They look at 2 strategies.

Strategy A allows students to add each number in terms of the value of each digit, written in expanded form. Strategy B follows the same logic, but without writing the full value that each digit represents. Then, students use the same strategies to subtract without decomposing a unit.

When students perform operations on the quantities in the situation, they reason abstractly and quantitatively (MP2).

• Groups of 2
• “Ahora veamos cuál fue la actividad física durante el fin de semana” // “Now let’s look at the weekend activity,”
• Display the image in the task.
• “¿Qué observan acerca del número de pasos que la profesora dio durante la semana en comparación con el número de pasos que dio el fin de semana?” // “What do you notice about the number of steps the teacher took during the week versus on the weekend?” (The teacher took a lot more steps each day during the weekend.)

• 2 minutes: quiet think time
• 6–7 minutes: partner work time

Students may accurately write numbers in expanded form to subtract, but add the values instead of subtracting them because of the addition symbols they see. Consider refocusing students to the original problem and asking: “¿Cómo podrías encontrar la diferencia entre los valores que hay en cada posición?” // “How might you find the difference between the values in each place?”

• Ask students to explain how the strategies are alike and how they are different. (They both add by place value and get the same answer, but one strategy breaks each number up and the other does not.)
• “¿Por qué un estudiante pudo haber usado una de las estrategias en lugar de la otra?” // “Why might a student have used one of the strategies instead of the other?”
• “La estrategia B se llama el algoritmo estándar y es útil cuando sumamos y restamos números grandes” // “Strategy B is called the standard algorithm and is useful when we add and subtract large numbers.”