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Activity 1

15 mins

Muchos ceros

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

to see where instructional routines fit in your journey.

Materials

To Gather

Grid paper

Activity Narrative

In this activity, students subtract multi-digit numbers. They do so in two ways: by using the standard algorithm for subtraction and by finding unknown addends. Students find the value of a string of related differences that encourage them to look for and express regularity in repeated reasoning (MP8).

Students may notice that when a subtraction problem requires them to decompose multiple units to subtract in one place when using the standard algorithm—as is the case when the minuend has multiple zeros and the subtrahend has mostly non-zero digits—the standard algorithm for subtraction may not be the most practical. Students use their work in the lesson activity to discuss alternatives to the standard algorithm in these cases, including methods based on the relationship between addition and subtraction and on reasoning about sums and differences that are easier to calculate (MP7).

MLR7 Compare and Connect. Synthesis: After all strategies have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask students: “¿Qué tenían en común las estrategias?” // “What did the approaches have in common?” “¿En qué eran diferentes?” // “How were they different?” or “¿Alguien resolvió el problema de la misma forma, pero lo explicaría de otra manera?” // “Did anyone solve the problem the same way but would explain it differently?”
Advances: Representing, Conversing

Engagement: Provide Access by Recruiting Interest. Leverage choice around perceived challenge while activating background knowledge. Provide access to materials that students found helpful in Unit 4, such as base-ten blocks,

grids, digit cards, and colored pencils. As the value of the numbers increase, invite students to consider how they might use mental pictures of these materials instead of the materials themselves.
Supports accessibility for: Conceptual Processing, Attention, Social-Emotional Functioning

Launch

Groups of 2
Display the first set of equations.
“¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
1 minute: quiet think time
Share responses.

Activity

6–8 minutes: independent work time
3–4 minutes: partner discussion
Monitor students who:
- Use the standard algorithm and record how they decompose each place.
- Think flexibly about how to decompose a larger place one time (for example, for , rather than thinking about decomposing by starting with 7 thousands, they think of decomposing 700 tens and record to show 7,000 as 699 tens and 10 ones).
- Use the results of solved problems to help solve new problems (by using known differences or by making use of a pattern).
- Use additive reasoning (for example, thinking about what number to add to 16 to find 100 and adding on to 100 to reach the total).

Activity Synthesis

Select previously identified students to share the strategies they used to find the value of .
Ask students who didn’t use the standard algorithm to subtract why they chose another way.
“¿En qué se parecen encontrar el valor de las diferencias del primer grupo de ecuaciones y encontrar el sumando desconocido del segundo grupo de ecuaciones?” // “How was finding the values of the differences in the first set of equations like finding the unknown addends in the second set of equations?” (Both had totals that kept adding a new place. The two-digit number in each did not have any zeros, but the total number in each had many zeros. There was a pattern in each. You could think about adding on and adding to a number like 100 first for each set.)

Activity 2

20 mins

Formas de encontrar diferencias

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

to see where instructional routines fit in your journey.

Materials

None

Activity Narrative

Previously, students used the standard algorithm for subtraction to find the differences involving minuends with multiple zeros. They also used the standard algorithm of addition to find an unknown addend that gives a sum with multiple zeros for its digits. In this activity, students make connections between these two ways of reasoning about differences. They also analyze another way to find differences between multi-digit numbers.

Launch

“Examinen los cálculos de Priya y de Han. ¿En qué se parecen sus planteamientos? ¿En qué son diferentes?” // “Look at Priya's and Han’s calculations. How are their setups alike? How are they different?”
1 minute: quiet think time
1 minute: share responses
Highlight that Priya is subtracting 472 from 20,000, while Han is finding a number to add to 472 to get 20,000, but both are finding the same unknown number.

Activity

6–8 minutes: independent work time on the first three questions
Pause for a discussion before the last question.
Select students to share their calculations, or display:

Priya

Han

Kiran

Ask a student to explain what is happening in each calculation.
“¿Alguien pensó en otra forma de encontrar la diferencia?” // “Did anyone think of another way to find the difference?” (See Student Responses.)
Poll the class on their preferred strategy. Ask a student from each camp to explain their reasoning.
3 minutes: independent work time on the last question
Monitor for students, who try Priya’s way, Han’s way, Kiran’s way, or a different way, to share in the Lesson Synthesis.