The purpose of this activity is to see that some equivalent ways of rewriting a division expression are more helpful than others for finding its value. In particular expressions, the value of which can be calculated mentally, are most helpful. This supports students in choosing their own ways of breaking up the dividend when they use a partial-quotients algorithm in future lessons.

When they identify expressions to find the value of a specific quotient, students notice that dividends readily identifiable as multiples of 14 are most useful for finding the value of the quotient (MP7).

This activity uses MLR2 Collect and Display. Advances: conversing, reading, writing.

• Refer to the display of the words students used during the activity.
• “Estas son las palabras que usaron para explicar cómo supieron que las tarjetas que escogieron representan una suma que tiene el mismo valor que ” // “These are the words you used to explain how you knew the cards you chose represent a sum that has the same value as .”
• “¿Qué otras palabras o frases deberíamos incluir en nuestra presentación?” // “Are there any other words or phrases that are important to include on our display?”
• As students share responses, update the display by adding (or replacing) language, diagrams, or annotations.
• Remind students to borrow language from the display as needed.
• Display the expression:
• Ask previously selected students to share.
• “¿Por qué escogieron ese grupo de expresiones para encontrar el valor de ?” // “Why did you choose that set of expressions to find the value of ?” (I could find the values of the expressions mentally.)
• Display the expression:
• “¿Por qué nos puede ayudar empezar con la expresión   ?” // “Why is a helpful expression to start with?” ( is a helpful expression to start with because and 280 is close to 308.)
• “¿Cómo sabemos que  es la expresión que corresponde a ?” // “How do we know that is the expression that matches ?” ( )

• Invite selected students to share their reasoning for and explain why they started with their expression.
• Invite students to share how they changed their mind about which expressions to use during the activity.