The purpose of this Warm-up is to elicit the idea of partial quotients, which will be useful when students learn a new way to record partial quotients in a later activity. While students may notice and wonder many things about these equations, the idea of dividing a number by decomposing the dividend into smaller and more-familiar parts are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Arrange students in groups of 2. Display the problem stem and four equations for all to see. Give students 1 minute of quiet think time and ask them to be prepared to share at least one thing they notice and one thing they wonder about. Give students another minute to discuss their observations and questions.
Here are Kiran’s calculations for finding 657÷3:
\begin{align} 600 ~\div~ 3 &= 200 \\[2ex] 30 ~\div~ 3 &= \phantom{2}10 \\[2ex] 27 ~\div~ 3 &=\phantom{21}9\\ \overline{\hspace{2mm} 657~\div~ 3} &\overline {\hspace{1mm}= 219 \hspace{2mm}} \end{align}
What do you notice? What do you wonder?
Students may notice:
Students may wonder:
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the equations. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If no students mentioned that Kiran did not decompose the 657 strictly by place value, ask students to discuss this idea and whether it would be just as productive to decompose 657 into 600, 50, and 7.
All skills for this lesson
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The purpose of this Warm-up is to elicit the idea of partial quotients, which will be useful when students learn a new way to record partial quotients in a later activity. While students may notice and wonder many things about these equations, the idea of dividing a number by decomposing the dividend into smaller and more-familiar parts are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Arrange students in groups of 2. Display the problem stem and four equations for all to see. Give students 1 minute of quiet think time and ask them to be prepared to share at least one thing they notice and one thing they wonder about. Give students another minute to discuss their observations and questions.
Here are Kiran’s calculations for finding 657÷3:
\begin{align} 600 ~\div~ 3 &= 200 \\[2ex] 30 ~\div~ 3 &= \phantom{2}10 \\[2ex] 27 ~\div~ 3 &=\phantom{21}9\\ \overline{\hspace{2mm} 657~\div~ 3} &\overline {\hspace{1mm}= 219 \hspace{2mm}} \end{align}
What do you notice? What do you wonder?
Students may notice:
Students may wonder:
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the equations. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If no students mentioned that Kiran did not decompose the 657 strictly by place value, ask students to discuss this idea and whether it would be just as productive to decompose 657 into 600, 50, and 7.