Lesson 25

The purpose of this Number Talk is to elicit strategies and understandings students have to divide whole numbers by decimals. These understandings help students develop fluency and will be helpful later in this lesson when students divide decimals greater than 1 by decimals less than 1.

• Display one problem.
• “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.
• Keep problems and work displayed.
• Repeat with each problem.

• “¿Por qué \(50 \div 2\) y \(5 \div 0.2\) tienen el mismo valor?” // “Why do \(50 \div 2\) and \(5 \div 0.2\) have the same value?” (Because 5 is 50 tenths and I am dividing that into groups of 2 tenths so that's \(50 \div 2\).)

The purpose of this activity is for students to divide decimal numbers by 0.1 and 0.01. They are given diagrams to help see that there are 10 tenths in each whole and 100 hundredths in each whole. The diagrams are not labeled with the whole so that the same diagram which shows \(1.6 \div 0.1 = 16\) can be interpreted as whole number division showing \(160 \div 10 = 16\). This dual way of interpreting one diagram is highlighted in the synthesis. When students interpret the diagram as representing two different equations they attend to precision in the meaning each part of the diagram (MP6).

• Groups of 2

• 5 minutes: independent work time
• 5 minutes: partner work time
• Monitor for students who:
  • Describe how Jada's diagram shows the value of \(1.6 \div 0.1\) as 16.
  • Describe how Jada's diagram also represents the expression \(160 \div 10\).

• Ask selected students to share their reasoning for each problem.
• Display: \(1.6 \div 0.1 = 160 \div 10\)
• “¿Cómo se muestra en el primer diagrama que esta ecuación es verdadera?” // “How does the first diagram show that this equation is true?” (If each large square is a whole then the number of shaded strips is \(1.6 \div 0.1\) and if each large square is 100 then the number of those strips is \(160 \div 10\). The same diagram represents both expressions so they are equal.)
• Display: \(1.3 \div 0.01  =130 \div 1\)
• “¿Cómo se muestra en el segundo diagrama que esta ecuación es verdadera?” // "How does the second diagram show that this equation is true?" (If each large square is a whole then the number of small pieces represents \(1.3 \div 0.01\) and if each large square is 100 then the number of small pieces represents \(130 \div 1\).)

In this activity, students practice finding quotients of decimals divided by 0.1 and 0.01. Students find the value of different expressions without the scaffold of a diagram. Monitor for these approaches:

• diagrams
• whole number quotient facts
• multiples of the divisor

• Groups of 2
• Give students access to blackline master of grids.

• 8 minutes: independent work time
• 2 minutes: partner discussion

• Display:

  \(0.5 \div 0.1 = 5\)

  \(0.50 \div 0.01 = 50\)

• “¿Cómo podemos usar el significado de los valores que están en las posiciones decimales para explicar estas ecuaciones?” // “How can we use the meaning of decimal place values to explain these equations?” (5 tenths is the same as 50 hundredths so that’s 5 groups of 0.1 or 50 groups of 0.01.)
• “¿Cómo nos ayuda usar el significado de los valores que están en las posiciones decimales a encontrar el valor de \(1.53 \div 0.01\)?” // “How can we use the meaning of decimal place values to help find the value of \(1.53 \div 0.01\)?” (The three is in the hundredths place so there are 3 one hundredths in three hundredths. The 5 is in the tenths place and there are 10 hundredths in each tenth so that's 50 more hundredths. There are 100 hundredths in one whole. That's 153 hundredths altogether in 1.53.)