Lesson 3

This Number Talk encourages students to think about equivalent forms of whole numbers and decomposing fractions in order to subtract. When students consider equivalent fractions, look for ways to decompose fractions, or use the structure of mixed numbers to find the value of each difference, they look for and make use of structure (MP7). 

• Display one expression.
• “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 expressions and work displayed.
• Repeat with each expression.

• “¿En qué se parecen estas expresiones?” // “How are these expressions alike?” (They all involve subtracting \(\frac{8}{10}\) from a number that is at least 1. To subtract, it’s helpful or necessary to decompose a 1 or to write an equivalent fraction.)
• “¿Cómo usaron las primeras expresiones como ayuda para encontrar el valor de las últimas expresiones?” // “How did you use earlier expressions to help you find the value of later expressions?”

In previous lessons, students have used their understanding of fraction equivalence to compare fractions and solve problems. The purpose of this activity is to practice solving addition and subtraction problems involving decimal fractions (MP2). Students use what they know about equivalent fractions and the relationship between 10 and 100 to add tenths and hundredths.

• Groups of 2

• 1–2 minutes: independent work time
• “Comparen sus estrategias con las de su compañero” // “Compare your strategies with your partner’s.”
• 5 minutes: partner discussion
• Monitor for expressions, strategies, and representations students use to determine connections between strategies and evidence of reasoning about equivalence.

• Invite previously identified students to share how they solved the problems.
• “¿En qué se parecen resolver estos problemas y resolver los problemas de las lecciones anteriores? ¿En qué son diferentes?” // “How was solving these problems the same as the problems we solved in previous lessons? How was it different?” (It was the same because we were adding and subtracting mixed numbers. We still looked for ways to make a new whole number when we could. We had to add up fractions that had different denominators in these problems. We had to compare with a decimal fraction written with decimal notation.)

The purpose of this activity is to create and solve addition and subtraction problems with fractions. Students first create stories to match a given value or equation and some given constraints. 

• Groups of 2
• “Piensen en una situación que tenga un problema que se pueda resolver encontrando el valor de \(3\frac{4}{10} + \frac{2}{10} + \frac{1}{2}\)” // “Think of a situation with a problem that could be solved by finding the value of \(3\frac{4}{10} + \frac{2}{10} + \frac{1}{2}\).”
• 1–2 minutes: partner discussion
• Share responses.

• 5–6 minutes: independent work time
• 4–5 minutes: compare with a partner
• Monitor for students who create situations that involve different problem types. For example, for the problem that can be solved with addition, look for students who create an Add to, Result Unknown problem and a student who creates a Compare, Difference Unknown problem.

• Invite 1–2 previously identified students to share their situations for each problem.
• “¿En qué se parecen estas situaciones? ¿En qué son diferentes? ¿De qué manera cada una corresponde a las instrucciones?” // “How are these situations the same? How are they different? How does each one match the directions?”