Lesson 3

The purpose of this Number Talk is to elicit strategies and understandings students have for adding and subtracting multi-digit numbers. These understandings help students develop fluency and will be helpful in later units as students add and subtract multi-digit numbers fluently using the standard algorithm.

When students decompose addends to support mental addition they are looking for and making use of the base-ten structure of numbers (MP7). 

• Display one expression.
• “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.

• “How did the first couple of expressions help you reason about last two expressions?”
• Consider asking:
  • “Who can restate _____’s reasoning in a different way?”
  • “Did anyone have the same strategy but would explain it differently?”
  • “Did anyone approach the expression in a different way?”
  • “Does anyone want to add on to _____’s strategy?”

The purpose of this activity is to prompt students to reason about the relative sizes of two fractions with the same numerator and articulate how they know which one is greater. Students have done similar reasoning work (and used similar tools to support their reasoning) in grade 3, but here the fractions include those with denominators 5 and 10. When students observe that 5 equal parts are greater than 3 of the same equal part, regardless of the size of those parts, they see regularity in repeated reasoning (MP8).

To add movement to this activity and if time permits, assign each group a pair of fractions in the second question and ask them to create a visual display showing their reasoning. Then, allow a few minutes for a gallery walk. Ask students to identify any patterns they notice on the displays.

• Groups of 2

• “Take a few quiet minutes to answer the first three questions. Discuss your work with your partner before moving on to the last question.”
• 5–7 minutes: independent work time
• 3–4 minutes: partner discussion
• 2–3 minutes: independent work time on the last question

• “What do you notice about each pair of fractions in the second question?” (They all have 3 and 5 for the numerators, and they have the same denominator.)
• “What does it mean when two fractions, say \(\frac{3}{8}\) and \(\frac{5}{8}\), have the same denominator?” (They are made up of the same fractional part—eighths in this case.)
• “How can we tell which fraction is greater?” (Because the fractional parts are the same size, we can compare the numerators. The fraction with the greater numerator is greater.)

The purpose of this activity is for students to reason about the relative sizes of two fractions with the same numerator. As before, a diagram of fraction strips can be used to help students visualize the sizes of various fractional parts. When students discuss and improve their explanation for why \(\frac{70}{20}\) is greater than \(\frac{70}{100}\) they develop their mathematical communication skills (MP3).

This activity uses MLR1 Stronger and Clearer Each Time. Advances: Reading, Writing

• Groups of 2
• “What do you notice about the fractions in the first question?” (Each pair has the same numerator and has 3 and 5 for the denominators.)

• “Think quietly for a moment about how you can find out which fraction in each pair is greater. Then, share your thinking with your partner.”
• 1 minute: quiet think time
• 2 minutes: partner discussion
• Monitor for students who use the size of a unit fraction or one fractional part to help them make comparisons.
• “Take a few quiet minutes to work on the questions.”
• 7–8 minutes: independent work time

• Select students to share their responses to the first two questions. 
• “In the set of fractions you saw, why are the fractions with 3 for the denominator always greater than fractions with 5 for the denominator?” (A third is always greater than a fifth, so some number of thirds will always be greater than the same number of fifths.)

MLR1 Stronger and Clearer Each Time

• “Share your response to the third question with your partner. Take turns being the speaker and the listener. If you are the speaker, share your explanation. If you are the listener, ask questions and give feedback to help your partner improve their explanation.”
• 3–5 minutes: structured partner discussion 
• Repeat with 2–3 different partners.
• “Revise your initial explanation based on the feedback from your partners.”
• 2–3 minutes: independent work time