Lesson 9

The purpose of this Number Talk is to elicit strategies and understandings students have for finding the value of differences when they may need to decompose a ten. When students consider how they can use known differences, like \(10 - 6\) or \(14 - 6\), to find the value of the other expressions, they look for and make use of structure and express regularity in repeated reasoning (MP7, MP8).

• 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 can you use the result of \(14 - 6\) to find the value of \(54 - 6\)?” (54 has 4 more tens than 14 so add 4 tens or 40 to the result of \(14 - 6\).)
• “How can you use the result of \(54 - 6\) to find the value of \(54 - 26\)?” (26 has 2 more tens than 6 so that means 2 tens need to be taken away from the answer to \(54 - 6\).)

The purpose of this activity is to sort story problems into categories students choose. Monitor for students who identify these types of story problems:

• one-step problems
• two-step problems
• problems that compare quantities

Students may also use addition, subtraction, or both addition and subtraction as their categories. This may create some ambiguity since students might sort based on the operation suggested by the overall story structure or by the operation they would use to solve the problem. Some of the two-step stories may require both operations to solve. If students use the operations to sort and sort in different ways, this provides a good opportunity for discussion.

The goal of the activity synthesis is to share the different characteristics students used to sort the problems.

• Create a set of cards from the blackline master for each student.

• Groups of 2
• “At the end of each school year, some schools donate books to families or charities to encourage summer reading. The students and teachers sort books, so they can decide which ones to keep and which ones to give away.”
• “Some students reflect on the books they have read and choose their favorites. Many students think about the books they hope to read over the summer.”
• “You will be sorting and solving story problems about books and reading.”
• As needed, consider asking:
  • “Which of the books that you read this year would you want to keep and which would you be fine giving away?”
  • “What ways could you sort the books in our (classroom) library?”
  • “How many books are you hoping to read this summer?”

• “In this activity, you are going to sort the story problems in a way that makes sense to you.”
• “You can think about the categories you would like based on what you notice is the same or different about the stories and how you might solve them.”
• 5 minutes: independent work time
• “Compare your sort with your partner’s. How are your sorts the same? How are they different?”
• 5 minutes: partner discussion
• Monitor for students who sort their cards in different ways.

If students sort the story problems based on non-mathematical characteristics (for example, character names), consider asking:

• “Can you explain how you decided the groups for your sort?”
• “How could you sort the cards based on what you know from the story and what is unknown?”

• Invite selected students to share the categories for their sorts.
• Record the various categories.
• If students do not sort in any of the ways suggested in the student responses, propose these categories and ask them to sort.

The purpose of this activity is to solve the story problems from the first activity. Monitor for the different ways students represent their thinking and solve their selected problems including:

• tape diagrams to make sense of the problems
• base-ten diagrams
• equations

The goal of the activity synthesis is to share the different methods students used to make sense of and solve story problems (MP2).

• Groups of 2

• “Choose one of the story problems from the first activity to solve. Pick a different problem than your partner.”
• 5 minutes: independent work time
• “Share the method you used and the solution to your problem with your partner.”
• 5 minutes: partner discussion
• Monitor for students who solved the story with Jada’s stacks of books in different ways. 

• Invite selected students to share their solutions for the story with Jada’s pile of books in stacks of 10.
• “How are their methods the same? How are they different?”