Lesson 17

The purpose of this True or False is to elicit strategies and understandings students have for multiplying one-digit whole numbers by multiples of 10. The reasoning students do here helps to deepen their understanding of the associative property as they decompose multiples of ten to make multiplying easier.

• Display one statement.
• “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

• Share and record answers and strategy.
• Repeat with each statement.

• “How can you justify your answer without finding the value of both sides?”
• Consider asking:
  • “Who can restate _____’s reasoning in a different way?”
  • “Does anyone want to add on to _____’s reasoning?”
  • “Can we make any generalizations based on the statements?”

The purpose of this activity is for students to consider a situation and think about all the mathematical questions they could ask about it. This gives students a chance to make sense of the situation before they are asked to solve problems. Students might choose to write a multiplication equation like \((g \times 6) + 94 = 142\). Acknowledge that this represents this situation, but focus the discussion in the synthesis on division to connect to the work in the next section.

• Groups of 2
• “This situation is about planning for a party. What are some things that you have to think of when you plan for a party?” (Making enough food. Places for people to sit or hang out. Activities for people to do.)
• 1 minute: quiet think time
• Share responses.

• “Now, work with your partner to come up with as many questions as you can about this situation.”
• 3–5 minutes: partner work time
• Share and record responses.
• Display: “How many guests fit at each table in Room B?” or circle the question if mentioned by a student.
• “Now work with your partner to answer this question.” (I found \(142 - 94\) to find out how many guests were in Room B. There were 48 guests and 6 tables, I put the same amount of guests at each table and there were 8 guests at each table.)
• 3–5 minutes: partner work time

• “What information did we use in the problem?” (The number of guests at the party. The number of guests in Room A. The number of tables in Room B.)
• “How could we record an equation with a letter for the unknown quantity that would represent the problem? Explain your reasoning.” (\((142 - 94) \div 6 = g\). We had to find \(142 - 94\) to find out how many people were in Room B. We had to divide the number of people in room B by 6 to find out how many guests were at each table. The g represents how many guests fit at each table in Room B.)
• Display: \((142 - 94) \div 6 = g\)
• If students don’t use parentheses, say: “In this equation, we can use parentheses to show that we subtracted first.”
• “The parentheses show us that the subtraction is done first in the equation to represent the problem. Keep this in mind as you work on the next activity.”

The purpose of this activity is for students to solve two-step word problems using all four operations. Students should be encouraged to solve the problem first or write the equation first, depending on their preference. Encourage students to use parentheses if needed to show what is being done first in their equations.

When students make sense of situations to solve two-step problems they reason abstractly and quantitatively (MP2).

• Groups of 2
• Give students access to grid paper and base-ten blocks.

• “Work independently to solve these problems and write an equation with a letter for the unknown quantity to represent each situation. You can choose to solve the problem first or write the equation first.”
• 5–7 minutes: independent work time
• “Share your solutions and your equations with your partner. Also, tell your partner if you think their solutions and equations make sense or why not.”
• 5–7 minutes: partner discussion

• “What equations did you write for each part of the problem?”
• “How could you combine your equations into one equation that would represent the problem?”

• For each problem have a student share their equation and discuss how it represents the problem.
• Consider asking:
  • “Where do we see ______ from the problem in the equation?”
  • “What information from the situation did we need to solve and write our equation?”
  • “How are parentheses used in the equation?”