Lesson 12

The purpose of this warm-up is to elicit students’ knowledge about 1 year as a measure of time and the ways it can be represented. The reasoning and conversations here will be helpful as students solve problems that involve time in years later in the lesson.

• Display: “1 year”
• “What do you know about 1 year?”
• 1 minute: quiet think time

• Record responses.

• “What does a year measure?” (time) 
• “What are some aspects of time that are related to a year?” (seasons, months, weeks, days)

In this activity, students use what they learned about multiplication of multi-digit numbers and unit conversion to solve problems involving measurements. Students may choose to represent the situations in a number of ways—concretely or visually (by drawing diagrams) or abstractly (by writing expressions and equations). While some problems can be reasoned additively, students may opt to reason multiplicatively for practical reasons.

Regardless of their chosen representations and reasoning strategy, students reason quantitatively and abstractly when they interpret and solve the questions about different units of time (MP2).

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

• Groups of 2–4
• Give each group tools for creating a visual display.
• “Today we’ll solve some problems that involve measurements.”
• “Before we solve any problem, let’s do some estimation.”
• Read the first problem as a class.
• “Estimate: About how many days old is the baby elephant?”
• 1 minute: quiet think time
• Display the following ranges and poll the class on their estimate. (Alternatively, post each range in a different part of the classroom and ask students to stand by the range that reflects their estimate.)
  • 280 to 299
  • 300 to 349 
  • 350 to 400
• Select a student who selected each range to explain their estimate. Then, ask students if they’d revise their estimate.

• “Take a few quiet minutes to solve the first two problems. Then, discuss your responses with your group and work on the last problem together.”
• 5 minutes: independent work time
• 5 minutes: group work time
• Monitor for the different representations and strategies used to solve the problems. 
• Assign one problem to each group.

MLR7 Compare and Connect

• “Create a visual display to show how you solved the problem assigned to your group. Organize your work so that it can be followed by others.”
• 3 minutes: group work time
• 5 minutes: gallery walk
• Prompt students to make note of the different strategies they see and any solutions that they question.

• “Most of the problems can be solved by multiplication. What is the same between the solutions and multiplication strategies that you saw? What’s different?”
• 30 seconds quiet think time
• 1 minute: partner discussion
• Record students’ responses, or display students’ diagrams and representations.
• “What are some common strategies for multiplying a multi-digit number by a one-digit number (48 and 7, or 366 and 3)?” 
• “What are some strategies you saw for multiplying 2 two-digit numbers (12 and 31)?”

This activity offers students more practice with using multiplication to solve contextual problems (MP2), including situations in which at least one factor is four digits long, and to generate a new problem according to some parameters. 

• Groups of 2–4

• 6–7 minutes: independent work time 
• 2–3 minutes: group discussion
• Monitor for the different ways students represent the situations and solve the problems.

• See lesson synthesis.