Lesson 18

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information.

The expression allows students to preview the work of this lesson and give teachers insight into how students think about subtraction.

• Groups of 2
• Display the expression.
• “What is an estimate that’s too high?” “Too low?” “About right?”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

• “Is anyone’s estimate less than 30,000?”
• “Is anyone’s estimate greater than 40,000?”
• “Based on this discussion, does anyone want to revise their estimate?”
• “Let’s find out how to add and subtract numbers like these.”

The purpose of this activity is for students to add and subtract numbers through the thousands place in a way that makes sense to them. The numbers here do not require regrouping when subtracting. Throughout the activity, teachers have the opportunity to learn what students know about addition and subtraction through the hundreds place and how they apply that prior knowledge to work with four-digit numbers. Working with larger numbers sets the stage for students to think about the standard algorithm as an efficient way to add and subtract.

Students may need an orientation to the context. To give students an idea of what the number of steps means, share that it takes about 1,700 steps to walk a mile.

• Groups of 2
• Display the image in the task.
• “What do you notice? What do you wonder?”
• “Based on the data, when was the teacher most active that week? Least active?”

• 5 minutes: independent work time
• 3 minutes: partner work time

• Ask students to share responses and strategies for finding sums and differences. Record strategies.
• “Were there certain strategies that showed up a lot in this activity? Can we describe them?” (Yes, a lot of us added and subtracted by place value.)

The purpose of this activity is for students to analyze strategies for adding and subtracting numbers to the ten-thousands place. Students look at addition problems that require composing new units, when the sum of the digits in a particular place value exceeds 10. The subtraction problems do not require students to decompose a unit, as this will be addressed in future lessons. They look at 2 strategies.

Strategy A allows students to add each number in terms of the value of each digit, written in expanded form. Strategy B follows the same logic, but without writing the full value that each digit represents. Then, students use the same strategies to subtract without decomposing a unit.

When students perform operations on the quantities in the situation, they reason abstractly and quantitatively (MP2).

• Groups of 2
• “Now let’s look at the weekend activity,”
• Display the image in the task.
• “What do you notice about the number of steps the teacher took during the week versus on the weekend?” (The teacher took a lot more steps each day during the weekend.)

• 2 minutes: quiet think time
• 6–7 minutes: partner work time

• Ask students to explain how the strategies are alike and how they are different. (They both add by place value and get the same answer, but one strategy breaks each number up and the other does not.)
• “Why might a student have used one of the strategies instead of the other?”
• “Strategy B is called the standard algorithm and is useful when we add and subtract large numbers.”