Field Trip

Est. Class Sessions: 2

Developing the Lesson

Subtraction Problems on a Field Trip. Direct students' attention to the Field Trip pages in the Student Guide.

Discuss the first paragraph and ask:

If it is hard for the students to write, how are they going to solve the problems? (They can try to do them in their heads or just make a few notes.)

Ask students to work in pairs to answer Question 1. Encourage them to pretend that they are on the field trip with Mrs. Dewey's students, so they must answer the question while standing in the museum with a clipboard. Tell them they can make notes on scrap paper, but they should try to solve the problems using mental math as much as possible.

For example, Question 1 asks how many empty seats there are on a 40-seat bus if there are 25 students, the teacher, and two parents on the bus. Students may want to jot down the total number of people on the bus (28) before subtracting it from 40. Possible strategies include:

Counting up from 28 to 40: 28 + = 30 and 30 + = 40. Then 2 + 10 = 12.
Counting back from 40: 40 − 20 = 20 and 20 − 8 = 12.

Students may count in their heads or visualize a number line.

Although students would probably not carry a number line to a museum, encourage students to use their desk number lines. This will help them learn to visualize working with number lines in their heads.

When students have solved the problem, ask volunteers to share their strategies with the class. Help students record their thinking on chart paper or the board, and label the strategies with students' names. As volunteers explain their thinking, encourage students to ask clarifying questions.

When a few strategies have been recorded, ask:

Suppose there were 50 seats on the bus and 36 passengers. How many empty seats would there be? Use the strategy [student's name] used to solve Question 1 to solve this problem.

Ask students to work in pairs to solve Questions 2–6. Remind them to be prepared to share their strategies with the class.

As students work, use the following prompts as appropriate:

Tell me what you were thinking when you solved the problem.
What did you “see” in your head? Did you see a number line?
Did you count in your head? If so, how?
Did you take the number apart? If so, how?
How did you use tens and ones?

Comparing Strategies. Ask students to solve the problem in Question 7 in the Student Guide using their own strategies before reading further. Students must subtract 19 from 42. This question is followed by three possible strategies: Jerome uses a number line strategy; Tanya counts up from 19 to 42; and Nila uses expanded form.

Ask students to study the three strategies and to compare them using prompts similar to those use with Questions 2–6 and the following:

How did Jerome use tens and ones? (Jerome used a number line. He knew that 20 was 1 more than 19, so he first subtracted 20 to go from 42 to 22. Then he went forward one.)
How did Tanya use tens and ones? (Tanya counted on two tens and got close to 42. Then she counted by ones.)
How did Nila use tens and ones? (Nila broke each number into tens and ones and then she wrote them in expanded form. She got stuck when she tried to subtract, so she wrote 42 a different way so she could subtract the 9 ones. Then all she had to do was subtract the tens.)
Are any of the strategies that you used for Questions 1–6 like any of these three strategies? How are they alike? How are they different?
Did you count by tens or ones? If so, how?
Did you use your desk number line? If so, how?
Which of the strategies is the easiest to use or understand? Why do you think so?
Which is the most efficient?

While Nila's strategy is not efficient, it is included here in preparation for developing paper-and-pencil methods that involve regrouping in Lessons 3 and 4. This strategy helps students understand that when they regroup, the value of the number does not change. They have just partitioned the number in a different way using tens and ones.

Ask students to solve Question 8. Students must solve the problem using one of the three strategies discussed above. Discuss students' solutions and why they chose the method they did.

Students complete the problems in Question 9. Encourage them to try new methods that they have learned through the class discussions and to check their solutions using a second solution strategy. As students work, ask them to explain their thinking. It may be useful for students to make a table similar to the table in Figure 1.

When students have completed the problems, use the bulleted questions you asked for Questions 1–7 to discuss their choice of strategies.

Student Guide: 155 156 157

Answers