Lesson 1

Lizardland Problems

Est. Class Sessions: 1–2

Developing the Lesson

Discuss Math Practices. Tell students they will work in pairs to solve the questions on the Lizardland Problems pages in the Student Guide. Explain that they will have to read problems and look carefully at the pictures in their books to find the information needed to answer the problems. Display and refer students to the Math Practices page in the Student Guide Reference section as you discuss the Math Practices Expectations as related to Question 1A in the Student Guide.

Use the following prompts:

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  • Tell in your words what question needs to be answered. (Possible response: We need to find out how many people can ride on the roller coaster together if all the seats are filled.)
  • What is the important information needed to solve this problem? (eight cars on the roller coaster; four people can ride in each car)
  • Where did you find the needed information? (The problem said there were eight cars, and the picture shows four people in one car.)
  • What are some strategies and tools you might use to solve this problem? (Answers will vary. Some possible strategies: draw a picture, use the picture to count, use repeated addition, or multiply 4 × 8)
  • How would you label your answer? How do you know which word to use? (The question asks, “How many people …,” so I would label the answer with the word people. Some number of people can ride in 8 cars on the roller coaster.)
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Children often invent their own strategies for solving multiplication problems. Other strategies are developed through conversations with others. Even after students have developed proficiency with paper-and-pencil algorithms, these invented methods are helpful for mental arithmetic and estimation. Allowing students to explore their own ideas and hear the ideas of their classmates helps them develop flexibility with numbers and computation.

Use Strategies to Solve Multiplication Problems. Tell student pairs to solve Questions 1–9 reminding them to use the Math Practices while solving the problems. Students can solve all of the problems using multiplication, but allow them to solve the problems in any way that makes sense to them. Encourage them to use a different strategy on each problem. Have counters available.

While students are working, identify some students to share their strategies with the class. Try to select a variety of strategies. Ask selected students to record their strategies on pieces of chart paper or other display and to name the strategy they used. Some students will use strategies they have learned (e.g., skip counting, repeated addition, reasoning from known facts) and others will invent strategies (e.g., using money, using number lines). When using a calculator students should represent and explain their keystrokes with a number sentence. See Sample Dialog 1 and Figures 1–4 for examples of strategies used by students to solve Questions 1 and 2. See Sample Dialog 2 and Figures 5–7 for examples of strategies used by students to solve Questions 4 and 5.

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Use Check-In: Questions 8–9 on the Lizardland Problems pages in the Student Guide to assess students' abilities to represent multiplication problems with number lines, drawings, and number sentences [E1]; use appropriate and efficient strategies to solve multiplication problems [E2, MPE2]; read problems carefully to find what information is important [MPE1]; show work [MPE5]; and use labels to explain solutions and strategies [MPE6].

The workshop in Lesson 10 provides targeted practice with representing and using strategies to solve the multiplication facts.

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To better facilitate students' writing and solving of a multiplication problem in Question 9, give each student a piece of paper folded in half. Ask each student to write a multiplication problem on the front of the folded paper and write a solution on the inside of the folded paper. When a classmate solves the problem, the student writes his or her solution on the back of the folded paper.

Write and Solve Story Problems. Question 9 asks students to write their own multiplication problems. Students enjoy working with larger numbers, so their problems might involve numbers that they do not yet know how to multiply. Do not discourage students from using large numbers; problems that are too hard can be modeled with base-ten pieces or solved using calculators.

Ask students to trade and solve each other's problems. Encourage partners to ask each other clarifying questions to be sure they understand their partners' problems.

Ask student volunteers to share a few of the multiplication problems they have written.

As a problem is shared, ask:

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  • What question needs to be answered [MPE1]?
  • What is the important information needed to solve [student name]'s problem [MPE1]?
  • Share your strategy for solving this problem [MPE2], and show your work with a number sentence, number line, or pictures [MPE5].
  • What do the numbers in the solution stand for? Are labels included [MPE6]?

If the problem is unclear, encourage students to make helpful editing suggestions to the author.

Student Guide: 190 191 192 193
Answers
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Student Activity Book:
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