Lesson 3

Doubles and Halves

Est. Class Sessions: 2

Summarizing the Lesson

To introduce the Guess My Rule game, show the Guess My Rule Machine Master or a box decorated to look like a Guess My Rule Machine. Tell students that they will give you a small number, and you will tell them the result of what happens to the number after you put it in the Guess My Rule Machine. To begin, add one to the number a student suggests. Write down their suggestions as well as the output from the machine in a data table with two columns: Input and Output. Let students guess the rule. Students should be able to explain how they guessed the rule. When the rule is guessed, write the rule at the top of the table. See Figure 7.

Play a few more rounds of Guess My Rule. Some suggestions for rules to guess:

  • Add two.
  • Add ten.
  • Number partner to make a ten (the numbers must be ten or less). For example, if a student suggests the number 7, then the output is 3 because 7 + 3 = 10.
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For each of the rules, students might want to use their connecting cubes to verify their guesses.

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Some students are going to be comfortable guessing rules; others may be more confident testing those rules but not generating their own guesses. Record rules from several students, then ask students to test each rule and explain why it works or why it does not.

When you have almost full participation from the class, go to doubling the number for the next game. For the final game, ask students for an even number input for halving.

After students identify the doubling and halving rules, ask:

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  • How are doubling and halving related? Think about your papers with holes [dots], cube towers, and the Guess My Rule Machine. (Possible responses: Doubling is making two of the same thing and halving is dividing it into two equal things. When you find half, you are back to the original number.)
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Halving only even numbers allows students to verify that the two towers of connecting cubes are the same height. As students are not really familiar with one-half, and cannot take one-half of a connecting cube, it is best to ask students to halve only even numbers. Halving an even number will always result in a whole number. You can ask a student who is ready for a challenge to halve a number like 7. Encourage them to share their thinking with drawings or connecting cubes.

Play one Guess My Rule game again with a variation. To vary the game, start by telling the rule and alternate between giving the input or output, leaving the other column blank. For example, tell the rule "add one" and fill in 7 in the output column. Students then determine that the input is 6. Or, fill in 8 in the input column, then students determine the output is 9.

Assign the Guess the Output Homework Master to promote critical thinking skills and reinforce computation strategies.

Provide connecting cubes or other counters and tools for students to independently complete the Doubles and Halves page from the Student Activity Book on which students are asked to fill in tables for doubles and halves.

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Use the Doubles and Halves page from the Student Activity Book to assess students' abilities to represent doubles and halves using counters and number sentences [E1] and use mental math strategies and reasoning strategies (e.g., using doubles) to solve addition and the related subtraction problems with sums up to 20 [E5].

Place several different copies of the Guess My Rule Machine Master in a center to provide targeted practice.

Student Guide:
Student Activity Book: 369
Answers
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SAB_Mini
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Master:
Data table for the add one rule
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