standard_description: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., p^(2)). For example, by truncating the decimal expansion of Ö2, show that Ö2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
problem_activity: Optional activity
This optional activity is an opportunity to practice the methods in this lesson to calculate products of decimals, and students have an opportunity to practice multiplying decimals in a real-world context. Students can choose to use area diagrams to help organize their work and support their reasoning. However, the goal of the activity is to have students practice using the multiplication algorithm on decimals.
Launch
Give students quiet think time to complete the activity and then time to share their explanation with a partner. Follow with whole-class discussion.
Representation: Internalize Comprehension.
Activate or supply background knowledge. Provide students with access to a blank area diagram to support information processing.
Supports accessibility for: Visual-spatial processing; Organization
Student Facing
Calculate each product. Show your reasoning. If you get stuck, consider drawing an area diagram to help.
\((5.6) \boldcdot (1.8)\)
\((0.008) \boldcdot (7.2)\)
A rectangular playground is 18.2 meters by 12.75 meters.
Find its area in square meters. Show your reasoning.
If 1 meter is approximately 3.28 feet, what are the approximate side lengths of the playground in feet? Show your reasoning.
Student Response
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Student Facing
Are you ready for more?
Write the following expressions as decimals.
\(1-0.1\)
\(1-0.1+10-0.01\)
\(1-0.1+10-0.01+100-0.001\)
Describe the decimal that results as this process continues.
What would happen to the decimal if all of the addition and subtraction symbols became multiplication symbols? Explain your reasoning.
Student Response
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Activity Synthesis
Select students to share their strategies, being sure to highlight approaches using area diagrams and vertical calculations. Record the representations or strategies students share and display them for all to see.
Representing, Conversing: MLR8 Discussion Supports.
Use this routine help students prepare to share their strategies with the class. Give students time to discuss how they calculated each product for the first problem with a partner. Consider using this prompt to begin the conversation: “How did you use the multiplication algorithm to calculate the product of these two decimals? Provide a step-by-step explanation.” The listener should press for details by asking clarifying questions such as, “Why did you do that first?” and “Could you explain that a different way?” Allow each student an opportunity as the speaker and listener. This will help students build confidence in explaining the process of multiplying decimals before students are selected in the whole-class discussion.
Design Principle(s): Support sense-making; Cultivate conversation


aligns: no