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Place Value up to 100,000
Read How Much is a Million by David M. Schwartz and Steven Kellog
This book motivates kids to learn more about large numbers and place value with illustrations and examples that include:
- It would take twenty-three days to even count to a million and that a goldfish bowl large enough to hold a million goldfish could hold a whale.
- Seven pages are printed with tiny white stars on a grid pattern against a blue sky -- adding up to only one hundred thousand stars!
- A trillion children standing on each other's shoulders would almost reach to the rings of Saturn.
The author concludes with several pages of the mathematical calculations which support his examples, very clearly and humorously explained. An unusual idea, smoothly and amusingly presented.
Save the end of the story for wrap-up.
2 Direct Instruction
Students should already have a basic understanding of place value. This review is intended to prepare students for single and multi-digit multiplication and division.
Explain the importance of understanding place value: "Place value is the idea that each digit in a number represents a certain amount, depending on the position that it occupies (quick note: a “digit” is a particular number within a larger number; the “number” refers to the entire group of digits). Thus, a number like 465 has a 4 in the hundreds place, a 6 in the tens place, and a 5 in the ones place. The digit 4, in the hundreds place, does not represent 4 – it represents 400. Understanding this concept will make it easier to add or subtract numbers, as well as use multiplication in the future grades."--Ruth Rumack, http://ruthrumack.wordpress.com/2011/06/02/the-importance-of-place-value/
Show the following video to students: https://www.khanacademy.org/math/cc-fourth-grade-math/cc-5th-place-value...
In this 00:02:24 video, Sal Khan demonstrates how to find the value of a digit by writing numbers in expanded notation as well as word form. He breaks down the number 4,356 into their individual values and names the value of each.
This video provides a concrete example of finding the value of a digit within a number.
3 Guided Practice
Students will glue a template into their math notebooks that reflects the format of their work:
Model the first number for students using the same format shown in the video on the template pasted into their math notebooks. Explain that they must use that same format for the rest of the numbers.
Have students work in small, collaborative groups to practice writing numbers in expanded form and naming the value of each digit using the format in the template. The teacher should preselect the numbers.
While students work the teacher should check in with groups to check for understanding. During that time students will have the opportunity to ask clarifying questions. Pause for a mid-workshop interruption if neccessary.
4 Independent Practice
Have students create their own tutorial videos for writing numbers in expanded form and naming the value of each digit using Explain Everything. They can record themselves explaining the problem solving process, including any tips and hints they value. They can end with challenging practice questions for fellow classmates.
Finish reading How Much is a Million.
Encourage students to look for examples around their school and community of a large group of items (bricks on a wall, chairs in the media center) and share them with the class the next day.