Title: Oral and written numerals

Grade Level 5 - 6

Name Dr. Robert Sweetland

Concept Assessment Information

Concepts

Supporting Information

Misconceptions

Assessment

Patterns in place value help us write and read numbers.

1. Numbers are written following a certain pattern.
2. Three digits are grouped with commas.
3. Decimal place is a marker not a place.
4. There is only one units place.
5. Pattern of thousand, million...
6. Pattern of ___, ten, hundred,

1. Each number has a certain way to be said and written that must be memorized .
2. A pattern for determining how numbers are written and said orally is too complicated for most people to understand.

Diagnostic
Ask students to describe how they can use a pattern to help them say and write number words.

Concepts

Supporting Information

Misconceptions

Assessment

Numbers are communicated in a standard way.

1. Numbers are represented orally.
2. Numbers are represented in writing.
3. Number words have correct spellings.
4. Number words have a grammar.

1. There are many standard ways to write numbers.

Diagnostic
Ask a student to write a number on the board and another to read the numeral and another to write the numeral in words.

Summative
Repeat with all possible combinations until students say they could do any number in the world.

Procedure for Concept Conceptualization and Generalization

Students will look for patterns in a place value chart and use it to create a procedure for writing, reading, and saying numbers from millionths to millions.

Materials: ------ Number facts sheet,-------- place value number line

Exploration

1. Put students in pairs.
2. Pass out place value chart and challenge students to find as many patterns as they can in five minutes.
3. Put pairs of students into groups of four and ask them to consolidate their list.

Invention

1. Have students consolidate all group’s lists into one class list on the board or overhead.
2. Discuss results.
3. Be sure that all patterns outlined in the supporting information are discussed.

Exploration

1. Tell students they will explore in groups of four.
2. Give students the number facts sheet.
3. Ask students to do two things:

• Use the place value chart and the information on the fact sheet to explain how all the 14 examples are read and written.
• Create a rule that would explain how to read or write any number less than one million and greater than one millionth.

Invention

1. Have each group share their rule.
2. As each group shares have other groups give them numerals to read and write to see if the rule works or not.
3. Continue until all groups share their rule.
4. Have students identify which rule(s) they will use.
5. Have students create a problem they believe will test the limits of their rule.
6. Have students exchange their problems with their original partner, use their preferred rule, write the word number, read it to each other, and determine if the rule works.
7. Ask students if patterns can help them solve real world problems.

1. Have students create a list of nine numbers: three written in words, three in numberals, and three either way for a partner to read.
2. Have students exchange and write or say the numbers in different ways.