wikisori - User contributions [en]

Decimals Operations Subtraction (lesson 2)

2020-08-20T17:32:20Z

Kdmullins: /* Variation */

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Decimal beads and disks
* Three sets of decimal numeral cards
* Cardboard strip as long as the decimal board
* Prepared problems
* Paper and pencil

* Optional/Alternative: Montessori bead bars

 

=== Preparation ===

Students should have had the Introductory Decimal Lessons 1-9 and Addition with Decimals lesson 1.

 

=== Presentation ===

*Teacher can choose to use bead bars for this lesson to help make an impression for the difference in values.

* 1. Select the first problem: 6.4 - 2.8
* 2. Form the minuend and subtrahend with cards, placing the cards to the left of the board with the cardboard strip underneath (emphasizing the importance of placing the decimal disks in the proper place values).
* 3. Place the beads and disks for the minuend on the board. Beginning with the tenths, remove the amount in the subtrahend, exchanging a unit for ten more tenths. Place the quantity taken away on the table beside the board, so it can be used to check work at the end.
* 4. Form the remainder with cards, and place them under the other cards. Have the child record the problem in his notebook.

[[File:Subtracting_with_decimals_page_61.jpg|300px]]

NOTE: Provide problems which involve a great deal of exchanging, e.g., 3.000 - 0.123 and 1.000000- 0.999999

* Again, most students will work with this material for a very short time, because they will be able to internalize the procedure and proceed abstractly.

=== Control Of Error ===

Teacher guided; lining up the disks in the proper decimal place values. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the student on how to perform operations with decimals.

 

=== Variation ===

Alternative: Use bead bars instead of beads and disks.

[[File:Alternative_subtracting_decimals.jpg|300px]]

 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Operations Subtraction (lesson 2)

2020-08-20T17:31:13Z

Kdmullins: /* Presentation */

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Decimal beads and disks
* Three sets of decimal numeral cards
* Cardboard strip as long as the decimal board
* Prepared problems
* Paper and pencil

* Optional/Alternative: Montessori bead bars

 

=== Preparation ===

Students should have had the Introductory Decimal Lessons 1-9 and Addition with Decimals lesson 1.

 

=== Presentation ===

*Teacher can choose to use bead bars for this lesson to help make an impression for the difference in values.

* 1. Select the first problem: 6.4 - 2.8
* 2. Form the minuend and subtrahend with cards, placing the cards to the left of the board with the cardboard strip underneath (emphasizing the importance of placing the decimal disks in the proper place values).
* 3. Place the beads and disks for the minuend on the board. Beginning with the tenths, remove the amount in the subtrahend, exchanging a unit for ten more tenths. Place the quantity taken away on the table beside the board, so it can be used to check work at the end.
* 4. Form the remainder with cards, and place them under the other cards. Have the child record the problem in his notebook.

[[File:Subtracting_with_decimals_page_61.jpg|300px]]

NOTE: Provide problems which involve a great deal of exchanging, e.g., 3.000 - 0.123 and 1.000000- 0.999999

* Again, most students will work with this material for a very short time, because they will be able to internalize the procedure and proceed abstractly.

=== Control Of Error ===

Teacher guided; lining up the disks in the proper decimal place values. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the student on how to perform operations with decimals.

 

=== Variation ===

Alternative: Use bead bars instead of beads and disks:
Picture 4

 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Operations Addition (lesson 1)

2020-08-20T17:29:06Z

Kdmullins: /* Variation */

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Decimal beads and disks
* Three sets of decimal numeral cards
* Cardboard strip as long as the decimal board
* Prepared problems
* Paper and pencil

* Optional/Alternative: Montessori bead bars

 

=== Preparation ===

Students should have had the Introductory Decimal Lessons 1-9.

 

=== Presentation ===

*Teacher can choose to use bead bars for this lesson to help make an impression for the difference in values.
* 1. Select the first problem: 8.38 + 6.75
* 2. Make the top addend with cards, and place it to the left of the board. Then make the second addend with cards, placing it under the first. Place the cardboard strip under both.
* 3. Form the first addend with beads and disks on the board. Then form the second addend on the board, leaving a space between the two addends.

[[File:Adding_with_decimals_1_page_59.jpg|300px]]

* 4. Begin adding with hundredths: 8 + 5 = 13. Exchange the hundredths for a tenth, leaving three thousandths. continue adding tenths, then units- exchanging when necessary, until the sum is reached. When the addition is complete, get the small cards corresponding to the sum, and place them under the addend cards.

[[File:Adding_with_decimals_2_page_59.jpg|300px]]

NOTE:
* Provide examples that offer many opportunities for exchanging, e.g., 0.999999 + 0.000001
* Provide other problems with addends having unequal numbers of decimal places, '''''Italic text'''Pointing out the importance of lining up the decimal mounts inside the proper place values.'' Example: 32.285 + 7.94
* Provide other problems with more than two addends or with addends written horizontally, e.g. 52.74 + 6.5 + 23.88 =

* Most students will work with this material for a very short time, because they will be able to internalize the procedure and proceed abstractly.

=== Control Of Error ===

Teacher guided; lining up the disks in the proper decimal place values. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the student on how to perform operations with decimals.

 

=== Variation ===

Alternative: Use bead bars instead of beads and disks.

[[File:Adding_decimals_alternative.jpg|300px]]

 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Operations Addition (lesson 1)

2020-08-20T17:27:57Z

Kdmullins: /* Presentation */

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Decimal beads and disks
* Three sets of decimal numeral cards
* Cardboard strip as long as the decimal board
* Prepared problems
* Paper and pencil

* Optional/Alternative: Montessori bead bars

 

=== Preparation ===

Students should have had the Introductory Decimal Lessons 1-9.

 

=== Presentation ===

*Teacher can choose to use bead bars for this lesson to help make an impression for the difference in values.
* 1. Select the first problem: 8.38 + 6.75
* 2. Make the top addend with cards, and place it to the left of the board. Then make the second addend with cards, placing it under the first. Place the cardboard strip under both.
* 3. Form the first addend with beads and disks on the board. Then form the second addend on the board, leaving a space between the two addends.

[[File:Adding_with_decimals_1_page_59.jpg|300px]]

* 4. Begin adding with hundredths: 8 + 5 = 13. Exchange the hundredths for a tenth, leaving three thousandths. continue adding tenths, then units- exchanging when necessary, until the sum is reached. When the addition is complete, get the small cards corresponding to the sum, and place them under the addend cards.

[[File:Adding_with_decimals_2_page_59.jpg|300px]]

NOTE:
* Provide examples that offer many opportunities for exchanging, e.g., 0.999999 + 0.000001
* Provide other problems with addends having unequal numbers of decimal places, '''''Italic text'''Pointing out the importance of lining up the decimal mounts inside the proper place values.'' Example: 32.285 + 7.94
* Provide other problems with more than two addends or with addends written horizontally, e.g. 52.74 + 6.5 + 23.88 =

* Most students will work with this material for a very short time, because they will be able to internalize the procedure and proceed abstractly.

=== Control Of Error ===

Teacher guided; lining up the disks in the proper decimal place values. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the student on how to perform operations with decimals.

 

=== Variation ===

Alternative: Use bead bars instead of beads and disks:
Picture 3

 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

File:Subtracting with decimals page 61.jpg

2020-08-20T17:08:09Z

Kdmullins:

File:Alternative subtracting decimals.jpg

2020-08-20T17:06:15Z

Kdmullins:

File:Adding with decimals 2 page 59.jpg

2020-08-20T17:04:42Z

Kdmullins:

File:Adding with decimals 1 page 59.jpg

2020-08-20T17:03:51Z

Kdmullins:

File:Adding decimals alternative.jpg

2020-08-20T17:02:46Z

Kdmullins:

Decimals Operations Subtraction (lesson 2)

2020-08-20T15:57:36Z

Kdmullins: Initial presentation of subtracting with decimals.

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Decimal beads and disks
* Three sets of decimal numeral cards
* Cardboard strip as long as the decimal board
* Prepared problems
* Paper and pencil

* Optional/Alternative: Montessori bead bars

 

=== Preparation ===

Students should have had the Introductory Decimal Lessons 1-9 and Addition with Decimals lesson 1.

 

=== Presentation ===

*Teacher can choose to use bead bars for this lesson to help make an impression for the difference in values.

* 1. Select the first problem: 6.4 - 2.8
* 2. Form the minuend and subtrahend with cards, placing the cards to the left of the board with the cardboard strip underneath (emphasizing the importance of placing the decimal disks in the proper place values).
* 3. Place the beads and disks for the minuend on the board. Beginning with the tenths, remove the amount in the subtrahend, exchanging a unit for ten more tenths. Place the quantity taken away on the table beside the board, so it can be used to check work at the end.
* 4. Form the remainder with cards, and place them under the other cards. Have the child record the problem in his notebook.

Picture on 61

NOTE: Provide problems which involve a great deal of exchanging, e.g., 3.000 - 0.123 and 1.000000- 0.999999

* Again, most students will work with this material for a very short time, because they will be able to internalize the procedure and proceed abstractly.

=== Control Of Error ===

Teacher guided; lining up the disks in the proper decimal place values. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the student on how to perform operations with decimals.

 

=== Variation ===

Alternative: Use bead bars instead of beads and disks:
Picture 4

 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Operations Addition (lesson 1)

2020-08-20T15:14:39Z

Kdmullins: A concrete experience of adding decimals, stressing the importance of lining up the decimal points.

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Decimal beads and disks
* Three sets of decimal numeral cards
* Cardboard strip as long as the decimal board
* Prepared problems
* Paper and pencil

* Optional/Alternative: Montessori bead bars

 

=== Preparation ===

Students should have had the Introductory Decimal Lessons 1-9.

 

=== Presentation ===

*Teacher can choose to use bead bars for this lesson to help make an impression for the difference in values.
* 1. Select the first problem: 8.38 + 6.75
* 2. Make the top addend with cards, and place it to the left of the board. Then make the second addend with cards, placing it under the first. Place the cardboard strip under both.
* 3. Form the first addend with beads and disks on the board. Then form the second addend on the board, leaving a space between the two addends.

Picture 1 from page 59

* 4. Begin adding with hundredths: 8 + 5 = 13. Exchange the hundredths for a tenth, leaving three thousandths. continue adding tenths, then units- exchanging when necessary, until the sum is reached. When the addition is complete, get the small cards corresponding to the sum, and place them under the addend cards.

Picture 2 on page 59

NOTE:
* Provide examples that offer many opportunities for exchanging, e.g., 0.999999 + 0.000001
* Provide other problems with addends having unequal numbers of decimal places, '''''Italic text'''Pointing out the importance of lining up the decimal mounts inside the proper place values.'' Example: 32.285 + 7.94
* Provide other problems with more than two addends or with addends written horizontally, e.g. 52.74 + 6.5 + 23.88 =

* Most students will work with this material for a very short time, because they will be able to internalize the procedure and proceed abstractly.

=== Control Of Error ===

Teacher guided; lining up the disks in the proper decimal place values. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the student on how to perform operations with decimals.

 

=== Variation ===

Alternative: Use bead bars instead of beads and disks:
Picture 3

 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Comparing Decimal Numbers (lesson 9)

2020-08-19T02:32:17Z

Kdmullins: /* Variation */

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Decimal beads and disks
* Cardboard strip as long as the decimal board
* Prepared problems
* Paper and pencil

* Optional/Alternative: Montessori bead bars

 

=== Preparation ===

Students should have had the Decimal Lessons 1-8 (We are moving from the concrete toward the abstract).

 

=== Presentation ===

*Teacher can choose to use bead bars for this lesson to help make an impression for the difference in values.

* 1. "In this activity we're going to compare two numbers to see which is the larger, or whether both are equal to each other. Let's start with two whole numbers, so we can see the steps to follow."
* 2. Place the cardboard strip horizontally across the middle of the decimal board. Above the strip, form the quantity 138 with the beads; below the strip, form the quantity 161 (Teacher can choose to write the numeral on a slip, put at the bottom of Decimal Board)

[[File:Comparing_decimals_number_1_page_57.jpg|300px]]

* 3. "How do we know which number is larger? They both have the same number of hundreds, so we can't tell from that. One number has three tens, and the other has six. The number with six tens will be larger, regardless of any other differences after that."

Even if the first number were 139.999999999, and the other numbers were 160.000000000, the first number would still be smaller because it has fewer tens.

* 4. Replace the beads, and form the next pair of numbers on the board. In the top half, form the numeral 0.78. In the bottom half, form 0.6

[[File:Comparing_Decimal_number_2_page_57.jpg|300px]]

"Are there any whole numbers (hundreds, tens, units) at all in either number?" (no) "So we can't tell from the whole numbers which is the larger number. Let's go on the the tenths."

* 5. "The top number has seven tenths. The bottom number has six tenths. We don't have to look any further. The top number is larger, no matter what the rest of the number looks like." Invite the students to write this statement in their Math Journals: 0.78 > 0.6
* 6. Remove the disks, and form the next pair of numbers: 0.6 in the top and 0.60 in the bottom.

[[File:Comparing_decimal_number_1_page_58.jpg|300px]]

Compare whole numbers: neither number has any compare tenths: both numbers have six tenths: both numbers have six tenths. compare hundredths and other categories after that: neither number has any.

Both numbers are equal. Direct the students to write a statement in their Math journal: 0.6 = 0.60

Point out to the student that we can add zeros forever to the right of either number, and the value of the number wouldn't change.

* 7. Continue with other number pairs, increasing the level of difficulty gradually as you go. An example of a more complicated one is:
form 3.6667 in the top half, and 3.6671 in the bottom half.

[[File:Comparing_decimal_number_2_page_58.jpg|300px]]

"Compare whole numbers: both are equal there. Compare tenths: both have six. Compare hundredths: both have six."

"Compare thousandths: the top number has six the bottom number has seven. It is larger regardless of anything else after that."

Extension: Ordering three decimal numbers from least to greatest.

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Alternative: Use bead bars instead of beads and disks:

138 < 161:

[[File:Alternative_138_is_less_than_161.jpg|300px]]

0.78 > 0.6

[[File:Alternative_0.78_is_greater_than_0.6.jpg|300px]]
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Comparing Decimal Numbers (lesson 9)

2020-08-19T02:24:30Z

Kdmullins: /* Presentation */

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Decimal beads and disks
* Cardboard strip as long as the decimal board
* Prepared problems
* Paper and pencil

* Optional/Alternative: Montessori bead bars

 

=== Preparation ===

Students should have had the Decimal Lessons 1-8 (We are moving from the concrete toward the abstract).

 

=== Presentation ===

*Teacher can choose to use bead bars for this lesson to help make an impression for the difference in values.

* 1. "In this activity we're going to compare two numbers to see which is the larger, or whether both are equal to each other. Let's start with two whole numbers, so we can see the steps to follow."
* 2. Place the cardboard strip horizontally across the middle of the decimal board. Above the strip, form the quantity 138 with the beads; below the strip, form the quantity 161 (Teacher can choose to write the numeral on a slip, put at the bottom of Decimal Board)

[[File:Comparing_decimals_number_1_page_57.jpg|300px]]

* 3. "How do we know which number is larger? They both have the same number of hundreds, so we can't tell from that. One number has three tens, and the other has six. The number with six tens will be larger, regardless of any other differences after that."

Even if the first number were 139.999999999, and the other numbers were 160.000000000, the first number would still be smaller because it has fewer tens.

* 4. Replace the beads, and form the next pair of numbers on the board. In the top half, form the numeral 0.78. In the bottom half, form 0.6

[[File:Comparing_Decimal_number_2_page_57.jpg|300px]]

"Are there any whole numbers (hundreds, tens, units) at all in either number?" (no) "So we can't tell from the whole numbers which is the larger number. Let's go on the the tenths."

* 5. "The top number has seven tenths. The bottom number has six tenths. We don't have to look any further. The top number is larger, no matter what the rest of the number looks like." Invite the students to write this statement in their Math Journals: 0.78 > 0.6
* 6. Remove the disks, and form the next pair of numbers: 0.6 in the top and 0.60 in the bottom.

[[File:Comparing_decimal_number_1_page_58.jpg|300px]]

Compare whole numbers: neither number has any compare tenths: both numbers have six tenths: both numbers have six tenths. compare hundredths and other categories after that: neither number has any.

Both numbers are equal. Direct the students to write a statement in their Math journal: 0.6 = 0.60

Point out to the student that we can add zeros forever to the right of either number, and the value of the number wouldn't change.

* 7. Continue with other number pairs, increasing the level of difficulty gradually as you go. An example of a more complicated one is:
form 3.6667 in the top half, and 3.6671 in the bottom half.

[[File:Comparing_decimal_number_2_page_58.jpg|300px]]

"Compare whole numbers: both are equal there. Compare tenths: both have six. Compare hundredths: both have six."

"Compare thousandths: the top number has six the bottom number has seven. It is larger regardless of anything else after that."

Extension: Ordering three decimal numbers from least to greatest.

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Alternative: Use bead bars instead of beads and disks:
pictures
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Comparing Decimal Numbers (lesson 9)

2020-08-19T02:15:58Z

Kdmullins: /* Presentation */

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Decimal beads and disks
* Cardboard strip as long as the decimal board
* Prepared problems
* Paper and pencil

* Optional/Alternative: Montessori bead bars

 

=== Preparation ===

Students should have had the Decimal Lessons 1-8 (We are moving from the concrete toward the abstract).

 

=== Presentation ===

*Teacher can choose to use bead bars for this lesson to help make an impression for the difference in values.

* 1. "In this activity we're going to compare two numbers to see which is the larger, or whether both are equal to each other. Let's start with two whole numbers, so we can see the steps to follow."
* 2. Place the cardboard strip horizontally across the middle of the decimal board. Above the strip, form the quantity 138 with the beads; below the strip, form the quantity 161 (Teacher can choose to write the numeral on a slip, put at the bottom of Decimal Board)

[[File:Comparing_decimals_number_1_page_57.jpg|300px]]

* 3. "How do we know which number is larger? They both have the same number of hundreds, so we can't tell from that. One number has three tens, and the other has six. The number with six tens will be larger, regardless of any other differences after that."

Even if the first number were 139.999999999, and the other numbers were 160.000000000, the first number would still be smaller because it has fewer tens.

* 4. Replace the beads, and form the next pair of numbers on the board. In the top half, form the numeral 0.78. In the bottom half, form 0.6

[[File:Comparing_decimal_number_2_page_57.jpg|300px]]

"Are there any whole numbers (hundreds, tens, units) at all in either number?" (no) "So we can't tell from the whole numbers which is the larger number. Let's go on the the tenths."

* 5. "The top number has seven tenths. The bottom number has six tenths. We don't have to look any further. The top number is larger, no matter what the rest of the number looks like." Invite the students to write this statement in their Math Journals: 0.78 > 0.6
* 6. Remove the disks, and form the next pair of numbers: 0.6 in the top and 0.60 in the bottom.

[[File:Comparing_decimal_number_1_page_58.jpg|300px]]

Compare whole numbers: neither number has any compare tenths: both numbers have six tenths: both numbers have six tenths. compare hundredths and other categories after that: neither number has any.

Both numbers are equal. Direct the students to write a statement in their Math journal: 0.6 = 0.60

Point out to the student that we can add zeros forever to the right of either number, and the value of the number wouldn't change.

* 7. Continue with other number pairs, increasing the level of difficulty gradually as you go. An example of a more complicated one is:
form 3.6667 in the top half, and 3.6671 in the bottom half.

[[File:Comparing_decimal_number_2_page_58.jpg|300px]]

"Compare whole numbers: both are equal there. Compare tenths: both have six. Compare hundredths: both have six."

"Compare thousandths: the top number has six the bottom number has seven. It is larger regardless of anything else after that."

Extension: Ordering three decimal numbers from least to greatest.

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Alternative: Use bead bars instead of beads and disks:
pictures
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Comparing Decimal Numbers (lesson 9)

2020-08-19T02:13:21Z

Kdmullins: /* Presentation */ Pictures to go with lessons

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Decimal beads and disks
* Cardboard strip as long as the decimal board
* Prepared problems
* Paper and pencil

* Optional/Alternative: Montessori bead bars

 

=== Preparation ===

Students should have had the Decimal Lessons 1-8 (We are moving from the concrete toward the abstract).

 

=== Presentation ===

*Teacher can choose to use bead bars for this lesson to help make an impression for the difference in values.

* 1. "In this activity we're going to compare two numbers to see which is the larger, or whether both are equal to each other. Let's start with two whole numbers, so we can see the steps to follow."
* 2. Place the cardboard strip horizontally across the middle of the decimal board. Above the strip, form the quantity 138 with the beads; below the strip, form the quantity 161 (Teacher can choose to write the numeral on a slip, put at the bottom of Decimal Board)

[[File:Comparing_decimals_number_1_page_57.jpg|300px]]

* 3. "How do we know which number is larger? They both have the same number of hundreds, so we can't tell from that. One number has three tens, and the other has six. The number with six tens will be larger, regardless of any other differences after that."

Even if the first number were 139.999999999, and the other numbers were 160.000000000, the first number would still be smaller because it has fewer tens.

* 4. Replace the beads, and form the next pair of numbers on the board. In the top half, form the numeral 0.78. In the bottom half, form 0.6

[[File:comparing_decimal_number_2_page_57.jpg|300px]]

"Are there any whole numbers (hundreds, tens, units) at all in either number?" (no) "So we can't tell from the whole numbers which is the larger number. Let's go on the the tenths."

* 5. "The top number has seven tenths. The bottom number has six tenths. We don't have to look any further. The top number is larger, no matter what the rest of the number looks like." Invite the students to write this statement in their Math Journals: 0.78 > 0.6
* 6. Remove the disks, and form the next pair of numbers: 0.6 in the top and 0.60 in the bottom.

[[File:Comparing_decimal_number_1_page_58.jpg|300px]]

Compare whole numbers: neither number has any compare tenths: both numbers have six tenths: both numbers have six tenths. compare hundredths and other categories after that: neither number has any.

Both numbers are equal. Direct the students to write a statement in their Math journal: 0.6 = 0.60

Point out to the student that we can add zeros forever to the right of either number, and the value of the number wouldn't change.

* 7. Continue with other number pairs, increasing the level of difficulty gradually as you go. An example of a more complicated one is:
form 3.6667 in the top half, and 3.6671 in the bottom half.

[[File:Comparing_decimal_number_2_page_58.jpg|300px]]

"Compare whole numbers: both are equal there. Compare tenths: both have six. Compare hundredths: both have six."

"Compare thousandths: the top number has six the bottom number has seven. It is larger regardless of anything else after that."

Extension: Ordering three decimal numbers from least to greatest.

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Alternative: Use bead bars instead of beads and disks:
pictures
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

File:Comparing decimal number 2 page 58.jpg

2020-08-19T02:05:38Z

Kdmullins:

File:Comparing decimal number 1 page 58.jpg

2020-08-19T02:03:39Z

Kdmullins:

File:Comparing Decimal number 2 page 57.jpg

2020-08-19T02:01:58Z

Kdmullins:

File:Comparing decimals number 1 page 57.jpg

2020-08-19T01:59:58Z

Kdmullins:

File:Alternative 0.78 is greater than 0.6.jpg

2020-08-19T01:58:22Z

Kdmullins:

File:Alternative 138 is less than 161.jpg

2020-08-19T01:56:49Z

Kdmullins:

Decimals Comparing Decimal Numbers (lesson 9)

2020-08-19T01:30:36Z

Kdmullins: This is a very important lesson that forms and impression on comparing decimal values.

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Decimal beads and disks
* Cardboard strip as long as the decimal board
* Prepared problems
* Paper and pencil

* Optional/Alternative: Montessori bead bars

 

=== Preparation ===

Students should have had the Decimal Lessons 1-8 (We are moving from the concrete toward the abstract).

 

=== Presentation ===

*Teacher can choose to use bead bars for this lesson to help make an impression for the difference in values.

* 1. "In this activity we're going to compare two numbers to see which is the larger, or whether both are equal to each other. Let's start with two whole numbers, so we can see the steps to follow."
* 2. Place the cardboard strip horizontally across the middle of the decimal board. Above the strip, form the quantity 138 with the beads; below the strip, form the quantity 161 (Teacher can choose to write the numeral on a slip, put at the bottom of Decimal Board)

Picture # 1 picture 57

* 3. "How do we know which number is larger? They both have the same number of hundreds, so we can't tell from that. One number has three tens, and the other has six. The number with six tens will be larger, regardless of any other differences after that."

Even if the first number were 139.999999999, and the other numbers were 160.000000000, the first number would still be smaller because it has fewer tens.

* 4. Replace the beads, and form the next pair of numbers on the board. In the top half, form the numeral 0.78. In the bottom half, form 0.6

picture # 2 page 57

"Are there any whole numbers (hundreds, tens, units) at all in either number?" (no) "So we can't tell from the whole numbers which is the larger number. Let's go on the the tenths."

* 5. "The top number has seven tenths. The bottom number has six tenths. We don't have to look any further. The top number is larger, no matter what the rest of the number looks like." Invite the students to write this statement in their Math Journals: 0.78 > 0.6
* 6. Remove the disks, and form the next pair of numbers: 0.6 in the top and 0.60 in the bottom.

picture #1 pg. 58

Compare whole numbers: neither number has any compare tenths: both numbers have six tenths: both numbers have six tenths. compare hundredths and other categories after that: neither number has any.

Both numbers are equal. Direct the students to write a statement in their Math journal: 0.6 = 0.60

Point out to the student that we can add zeros forever to the right of either number, and the value of the number wouldn't change.

* 7. Continue with other number pairs, increasing the level of difficulty gradually as you go. An example of a more complicated one is:
form 3.6667 in the top half, and 3.6671 in the bottom half.

picture #2 pg. 58

"Compare whole numbers: both are equal there. Compare tenths: both have six. Compare hundredths: both have six."

"Compare thousandths: the top number has six the bottom number has seven. It is larger regardless of anything else after that."

Extension: Ordering three decimal numbers from least to greatest.

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Alternative: Use bead bars instead of beads and disks:
pictures
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Forming and Reading Decimal Numerals Second Presentation(Lesson 8)

2020-08-18T21:55:36Z

Kdmullins:

=== Age ===

9-12 

=== Materials ===

* Numeral cards from the bank game-to millions
* Decimal numerals cards- to millionths
* Decimal board

 

=== Preparation ===

Students should have had the Decimal Lessons 1-7 (We are moving from the concrete toward the abstract).

 

=== Presentation ===

This lesson is moving toward standard form.

* 1. From the numeral 16.5 with the cards. Have the student(s) place it on the appropriate place on the board. "This is read 'sixteen... (point to the 16) ... "AND"... (point to the decimal point) ... 'five tenths'." (point to the 5). "This five is in the tenths' place. The tenths' place is the last decimal place we have a numeral in."
* 2. Form a numeral 16.05 with the cards. Have the student place it on the appropriate place on the board. Point to the numerals as you read them: "This is read 'sixteen AND five hundredths.' " "The five is in the hundredths' place. There aren't any tenths."
* 3. Do the same thing with 16.15. "sixteen.. AND...("The word 'and' is always used to indicate the decimal point.")...fifteen hundredths." ("The numeral after the decimal point is fifteen, and it ends in the hundredths' place.")
* 4. Form a numeral 16.34 with the cards. Have the student place them on the board, and name the numeral. Form other similar numerals-with two decimal places- if necessary until the child is comfortable with them. Then continue with the next step.
* 5. Form a numeral 27.132 with the cards. Have the student place them on the board, and guide him in naming the numeral: "Twenty seven...AND...(the decimal point)...one hundred thirty-two...(just read the numeral normally)...thousandths."...(we ended in the thousandths' place)
*6. Practice more similar numerals until the student(s) can easily read numerals with three decimal places.

Continue with more practice: Teachers can access the link below to copy, cut and mount on cards for students to practice with partners or independently.

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can recreate the symbols in these lessons in their Math journals.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Practice exchanging (after lesson 8)

2020-08-18T21:52:14Z

Kdmullins: /* Presentation */

=== Age ===

9-12 

=== Materials ===

* Decimal beads and disks
* Decimal Board
* Paper and pencil
 

=== Preparation ===

Students should have had the Decimal Lessons 1-8 (We are moving from the concrete toward the abstract).

 

=== Presentation ===

Progressive Counting

* 1. Remind students of instances in the past when they have done progressive counting- with bead chains, games involving multiples, and so on.
"The only difference is that we will be doing progressive counting with decimal numbers."
* 2. Select the 0.03 decimal card and have the students write the number as it is in their notebooks and then write 0.36. 0.03------>0.36
Say, "This means that we are going to count by three hundredths until we get to thirty-six hundredths." (like skip counting)
* 3. Have the students lay out three red disks and place them in the hundredth column. The students will then write 0.03 in their Math journals.
* 4. Direct the students to lay out three more hundredth disks to the board, and write the new total (0.06) underneath 0.03 in Math journal.
* 5. Students will continue adding three hundredth disks, exchanging when necessary and recording the new amounts until they have reached 0.36.
0.03 -->0.36 =
* 0.33
* 0.30
* 0.27
* 0.24
* 0.21
* 0.18
* 0.15
* 0.12
* 0.09
* 0.06
* 0.03
* 6. Provide practice problems and eventually let the students plan their own set.

EXTENSION: Regressive Counting
Invite the students to practice counting backwards from some decimal number to a lower one. for instance: 0.50 ---->0.05 or 0.36 ---> 0.03

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can practice these problems with or without materials and record them in their Math journals:

PROGRESSIVE COUNTING:
* 0.4 --> 2.0
* 0.02 --> 0.12
* 0.0005 ---> 0.050
* 0.02 ---> 0.022
* 4.04 ---> 60.60
* 0.08 ---> 0.72
* 0.0006 ---> 0.0162
* 0.24 ---> 2.40
* 0.13 ---> 1.30
* 33.33 ---> 333.30
* 7.07 ---> 106.05
* Plan your own set

 

===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Practice exchanging (after lesson 8)

2020-08-18T21:50:58Z

Kdmullins: /* Variation */

=== Age ===

9-12 

=== Materials ===

* Decimal beads and disks
* Decimal Board
* Paper and pencil
 

=== Preparation ===

Students should have had the Decimal Lessons 1-8 (We are moving from the concrete toward the abstract).

 

=== Presentation ===

Progressive Counting

* 1. Remind students of instances in the past when they have done progressive counting- with bead chains, games involving multiples, and so on.
"The only difference is that we will be doing progressive counting with decimal numbers."
* 2. Select the 0.03 decimal card and have the students write the number as it is in their notebooks and then write 0.36. 0.03------>0.36
Say, "This means that we are going to count by three hundredths until we get to thirty-six hundredths." (like skip counting)
* 3. Have the students lay out three red disks and place them in the hundredth column. The students will then write 0.03 in their Math journals.
* 4. Direct the students to lay out three more hundredth disks to the board, and write the new total (0.06) underneath 0.03 in Math journal.
* 5. Students will continue adding three hundredth disks, exchanging when necessary and recording the new amounts until they have reached 0.36.
0.03 -->0.36 =
0.33
0.30
0.27
0.24
0.21
0.18
0.15
0.12
0.09
0.06
0.03
* 6. Provide practice problems and eventually let the students plan their own set.

EXTENSION: Regressive Counting
Invite the students to practice counting backwards from some decimal number to a lower one. for instance: 0.50 ---->0.05 or 0.36 ---> 0.03

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can practice these problems with or without materials and record them in their Math journals:

PROGRESSIVE COUNTING:
* 0.4 --> 2.0
* 0.02 --> 0.12
* 0.0005 ---> 0.050
* 0.02 ---> 0.022
* 4.04 ---> 60.60
* 0.08 ---> 0.72
* 0.0006 ---> 0.0162
* 0.24 ---> 2.40
* 0.13 ---> 1.30
* 33.33 ---> 333.30
* 7.07 ---> 106.05
* Plan your own set

 

===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Practice exchanging (after lesson 8)

2020-08-18T21:49:34Z

Kdmullins: This exercise provides practice exchanging amounts for decimals and whole numbers.

=== Age ===

9-12 

=== Materials ===

* Decimal beads and disks
* Decimal Board
* Paper and pencil
 

=== Preparation ===

Students should have had the Decimal Lessons 1-8 (We are moving from the concrete toward the abstract).

 

=== Presentation ===

Progressive Counting

* 1. Remind students of instances in the past when they have done progressive counting- with bead chains, games involving multiples, and so on.
"The only difference is that we will be doing progressive counting with decimal numbers."
* 2. Select the 0.03 decimal card and have the students write the number as it is in their notebooks and then write 0.36. 0.03------>0.36
Say, "This means that we are going to count by three hundredths until we get to thirty-six hundredths." (like skip counting)
* 3. Have the students lay out three red disks and place them in the hundredth column. The students will then write 0.03 in their Math journals.
* 4. Direct the students to lay out three more hundredth disks to the board, and write the new total (0.06) underneath 0.03 in Math journal.
* 5. Students will continue adding three hundredth disks, exchanging when necessary and recording the new amounts until they have reached 0.36.
0.03 -->0.36 =
0.33
0.30
0.27
0.24
0.21
0.18
0.15
0.12
0.09
0.06
0.03
* 6. Provide practice problems and eventually let the students plan their own set.

EXTENSION: Regressive Counting
Invite the students to practice counting backwards from some decimal number to a lower one. for instance: 0.50 ---->0.05 or 0.36 ---> 0.03

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can practice these problems with or without materials and record them in their Math journals:

PROGRESSIVE COUNTING:
0.4 --> 2.0
0.02 --> 0.12
0.0005 ---> 0.050
0.02 ---> 0.022
4.04 ---> 60.60
0.08 ---> 0.72
0.0006 ---> 0.0162
0.24 ---> 2.40
0.13 ---> 1.30
33.33 ---> 333.30
7.07 ---> 106.05
Plan your own set

 

===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Forming and Reading Decimal Numerals Second Presentation(Lesson 8)

2020-08-18T18:49:15Z

Kdmullins: /* Handouts/Attachment */

=== Age ===

9-12 

=== Materials ===

* Numeral cards from the bank game-to millions
* Decimal numerals cards- to millionths
* Decimal board

 

=== Preparation ===

Students should have had the Decimal Lessons 1-7 (We are moving from the concrete toward the abstract).

 

=== Presentation ===

This lesson is moving toward standard form.

* 1. From the numeral 16.5 with the cards. Have the student(s) place it on the appropriate place on the board. "This is read 'sixteen... (point to the 16) ... "AND"... (point to the decimal point) ... 'five tenths'." (point to the 5). "This five is in the tenths' place. The tenths' place is the last decimal place we have a numeral in."
* 2. Form a numeral 16.05 with the cards. Have the student place it on the appropriate place on the board. Point to the numerals as you read them: "This is read 'sixteen AND five hundredths.' " "The five is in the hundredths' place. There aren't any tenths."
* 3. Do the same thing with 16.15. "sixteen.. AND...("The word 'and' is always used to indicate the decimal point.")...fifteen hundredths." ("The numeral after the decimal point is fifteen, and it ends in the hundredths' place.")
* 4. Form a numeral 16.34 with the cards. Have the student place them on the board, and name the numeral. Form other similar numerals-with two decimal places- if necessary until the child is comfortable with them. Then continue with the next step.
* 5. Form a numeral 27.132 with the cards. Have the student place them on the board, and guide him in naming the numeral: "Twenty seven...AND...(the decimal point)...one hundred thirty-two...(just read the numeral normally)...thousandths."...(we ended in the thousandths' place)
*6. Practice more similar numerals until the student(s) can easily read numerals with three decimal places.

Continue with more practice: Teachers can access the link below to copy, cut and mount on cards for students to practice with partners or independently.

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can recreate the symbols in these lessons in their Math journals.
 

[[Media:https://docs.google.com/document/d/1yy0lWFVSlpc-erkw9CW03GJQVbAcRiaCr1QXfb-MDSM/edit.ogg]]=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Forming and Reading Decimal Numerals Second Presentation(Lesson 8)

2020-08-18T16:44:59Z

Kdmullins: /* Presentation */

Decimals Forming and Reading Decimal Numbers (Lesson 7)

2020-08-18T16:33:53Z

Kdmullins: /* Presentation */

=== Age ===

9-12 

=== Materials ===

* Numeral cards from the bank game-to millions
* Decimal numerals cards- to millionths
* Decimal board

 

=== Preparation ===

Students should have had the Decimal Lessons 1-6 (We are moving from the concrete toward the abstract).

 

=== Presentation ===
[[File:Reading_decimals_L7.jpg|600px]]

This lesson is combining everything: spolen word, written symbol, quantity on the Decimal Board.

* 1. Form a whole number with two or three numeral cards, for instance, 324. Have the student(s) read the numeral and place the cards above the appropriate columns of the decimal board.
* 2. If the student is able to do that easily, form a number which includes decimals, e.g., 3.84. Invite the student to read it it; "Three AND eight tenths and four hundredths". Place the cards above the appropriate columns on the Decimal Board.
* 3. continue with several other examples of numerals combining whole numbers and decimals. Include a few numbers containing zeros, e.g., 45.067.
* 4. When the student(s) is/are able to do this comfortably, dictate a numeral to the student, again beginning with whole numbers. Have student(s) assemble the numeral from the correct cards and place them appropriately on the board. Continue doing this for numerals containing decimals: "three units, nine tenths, six hundredths."

In the process, challenge the students by dictating a number that omits one category, e.g., "three tens, two unitis, AND four hundredths." Also, ask the student(s) for the card four "ten tenths", and see if she/he realizes he/she umst give you the card for an equivalent amount = one unit.
* 5. When the student(s) can accomplish this easily, have them do the whole work: form a numeral, read it, and place it on the board.

NOTE: Students may stay on this level for a while, until all that has been learned to date has been assimilated. There is a large leap between this step and the following step.

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can recreate the symbols in these lessons in their Math journals.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

File:Reading decimals L7.jpg

2020-08-18T16:31:51Z

Kdmullins:

Decimals Forming and Reading Decimal Numerals Second Presentation(Lesson 8)

2020-08-18T15:39:54Z

Kdmullins: Created page with "=== Age === 9-12 === Materials === * Numeral cards from the bank game-to millions * Decimal numerals cards- to millionths * Decimal board === Preparation ===..."

=== Age ===

9-12 

=== Materials ===

* Numeral cards from the bank game-to millions
* Decimal numerals cards- to millionths
* Decimal board

 

=== Preparation ===

Students should have had the Decimal Lessons 1-7 (We are moving from the concrete toward the abstract).

 

=== Presentation ===

This lesson is moving toward standard form.

* 1. From the numeral 16.5 with the cards. Have the student(s) place it on the appropriate place on the board. "This is read 'sixteen... (point to the 16) ... "AND"... (point to the decimal point) ... 'five tenths'." (point to the 5). "This five is in the tenths' place. The tenths' place is the last decimal place we have a numeral in."
* 2. Form a numeral 16.05 with the cards. Have the student place it on the appropriate place on the board. Point to the numerals as you read them: "This is read 'sixteen AND five hundredths.' " "The five is in the hundredths' place. There aren't any tenths."
* 3. Do the same thing with 16.15. "sixteen.. AND...("The word 'and' is always used to indicate the decimal point.")...fifteen hundredths." ("The numeral after the decimal point is fifteen, and it ends in the hundredths' place.")
* 4. Form a numeral 16.34 with the cards. Have the student place them on the board, and name the numeral. Form other similar numerals-with two decimal places- if necessary until the child is comfortable with them. Then continue with the next step.
* 5. Form a numeral 27.132 with the cards. Have the student place them on the board, and guide him in naming the numeral: "Twenty seven...AND...(the decimal point)...one hundred thirty-two...(just read the numeral normally)...thousandths."...(we ended in the thousandths' place)
*6. Practice more similar numerals until the student(s) can easily read numerals with three decimal places.

Continue with more practice:

To be added

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can recreate the symbols in these lessons in their Math journals.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Forming and Reading Decimal Numbers (Lesson 7)

2020-08-18T15:11:47Z

Kdmullins: combining everything: spoken word, written symbol, decimal quantities on the Decimal Board.

=== Age ===

9-12 

=== Materials ===

* Numeral cards from the bank game-to millions
* Decimal numerals cards- to millionths
* Decimal board

 

=== Preparation ===

Students should have had the Decimal Lessons 1-6 (We are moving from the concrete toward the abstract).

 

=== Presentation ===

This lesson is combining everything: spolen word, written symbol, quantity on the Decimal Board.

* 1. Form a whole number with two or three numeral cards, for instance, 324. Have the student(s) read the numeral and place the cards above the appropriate columns of the decimal board.
* 2. If the student is able to do that easily, form a number which includes decimals, e.g., 3.84. Invite the student to read it it; "Three AND eight tenths and four hundredths". Place the cards above the appropriate columns on the Decimal Board.
* 3. continue with several other examples of numerals combining whole numbers and decimals. Include a few numbers containing zeros, e.g., 45.067.
* 4. When the student(s) is/are able to do this comfortably, dictate a numeral to the student, again beginning with whole numbers. Have student(s) assemble the numeral from the correct cards and place them appropriately on the board. Continue doing this for numerals containing decimals: "three units, nine tenths, six hundredths."

In the process, challenge the students by dictating a number that omits one category, e.g., "three tens, two unitis, AND four hundredths." Also, ask the student(s) for the card four "ten tenths", and see if she/he realizes he/she umst give you the card for an equivalent amount = one unit.
* 5. When the student(s) can accomplish this easily, have them do the whole work: form a numeral, read it, and place it on the board.

NOTE: Students may stay on this level for a while, until all that has been learned to date has been assimilated. There is a large leap between this step and the following step.

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can recreate the symbols in these lessons in their Math journals.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Forming and Reading Decimal Quantities (Lessons 4 & 5)

2020-08-18T03:19:41Z

Kdmullins: /* Control Of Error */

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Box of beads and disks

 

=== Preparation ===

Students should have had the Introduction to Decimals, Lesson 1 and Second Presentation of Quantity and Introduction to the Decimal Board and Unit as the Center

 

=== Presentation ===
These lessons are providing an opportunity for the student to be comfortable with decimal place values. These experiences are assisting the student to move toward abstraction.

NOTE: The ability to read decimal numeral or quantities depends on a very solid understanding of the names of each category and the relationships between them.

Therefore, a great deal of time for practice with decimal quantities symbols must be given, so the child can internalize these relationships (basically, don't hurry written words too fast).

First Presentation (Lesson 4):
* 1. Place several beads representing whole numbers (e.g., four hundred) on the board and have the student read the quantity: "four hundred". continue with more complex quantities, still composed entirely of whole numbers, until the student is familiar with the whole number side of the board.
* 2. Place two beads in the units column and three blue disks in the tenths column. Ask the student to read this quantity, one column at a time: "two units and three tenths"
* 3. Continue with several other quantities on this level of difficulty.
* 4. Begin forming quantities with hundredths also asking the student to identify them (e.g., "six units and four tenths and two hundredths") NOTE: At this point this is an acceptable answer, since the purpose is to solidify the names of the different place values/categories.
Continue with several more of these.
* 5. Review this much by saying a quantity and having the child form it with the beads: "seven units and three tenths and nine hundredths"
* 6. Have the students form a quantity and name it themselves.
* 7. During later presentations, or now if appropriate, continue into thousandths and other decimal places.

Second Presentation (Lesson 5)
* 1. Review a couple quantities from the previous presentation, for instance, asking the student to form three units and eight tenths and six hundredths.
* 2. Now as the student to put out thirteen hundredths. The student will probably place thirteen red disks in the hundredths column.
* 3. Say, "We can't have thirteen hundredths this way." Give the student a chance to see if they can be arranged another way. If students can't see what to do, tell them: "We have more than ten hundredths here; what does ten hundredths equal?" (one tenth). Have them make the exchange:

[[File:Page_50.jpg|300px]]

* 4. Give several other examples such as this, then try an example like "twenty four thousandths" (Here the exchange will have to be made twice, and the students will end up with two hundredths and four thousandths). Try several other challenges like this, increasing the level of difficulty as it seems appropriate.

The presentation can stop here, or you can go on to the next step.

* 5. Say, "Take a deep breath! Let's put out one hundred eight thousandths!" There may not be enough disks; but ask the students if there is a very fast way to put down ten thousandths with just one disk. Put one disk in the hundredths place: "that stands for ten thousandths." Put out another hundredth disk: "Twenty thousandths." Keep lacing hundredth disks and counting until you reach one hundred thousandths. Say, "The quantity we want here is one hundred eight thousandths; so what do we have to add next?" Have the students add eight disks to the thousandths; column.

[[File:Page_51_after_5.jpg|300px]]

* 6. Say, "Let's see how many hundredths we have." Count them-there are ten. "What does ten hundredths equal?" (one tenth). Exchange the hundredths for a tenth disk. "We now have this arrangement: the tenth represents one hundred thousandths; there are one hundred thousandths; there are one hundred thousandths in one tenth."

[[File:Page_51_after_6.jpg|300px]]

The total represented on this board is one hundred eight thousandths (0.108)

* 7. Continue with other such quantities, if you feel students need more practice.

 

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can recreate the quantities in these lessons in their Math journals.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Forming and Reading Decimal Quantities (Lessons 4 & 5)

2020-08-18T03:14:29Z

Kdmullins:

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Box of beads and disks

 

=== Preparation ===

Students should have had the Introduction to Decimals, Lesson 1 and Second Presentation of Quantity and Introduction to the Decimal Board and Unit as the Center

 

=== Presentation ===
These lessons are providing an opportunity for the student to be comfortable with decimal place values. These experiences are assisting the student to move toward abstraction.

NOTE: The ability to read decimal numeral or quantities depends on a very solid understanding of the names of each category and the relationships between them.

Therefore, a great deal of time for practice with decimal quantities symbols must be given, so the child can internalize these relationships (basically, don't hurry written words too fast).

First Presentation (Lesson 4):
* 1. Place several beads representing whole numbers (e.g., four hundred) on the board and have the student read the quantity: "four hundred". continue with more complex quantities, still composed entirely of whole numbers, until the student is familiar with the whole number side of the board.
* 2. Place two beads in the units column and three blue disks in the tenths column. Ask the student to read this quantity, one column at a time: "two units and three tenths"
* 3. Continue with several other quantities on this level of difficulty.
* 4. Begin forming quantities with hundredths also asking the student to identify them (e.g., "six units and four tenths and two hundredths") NOTE: At this point this is an acceptable answer, since the purpose is to solidify the names of the different place values/categories.
Continue with several more of these.
* 5. Review this much by saying a quantity and having the child form it with the beads: "seven units and three tenths and nine hundredths"
* 6. Have the students form a quantity and name it themselves.
* 7. During later presentations, or now if appropriate, continue into thousandths and other decimal places.

Second Presentation (Lesson 5)
* 1. Review a couple quantities from the previous presentation, for instance, asking the student to form three units and eight tenths and six hundredths.
* 2. Now as the student to put out thirteen hundredths. The student will probably place thirteen red disks in the hundredths column.
* 3. Say, "We can't have thirteen hundredths this way." Give the student a chance to see if they can be arranged another way. If students can't see what to do, tell them: "We have more than ten hundredths here; what does ten hundredths equal?" (one tenth). Have them make the exchange:

[[File:Page_50.jpg|300px]]

* 4. Give several other examples such as this, then try an example like "twenty four thousandths" (Here the exchange will have to be made twice, and the students will end up with two hundredths and four thousandths). Try several other challenges like this, increasing the level of difficulty as it seems appropriate.

The presentation can stop here, or you can go on to the next step.

* 5. Say, "Take a deep breath! Let's put out one hundred eight thousandths!" There may not be enough disks; but ask the students if there is a very fast way to put down ten thousandths with just one disk. Put one disk in the hundredths place: "that stands for ten thousandths." Put out another hundredth disk: "Twenty thousandths." Keep lacing hundredth disks and counting until you reach one hundred thousandths. Say, "The quantity we want here is one hundred eight thousandths; so what do we have to add next?" Have the students add eight disks to the thousandths; column.

[[File:Page_51_after_5.jpg|300px]]

* 6. Say, "Let's see how many hundredths we have." Count them-there are ten. "What does ten hundredths equal?" (one tenth). Exchange the hundredths for a tenth disk. "We now have this arrangement: the tenth represents one hundred thousandths; there are one hundred thousandths; there are one hundred thousandths in one tenth."

[[File:Page_51_after_6.jpg|300px]]

The total represented on this board is one hundred eight thousandths (0.108)

* 7. Continue with other such quantities, if you feel students need more practice.

 

=== Control Of Error ===

Directress guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can recreate the quantities in these lessons in their Math journals.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Forming and Reading Decimal Quantities (Lessons 4 & 5)

2020-08-18T03:11:35Z

Kdmullins: /* Control Of Error */

Decimals Introduction Lesson 1

2020-08-18T03:10:51Z

Kdmullins: /* Control Of Error */

=== Age ===

9-12 

[[File:20190912_113625_To_go_with_Decimal_Board_lessons.jpg|600px]]

=== Materials ===

* Fraction insets: the whole circle, circle divided into tenths
* Cardboard or construction paper sector of the circle: 1/10 (you will need to trace a 1/10 sector ahead of time)
*Scissors
* One green unit bead in small dish
* Box of decimal material: red, blue, green beads for whole numbers and red, blue, green discs (light and dark of each color) for decimal numbers

 

=== Preparation ===

Students should have a comfortable knowledge of fractions and the definition that a fraction is an equal part of a whole (a fraction is the result of dividing a whole).

 

=== Presentation ===
[[File:20200813_123857_Introduction_to_the_Quantities_of_Decimals.jpg|300px]]

* 1. Take out the whole circle, and ask the student what its value is(It represent on whole). Show the green unit bead- It also represents on whole. "Both have the same value- one unit."
* 2. "If we divide the circle into ten equal parts, we have this." (Show the circle divided into tenths). "Each of the small sectors is 1/10 of the whole circle. Ten of these tenths equal one whole."
* 3. Gather 10 blue disks and hide them in one hand. "I'm going to perform magic. I will take this unit bead (green) and make ten pieces." Hold the unit bead between your fingers next to the hand holding the 10 discs. "If I were to split this unit into ten equal pieces, I would have this..." (be as dramatic as you feel comfortable, squeezing the unit bead, slowly moving it close to your wrist and then open your fist allowing the 10 discs to fall onto the presentation rug or desk. Pick up one disk and say, "This represents one tenth of the unit bead. Ten of these disks equal one whole."
* 4. Place the small blue disks on the sectors of the divided circle. "Each has the same value: the sector 1/10 and the blue disk."
* 5. Take the cardboard or construction paper sector that you prepared for 1/10 and cut off a thin piece saying, "If I were to cut this tenth into ten equal pieces, each piece would be 1/100 of the whole." ''(You can stop there or continue trying to cut the 1/10 sector into 10 equal strips.It's extremely difficult, but I have found that the students are engaged, and the impression of making one tenth into ten hundredths forms a clear understanding of how decimals are smaller forms of a whole.)''
While holding one of the hundredth strips say, "If I take this blue disk, this tenth and do the same; if I smash it into ten pieces, each will have the value of one hundredth of the whole."
* 6. Review by displaying the circle, bead, sectors and disks in a display with the unit on the left and tenth and hundredth to the right. (You can choose to have the students record this image in their Math journals.)
* 7. If you chose to cut 10 pieces of the 1/10 sector, pick up one of them or cut a strip from the 1/10 sector to represent one hundredth and say, "If I were to cut this hundredth into ten equal pieces, each piece will have the value of 1/1000 ''(Again, I choose to try to cut 10 equal pieces and then pull out one of them)'' . Hold the hundredth disc (red) and then say, "In the same way, if I were to break this hundredth disk into ten equal pieces, each piece will have the value of one thousandth." Show the green thousandth disk.
* 8. With the final display in front of you, review the names of units, tenths, hundredths, and thousandths (you can choose to create labels with names to place under the discs). Review how many tenths equal a unit, how many hundredths equal a tenth and so on. The teacher can do this by conducting the Montessori Three Period Lesson.

DEPENDING ON TIME AND THE ENERGY OF YOUR STUDENTS, YOU CAN CHOOSE TO STOP HERE OR INTRODUCE THE NUMERIC SYMBOLS:

Materials: whole number and decimal numeric symbol cards/tablets
Presentation:
* 1. Show the card for 10. "This is ten. If I turn it upside down and add a decimal point, it is no longer a ten, but a tenth." Show the 0.1 tablet.
* 2. Show the card for 100. "This is a hundred. If I turn it upside down and add a decimal point, it is no loner a hundred, but a hundredth." Show the 0.01 tablet.
* 3. Show the card for 1,000. "This is a thousand. If I turn it upside down and add a decimal point, it is no longer a thousand but a thousandth." Show the 0.001 tablet.

 

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

dec is the root to the Latin word for ten- decem 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
The contributor of this lesson introduces the numerals at the same time she cuts the fraction pieces apart.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Second Presentation of Quantity & Introduction of the Decimal Board and the unit as the center (Lessons 2 & 3)

2020-08-18T03:10:08Z

Kdmullins: /* Control Of Error */

=== Age ===

9-12 

=== Materials ===

* Decimal beads and disks
* a small saucer

 

=== Preparation ===

Students should have had the Introduction to Decimals, Lesson 1

 

=== Presentation ===
* 1. Place the box of decimal material on the table or presentation rug. In this presentation, we want to show the relationship between one category and another.
* 2. (This is review) Begin with one of the whole number beads-for instance, a hundred. Take out one red bead, and place it in front of the child, to his/her left. Recall that it is possible to change one hundred for ten tens. Place the hundred bead in the saucer, and take out ten blue beads, arranging them in a column to the right of where the hundred bead was (exchanging).
* 3. (This is review) It is also possible to change one ten for ten units. Remove one ten bead, and place it in the saucer. Take out ten green beads, and place them in a column to the right of the ten beads.
* 4. It is possible to change one unit for ten tenths, since we know that a unit is made up of ten tenths. Remove one unit, placing it in the saucer; and bring out ten disks to represent tenths. Arrange them to the right of the units.
* 5. Continue with hundredths and thousandths; then continue, introducing ten-thousandths, hundred-thousandths, and millionths.
[[File:Presentation_of_Quantity_after_no._5.jpg|300px]]

* 6. Review- "How many tenths equal one unit?" "How many ten-thousandths equal one thousandth?" And so on.
* 7. Then: "How many units equal a ten?" (10) "How many tens equal a hundred?" (10) "Therefore, how many ones equal a hundred?" (100)

"How many hundredths equal a tenth?" (10) "How many tenths equal a unit?" (10) "Therefore, how many hundredths equal a unit?" (100)

Note: You can keep on going all the way back with exchanging to the unit, but it could also be 'over kill'

INTRODUCTION OF THE DECIMAL BOARD AND THE UNIT AS THE CENTER (CROWN): A REINFORCEMENT:

[[File:Introduction_of_the_Decimal_Board_and_the_Unit_as_the_Center_(crown).jpg|300px]]

Materials: Decimal beads, Teacher made paper or foil crown, Decimal Board

* 1. Take a unit bead and place it on the table or presentation rug saying, "This unit is so important that we are going to give it a crown: Place the crown at the top of the unit place on the decimal board and then place the unit bead in the unit's place on the decimal board. "In the world of Math, numeral gets a crown. Every numeral gets its name from a unit."
* 2. Ask, "What is to the left of the unit?" (tens). Place a ten bead in the ten's place on the decimal board . "What is to the right of the unit?" (tenths). Place a tenth disk in the tenth's place on the decimal board. "The ten is ten times the unit; the tenth is a tenth PART of the unit."
* 3. Ask, "What is to the left of the ten?" (hundreds). Place a hundred bead in the hundred's place on the decimal board. "What is to the right of the tenths?" (hundredths). Place a hundredths disk in the hundredth's place on the decimal board. "The hundred is one hundred times the unit; the hundredth is a hundredth PART of the unit."
* 4. Continue in this way through million and millionth.

 

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can recreate the decimal board in their Math journals.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Presentation of Decimal Symbols Lesson 6

2020-08-18T03:09:10Z

Kdmullins: Created page with "=== Age === 9-12 === Materials === * Bank game cards from units to millions * Decimal numbers from tenths to millionths * Decimal board === Preparation ===..."

=== Age ===

9-12 

=== Materials ===

* Bank game cards from units to millions
* Decimal numbers from tenths to millionths
* Decimal board

 

=== Preparation ===

Students should have had the Decimal Lessons 1-5 (We are moving from the concrete toward the abstract).

 

=== Presentation ===
These lessons are providing an opportunity for the student to be comfortable with decimal place values. These experiences are assisting the student to move toward abstraction.

* 1. Lay out the cards for units 1 to 9 in the center of the floor. Ask the student(s), "What is to the left of unts?" (tens). Place the column of ten numbers (10-90) to the left of the units. continue in the same manner for the hundreds, thousands, and so on to the millions.
* 2. Say, "All of these are whole numbers; but, as we've seen before, there are numbers that are smaller than whole numbers: decimals." Take the decimal cards out.
* 3. Ask, "What is immediately to the right of the units?" (tenths). Place the row of tenths numerals from 0.1 to 0.9, naming them as you go (Note that these are blue, like the disks and like the tens.)
* 4. Ask, "What is immediately to the right of the tenths?" (hundredths). Place the hundredths numerals form 0.01 to 0.09, naming them as you go (Note the red color, like the disks and like hundreds.)
* 5. Continue for thousandths, ten-thousandths, hundred-thousandths, and millionths.
* 6. Show the corresponding numerals on each column of the decimal board.
* 7. Point out to the child that as we go toward the left with these numerals, they become larger; and as we go toward the right, the numerals become smaller.

Point out also that, with the whole number cards, longer numerals mean larger quantities; but with the decimal cards, longer numerals mean smaller quantities.

[[File:Presentation_of_Decimal_Symbols.jpg|300px]]
 

=== Control Of Error ===

Teacher guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can recreate the symbols in these lessons in their Math journals.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

File:Presentation of Decimal Symbols.jpg

2020-08-18T02:26:33Z

Kdmullins:

Decimals Forming and Reading Decimal Quantities (Lessons 4 & 5)

2020-08-18T01:57:23Z

Kdmullins: /* Presentation */

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Box of beads and disks

 

=== Preparation ===

Students should have had the Introduction to Decimals, Lesson 1 and Second Presentation of Quantity and Introduction to the Decimal Board and Unit as the Center

 

=== Presentation ===
These lessons are providing an opportunity for the student to be comfortable with decimal place values. These experiences are assisting the student to move toward abstraction.

NOTE: The ability to read decimal numeral or quantities depends on a very solid understanding of the names of each category and the relationships between them.

Therefore, a great deal of time for practice with decimal quantities symbols must be given, so the child can internalize these relationships (basically, don't hurry written words too fast).

First Presentation (Lesson 4):
* 1. Place several beads representing whole numbers (e.g., four hundred) on the board and have the student read the quantity: "four hundred". continue with more complex quantities, still composed entirely of whole numbers, until the student is familiar with the whole number side of the board.
* 2. Place two beads in the units column and three blue disks in the tenths column. Ask the student to read this quantity, one column at a time: "two units and three tenths"
* 3. Continue with several other quantities on this level of difficulty.
* 4. Begin forming quantities with hundredths also asking the student to identify them (e.g., "six units and four tenths and two hundredths") NOTE: At this point this is an acceptable answer, since the purpose is to solidify the names of the different place values/categories.
Continue with several more of these.
* 5. Review this much by saying a quantity and having the child form it with the beads: "seven units and three tenths and nine hundredths"
* 6. Have the students form a quantity and name it themselves.
* 7. During later presentations, or now if appropriate, continue into thousandths and other decimal places.

Second Presentation (Lesson 5)
* 1. Review a couple quantities from the previous presentation, for instance, asking the student to form three units and eight tenths and six hundredths.
* 2. Now as the student to put out thirteen hundredths. The student will probably place thirteen red disks in the hundredths column.
* 3. Say, "We can't have thirteen hundredths this way." Give the student a chance to see if they can be arranged another way. If students can't see what to do, tell them: "We have more than ten hundredths here; what does ten hundredths equal?" (one tenth). Have them make the exchange:

[[File:Page_50.jpg|300px]]

* 4. Give several other examples such as this, then try an example like "twenty four thousandths" (Here the exchange will have to be made twice, and the students will end up with two hundredths and four thousandths). Try several other challenges like this, increasing the level of difficulty as it seems appropriate.

The presentation can stop here, or you can go on to the next step.

* 5. Say, "Take a deep breath! Let's put out one hundred eight thousandths!" There may not be enough disks; but ask the students if there is a very fast way to put down ten thousandths with just one disk. Put one disk in the hundredths place: "that stands for ten thousandths." Put out another hundredth disk: "Twenty thousandths." Keep lacing hundredth disks and counting until you reach one hundred thousandths. Say, "The quantity we want here is one hundred eight thousandths; so what do we have to add next?" Have the students add eight disks to the thousandths; column.

[[File:Page_51_after_5.jpg|300px]]

* 6. Say, "Let's see how many hundredths we have." Count them-there are ten. "What does ten hundredths equal?" (one tenth). Exchange the hundredths for a tenth disk. "We now have this arrangement: the tenth represents one hundred thousandths; there are one hundred thousandths; there are one hundred thousandths in one tenth."

[[File:Page_51_after_6.jpg|300px]]

The total represented on this board is one hundred eight thousandths (0.108)

* 7. Continue with other such quantities, if you feel students need more practice.

 

=== Control Of Error ===

Directress guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can recreate the quantities in these lessons in their Math journals.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

File:Page 51 after 6.jpg

2020-08-18T01:52:33Z

Kdmullins:

File:Page 51 after 5.jpg

2020-08-18T01:48:13Z

Kdmullins:

File:Page 50.jpg

2020-08-18T01:45:42Z

Kdmullins:

Decimals Forming and Reading Decimal Quantities (Lessons 4 & 5)

2020-08-18T01:43:33Z

Kdmullins: /* Presentation */

=== Age ===

9-12 

=== Materials ===

* Decimal board
* Box of beads and disks

 

=== Preparation ===

Students should have had the Introduction to Decimals, Lesson 1 and Second Presentation of Quantity and Introduction to the Decimal Board and Unit as the Center

 

=== Presentation ===
These lessons are providing an opportunity for the student to be comfortable with decimal place values. These experiences are assisting the student to move toward abstraction.

NOTE: The ability to read decimal numeral or quantities depends on a very solid understanding of the names of each category and the relationships between them.

Therefore, a great deal of time for practice with decimal quantities symbols must be given, so the child can internalize these relationships (basically, don't hurry written words too fast).

First Presentation (Lesson 4):
* 1. Place several beads representing whole numbers (e.g., four hundred) on the board and have the student read the quantity: "four hundred". continue with more complex quantities, still composed entirely of whole numbers, until the student is familiar with the whole number side of the board.
* 2. Place two beads in the units column and three blue disks in the tenths column. Ask the student to read this quantity, one column at a time: "two units and three tenths"
* 3. Continue with several other quantities on this level of difficulty.
* 4. Begin forming quantities with hundredths also asking the student to identify them (e.g., "six units and four tenths and two hundredths") NOTE: At this point this is an acceptable answer, since the purpose is to solidify the names of the different place values/categories.
Continue with several more of these.
* 5. Review this much by saying a quantity and having the child form it with the beads: "seven units and three tenths and nine hundredths"
* 6. Have the students form a quantity and name it themselves.
* 7. During later presentations, or now if appropriate, continue into thousandths and other decimal places.

Second Presentation (Lesson 5)
* 1. Review a couple quantities from the previous presentation, for instance, asking the student to form three units and eight tenths and six hundredths.
* 2. Now as the student to put out thirteen hundredths. The student will probably place thirteen red disks in the hundredths column.
* 3. Say, "We can't have thirteen hundredths this way." Give the student a chance to see if they can be arranged another way. If students can't see what to do, tell them: "We have more than ten hundredths here; what does ten hundredths equal?" (one tenth). Have them make the exchange:

Picture from pg. 50

* 4. Give several other examples such as this, then try an example like "twenty four thousandths" (Here the exchange will have to be made twice, and the students will end up with two hundredths and four thousandths). Try several other challenges like this, increasing the level of difficulty as it seems appropriate.

The presentation can stop here, or you can go on to the next step.

* 5. Say, "Take a deep breath! Let's put out one hundred eight thousandths!" There may not be enough disks; but ask the students if there is a very fast way to put down ten thousandths with just one disk. Put one disk in the hundredths place: "that stands for ten thousandths." Put out another hundredth disk: "Twenty thousandths." Keep lacing hundredth disks and counting until you reach one hundred thousandths. Say, "The quantity we want here is one hundred eight thousandths; so what do we have to add next?" Have the students add eight disks to the thousandths; column.

Picture page 51

* 6. Say, "Let's see how many hundredths we have." Count them-there are ten. "What does ten hundredths equal?" (one tenth). Exchange the hundredths for a tenth disk. "We now have this arrangement: the tenth represents one hundred thousandths; there are one hundred thousandths; there are one hundred thousandths in one tenth."

Picture 2 on page 51

The total represented on this board is one hundred eight thousandths (0.108)

* 7. Continue with other such quantities, if you feel students need more practice.

 

=== Control Of Error ===

Directress guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can recreate the quantities in these lessons in their Math journals.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Second Presentation of Quantity & Introduction of the Decimal Board and the unit as the center (Lessons 2 & 3)

2020-08-18T01:37:31Z

Kdmullins: /* Presentation */

=== Age ===

9-12 

=== Materials ===

* Decimal beads and disks
* a small saucer

 

=== Preparation ===

Students should have had the Introduction to Decimals, Lesson 1

 

=== Presentation ===
* 1. Place the box of decimal material on the table or presentation rug. In this presentation, we want to show the relationship between one category and another.
* 2. (This is review) Begin with one of the whole number beads-for instance, a hundred. Take out one red bead, and place it in front of the child, to his/her left. Recall that it is possible to change one hundred for ten tens. Place the hundred bead in the saucer, and take out ten blue beads, arranging them in a column to the right of where the hundred bead was (exchanging).
* 3. (This is review) It is also possible to change one ten for ten units. Remove one ten bead, and place it in the saucer. Take out ten green beads, and place them in a column to the right of the ten beads.
* 4. It is possible to change one unit for ten tenths, since we know that a unit is made up of ten tenths. Remove one unit, placing it in the saucer; and bring out ten disks to represent tenths. Arrange them to the right of the units.
* 5. Continue with hundredths and thousandths; then continue, introducing ten-thousandths, hundred-thousandths, and millionths.
[[File:Presentation_of_Quantity_after_no._5.jpg|300px]]

* 6. Review- "How many tenths equal one unit?" "How many ten-thousandths equal one thousandth?" And so on.
* 7. Then: "How many units equal a ten?" (10) "How many tens equal a hundred?" (10) "Therefore, how many ones equal a hundred?" (100)

"How many hundredths equal a tenth?" (10) "How many tenths equal a unit?" (10) "Therefore, how many hundredths equal a unit?" (100)

Note: You can keep on going all the way back with exchanging to the unit, but it could also be 'over kill'

INTRODUCTION OF THE DECIMAL BOARD AND THE UNIT AS THE CENTER (CROWN): A REINFORCEMENT:

[[File:Introduction_of_the_Decimal_Board_and_the_Unit_as_the_Center_(crown).jpg|300px]]

Materials: Decimal beads, Teacher made paper or foil crown, Decimal Board

* 1. Take a unit bead and place it on the table or presentation rug saying, "This unit is so important that we are going to give it a crown: Place the crown at the top of the unit place on the decimal board and then place the unit bead in the unit's place on the decimal board. "In the world of Math, numeral gets a crown. Every numeral gets its name from a unit."
* 2. Ask, "What is to the left of the unit?" (tens). Place a ten bead in the ten's place on the decimal board . "What is to the right of the unit?" (tenths). Place a tenth disk in the tenth's place on the decimal board. "The ten is ten times the unit; the tenth is a tenth PART of the unit."
* 3. Ask, "What is to the left of the ten?" (hundreds). Place a hundred bead in the hundred's place on the decimal board. "What is to the right of the tenths?" (hundredths). Place a hundredths disk in the hundredth's place on the decimal board. "The hundred is one hundred times the unit; the hundredth is a hundredth PART of the unit."
* 4. Continue in this way through million and millionth.

 

=== Control Of Error ===

Directress guided. 

=== Points Of Interest ===

Participating with the new knowledge helps move the concrete experiences toward abstract thinking 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
Students can recreate the decimal board in their Math journals.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

File:Introduction of the Decimal Board and the Unit as the Center (crown).jpg

2020-08-18T01:34:02Z

Kdmullins:

File:Presentation of Quantity after no. 5.jpg

2020-08-18T01:27:37Z

Kdmullins:

Decimals Introduction Lesson 1

2020-08-18T00:49:08Z

Kdmullins: /* Age */

=== Age ===

9-12 

[[File:20190912_113625_To_go_with_Decimal_Board_lessons.jpg|600px]]

=== Materials ===

* Fraction insets: the whole circle, circle divided into tenths
* Cardboard or construction paper sector of the circle: 1/10 (you will need to trace a 1/10 sector ahead of time)
*Scissors
* One green unit bead in small dish
* Box of decimal material: red, blue, green beads for whole numbers and red, blue, green discs (light and dark of each color) for decimal numbers

 

=== Preparation ===

Students should have a comfortable knowledge of fractions and the definition that a fraction is an equal part of a whole (a fraction is the result of dividing a whole).

 

=== Presentation ===
[[File:20200813_123857_Introduction_to_the_Quantities_of_Decimals.jpg|300px]]

* 1. Take out the whole circle, and ask the student what its value is(It represent on whole). Show the green unit bead- It also represents on whole. "Both have the same value- one unit."
* 2. "If we divide the circle into ten equal parts, we have this." (Show the circle divided into tenths). "Each of the small sectors is 1/10 of the whole circle. Ten of these tenths equal one whole."
* 3. Gather 10 blue disks and hide them in one hand. "I'm going to perform magic. I will take this unit bead (green) and make ten pieces." Hold the unit bead between your fingers next to the hand holding the 10 discs. "If I were to split this unit into ten equal pieces, I would have this..." (be as dramatic as you feel comfortable, squeezing the unit bead, slowly moving it close to your wrist and then open your fist allowing the 10 discs to fall onto the presentation rug or desk. Pick up one disk and say, "This represents one tenth of the unit bead. Ten of these disks equal one whole."
* 4. Place the small blue disks on the sectors of the divided circle. "Each has the same value: the sector 1/10 and the blue disk."
* 5. Take the cardboard or construction paper sector that you prepared for 1/10 and cut off a thin piece saying, "If I were to cut this tenth into ten equal pieces, each piece would be 1/100 of the whole." ''(You can stop there or continue trying to cut the 1/10 sector into 10 equal strips.It's extremely difficult, but I have found that the students are engaged, and the impression of making one tenth into ten hundredths forms a clear understanding of how decimals are smaller forms of a whole.)''
While holding one of the hundredth strips say, "If I take this blue disk, this tenth and do the same; if I smash it into ten pieces, each will have the value of one hundredth of the whole."
* 6. Review by displaying the circle, bead, sectors and disks in a display with the unit on the left and tenth and hundredth to the right. (You can choose to have the students record this image in their Math journals.)
* 7. If you chose to cut 10 pieces of the 1/10 sector, pick up one of them or cut a strip from the 1/10 sector to represent one hundredth and say, "If I were to cut this hundredth into ten equal pieces, each piece will have the value of 1/1000 ''(Again, I choose to try to cut 10 equal pieces and then pull out one of them)'' . Hold the hundredth disc (red) and then say, "In the same way, if I were to break this hundredth disk into ten equal pieces, each piece will have the value of one thousandth." Show the green thousandth disk.
* 8. With the final display in front of you, review the names of units, tenths, hundredths, and thousandths (you can choose to create labels with names to place under the discs). Review how many tenths equal a unit, how many hundredths equal a tenth and so on. The teacher can do this by conducting the Montessori Three Period Lesson.

DEPENDING ON TIME AND THE ENERGY OF YOUR STUDENTS, YOU CAN CHOOSE TO STOP HERE OR INTRODUCE THE NUMERIC SYMBOLS:

Materials: whole number and decimal numeric symbol cards/tablets
Presentation:
* 1. Show the card for 10. "This is ten. If I turn it upside down and add a decimal point, it is no longer a ten, but a tenth." Show the 0.1 tablet.
* 2. Show the card for 100. "This is a hundred. If I turn it upside down and add a decimal point, it is no loner a hundred, but a hundredth." Show the 0.01 tablet.
* 3. Show the card for 1,000. "This is a thousand. If I turn it upside down and add a decimal point, it is no longer a thousand but a thousandth." Show the 0.001 tablet.

 

=== Control Of Error ===

Directress guided. 

=== Points Of Interest ===

dec is the root to the Latin word for ten- decem 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
The contributor of this lesson introduces the numerals at the same time she cuts the fraction pieces apart.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Introduction Lesson 1

2020-08-18T00:45:51Z

Kdmullins: /* Age */

=== Age ===

9-12 

[[File:20190912_113625_To_g0_with_Decimal_Board_lessons.jpg|500px]]

=== Materials ===

* Fraction insets: the whole circle, circle divided into tenths
* Cardboard or construction paper sector of the circle: 1/10 (you will need to trace a 1/10 sector ahead of time)
*Scissors
* One green unit bead in small dish
* Box of decimal material: red, blue, green beads for whole numbers and red, blue, green discs (light and dark of each color) for decimal numbers

 

=== Preparation ===

Students should have a comfortable knowledge of fractions and the definition that a fraction is an equal part of a whole (a fraction is the result of dividing a whole).

 

=== Presentation ===
[[File:20200813_123857_Introduction_to_the_Quantities_of_Decimals.jpg|300px]]

* 1. Take out the whole circle, and ask the student what its value is(It represent on whole). Show the green unit bead- It also represents on whole. "Both have the same value- one unit."
* 2. "If we divide the circle into ten equal parts, we have this." (Show the circle divided into tenths). "Each of the small sectors is 1/10 of the whole circle. Ten of these tenths equal one whole."
* 3. Gather 10 blue disks and hide them in one hand. "I'm going to perform magic. I will take this unit bead (green) and make ten pieces." Hold the unit bead between your fingers next to the hand holding the 10 discs. "If I were to split this unit into ten equal pieces, I would have this..." (be as dramatic as you feel comfortable, squeezing the unit bead, slowly moving it close to your wrist and then open your fist allowing the 10 discs to fall onto the presentation rug or desk. Pick up one disk and say, "This represents one tenth of the unit bead. Ten of these disks equal one whole."
* 4. Place the small blue disks on the sectors of the divided circle. "Each has the same value: the sector 1/10 and the blue disk."
* 5. Take the cardboard or construction paper sector that you prepared for 1/10 and cut off a thin piece saying, "If I were to cut this tenth into ten equal pieces, each piece would be 1/100 of the whole." ''(You can stop there or continue trying to cut the 1/10 sector into 10 equal strips.It's extremely difficult, but I have found that the students are engaged, and the impression of making one tenth into ten hundredths forms a clear understanding of how decimals are smaller forms of a whole.)''
While holding one of the hundredth strips say, "If I take this blue disk, this tenth and do the same; if I smash it into ten pieces, each will have the value of one hundredth of the whole."
* 6. Review by displaying the circle, bead, sectors and disks in a display with the unit on the left and tenth and hundredth to the right. (You can choose to have the students record this image in their Math journals.)
* 7. If you chose to cut 10 pieces of the 1/10 sector, pick up one of them or cut a strip from the 1/10 sector to represent one hundredth and say, "If I were to cut this hundredth into ten equal pieces, each piece will have the value of 1/1000 ''(Again, I choose to try to cut 10 equal pieces and then pull out one of them)'' . Hold the hundredth disc (red) and then say, "In the same way, if I were to break this hundredth disk into ten equal pieces, each piece will have the value of one thousandth." Show the green thousandth disk.
* 8. With the final display in front of you, review the names of units, tenths, hundredths, and thousandths (you can choose to create labels with names to place under the discs). Review how many tenths equal a unit, how many hundredths equal a tenth and so on. The teacher can do this by conducting the Montessori Three Period Lesson.

DEPENDING ON TIME AND THE ENERGY OF YOUR STUDENTS, YOU CAN CHOOSE TO STOP HERE OR INTRODUCE THE NUMERIC SYMBOLS:

Materials: whole number and decimal numeric symbol cards/tablets
Presentation:
* 1. Show the card for 10. "This is ten. If I turn it upside down and add a decimal point, it is no longer a ten, but a tenth." Show the 0.1 tablet.
* 2. Show the card for 100. "This is a hundred. If I turn it upside down and add a decimal point, it is no loner a hundred, but a hundredth." Show the 0.01 tablet.
* 3. Show the card for 1,000. "This is a thousand. If I turn it upside down and add a decimal point, it is no longer a thousand but a thousandth." Show the 0.001 tablet.

 

=== Control Of Error ===

Directress guided. 

=== Points Of Interest ===

dec is the root to the Latin word for ten- decem 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
The contributor of this lesson introduces the numerals at the same time she cuts the fraction pieces apart.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]

Decimals Introduction Lesson 1

2020-08-18T00:41:36Z

Kdmullins: /* Presentation */

=== Age ===

9-12 

=== Materials ===

* Fraction insets: the whole circle, circle divided into tenths
* Cardboard or construction paper sector of the circle: 1/10 (you will need to trace a 1/10 sector ahead of time)
*Scissors
* One green unit bead in small dish
* Box of decimal material: red, blue, green beads for whole numbers and red, blue, green discs (light and dark of each color) for decimal numbers

 

=== Preparation ===

Students should have a comfortable knowledge of fractions and the definition that a fraction is an equal part of a whole (a fraction is the result of dividing a whole).

 

=== Presentation ===
[[File:20200813_123857_Introduction_to_the_Quantities_of_Decimals.jpg|300px]]

* 1. Take out the whole circle, and ask the student what its value is(It represent on whole). Show the green unit bead- It also represents on whole. "Both have the same value- one unit."
* 2. "If we divide the circle into ten equal parts, we have this." (Show the circle divided into tenths). "Each of the small sectors is 1/10 of the whole circle. Ten of these tenths equal one whole."
* 3. Gather 10 blue disks and hide them in one hand. "I'm going to perform magic. I will take this unit bead (green) and make ten pieces." Hold the unit bead between your fingers next to the hand holding the 10 discs. "If I were to split this unit into ten equal pieces, I would have this..." (be as dramatic as you feel comfortable, squeezing the unit bead, slowly moving it close to your wrist and then open your fist allowing the 10 discs to fall onto the presentation rug or desk. Pick up one disk and say, "This represents one tenth of the unit bead. Ten of these disks equal one whole."
* 4. Place the small blue disks on the sectors of the divided circle. "Each has the same value: the sector 1/10 and the blue disk."
* 5. Take the cardboard or construction paper sector that you prepared for 1/10 and cut off a thin piece saying, "If I were to cut this tenth into ten equal pieces, each piece would be 1/100 of the whole." ''(You can stop there or continue trying to cut the 1/10 sector into 10 equal strips.It's extremely difficult, but I have found that the students are engaged, and the impression of making one tenth into ten hundredths forms a clear understanding of how decimals are smaller forms of a whole.)''
While holding one of the hundredth strips say, "If I take this blue disk, this tenth and do the same; if I smash it into ten pieces, each will have the value of one hundredth of the whole."
* 6. Review by displaying the circle, bead, sectors and disks in a display with the unit on the left and tenth and hundredth to the right. (You can choose to have the students record this image in their Math journals.)
* 7. If you chose to cut 10 pieces of the 1/10 sector, pick up one of them or cut a strip from the 1/10 sector to represent one hundredth and say, "If I were to cut this hundredth into ten equal pieces, each piece will have the value of 1/1000 ''(Again, I choose to try to cut 10 equal pieces and then pull out one of them)'' . Hold the hundredth disc (red) and then say, "In the same way, if I were to break this hundredth disk into ten equal pieces, each piece will have the value of one thousandth." Show the green thousandth disk.
* 8. With the final display in front of you, review the names of units, tenths, hundredths, and thousandths (you can choose to create labels with names to place under the discs). Review how many tenths equal a unit, how many hundredths equal a tenth and so on. The teacher can do this by conducting the Montessori Three Period Lesson.

DEPENDING ON TIME AND THE ENERGY OF YOUR STUDENTS, YOU CAN CHOOSE TO STOP HERE OR INTRODUCE THE NUMERIC SYMBOLS:

Materials: whole number and decimal numeric symbol cards/tablets
Presentation:
* 1. Show the card for 10. "This is ten. If I turn it upside down and add a decimal point, it is no longer a ten, but a tenth." Show the 0.1 tablet.
* 2. Show the card for 100. "This is a hundred. If I turn it upside down and add a decimal point, it is no loner a hundred, but a hundredth." Show the 0.01 tablet.
* 3. Show the card for 1,000. "This is a thousand. If I turn it upside down and add a decimal point, it is no longer a thousand but a thousandth." Show the 0.001 tablet.

 

=== Control Of Error ===

Directress guided. 

=== Points Of Interest ===

dec is the root to the Latin word for ten- decem 

=== Purpose ===

*To make a visual, auditory and kinesthetic impression upon the child on how whole numbers are divided into smaller units-decimals.

 

=== Variation ===
The contributor of this lesson introduces the numerals at the same time she cuts the fraction pieces apart.
 

=== Handouts/Attachment ===

 

[[Category:Mathematics]] [[Category:Mathematics_9-12]]