http://www.uen.org/Lessonplan/preview.cgi?LPid=21500
Place Value (Cognitive Lesson)
Grade: 3
Objective: (Math Standard 1, objective 1) Students will be able to represent whole numbers up to 10,000, comprehend place value concepts, and identify relationships among whole numbers using base-ten models and symbolic notation.
Attention Getter: Students attention will be captured by triggering their sensory memory. Each students desk will be a card with a number on it. Numbers will represent every whole number place value between 1 and 10,000. Students will be asked to place their number card, backside (non-number side) showing, on the board under the appropriate heading (ones/1, tens/10, hundreds/100, one-thousands/1,000, ten-thousands/10,000). After all the cards are placed, the teacher will turn the card over and ask students to give a thumbs up or thumbs down based on whether the card was placed in the right column or not. (Sensory memory is triggered because students are experiencing learning through their senses here. They had to find/feel the card under the desk, physically move to place it under the appropriate heading, then use their body to indicate whether the cards were placed correctly or not.)
Thus far, students only had to have a declarative knowledge (knowing that) in relation to place value because both the name of the place value and an example of the number were written on the board. If students couldn’t yet distinguish the names of place values, they could place the number by matching it to the number written in numeral.
Activity
Students will continue to keep the idea of place value in their working memory through Rote Memorization—they will learn a song.
Before learning the song students will write an example of each number on a piece of paper on their desk. Students will now learn the song (rote memorization) to remember the place values. As they sing they will point to the numbers written on the board, triggering again their sensory memory. A link to the music for this song can be found at http://www.songsforteaching.com/math/placevalue/onestenshundredsplace.htm.
Ones, tens, hundredsOnes, tens, hundredsOnes, tens, hundredsThe places in the place value line.
Just find the one’s place.It’s on the far right.
The tens are next, In the place value line.
Move left one place,You’ll find the hundreds.Three places for hundreds every time.
Ones, tens, hundredsThe places in the place value line.
Just find the one’s place.It’s on the far right.
The tens are next, In the place value line.
Move left one place,You’ll find the hundreds.Three places for hundreds every time.
Ones, tens, hundredsOnes, tens, hundreds
Students have been keeping place value in their working memory. Working memory only lasts for approximately 20 seconds, so in order to keep something in working memory it must be rehearsed over and over. By practicing something over and over, knowledge is transferred from working memory to long-term memory.
Instruction: (taken from the UEN website)
Instructional Procedures Places, Everyone
1. Each student should receive a copy of the Place Value Houses. (attached at the end of the lesson plan)
2. The teacher should have a copy of the Place Value Houses on an overhead.
3. Have students cut out their Place Value Houses and glue them in their journal.
4. Teach students what each house represents. The first house on the right is called Units that have the values of ones, tens and hundreds. The second house is called Thousands with the values of ones, tens and hundreds and the third house is called Millions with the values of ones, tens and hundreds. Each house will have a group of three digits in a number. Each group is called a period. Explain to students that within each period the names are the same: hundreds, tens, and ones.
5. Write a four or five digit number on the overhead or chalkboard. (e.g. 6, 348 or 45, 823). Model how to say this number by pointing to where each number would be represented on the houses. Explain to students that when reading or writing a large numeral, it is helpful to break it down into periods and read each period as a simple one, two or three digit numeral. Also help students see that the commas between each house represent pauses when reading a numeral, just as they do in reading text. Whenever a student comes to a comma in reading or writing a large numeral, he knows to pause and say or write a period name. It is very important when you are modeling that you do not say “and” when reading the number. “And” represents a decimal, so when reading 6,348 you would not say six thousand three hundred and forty eight you would say six thousand three hundred forty eight. Model a few numbers to show students how to read large numbers. After you have modeled it a few times have students begin to say and point to the numbers that would be represented on their place value house chart.
6. Write a number on the overhead or chalkboard that has a 0 (e.g. 35, 207). Explain to students that the value of the first digit’s place determines how large the numeral will be and that any empty place to the right of the digit must have a zero place holder. Read this number to the students and point to where each digit would be represented on the place value house chart. Explain that even though you didn't say anything for the zero in the tens place it is very important that they don't forget to put it in when writing the number. Each place value on any digit has to be represented by a numeral.
7. Divide the class into two groups.
8. Give each student in each group a single digit card. (0-9)
9. Teacher reads a number (e.g. 12, 543) and the students arrange themselves in the proper order. Each student in the group will help each other to form the number. Once they have formed the number they raise their hand to show they have completed the number. The teacher then asks them to say the number out loud. You can continue this activity having them create many different numbers with their cards. (See extensions for more ideas to use with this activity.)
10. After each number they create they can write that number in their journal in standard form, expanded form and word form. They can also use the place value stamps to create the number.
11. Next, you will need a Place Value Chart there is a black line or your students can make their own by following these simple steps.
a. Lay a sheet of paper horizontally, fold one side in thirds and crease it and fold the other side in thirds and crease it.
b. Open up your sheet. Draw lines along the two vertical creases.
c. Measure and draw a horizontal line one inch from the top edge of your sheet.
d. Beginning on the left side, label the four resulting boxes: Millions, Thousands, and Units.
e. Measure and draw another horizontal line 1⁄2 inch below the first one.
f. Beginning on the right side of the paper, measure and draw a vertical line 1 1⁄4 inches from the edge. Extend this line from the first horizontal line down to the bottom edge of the paper.
g. Measure and draw another vertical line 1 1⁄4 inches from the first one. Extend this line from the first horizontal line down to the bottom edge of the paper.
h. From left to right, label the three resulting small boxes “H” (hundreds), “T” (tens), and “O” (ones).
i. Continue measuring and drawing vertical lines (1 1⁄4 inches apart) across the paper so that the thousands and millions sections are exactly like the units section.
j. Label the three column headings (“H”, “T”, and “0”) in each section.
k. If you want a pocket at the bottom to hold number strips just fold the bottom up 1 1⁄2 inches and tape or glue on each end.
12. Once they have their place value chart made you can laminate it and use overhead markers and/or use the Place Value Strips.
13. Read a number to them and have them place their Place Value Strips in the correct order to create the number provided.
14. Next have students go to a journal and write the number in standard form, expanded form, and word form. They can also use their place value stamps and stamp them in their journal to create the number given.
15. Students can work with partners and they can create numbers together or one partner can say a number and the other would create it on their place value chart.
Activity: peg-type mnemonics
In groups, students will come up with acronyms to help them remember the place values from one to ten-thousand. For an example, read the “one, two, buckle my shoe…” poem. Students get to create their own memory device for place value.
Homework 1: Mapping Students will be given a list of 15 numbers and asked to organize those numbers into a concept map, categorizing them by place value.
Homework 2: Tomorrow in class students will play “The Price is Right.” Items must be priced anywhere between one place value and ten-thousand place value. Each student, for homework, it to come up with an item and price for each place value. This homework assignment asks students to use conditional knowledge (when and why) because they are applying prices to real life objects. They need to know when and why numbers pertain to certain objects and are used in real life.
This homework assignment prevents decay. Decay is the weakening and fading of memories with the passing of time. By practicing place value again, at a later time, students bring place value back into working memory, and hopefully transfer it to long term memory. The time between class and when students do their , and then play the game in class the next day is called interference. Interference is the process that occurs when remembering certain information is hampered by the presence of other information.
Distributed practice is practice in brief periods with rest in between. Working on place value in class, then taking a break/rest, practicing it for homework, then practicing it again in class is distributed practice.
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