Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
- Students should be able to make relationships and connections between decimals, fractions and money as well as identify quarter, half and three quarters and 1 whole on the 100 grid.
- Students should be able to write all decimals and fractions from 0.01=$0.01=1/100 to 1.0=$1.00 (1 whole)=100/100.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be able to write and say given fractions and decimals as well as be proficient in decimal place value.
Students should have a basic understanding of tenths and hundredths when applied to decimals.
Students should also have a firm understanding that fractions and decimals are parts of a whole, and that a fraction such as 45/100 means 45 of 100.
Working on a 100 grid should be very familiar as well as identifying the 100 grid as a 10 x 10 array. In addition to decimal place value a basic, strong understanding of whole number place value is a needed prerequisite.
Guiding Questions: What are the guiding questions for this lesson?
The following question could be asked BEFORE and DURING the lesson:
- Are these numbers equal? (EX. 0.16 of one dollar and $0.16)
The following questions can be asked DURING and AFTER the lesson:
- How can you show 0.16 and $0.16 are equal?
- How are fractions and decimals similar?
- What patterns do you notice in the fractional representations and the decimal representations?
- How is money represented similarly to decimals?
Teaching Phase: How will the teacher present the concept or skill to students?
Using a 100 grid (chart) (make certain the squares are a bit larger than a normal hundreds chart so that the student can write each fraction, decimal and money amount in the box.) A sample is provided. blank100grid_3.pdf
- The teacher must stop students periodically to check and make certain all cells on the 100 grid are being filled in properly. Corrections will need to be made as they are discovered so that students are able to see the number/decimal pattern emerging.
- The teacher will have to walk to student desks/tables to check for understanding throughout the lesson. The teacher must see each mistake by students as an opportunity to reteach or clarify misconceptions.
- The teacher will start by explaining that each square is a hundredth because each square will be worth 1 penny or 1 cent and there are 100 cents in a dollar and there are 100 grid cells on the sheet.
- Students will then write and record 1 cent as money, a decimal and a fraction in the first grid cell ($0.01, 0.01, 1/100). A completed grid (chart) is provided. complete100grid_3.pdf
- The relationship should be made that each decimal and fraction are said orally in the same way. This pattern continues to the end of the row (0.10=10/100=$0.10). Students should realize that there is a pattern evolving and continue on to 0.25, 25/100, $0.25 where the teacher will do a check-in to make certain all students are in the same place and have correctly identified each fraction, decimal and money value. Teacher will also look to make certain that the second row has been identified as 20%.
CHECKPOINT #1 - At this benchmark number ($0.25, 0.25, 25/100) the teacher will identify this as 1/4. Noting that 1 of 4 parts of the chart is complete. Related to money, 1 of 4 quarters or $0.25/25 cents. There will be 4 benchmark numbers in this lesson or 4 parts/checkpoints.(25, 50, 75, 100). This is the first of the 4 checkpoints or 1 of 4. This will become clearer as you move on to the next three checkpoints (50, 75, 100).
Guiding Question after checkpoint #1 - "Based on what you have completed, how are fractions and decimals similar?"
CHECKPOINT #2 - Students will fill out the chart until they have completed up to 0.50=50/100=$0.50. The teacher will check work and ask how students know they have completed half of the chart and have students identify half as 0.50. Or, 50 is half of 100. Also, 2 of the 4 parts or benchmarks have been completed at this checkpoint. The teacher should have students highlight or circle the benchmark numbers 0.25, 0.5. Teacher will also discuss that 0.50 and 0.5 are equal. Students should be able to reason and explain this thinking. These numbers both represent ½ regardless of the zero after the 5, at the end . Students should also make the connection that 5 is half of 10, just as 50 is half of 100, which proves that both 0.5 and 0.50 represent half.
Guiding question after checkpoint #2 - "Explain how you know that 0.50 is equal to 1/2 ."
CHECKPOINT #3 - 0.75, $0.75, 75/100 or ¾. At this point, three of the four parts or checkpoints have been completed. Related to money this is similar to 3 of 4 quarters, which is equal to $0.75.
CHECKPOINT #4 - $1.00 or 100/100=1 or a whole. Related to money this is 100 pennies out of 100, which equals one or a whole or 1 dollar.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Students will correctly fill out the 100 grid with the guidance of the teacher and discover the number patterns that evolve as they fill out the grid writing all numbers from 0.01 to 1.0 in fraction, decimal and money form in each square of the grid.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Students will answer the following questions in a math journal or on an activity sheet. Students should be able to answer all questions correctly in the math journal AND be able to verbally state one answer correctly aloud to the teacher using correct mathematical language. The teacher will need to meet with each student briefly one-on-one to check for this understanding. Small group reteaching may be necessary for struggling learners.
Question #1 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXX Each "x" is worth 1 penny out of a dollar (1 of 100). Write the value of the "X's" shown in money, decimal and fraction form. (Answer –"x"=37…..$0.37, 0.37, 37/100)
Question #2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XX (Answer-"x"=52…..$0.52, 0.52, 52/100)
Question #3 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXX (Answer-"x"=78……$0.78, 0.78, 78/100)
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will bring closure by making certain that students understand that fractions decimals and money are related and have similarities and connections. Further closure can be made by having students write in their math journal explaining what they have learned or "3 BIG WOW's" that were discovered by doing this lesson. The teacher should read the journal responses and use them to probe further or clarify misconceptions.
Other math journal question stems may include:
I knew ________ but I didn't know __________.
Because I did___________I knew ____________.
I now know ___________ is = to ___________.
The teacher will close the lesson by having students preserve the 100 grid to be used later for more complex problem solving in the future for measurement and numbers greater than one, comparing and ordering fractions, etc. This teaching strategy can be extended later and the 100 grid used as a tool for that extension.
Students will be able to successfully represent a number of pennies between $0.01 and $1.00 with 80% accuracy. In a journal or on a sheet of paper, each student will draw any number of pennies (using circles or X's to represent pennies) 1-100 in an organized pattern that is easy to count ($0.01-$1.00) and write that number of pennies in fraction, decimal and money form 4 of 5 times accurately for 80% accuracy. Teacher may require that 3 of the 5 representations be more than $0.50 to get a true assessment of learning.
Note: Pennies may be represented as simple circles or X's. The organized pattern is most important as this shows understanding of place value. A detailed drawing of a penny is not required. For this particular lesson, the mathematical connection or depiction is more important than artistic quality.
BEFORE LESSON BEGINS:
JUMPSTART/BELLWORK (Activate Prior Knowledge)
The teacher will display the following 3 problems:
- In the number 23.56 what numeral is in the hundredths place? (Answer 6)
- What fraction is shown? (Answer 3/6 or 1/2)
- Write 8/10 as a decimal. (Answer 0.8)
INTRODUCTION OF WHOLE GROUP LESSON
In a whole group setting, the teacher will lay down a given number of pennies. (EX. 12 pennies) under the document camera in an organized pattern. The teacher will ask students to write the fractional representation (12/100) of these pennies as well as the decimal representation (0.12) of the pennies and the money representation ($0.12) of the pennies on a white board or blank sheet of paper. The teacher will then ask students to "show me" the answer by holding up their white boards or blank sheet of paper. The teacher will then pan the room to see that students wrote the number of pennies correctly in decimal, fraction and money form. The teacher will then ask students to say all of these representations out loud. Students should realize that both the fraction and decimals sound the same when said aloud.
THROUGHOUT LESSON TO CHECK FOR UNDERSTANDING
The teacher should repeat the above procedure 3 additional times with similar numbers of pennies, in an organized pattern under the document camera, not exceeding 100 pennies, having the students show their answers on the whiteboard or blank sheet of paper and have students say the fraction, decimal and money representations out loud.
(Examples—33 pennies shown=$0.33=0.33=33/100, 45 pennies shown=$0.45=0.45=45/100, 67 pennies shown=$0.67=0.67=67/100)
The teacher will be checking for understanding as students document and say these representations out loud. Teacher should take note of the students that do not write each of the representations correctly 2 of the 3 times. It will be necessary to pull these students aside for small group instruction after the lesson has been taught (see details below). The teacher will continue throughout the lesson to go back to these fractional relationships asking students the same questions with various amounts of pennies making certain that students are able to write and say each fraction, decimal and money representation correctly and make connections between them.
For those students who do not correctly write the fraction, decimal and money representation correctly 2 of the 3 times, it will be necessary to pull them aside in a small group setting and repeat the above process using real pennies. Different amounts than what are used in the lesson should be used for remediation. Also, using real quarters to clarify check points (1/4, 1/2, 3/4, 1 whole) would be helpful. This small group of no more than 5 or 6 students at one time should be called together after the lesson has been introduced and taught to the whole group. This will give the teacher an opportunity to provide individualized instruction, allow students to ask questions and work at a pace that is comparable to the students' learning. This strategy of differentiated learning will help the teacher better understand how students are learning, clarify misconceptions and provide support for any related mathematical deficits that may exist. Small group instruction should be supportive and flexible.
Feedback to Students
Students will be provided feedback from the teacher, in the form of clarification and correction, throughout the lesson as they fill in the 100 grid with decimals, fractions and money (0.01=1/100=$0.01 to 1.0=100/100=$1.00).
The following check-in points are given as suggested stopping points to check student work and make any needed corrections or provide further explanation.
These check-in points will be:
25/100=1/4=$0.25 (25 cents is one of four quarters that make a dollar)
50/100=1/2=$0.50 (50 cents is half of a dollar, 50 is half of 100)
75/100=3/4=$0.75 (75 cents is three of four quarters that make a dollar)
100/100=1 whole=$1.00 (100 pennies is equal to $1.00)
These check points are important as they will help make connections later in measurement and identifying points on a number line.