Equal Sharing
1.1 Integration of Learning Outcomes
- At the end of the lesson students will have a complete understanding of ‘Equal Sharing,’ or the principle behind division.
1.2 Standards
PA.M.2.6.5.A
> Organize and display data using pictures, tallies, tables, charts, bar graphs and circle graphs.
PA.M.2.8.5.D
> Use concrete objects and combinations of symbols and numbers to create expressions that model mathematical situations.
1.3 Anticipatory Set
- Ask for 4 volunteers and bring them up to the front of the classroom. I will then take out 8 stickers. Then, I will ask and discuss with the class how I can split up the 8 stickers equally between the 4 students.
1.4 Procedures
- After the anticipatory set question I will use the SmartBoard to ask another similar problem. Such as, “Kyle’s mom has 10 cookies. She wants to give each of her 4 children the same amount of cookies. How many cookies would each person get?”
o See if the students will be able to figure out that each person should get 2 ½ cookies.
o Use the SmartBoard to divide the cookies into four different columns (make sure 2 of the cookies are broken into halves)
- Next slide will connect these ‘everyday word problems’ to division.
- Explain that the idea of equal sharing is the same even when it is written out as 15 ÷ 3. Have the SMART board slide to a chart with 3 columns and 15 cubes below it. One at a time move each cube into the separate columns, until each column has 5 cubes.
- Assign each person a partner. Hand out a poster with 9 (or more if you wish) columns labeled on it. Make sure the columns are large enough for the base ten blocks to fit on it. Also hand each group a set of base ten blocks. I have included 10 rods and 30 cubes.
- Have the students mimic what you had just done on the board.
- Next ask the students a series of similar problems, first only focusing on the cubes and ignoring the rods. Put each problem up one at a time on the SMART board. Each pairing will work out the problems at their desks. Then once everyone is finished, select someone to come up to the SMART board to show the class what they have done. Repeat for 3-4 different problems.
o Optional- Play music while students are working with their partners. Once the music stops the students have to focus their attention to the front of the room. Once student comes up to board, award them with a piece of candy. This will allow for a lot of class participation.
- Once they understand the cube problems, slowly integrate using problems with the rods, (1 rod = 10 cubes). Demonstrate that once you get to higher numbers, it is difficult to keep track of all those small little cubes, when you can exchange ten of the units for one rod. Continue the activity with problems that can include a combination of rods and cubes.
- The next concept you want the students to understand is exchanging a rod for 10 cubes. With a problem such as 56 ÷ 4. Before telling the students what to do. See if they can figure it out for themselves. Continue the activity with problems that include exchanging rods with cubes.
- The final slide will show a completed problem with the standard division algorithm, such as 72 ÷ 6. Have the second to last slide include the same problem, with the students working out the problem with the base ten blocks. Discuss with the students where the numbers from the standard algorithm correlate with our base ten charts.
1.5 Differentiation
- Auditory learners—I will be speaking aloud about each equation, asking questions.
- Kinesthetic learners – The anticipatory set and the students answering the problems on the board allow for the students to get out of their seats
- Visual learners – Students will see it on the board, along with physically moving the blocks on their desk.
- Gold and Green learners – Students will be able to work independently to complete a worksheet
- Orange and Blue learners – Students will work with partners and have the opportunity to come up to the board.
1.6 Closure
- Have students independently work on a worksheet with problems similar to what we went over in class.
- Walk around the classroom to see if any of the students have questions.
1.7 Formative/ Summative Assessment of Students (P-12)
- Throughout the class ask the students to complete problems with their partner at the desk, with a few students answering the question on the board.
- Have the students complete a worksheet that will be collected to review how much the students understand.
1.8 Materials/ Equipment
- SMART board
- Notebook program for SMART board
- Base ten blocks
- 18’’ x 6’’ posters with 9 labeled columns
- Worksheet with assessment problems
- Optional – Candy
- Optional – Music
1.9 Technology
- SMART board
- Base ten blocks
2.1 Reflection on Planning
- I think that I have prepared for this lesson very well. I have started out by allowing students to get out of their seats. I believe that the activity I have prepared for the students is clear and concise, allowing for a lot of discussion between students and the teacher to occur. By playing music while the students are working with their partners and turning it off when I want them to look up at me allows me to keep control of the class without having to raise my voice. By rewarding people who come up to the board with candy will allow for a lot of class participation. At the end of the Power Point presentation I included a connection to the standard algorithm for division. This connection will allow me, or my co-op teacher, to start off the next lesson where I left off. Finally I included the worksheet to allow students who work better individually to have the opportunity to excel. The worksheet will also allow me to assess how well the students understood my lesson.
2.2 Reflection on Lesson
Overall I believe that the lesson went well and the children successfully understood the concept of ‘Equal Sharing.’ The first time I asked for a volunteer to come to the board, the entire class was very eager to be picked. Some of the students were very upset when they were not picked. I decided not to give candy as a reward for volunteering; I thought this would only cause more students to be upset when they were not chosen. If I were to give this lesson again I would include less of the simple questions with only the unit blocks. The students quickly grasped this idea. But I needed to spend more time focusing on exchanging a rod for ten units. Some of the students understood the concept quickly and others could not grasp the idea. Playing music while the students were allowed to talk with their partners was very successful; When I needed the classes attention all I had to do was turn off the music and they instantly focused on me. The worksheet after the lesson I thought was a very important factor, it allowed students who work better independently to ask questions.
1.1 Integration of Learning Outcomes
- At the end of the lesson students will have a complete understanding of ‘Equal Sharing,’ or the principle behind division.
1.2 Standards
PA.M.2.6.5.A
> Organize and display data using pictures, tallies, tables, charts, bar graphs and circle graphs.
PA.M.2.8.5.D
> Use concrete objects and combinations of symbols and numbers to create expressions that model mathematical situations.
1.3 Anticipatory Set
- Ask for 4 volunteers and bring them up to the front of the classroom. I will then take out 8 stickers. Then, I will ask and discuss with the class how I can split up the 8 stickers equally between the 4 students.
1.4 Procedures
- After the anticipatory set question I will use the SmartBoard to ask another similar problem. Such as, “Kyle’s mom has 10 cookies. She wants to give each of her 4 children the same amount of cookies. How many cookies would each person get?”
o See if the students will be able to figure out that each person should get 2 ½ cookies.
o Use the SmartBoard to divide the cookies into four different columns (make sure 2 of the cookies are broken into halves)
- Next slide will connect these ‘everyday word problems’ to division.
- Explain that the idea of equal sharing is the same even when it is written out as 15 ÷ 3. Have the SMART board slide to a chart with 3 columns and 15 cubes below it. One at a time move each cube into the separate columns, until each column has 5 cubes.
- Assign each person a partner. Hand out a poster with 9 (or more if you wish) columns labeled on it. Make sure the columns are large enough for the base ten blocks to fit on it. Also hand each group a set of base ten blocks. I have included 10 rods and 30 cubes.
- Have the students mimic what you had just done on the board.
- Next ask the students a series of similar problems, first only focusing on the cubes and ignoring the rods. Put each problem up one at a time on the SMART board. Each pairing will work out the problems at their desks. Then once everyone is finished, select someone to come up to the SMART board to show the class what they have done. Repeat for 3-4 different problems.
o Optional- Play music while students are working with their partners. Once the music stops the students have to focus their attention to the front of the room. Once student comes up to board, award them with a piece of candy. This will allow for a lot of class participation.
- Once they understand the cube problems, slowly integrate using problems with the rods, (1 rod = 10 cubes). Demonstrate that once you get to higher numbers, it is difficult to keep track of all those small little cubes, when you can exchange ten of the units for one rod. Continue the activity with problems that can include a combination of rods and cubes.
- The next concept you want the students to understand is exchanging a rod for 10 cubes. With a problem such as 56 ÷ 4. Before telling the students what to do. See if they can figure it out for themselves. Continue the activity with problems that include exchanging rods with cubes.
- The final slide will show a completed problem with the standard division algorithm, such as 72 ÷ 6. Have the second to last slide include the same problem, with the students working out the problem with the base ten blocks. Discuss with the students where the numbers from the standard algorithm correlate with our base ten charts.
1.5 Differentiation
- Auditory learners—I will be speaking aloud about each equation, asking questions.
- Kinesthetic learners – The anticipatory set and the students answering the problems on the board allow for the students to get out of their seats
- Visual learners – Students will see it on the board, along with physically moving the blocks on their desk.
- Gold and Green learners – Students will be able to work independently to complete a worksheet
- Orange and Blue learners – Students will work with partners and have the opportunity to come up to the board.
1.6 Closure
- Have students independently work on a worksheet with problems similar to what we went over in class.
- Walk around the classroom to see if any of the students have questions.
1.7 Formative/ Summative Assessment of Students (P-12)
- Throughout the class ask the students to complete problems with their partner at the desk, with a few students answering the question on the board.
- Have the students complete a worksheet that will be collected to review how much the students understand.
1.8 Materials/ Equipment
- SMART board
- Notebook program for SMART board
- Base ten blocks
- 18’’ x 6’’ posters with 9 labeled columns
- Worksheet with assessment problems
- Optional – Candy
- Optional – Music
1.9 Technology
- SMART board
- Base ten blocks
2.1 Reflection on Planning
- I think that I have prepared for this lesson very well. I have started out by allowing students to get out of their seats. I believe that the activity I have prepared for the students is clear and concise, allowing for a lot of discussion between students and the teacher to occur. By playing music while the students are working with their partners and turning it off when I want them to look up at me allows me to keep control of the class without having to raise my voice. By rewarding people who come up to the board with candy will allow for a lot of class participation. At the end of the Power Point presentation I included a connection to the standard algorithm for division. This connection will allow me, or my co-op teacher, to start off the next lesson where I left off. Finally I included the worksheet to allow students who work better individually to have the opportunity to excel. The worksheet will also allow me to assess how well the students understood my lesson.
2.2 Reflection on Lesson
Overall I believe that the lesson went well and the children successfully understood the concept of ‘Equal Sharing.’ The first time I asked for a volunteer to come to the board, the entire class was very eager to be picked. Some of the students were very upset when they were not picked. I decided not to give candy as a reward for volunteering; I thought this would only cause more students to be upset when they were not chosen. If I were to give this lesson again I would include less of the simple questions with only the unit blocks. The students quickly grasped this idea. But I needed to spend more time focusing on exchanging a rod for ten units. Some of the students understood the concept quickly and others could not grasp the idea. Playing music while the students were allowed to talk with their partners was very successful; When I needed the classes attention all I had to do was turn off the music and they instantly focused on me. The worksheet after the lesson I thought was a very important factor, it allowed students who work better independently to ask questions.