Counting Up/Vertical Addition Lesson Plan
Ariel Brisman
Grade: 1st / Subject Area: Math
Type of Setting: 1st grade general education classroom
Date of Lesson: March 8th 2012
PURPOSE:
What is vertical addition?
How do we add by counting up?
VOCABULARY & KEY TERMS:
SKILLS:
OBJECTIVES:
NEW YORK STATE LEARNING STANDARDS:
Common Core Standards:
1.NBT.4 Use place value understanding and properties of operations to add and subtract
PRE-ASSESSMENT:
LESSON PRESENTATION:
A. Set-Induction (10-12 minutes):
· Routinely the students are brought to the rug, introduced to the math message, and then sent back to their seats to copy and answer the problem and explain how they arrived at their answer.
· Math message will be – “Copy and find the sum of these problems. Explain how you found your answer: 5 + 7 = ________
· 3 + 8 = _______” (The problems will be written horizontally as shown).
· Teacher will first ask a student volunteer to define sum (students are expected to know that the sum of two numbers is the answer to an addition problem).
· After giving them a few minutes to complete the short problems at their seats the teacher will call the students back to the rug and go over the problems with them together.
· Teacher will ask for student volunteers to help her answer the problems.
· Teacher will guide students into thinking aloud while solving the problems and help students realize how they use their fingers or visuals to help them find the sum of two numbers.
· After the message is complete the teacher will explain that today the students will be learning about a different way to add called vertical addition.
B. Procedure (15-20 minutes):
· Teacher will start off by asking the students if they know what vertical means. If they know, teacher will then ask if they know what horizontal means (if the students cannot come up with an answer she will explain it to them by drawing lines on the board).
· Teacher will explain that horizontal means side-to-side and vertical means up and down.
· Teacher will ask the students to tell her what type of addition the math message asked them to complete, horizontal or vertical. Students are expected to recognize the math as horizontal.
· Teacher will then state that today they are going to be doing vertical math.
· Teacher will ask students what direction the numbers will be going in if the math is going to be vertical. Students are expected to respond that the numbers will be going up and down.
· Teacher will write a vertical math problem on the board (8 + 3 = _______). Teacher will show the students how the numbers are one on top of the other and the line under the addends is another way of putting an equals sign. It separates the addends from the sum.
· Teacher will then say that she has a trick that will help the students become better at adding. She will tell them trick is called counting up.
· The teacher will explain that the first step is finding the larger number. She will point out the larger number (8) and she will circle it on the board.
· Next the teacher will explain that because we know that we already have 8, when we add three we can start counting at 8.
· Teacher will explain that instead of starting at 1, then counting up to 8 and then 3 more, we can start at 8 and just count up three more.
· Teacher will model how to do this by saying, “Ok, so I already have 8 now I need to add three to that number. I will start with eight and then count up 3 more numbers. 8, 9, 10, 11. The teacher will use her fingers to show that she went up three. The teacher will write down 11 as the answer.
· The teacher will then take out linking cubes to show the students a better visual.
· Teacher will start out with 8 cubes linked together. The teacher will explain that she already knows that she has eight cubes so she doesn’t have to count them all up starting with 1.
· Teacher will them add three more and count up one number as she adds each so she will link one and say 9, link the second and say 10, and the link the third and say 11.
· Teacher will say she now wants the students to help her do a vertical addition problem by counting up.
· Teacher will write the problem (8 + 5 = _______) vertically on the board. She will ask the students what she should do first. Students should say find the bigger number.
· Teacher will ask students to locate the bigger number after they recognize that that is what they need to do. The students should easily be able to say the bigger number is 8.
· The teacher will ask the students what they would do next. The students should respond with answers such as, “Add 5,” “Count up by 5,” “Start at 8 and add 5 more,” etc.
· Teacher will ask the students that when she adds 5 more what number will she start with. Students should say start with 8 and count up. The first number they will count will be 9.
· Teacher will have the students count aloud with her and they will put up their fingers as they add to make sure they add only 5. The teacher and students will chant, “9, 10, 11, 12, 13.”
· The teacher will ask students where she should write thirteen on the board. Students should remember that the line separates the sum from the addends so they should be able to tell the teacher that the answer goes under the line.
· Teacher will put up another problem, (5 + 3 = _______). Teacher will ask a student volunteer who thinks they can do the problem to walk her through the steps.
· Teacher will ask what do I do first? Then next? And then have the student count up aloud using their fingers as a guide.
· The teacher will guide the student along through their answer to help avoid mistakes and will have them come up and write the answer in the correct space on the board.
· Teacher will put up one more example, (6 + 7 = ________). Teacher will have another student volunteer walk her through the steps and come up and write the answer once they know what it is.
· Teacher will then explain that students are going to receive a worksheet with a few problems on it so they can practice their counting up and vertical addition.
· Teacher will send the high and middle students back to their desks to work on the differentiated worksheets while the students that need extra help will come to the back and get more of a chance to practice.
** Students will now engage in 15-20 minutes of individual practice. The students at their seats will be completing the worksheets while one teacher circulates throughout the classroom to help them and make sure the students are on task. The students at the back will be given a few more practice problems while one teacher walks them through it using linking cubes as a visual. Those students will then start their independent worksheets in the back of the classroom with specialized attention from one of the teachers.
C. Closure (8-10 minutes):
· Before returning to the rug the teacher will have selected three students to share with the class one of the problems they completed and explain how they did it.
· The teacher will help guide the students through showing the class how they found the answer to the addition problem.
· The teacher will try to pick one tier 1 student, one tier 2 student, and one tier 3 student that way each level is represented and the teacher will know if the content was presented effectively and comprehended by each separate level.
· Teacher will explain that from then on students should keep counting up in mind because they can use it whether the problem is horizontal or vertical and it will help them become even better at addition problems.
MATERIALS:
FOLLOW UP ACTIVITY/ASSIGNMENT:
Students will be building on this skill as the math lessons progress in the days following the lesson. Students will be given plenty of time to practice counting up and using vertical addition. The math message each day calls on the student’s prior knowledge usually including the topic they learned the day before. The math message on Friday will probably be two vertical addition problems that the students will be given time to complete individually. As the students move on and start to learn about regrouping, vertical addition and counting up will become extremely important.
EVALUATION/ASSESSMENT:
I will be able to evaluate the students and determine whether they fully grasped the lesson by either circulating the room during their independent work or working with the students in the back of the classroom. The student’s independent work will be a very good indication of whether they understood the material or not. In addition, having a few students share with the class the way that they arrived at an answer will help me determine whether they not only understood the concept, but also knew how to apply it to their problem solving.
DIFFERENTIATED:
The lesson has been differentiated in a variety of ways to accommodate a multitude of learning styles and developmental levels in the classroom.
RESOURCES:
Grade: 1st / Subject Area: Math
Type of Setting: 1st grade general education classroom
Date of Lesson: March 8th 2012
PURPOSE:
What is vertical addition?
How do we add by counting up?
VOCABULARY & KEY TERMS:
- Vertical addition – An addition problem set up in a vertical direction (going up and down). The numbers appear one on top of the other with the answer at the bottom.
- Counting up – A method of adding two numbers together. You start with the larger number and simply continue counting the amount the smaller number allows in order to arrive at the correct answer.
- Sum – The combination of two or more numbers. The answer to an addition problem.
SKILLS:
- Recognize a vertical addition problem
- Place the sum in the correct place in a vertical addition problem
- Solve addition problems by counting up
OBJECTIVES:
- Students will demonstrate their ability to recognize a vertical addition problem.
- Students will demonstrate their ability to record a sum in the correct place in a vertical addition problem.
- Students will demonstrate their ability to solve addition problems by using the method of counting up.
NEW YORK STATE LEARNING STANDARDS:
Common Core Standards:
1.NBT.4 Use place value understanding and properties of operations to add and subtract
PRE-ASSESSMENT:
- Students have already been introduced to addition and subtraction and have the ability to solve addition and subtraction problems
- Students have only been introduced to addition and subtraction problems as horizontal number sentences so vertical addition will be a new perspective for them
- Students usually add by using their fingers to account for each number
- Counting up will allow them to still use their fingers as counters, but will be quicker and easier for them to do
- After this lesson the students should be able to recognize what a vertical addition problem is asking them to do and use the method of counting up in order to solve the problem correctly
LESSON PRESENTATION:
A. Set-Induction (10-12 minutes):
· Routinely the students are brought to the rug, introduced to the math message, and then sent back to their seats to copy and answer the problem and explain how they arrived at their answer.
· Math message will be – “Copy and find the sum of these problems. Explain how you found your answer: 5 + 7 = ________
· 3 + 8 = _______” (The problems will be written horizontally as shown).
· Teacher will first ask a student volunteer to define sum (students are expected to know that the sum of two numbers is the answer to an addition problem).
· After giving them a few minutes to complete the short problems at their seats the teacher will call the students back to the rug and go over the problems with them together.
· Teacher will ask for student volunteers to help her answer the problems.
· Teacher will guide students into thinking aloud while solving the problems and help students realize how they use their fingers or visuals to help them find the sum of two numbers.
· After the message is complete the teacher will explain that today the students will be learning about a different way to add called vertical addition.
B. Procedure (15-20 minutes):
· Teacher will start off by asking the students if they know what vertical means. If they know, teacher will then ask if they know what horizontal means (if the students cannot come up with an answer she will explain it to them by drawing lines on the board).
· Teacher will explain that horizontal means side-to-side and vertical means up and down.
· Teacher will ask the students to tell her what type of addition the math message asked them to complete, horizontal or vertical. Students are expected to recognize the math as horizontal.
· Teacher will then state that today they are going to be doing vertical math.
· Teacher will ask students what direction the numbers will be going in if the math is going to be vertical. Students are expected to respond that the numbers will be going up and down.
· Teacher will write a vertical math problem on the board (8 + 3 = _______). Teacher will show the students how the numbers are one on top of the other and the line under the addends is another way of putting an equals sign. It separates the addends from the sum.
· Teacher will then say that she has a trick that will help the students become better at adding. She will tell them trick is called counting up.
· The teacher will explain that the first step is finding the larger number. She will point out the larger number (8) and she will circle it on the board.
· Next the teacher will explain that because we know that we already have 8, when we add three we can start counting at 8.
· Teacher will explain that instead of starting at 1, then counting up to 8 and then 3 more, we can start at 8 and just count up three more.
· Teacher will model how to do this by saying, “Ok, so I already have 8 now I need to add three to that number. I will start with eight and then count up 3 more numbers. 8, 9, 10, 11. The teacher will use her fingers to show that she went up three. The teacher will write down 11 as the answer.
· The teacher will then take out linking cubes to show the students a better visual.
· Teacher will start out with 8 cubes linked together. The teacher will explain that she already knows that she has eight cubes so she doesn’t have to count them all up starting with 1.
· Teacher will them add three more and count up one number as she adds each so she will link one and say 9, link the second and say 10, and the link the third and say 11.
· Teacher will say she now wants the students to help her do a vertical addition problem by counting up.
· Teacher will write the problem (8 + 5 = _______) vertically on the board. She will ask the students what she should do first. Students should say find the bigger number.
· Teacher will ask students to locate the bigger number after they recognize that that is what they need to do. The students should easily be able to say the bigger number is 8.
· The teacher will ask the students what they would do next. The students should respond with answers such as, “Add 5,” “Count up by 5,” “Start at 8 and add 5 more,” etc.
· Teacher will ask the students that when she adds 5 more what number will she start with. Students should say start with 8 and count up. The first number they will count will be 9.
· Teacher will have the students count aloud with her and they will put up their fingers as they add to make sure they add only 5. The teacher and students will chant, “9, 10, 11, 12, 13.”
· The teacher will ask students where she should write thirteen on the board. Students should remember that the line separates the sum from the addends so they should be able to tell the teacher that the answer goes under the line.
· Teacher will put up another problem, (5 + 3 = _______). Teacher will ask a student volunteer who thinks they can do the problem to walk her through the steps.
· Teacher will ask what do I do first? Then next? And then have the student count up aloud using their fingers as a guide.
· The teacher will guide the student along through their answer to help avoid mistakes and will have them come up and write the answer in the correct space on the board.
· Teacher will put up one more example, (6 + 7 = ________). Teacher will have another student volunteer walk her through the steps and come up and write the answer once they know what it is.
· Teacher will then explain that students are going to receive a worksheet with a few problems on it so they can practice their counting up and vertical addition.
· Teacher will send the high and middle students back to their desks to work on the differentiated worksheets while the students that need extra help will come to the back and get more of a chance to practice.
** Students will now engage in 15-20 minutes of individual practice. The students at their seats will be completing the worksheets while one teacher circulates throughout the classroom to help them and make sure the students are on task. The students at the back will be given a few more practice problems while one teacher walks them through it using linking cubes as a visual. Those students will then start their independent worksheets in the back of the classroom with specialized attention from one of the teachers.
C. Closure (8-10 minutes):
· Before returning to the rug the teacher will have selected three students to share with the class one of the problems they completed and explain how they did it.
· The teacher will help guide the students through showing the class how they found the answer to the addition problem.
· The teacher will try to pick one tier 1 student, one tier 2 student, and one tier 3 student that way each level is represented and the teacher will know if the content was presented effectively and comprehended by each separate level.
· Teacher will explain that from then on students should keep counting up in mind because they can use it whether the problem is horizontal or vertical and it will help them become even better at addition problems.
MATERIALS:
- Linking cubes (a few for the lesson on the rug and enough to supply the students that will be using them for extra practice)
- Marker to write on white board throughout the lesson
- Three different levels of the worksheet with several addition problems on them
- Two cards “horizontal” and “vertical” to add to the math word wall
FOLLOW UP ACTIVITY/ASSIGNMENT:
Students will be building on this skill as the math lessons progress in the days following the lesson. Students will be given plenty of time to practice counting up and using vertical addition. The math message each day calls on the student’s prior knowledge usually including the topic they learned the day before. The math message on Friday will probably be two vertical addition problems that the students will be given time to complete individually. As the students move on and start to learn about regrouping, vertical addition and counting up will become extremely important.
EVALUATION/ASSESSMENT:
I will be able to evaluate the students and determine whether they fully grasped the lesson by either circulating the room during their independent work or working with the students in the back of the classroom. The student’s independent work will be a very good indication of whether they understood the material or not. In addition, having a few students share with the class the way that they arrived at an answer will help me determine whether they not only understood the concept, but also knew how to apply it to their problem solving.
DIFFERENTIATED:
The lesson has been differentiated in a variety of ways to accommodate a multitude of learning styles and developmental levels in the classroom.
- Visual learner: The visual learner will benefit from the examples placed on the board, the linking cubes, and using fingers as counters. All of these will show the same concept, but using three different visual aids. That way, if a student does not grasp the concept just by examining the numbers written on the board the linking cubes or the student’s fingers might be a better representation for accommodating that student’s thought process.
- Auditory learner: The auditory learner will benefit from counting aloud with the teacher during the examples. The student will be able to organize the concept in their head while verbally solving the problem. The student will also be given multiple opportunities to volunteer an answer verbally or listen to others volunteer answers. The students will also be able to listen to their peers explain the way they solved the problems if they don’t get the chance to share themselves.
- Intrapersonal learner: Students will be given a chance to explore vertical addition independently. The worksheets are meant to be completed individually and will provide independent practice that will help the intrapersonal learner understand the concept in their own way.
- Above grade level student: The high students will be asked to complete a worksheet that has more difficult problems. Some of the high problems will include one double-digit number. The students will be able to answer the problem the same way; the numbers will just be bigger. There will also be a space on their worksheet that will ask them to explain how they arrived at their answers.
- Meeting grade level student: The worksheet given to the middle student will provide problems very much like the problems used during the lesson. The problems will be a little less complex than the high worksheet in that the sum will not be such a large number. The students will only be asked to explain how they arrived at their answer if they finish completing the problems with time to spare.
- Below/Approaching grade level: These students will receive extra help in addition to the lesson being taught. The worksheet these students will be asked to complete will have fewer problems and will be the most simple of the three worksheets. A teacher will also be available for more individualized guidance while the students complete their worksheets. These students will also be encouraged to use linking cubes to help them complete the problems.
RESOURCES: