TEDU 522 – Math Lesson Sequence, Plan, and Reflection

Below is both the lesson sequence that I created for a second grade class, focusing on math, and the lesson plan that I conducted with a second grade, field placement class. Additionally, my reflection for the lesson is also included and helps to offer insight not only into what I had planned to do, but then what actually happened and what I was able to take away from the experience.

Lesson Sequence Assignment:

Strategies for Subtraction – 2nd Grade

Big Idea:

Different strategies that can be used to solve subtraction problems, such as:

  • Use a Ten
  • Round and Adjust
  • Subtract the Parts
  • Open Number Lines

Related SOL:

2.6 – The student will

  1. a) estimate sums and differences;
  2. b) determine sums and differences, using various methods; and
  3. c) create and solve single-step and two-step practical problems involving addition and subtraction.
  Before/ Intro

(Activate Prior Know.)

During/ Development

(Student Work)

After/ Summary

(Class Discussion)

Process Skills & Mathematical Practices
Day 1

 

“Use a Ten”

Number of the day discussion (What is 10?)

–        5+5, 6+4, 9+1, et.

–        My brother is ten

–        There are ten….

 

Discuss/model “Use a Ten” Method

–        Change number to the nearest ten and sub/add what was changed to make it a 10

–        72 – 5 à 70 – 5 + 2

“Use a Ten” Game

–        Tables/Groups work to change and then solve subtraction problems using the method

–        Examples of problems:

o   64 – 6

o   93 – 8

o   57 – 12

o   33 – 21

 

Discuss the method and game

–        Is it easier or not then other ways? Why?

–        Do you think you could use this in real life? How?

–        Communication

–        Connections (math to world)

–        Model w/ Math

–        Use tools strategically

 

Day 2

 

“Round & Adjust”

Number cards/PowerPoint (Which is easier?)

–        Numbers ending in 0s and 5s versus others

 

Discuss/model “Round & Adjust” Method

–        On board w/ marker to work through w/ students

–        Friendly numbers

–        Ex. 54 – 18 à 50 – 15

“Round & Adjust” Worksheet

–        Change subtraction problems to make them easier

–        i.e. 25 – 9 goes to 25 – 10 = 15

Go over worksheet w/ class

Discuss Method

–        What is important to remember w/ this way?

–        Why is it important?

–        How do you know it is important?

–        What else do you think we should remember?

–        Communication

–        Reasoning & Proof

–        Model w/ Math

–        Look/ Make use of structure

Day 3

 

“Round & Adjust” Part II

White board

(How to adjust it)

–        Students come to board and make problems easier

–        i.e. 10 – 6 — > 10 -__ (5)

“Round & Adjust” Worksheet Back

–        Using already changed subtraction problems, decide how much was taken away or added to make it easier

Go over worksheet w/ class

–        Model some of the problems

 

Discuss

–        How’s this different to the others ways we’ve learned?

–        Is it easier? Why?

–        Communication

–        Connections (math to math)

–        Look/ Make use of structure

–        Model w/ math

Day 4

 

“Subtract the Parts”

Read Shark Swimathon by Stuart J. Murphy

 

Discuss using parts of numbers to help subtract

–        W/ powerpoint showing numbers and what they can be broken into

–        9 à 5 & 4…

 

Group Trade Problems

–        Tables solve one step of parts problem then trade with another to solve another step until all steps done

Have tables share their answers

 

Discuss

–        Was it easier to do parts instead of whole?

–        Why?

–        Communication

–        Connections (Math to world)

–        Reasoning & Proof

–        Model w/ Math

–        Look/ Make use of structure

Day 5

“Open Number Line”

Help me make a number line

–        Have class tell teacher what and how to make a number line (scribe on board)

 

Discuss open number line & subtracting

–        Model it on board

–        Go over how it works both directions (sub vs. addition)

“Open Number Line” strips

–        Cut out strips of paper and have students solve problems with a number line

–        Give each group a different problem

–        Challenge to try addition/counting up if done early

 

Have each table share their original problem and number lines & WHY they did what they did

 

Number Talk

–        47 – 12

–        Students can use any strategy to see what they learned

 

 

–        Communication

–        Reasoning & Proof

–        Representation

–        Model w/ math

–        Look for & express regularity in repeated reasoning

Lesson Plan:

Open Number Line for Subtraction & Addition

Purpose

  • Students will gain an understanding of what an open number line is, as well as, how to use one to solve both subtraction and addition problems with numbers containing up to two digits.
  • SOL: 2.6 – The student will
  1. a) estimate sums and differences;
  2. b) determine sums and differences, using various methods; and
  3. c) create and solve single-step and two-step practical problems involving addition                                   and subtraction.
  • NCTM Process Skills and Mathematical Practices:
    • Communication, Reasoning and Proof, Representation
    • Model with Math, Looking for and expressing regularity in repeated reasoning

Objectives

  • The second-grade students will be able to correctly model using an open number line to solve a subtraction and an addition problem given a subtraction and addition problem, a strip of receipt paper, and a prior review of open numbers lines and operations without error.
  • The second-grade students will be able to correctly demonstrate an understanding of different strategies for solving subtraction problems, as they have learned in class, in a number talk given the number talk problem and prompting from the teacher without error.

Procedure

  • Introduction:
    • Begin the lesson by telling the class that you need their help. Tell them that you want to create a number line but cannot remember what one looks like. Ask them to think about what a number line is and then raise their hands to tell you. Scribe what they say on the board.
    • Afterwards, go over the parts of a number line and revise what is on the board if needed.
      • A number line is a straight line with two arrows or endpoints, one at each end of the line. It has lines on the actual number line that indicate how much each ‘jump’ is worth.
    • Next, tell students that you will be learning how to use a number line to subtract and add. Explain and model that they will use an open number line, which is a number line just without the ‘jumps’/integers. Draw an example on the board.
    • Then solve the problems 43 + 36 and 80 – 53 on an open number line, walking the class through the different steps you do to solve it (Model with Math).
      • For 43 + 36, start at 43 the make a jump forward of 30 to 73 then another jump of 2 to 75 and a final jump of 4 to 79.
      • For 80 – 53, start at 80 then jump backwards 30 to get to 50 then jump back 20 to get to 30 and finally jump back 3 to get to 27.
    • Take any questions about using an open number line.
  • Development:
    • Next, tell students that they will be working on their own open number lines to solve a problem.
    • Pass out the receipt paper, one strip to each student, and the index cards with the subtraction and the addition problems on them, one card per table.
      • See attached index cards for problems and answer key
    • Tell students that everyone will be making their own open number line, but that each person at a table will be working on the same problem. Ask them to do this individually and to start on the subtraction problem. When they finish, they should flip their number line over and try the addition problem on the back.
    • Allow students time to work and walk around observing and answering any questions that the students might have.
  • Summary:
    • When everyone has finished, ask the different tables, one at a time, to stand up in front of their desks and share with the class their original problem and the number lines that they created (Communication and Looking for and expressing regularity in repeated reasoning).
      • Be sure to prompt the students to what they did for their number line and why.
    • Once each table has gone, thank the class and collect the number lines.
    • Then tell them that you have one last thing for them to do and that you would like for them to join you at the front carpet, calling each table to join you at a time.
    • Write the problem 47 – 12 on the board and tell students that you will be doing a number talk.
    • Go over the rules of a number talk and ask students to think about how they would solve the problem. Tell them that they can use any subtraction strategy they want to.
    • Allow them time to think and then ask for some answers. Scribe them on the board and then have students raise their hands and tell you their various methods for solving the problem, scribe these as well (Reasoning and proof and Representation).
      • The answer to the problem is 35
    • Once students have shared, ask the class for their conclusion and answer and then thank them again for taking part in your lesson.
  • Differentiation
    • Visual and Auditory learners will have support through the explanation of using an open number line and the number talk.
    • Kinesthetic learners will have support through the actual activity of creating their own open number lines
    • Students who finish early can be prompted to share with other students, Kagan strategies, about what they think about open number lines.
    • Students who finish early can try and create their own problem and solve it on another number line.
    • Students who are struggling can have teacher support during their work on the number lines.
    • Students who are struggling can have peer support while taking part in the number talk.

Materials

  • Teacher
    • White board/ Smart board
    • Dry erase marker/ Smart board marker
    • Index cards w/ each table’s problems
    • Answer key for problems
  • Students
    • Pencils
    • Receipt paper strip

Evaluation A

  • Student learning will be evaluated by whether or not they have successfully solved their given subtraction and addition problem using the open number line strategy individually and without error.
  • Student learning will be evaluated as a class and by whether or not students were able to successfully use, talk about, and explain the different subtraction strategies during the number talk without error.

Lesson Reflection

The math lesson I taught with my second-grade, practicum class went over rather well. My students were very engaged and had a lot of fun making their own open numbers lines, so much so that they were begging their teacher to display them around the room afterwards. But aside from all of the fun, my students were also able to learn from my lesson as well. They not only learned about how to use open number lines to solve both addition and subtraction problems, they also gained more of an understanding that you can use whatever method you want to solve math problems, thanks to the number talk we had. I know they learned how to use open number lines based on the results that I got from each of my students’ open number lines on their receipt paper. My students, of all levels, were able to complete both subtraction and addition problems. Not only that, but they also seemed to realize that they were not limited to just one method for the number talk, though it did take some prompting and a suggestion of my own favorite method while we talked about the problem. Over all, I do feel like my students learned from my lesson and I would love the chance to go back and review subtraction strategies with them to see if it stuck.

My lesson, despite being a success, had its fair share of positives and challenges. First and foremost, my lesson was very engaging, at least for my second graders. Most all of my students absolutely loved being able to not only make their own open number lines, but they also really enjoyed being able to show me their skills at solving a problem during the number talk. Another positive is that the opening activity, with them telling me what a number line is, really helped me to see how much they already knew about the idea of one and how to use it. It turned out they knew a lot already and it helped me to be able to move more quickly with explaining what an open number line is and how to use one. On the other hand, one of the challenges I faced was that because the open number line activity was individual and all twenty-six of my students made their own, I had trouble trying to check everyone’s work to make sure it was correct. I was able to see that all my students had the method down and were trying to use the number lines, but not if everyone was able to get the right answers, though I did have them talk as a group and discuss how they solved it to share with the class so I do hope that students who were incorrect had a chance to realize it and change it. Another challenge was that not everyone was following along during all parts. All my students loved the number line activity and the number talk, I did have some students wandering off during my warm up activity and my actual going over of the concept of open number lines. Those were the most notable things about my lesson overall, and the next steps for me would be to go back through my lesson and try and see if I could change areas I know were challenging to better accommodate students hopefully better the lesson for the next time I teach it. I could also actually ask for my class’s feedback and whether or not they had anything they would suggest.

I learned a few things from this lesson. For one, I learned that when teaching, a great way to get students excited or interested is to get them to work on things that they can show off or take home. They love being able to show what they can do to those around them. Another thing is that it is super important to see where your students are before you teach a lesson. You do not want to try and teach students a new idea building on a concept if they do not know what the concept you are building on is. It would just lead to a lot of confusion. For myself, I learned that I am actually quite a bit better at direct instruction than I thought. I was able to properly convey my ideas and the concept to my students as they were able to take it and apply it afterwards. Not only that, but I also learned that I enjoy seeing the students make things that they are proud of just as much as they do. I loved seeing them complete their number lines and then have them share them with me.

If I had the chance to teach this lesson again in my own class, I would change a few things. I would be sure to try and make my warm up activity more appealing to everyone so that all students stayed focused, perhaps by incorporating a roleplay aspect into it or having them work in partners or groups to think of something. I would also see if I could do something similar with my direct instruction, having students help me with examples or finishing ideas. I would still, of course, make sure they were right though. And finally, I would definitely try and collect my students’ number lines once they finished, just so I could gain a real feel for whether or not everyone not only got the concept but could then correctly apply it. We would hopefully still have a lot of fun, but I could tweak the lesson to make sure that it was as effective as it could be.

This plan is a like to best practice in a few ways. One way is that it got students to not only communicate with me and each other about what they did to solve problems, but they also had to consider why and how they worked, which would be implementing reasoning and proof, for both the number line activity and the number talk. Not only that, but students also had a hand in using representations during the lesson with the number talk in which they were able to use any method or model they wanted to solve a problem. The number talk also helped to promote more conceptual understanding than just procedural. Students looked at a problem and then decided how they would work with it. There was no set method or prompt for them to follow. Students also worked through productive struggle when I would ask them about a method they used and to explain it for everyone. It really did take some thought for them to be able to do so. I feel that while my lesson could of course include more to fit with best practice, it also did have a lot of the ideas from best practice incorporated into it to help make student learning as focal as it could be.

 

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