
Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
When given 3 index cards containing addition and subtraction equations through the thousands, the student will be able to determine if the equations are true or false.
Students will justify their reasoning as they work in partners to explain how they know these equations are true or false. Students will use comparative relational thinking, without computing.

Prior Knowledge: What prior knowledge should students have for this lesson?
Prior to this lesson, students should have a thorough understanding of the place value system and numbers that add to 10. Students should be able to compute mentally through the thousands, using relational thinking, without using paper and pencil.

Guiding Questions: What are the guiding questions for this lesson?
What does it mean for an equation or number sentence to be true or false? Possible student answer: both sides of the equal sign have to be the same, or one side has to equal the other side like a balance scale.
Essential QuestionHow can you use relational thinking to solve a set of problems, without actually using paper and pencil computation?
Students need to be able to orally answer this at the end of the lesson.

Teaching Phase: How will the teacher present the concept or skill to students?
1. The teacher will begin the lesson by introducing equations to students.
Is the number sentence 129=3 true or false? How do you know?
Suggested answer: It is true because if I have 12 snickers and I eat 9, then I am left with 3.
Is the number sentence 14+16=30 true or false? How do you know?
Suggested answer: It is true. Possible reasons: I know because 10+10= 20 and 6+4=10, so 20+10=30 or "I can move one from the 16 over to the 14 and make the problem 15+15=30.
Is the number sentence 133=9 true or false? How do you know?
Suggested answer: It is false because when I take away 3 from 13, I have 10 left over, not 9.
**The teacher should notice which children are computing and which children are using relationships to determine which problems are true and which problems are false.
2. Now students need to be given problems in which there are two addends on each side of the problem.
Examples:
How do we know if 60+74=72+62 is true or false?
Possible answer includes students stating they used mental math to add their ones column and then their tens column on each side of the equation to figure out the equation is equal.
Let’s do some additional practice. Tell me how we know that 44+29=45+28 is true or false?
Possible answers: 44+29=45+28 is true because I can take one away from the 44, add it to 29 so now I'm working with 43+30 and that is 73 and 45+28 is also equal to 73 because if I take away 5 from the 28 and add it to the 45, I have 50+23 which also equals 73.
**Children must recognize they can use relational thinking to solve these problems without the use of all the calculations.
Give an example through the thousands place.
The teacher will use the several examples mentioned and build upon them into multidigit numbers through the thousands place. (Some student will have to use paper/pencil or white board/marker to show their thinking process before they begin using comparative relational thinking)

Guided Practice: What activities or exercises will the students complete with teacher guidance?
The teacher will then have students work in pairs with the three provided teachermade index cards (see attachments). During this time the students will try and determine for each card whether the equation is true or false, and then share their thinking with their partner. The teacher will guide the struggling students with their relational thinking (if needed, use the individual white boards to model the students thinking so they can understand their own thinking process). Students will document their answers (on paper or white boards) so a whole group check can be done.
The teacher should remind students to "Keep in mind the strategies we have used when solving these "warm up" problems today, throughout the rest of math today."
While the teacher is walking around monitoring students working in their pairs to solve the example problems, the teacher might ask some of the following probing questions:
1. Can you explain to me what you are thinking?
2. Why do you say that this equation is true but this one is false?
3. How is this equation false? What is it missing to make it true?
4. Did your partner use a different method to figure out if it was true or false?
5. Ok, now explain that to your partner again because I don't think he understood that.
6. Can you share that thinking with the whole class please?

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
After working in pairs with index cards, students will then work on an additional three index cards (see attachments) independently to solve for true or false. The students will not only solve true or false, but also demonstrate their relational thinking through a written justification for their true or false answer. (1520 min)
Independent Practice Instructions
1. I am going to provide you with three additional Independent Practice Index Cards.
2. I want you to write on these because I want you to explain and justify your thinking in writing.
3. So, you are going to write TRUE or FALSE AND I want you to explain in writing your relational thinking on how you figured out the answer.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will collect student work and use student responses to their index cards as examples on the board (without using student names) to ask if the methods used make sense and compare them to other student responses while asking the students if both responses are reasonable. (Use of a document camera is possible here or the teacher can just copy the student work on to the board)
Once the teacher collects and begins to review student answers she/he will ask:
1. Can this person’s method be used AND this person method be used to solve for true or false? Why? Why not?
2. Is one strategy better than the other? Or is it depending on how you think about numbers?
3. How does knowing what numbers add up to ten help you with this skills?
4. Now I will give you the correct answers so you can check and see if you were correct before we do our independent practice.
FINAL QUESTION REFER BACK TO THE ESSENTIAL QUESTION How can you use relational thinking to solve the next set of problems, without actually using paper and pencil computation? HAVE STUDENTS ORALLY RESPOND TO THIS QUESTION

Summative Assessment
At the completion of the three independent practice index cards and the teacher reviews/compares student answers, index cards will be used as a summative assessment. The teacher should be looking for how the student uses written form to verbalize their relational thinking. Although there is no "right" or "wrong" answer to a student's relational thinking, the teacher is looking for the students' use of mental math strategies as modeled in the guiding questions and reasonableness.

Formative Assessment
While teaching whole group, the teacher will pose a situational story problem on the board to students. Using white boards and markers, or paper and pencil, the students will write the answer to the question that has been posed with the words true or false, followed by either a written or oral description of their relational thinking. The teacher will walk around and put a sticker on the desk (stickers are not necessary, a high five or some acknowledgment is all that is necessary) for the students who are correct and ask the students who are still struggling what their relational thinking process is. If needed, the teacher will use manipulatives or numerical representations to demonstrate to those students how they can make groups of ten to solve the problems with comparative relational thinking.

Feedback to Students
During the whole group lesson, the teacher will provide students stickers for their correct answer for the true/false answer. The students who are struggling will get immediate feedback from the teacher by reviewing the lesson, reminding them of the other examples that were given and asking them to explain what their relational thinking process is.
Once students have been given their independent practice assignment in pairs, they will solve the equations independently and then share with their partner their method of thinking and explain how they figured out if the equation is true or false and why. The teacher will be walking around listening to the students talk, and participating with them as she/he deems necessary. The teacher will remind students to stay on task, provide probing/guiding questions, and use phrases with the class "I like the way student a and b are working and talking about their true and false equations"
Students will write their "true" "false" answers to the index cards on a piece of paper or a dry erase board (depending on available teacher resources or teacher preference)