Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
- Students will be able to compare both sides of an equation and determine if the equation is true or false.
- Students will reason and explain their reasoning about the relationship between the two sides of the equal sign to determine if the equation is true rather than solving to find out if the equation is true.
- Students will be able to find the missing whole number in an equation by reasoning about what is the same and what is different in the two sides of an equation.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should know and understand the following:
- The meaning of the equal sign.
- In addition, you add the parts to make the total (whole).
- Comparison of numbers.
- The meaning of true and false.
- Some ability to add and subtract mentally.
Students may get confused with the equal sign when comparing equations. They may want to make both sides equal when looking for the relationship between the two numbers instead of comparing the sides to see if the equation is true or false.
Guiding Questions: What are the guiding questions for this lesson?
- What is the meaning of true and false? (This is the first question the student should be asked.)
- What does the equal sign mean? (the same as)
- What does the equal sign mean in an equation? (both sides have the same value)
- What are the parts in this equation?
- How have the parts changed from one side of the equal sign to the other side? Would this change the total? Why? or Why not?
- How do we find a missing number in an equation? Why does that work?
- What do you know about the parts and whole in addition that might help you?
Teaching Phase: How will the teacher present the concept or skill to students?
Teacher Note: The difference in this new standard as compared to other standards addressing equations is that students are looking for relationships or what is the same and different about both sides of the equal side. It states that students are not to solve the equations to find if it is true but rather compare the sides. Because of this newness, this lesson begins with a rather simple addition problem. As the years progress, and more students gain the math understanding expected in the Florida Standards in the primary years, the beginning of this lesson might only be used as remedial work.
Each student should have a paper with two lines on it and 8 cubes or counters.
Tell the following quick story. You might substitute the name for a student in your class and the item for something of more interest to your students.
Pete loves to collect dead insects, put them into jars and study them. It is his joy in the morning (before school) and his delight in the evening to overturn rocks and logs hunting for dead insects. Pete's mom is not overjoyed or delighted by the amount of dead insects she finds in Pete's pockets and on his desk. Like all moms, she came up with a plan to help Pete organize his insects. She and Pete hung 2 shelves in Pete's room and bought 8 insect viewing jars to hold Pete's collection. Pete's mom has warned him that all insects go into the jars and he may only use 8 jars. If she finds one more insect in Pete's pocket, she will ground Pete for the rest of his life or send him to Siberia! Brr...
Pete is trying to decide how many jars he should put on each shelf. Use the two lines as shelves and the cubes as jars and come up with at least 3 ways Pete may organize the two shelves. Write these ways on the bottom of your shelf paper.
Encourage student to actually use the cubes and move them between the two shelves. This helps reinforce later more abstract ideas about addition.
Ask the students to report their solutions. Record them on a chart paper or the board in the order listed on this attachment. (I like to use chart paper so I can keep in hanging up in the classroom while we are studying these ideas.)
Ask the students what patterns they see in this arrangement. You will want to highlight two patterns. I suggest discussing the first one listed below first. If students don't say this one first, keep asking for patterns until someone does.
- If you add the amount on the 2 shelves, it always equals 8. Write the equation for each shelf letting the children say the total (8) for each equation. Emphasize this point by asking the students if they are sure. Ask them to explain why this is true. Probably they will say these addition facts are ones they know or count on their fingers to prove the addition fact. If that is all they say, you will need to ask these questions:
- Did I add any to this part? or this part? (point to the shelves). (No)
- Did I take any away from this part or this part? (No)
- Say, so if I didn't add any or take any away from the parts, I still have a total of 8. Right? Write this on the chart.
Second Important Pattern
- By organizing your chart chronologically, the students should find the pattern that you can take one jar from one shelf, put it on the other shelf and the total is still 8. One shelf decreases by 1 while the other shelf increases by 1 but there are still 8 jars.
- Ask the students, if they think this idea would work with numbers other than 1. What if I take 3 from one shelf and move it to the other shelf, is my total still the same? (You can show this is true by pointing this out on the chart.) Ask, why does this work? Hopefully a student will repeat the generalization from the first pattern. We haven't added any to the parts or taken away from the parts, we have just moved the amounts between the parts so the total stays the same.
- Ask the students to help you generalize this idea about addition. You should create something like, "If you move an amount from one part and add it to the other part the total does not change."Add this statement to the chart so your chart now looks like this.
Tell the students they have done a great job helping Pete organize his dead bugs and you are sure he can now make his mom happy. However, this is a math class and we need to pull a bit more math learning from our story.
Pointing to the chart, remind the students they told you that all of the addition equation equal 8. Point to two of the equations and ask the students to come up with a way we can record in mathematics language that the two equations are equal. Let the students think and explore on their own before sharing ideas.
If a student has found the appropriate way then use the student's example. For now, we will use this one.
7 + 1 = 6 + 2
Ask the students what is the difference in the expressions on each side of the equal sign. (6 is one less than 7 and 2 is one more than 1). Point to the generalization on the chart and state that we have taken an amount from one part and given it to the other part so our total does not change.
Try another equation that does not use a difference of 1, such as
4 + 4 = 1 + 7
Ask the students to think about the relationship (what is the same, what is different) about the two sides of the equation and explain why this equation is true. Discuss and clarify their ideas.
(Move the 3 from one part so it becomes 1 and give it to the other part so it becomes 7.)
Explain to the students that because they are now 4th graders they should not have to always solve to know if equations or true, but should be able to use reasoning, such as we just did. Tell them to not solve or find the total but rather use their reasoning to figure out if the next equation is true.
Post: 44 + 4 = 41 + 7
The students should explain we haven't added or taken anything away, we have move 3 from 44 so it becomes 41 and added it to the 4 so it becomes 7. Yes, this equation is true. If it helps you could use cloud writing to explain the thinking as seen in the attached picture. This picture gives further examples to try with the students. Please note, the students can reason mentally (that is the goal) and not do the cloud writing. The cloud writing allows the mental math to become visible. Also, problem numbers 5 and 6 use large numbers. It is a lot easier to reason relationally to determine this is a true equation than it is to add the parts. You will want to point this out to students.
Sample practice problems with cloud writing
The second standard is an extension of the first standard so if you still have the students' attention, you could go ahead and do the next part. If the students are getting tired, do this part on another day.
Sometimes, we don't have complete equations such as the ones we just did. Sometimes there are parts missing to the equations. We can still use our relational thinking (reasoning about the parts) to find a missing part. You do not always have to solve the equations to find the missing part.
For example, (post on the board) 7 + 5 = 8 + ?
Ask the students how they might find out what the question mark represents using the same strategies we have been using in this lesson.
(We know 8 is 1 more than 7 so we would need to take 1 from the 5 to find the other part. The complete equation would be 7 + 5 = 8 + 4. If needed, you could use the cloud writing to record the steps.) If the class seems to have a hard time grasping this go back to the shelves story and tell them Pete has 7 jars on one shelf and 5 jars on the other shelf. He decides to rearrange by moving 1 jar from the bottom shelf to the top shelf. You and/or the students model this. Ask, how to write the new arrangement using addition.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Group the students as best meets the needs of your class. Here is one possible way. The students will be given a piece of paper with a number on it 1-4. They will be grouped according to the numbers they have, the 1s will be grouped together and so on.
In the groups each table will have two envelopes. Envelope one has equations inside and the second envelope will have equations with numbers and unknown variables. (These can be printed in card stock or copy paper.)
Click the link envelope_1.docx
The teacher will assign each group to open envelope one.
Each group will have equations inside with the options of true or false. The students will sort the equations by whether they are true or false. Tell the students they should not be solving the equations but using their relational reasoning to classify the equation. Each equation classification must be justified by using the relational reasoning. Listen for this reasoning and stop the group if you hear then solving the equation. The teacher will monitor each group for participation and understanding. The teacher will assist groups as needed.
After the students have completed this task, selected groups will report with an explanation of what they chose and why they chose it.
If you have done the work on the unknown variable, you can assign envelope 2.
In the envelope there are equations with unknown variables. Each group will work on the equations and come up with the missing number. This number will make these equations true. A set of possible numbers are given, so the activity is somewhat self checking. Once the groups have finished with the second envelope, you can call the class together to discuss their findings. Be sure to require explanations.
At any point in the lesson, you can click on the following link to open an interactive game about equations. The game allows students to balance equations.
Pan Balance Interactive Game
The teacher can enter equations on the balance or the students can enter and play independently of the teacher. Students will get a visual on the balancing of the equations.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
- Students will work on this assignment independently.
- Students will create their own equations that are true and false. (3 of each type) They will also create an unknown equation with an answer key.
- The teacher will circulate throughout the room to observe the work of the students.
- After completing the assignment each student will present their equations with the answers.
- While the pairs are presenting students can agree or disagree with the outcome of a group. The students that disagree must state why they disagree.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Call the class together to summarize the learning in this lesson. It should be some think like
Sometimes you can reason about what is the same and what is different in the parts of an equation to find out if equations are equal and/or to find out what number a variable represents.
The students will share their creations with the class. They will explain their thinking process when solving.
Give the assessment.
Administer the attached assessment as the summative assessment. The assessment will show the students level of understanding. Click the link for the assessment:
On the assessment worksheet the students will explain why the item is true or false. After the explanation the teacher will know if the student really understands the concept. Students that demonstrated a lack of understanding will need more support and/or re-teaching.
Essential Prior Knowledge for this lesson is the understanding of the meaning of the equal sign. A day before the lesson put the following equation on the board and ask the students to identify what number should replace the question mark. Then ask the students to explain the meaning of the equal sign. Collect these responses. If students do not show the understanding that the equal sign means that both sides have the same value then you will have to teach this concept first.
Equation and instruction to put on the board:
7 + 5 = ? + 8
Explain the meaning of the equal sign.
7 + 5 = 4 + 8
The equal sign means that the quantities on its two sides have the same value.
Teacher Note: The meaning of the equal sign is now a first grade standard in the Florida Standards so hopefully as the years progress, more students will come to 4th grade knowing this concept.
The teacher will assess to see if the students are able to determine if an equation is true or false without calculating. This quick assessment may be done at any point in the lesson.
The teacher will present a true or false equation on the board and ask the students to state if it is true or false and explain why. Example equations include:
- 24 + 15 = 13 + 23 (Answer: False. 13 is 2 less than 15 and 23 is 1 less than 24 so when compared to the first equation, the second equation is 3 less.)
- 30 + 12 = 25 + 17 (Answer: True. 25 is 5 less than 30 but 17 is 5 more than 12 so the parts have changed but nothing was added or taken away so the total is still the same.)
Students will respond by writing true or false and explaining their reasoning on index cards. The teacher will need to assess the students' understanding.
After the teacher sees the responses he/she will be able to determine if the students have grasped the concept. If the student has not grasped the concept the teacher may modify the lesson using the suggested accommodations:
- Modify the lesson using concrete models by allowing students to solve equations using cubes or base-ten blocks. The students will show their work using the manipulative.
The teacher may also wish to pull a small group of struggling students for extra review of the skills.
Feedback to Students
Students that are not successful in determining the correct answers will be asked by the teacher to explain their thinking process. This will help the teacher to understand where the student's misunderstanding may have occurred. Ask the student:
- How did you solve the equation?
- What is the same and what is different in the two sides of the equation?
- What is the relationship between one part and another part?
- Why was the equation true or false?
After asking these questions the teacher should be able to the identify the student's error and correct it by re-teaching the area of confusion (for example, the equal sign or decomposing).