Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 73435
Creating a Balanced Equation
Students will relate using a balance to the mathematical symbol, the equal sign. Students will use their knowledge of the equal sign and addition and
subtraction to find the unknown number in an equation with four or more numbers.
Subject(s): Mathematics
Grade Level(s): 2
Intended Audience: Educators
Suggested Technology: Computer for Presenter,
Interactive Whiteboard, Overhead Projector, Microsoft
Office
Instructional Time: 2 Hour(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: unknown, equation, equal sign
Resource Collection: FCR-STEMLearn Mathematics General
ATTACHMENTS
Creating a Balanced Equation.docx
Creating a Balanced Equation.pptx
Student Scale.docx
LESSON CONTENT
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 determine the unknown whole number in an equation relating four or more whole numbers using numerals or pictures.
Students will make sense of problems using addition and subtraction strategies mentally or in written form and persevere in solving them.
Prior Knowledge: What prior knowledge should students have for this lesson?
In order to be successful in this lesson, students must either have mastered the following skills or have been exposed to the following skills from
their current or previous grade levels:
1. MAFS.K.CC.2.4 – Understand the relationship between numbers and quantities; connect counting to cardinality.
2. MAFS.1.OA.4.7 – Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of
the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
3. MAFS.1.OA.4.8 – Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the
unknown number that makes the equation true in each of the equations 8 + ___ = 11, 5 = ___ – 3, 6 + 6 = ___.
4. MAFS.2.NBT.2.6 – Add up to four two­digit numbers using strategies based on place value and properties of operations.
Guiding Questions: What are the guiding questions for this lesson?
1. What does the equal sign tell us?
2. How do you know if the equation is true?
3. What can I do to make my equation true?
Teaching Phase: How will the teacher present the concept or skill to students?
page 1 of 4 Teacher will bring students to the carpet ("carpet" in this sense refers to a shared space. Teacher will need to be located by something they can write on). Teacher
will introduce students to a balance. Teacher will ask students to explain what they think the object is and what it could be used for. Teacher will record student
thinking on the board using a circle map. A circle map is a large circle with a smaller circle inside of it. Inside the smaller circle would be the main idea (in this case
the word "balance"). Within the outside circle could be words or phrases that relate to the main idea (in this case, the outside circle would have explanations of the
object and what it could be used for).
After the students have hypothesized what they think the balance is, the teacher will put 5 snap cubes on one side of the balance. The teacher will then ask the
students to explain what they think happened. The teacher will then put 10 snap cubes on the other side of the balance and ask the students to explain what
happened this time. The teacher will ask students if they can add any more ideas to the circle map about what a balance does. The balance will be used to
emphasize the concept of equal. Students will not be comparing numbers, but rather, trying to make them equal.
The teacher will then add 2 snap cubes to both sides of the balance. The teacher will ask students to explain what is happening to the balance when both sides are
the same.
Relate this concept to math. "Hmmm…I am thinking I can relate this to math somehow. Is there anything in math that shows me that both sides are the same
thing?"
Guide students to the equal sign. "That's right! The equal sign is a symbol we use in math that tells us both sides are the same or equal!"
Ask students: "Who thinks they can come to the board and show me what the equal symbol looks like?" Have a student come to the board to draw the symbol.
Praise and encourage.
"So, you all told me that the equal symbol in math means that both sides are the same right?" Who thinks they can come to the board and show me an example of
that… where both sides are the same?" Allow students to show you in a variety of ways by prompting, "Does anyone else have a different way?"
Depending on student examples, you may need to show your thinking as well. For example: "I think I may have an example too!" If no pictures have been drawn,
draw a simple picture where the picture is on both sides of the equal sign. Ask, "Is this equation true, why?" Draw another example but draw more than one picture
on each side of the equal sign. "What about this equation, is it true?" Ask students if there is any other way to write that equation. Guide students to notice the
numeral associated with the value of the pictures (If there is a picture of three circles = three circles, have students take notice that 3 = 3).
"I can see we are getting really good at this. Let's try something a little harder this time." Example: three circles + four circles = _______. "Who thinks they can
show me how to make this equation true?" The student should draw seven circles on the other side of the equal symbol to make the equation true. "So let's see
what we have. Seven circles on one side, and seven circles on another side. Is this equation correct?" Give another example but now transition to only numerals.
"Alright, so we had some picture examples, what if we only used numbers in our equation." 3 + 4 = _____ + 5. "Who thinks they can show me how to make this
equation true?"
Misconception – Students may think that the number 7 will be the unknown number. However, guide students to see that 3 + 4 on one side is 7, which means that
we need to find out how to get 7 on the other side and 7 + 5 does not make 7. Move into guided practice of the skill.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Give several more examples until it is clear most of the class has an understanding and the misconception (if any) has been solved.
Example problems:
5 + 9 = 7 + _____
_____ – 6 = 3 + 2
12 – 7 = _____ + 2
20 – 10 = 9 + _____
9 + 8 = 20 – _____
Dismiss students to their seats.
Explain to students that they will now play a game. They will be playing the game Telephone.
Kagan Strategy Telephone (modified): Students will all sit at their desks. The teacher will ask or show a question. Teacher will choose one student to start the game.
The student chosen will solve the problem in their head and then stand up. The teacher will then say, "Ok, now go tell your answer to _____." The student who is told
the answer has two options; they either agree with the other student or disagree. If they agree, that student will now stand while the other sits, and be prompted to
tell another student the response they agreed with. If they do not agree, both students will stand up and give and defend their answers. The teacher will clarify
misconceptions of the answers or allow students to self-correct. Continue playing the game until all students have gotten the chance to play (You may play more than
one round).
Follow the rules of the game to play. Allow students to use paper and pencil if they choose.
Examples:
9 – 8 = _____ + 0
10 + 6 = 20 – _____
1 + 3 + 5 = _____ – 1
20 – 5 – 5 = 15 – _____
8 – 6 + 1 = 2 + _____
18 – 6 = 2 + 6 + _____
1 + 10 – 1 = _____ + 5
7 + 5 = 6 + _____
_____ + 1 = 4 + 6
1 + 1 + 1 = _____ – 3
Move to independent practice.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Students will be given a worksheet to complete individually. On the assignment, students will be determining the unknown in the equation. The equation may be
with pictures or numerals. Students will not only need to determine the unknown, but they will also need to show their thinking and defend their answers.
The amount of reading students will need to perform to complete the assignment is minimal. By grade 2, students should be able to read and comprehend the
directions given.
The teacher will circulate around the room while students are working. The teacher may help explain directions and vocabulary and probe students for
page 2 of 4 explanations. If the teacher is noticing a large struggle in completing the assignment, the teacher can pull the student for one-on-one intervention and give several
more examples for the skill.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Class Discussion:
The class will come back together on the carpet (or shared space in the classroom) after the summative assessment. Teacher will ask:
"Who can share their favorite part of our lesson today?"
Take several examples.
"Who thinks they can tell me what the equal symbol tells us?"
"What are times in our lives that we see things that are equal?"
Summative Assessment
The teacher will pass out dry erase boards, markers, and erasers to each student in the class. The teacher will project 5 different equations on the board where
students will be asked to find the unknown individually. (See PowerPoint Presentation for equations) Students can use their dry-erase boards to solve the problem.
The teacher will give the students ample time to complete each question. Once each student has decided on an answer, the teacher will use the Kagan Strategy,
"Showdown", to see students' answers. (Kagan Strategy: "Showdown" – Students will be given a problem to complete on paper, dry­erase boards, etc. Students will
work individually or in groups (This strategy is usually down in groups for cooperative learning. For the purpose of accurate summative assessment, this strategy can
be used for individual students). The students will hide their solution from others until the teacher calls "Showdown." The students will then reveal their solution to the
class.) The teacher will scan the students' answers and use a checklist or notes to record the students who have still not mastered the skill. The following are
suggestions for intervention when students produce an incorrect response:
1 incorrect – Teacher may want to pull these students one­on­one or in a group to allow them to try the problem again. Students may have made a simple mistake
and could self-correct when given a second chance. If the student self-corrects, they will not need any further intervention.
2 or more incorrect – It is possible that these students lack full mastery of prerequisite skills. Teacher will need to pull them individually or in small groups to
determine the area of need. Once the teacher has determined the area of need, students will need additional guidance in that area to fill the gaps before being able to
master the new skill.
If you are unable to use PowerPoint Presentations, example equations are as follows:
16 – 2 +1 = _____ + 6 + 4
_____ + 3 + 7 = 22 – 10 + 7
29 + 26 = 45 + _____
12 – 8 = _____ + 2
_____ – 6 + 12 = 16 + 5 – 2
These are simply sample problems that can be used for assessment. Feel free to create your own within the perimeters of the standard. These may be written on the
board one at a time for students to complete the assessment.
Formative Assessment
The following are a list of suggestions to elicit students' prior knowledge on the previous skills:
1. Show students a group of pictures or objects to represent a set quantity. Ask the students to identify the value of the set.
2. Relate a game of Tug-O-War to the equal sign when the game results in a tie. Discuss the game of Tug-O-War asking what it means when the game ends in a tie.
The goal would be for students to come up with the idea that a tie meant both sides were the same. Ask the students to relate this idea to Math; what symbol in math
tells us both sides are the same?
3. When moving the lesson towards equations, start the equation examples with simple equations that students should have already been exposed to. For example: In
first grade, students should be able to find an unknown in an equation with three numbers; 8 - __ = 2. Give a variety of these examples first, to remind them of the
skill before moving on to four or more numbers.
4. When discussing equations with three numbers and an unknown, expose the students to a variety of strategies to add and subtract; such as using pictures, making
tens, etc. When you begin to expose them to four or more numbers in an equation with an unknown, model and accept a variety of strategies to add or subtract three
or more numbers.
Common Misconceptions:
Students may think that when completing an equation with an unknown (8 - 2 + 4 = 5 + __ ), that the unknown is the answer to the first three numbers. It is
essential that the students understand that the equal sign makes both sides the same.
Teacher will gather information about the students' understanding through observation of their responses and justifications of their answers. Teacher will take
anecdotal notes while students are working to interpret which students are "getting it" and which students continue to have misconceptions. Teacher will accept a a
variety of answers from the class to ensure misconceptions are corrected.
Based on this information, teacher will guide students to self-correct, allow other students to clarify, or clarify misconceptions through discussion.
Teacher will use independent work to monitor the students who grasp the concept and who still need help.***Summative assessment should not be given if: Over
25% of the class does not show mastery of the concept. Teacher will re-teach concept and allow students to continue practice. If under 25% do not show mastery,
teacher will pull those students one-on-one for re-teaching.
Feedback to Students
The teacher will circulate around the room throughout the lesson.
While circulating the room, the teacher will ask students to justify why they believe their answer is correct and have them show or explain how they got to that
answer.
Teacher will record the misconceptions on their anecdotal records while talking with the students.
The teacher can ask such things as "How do you know?" or "How did you get that answer?"
Teacher will help clarify misconceptions with probing and encouragement.
Students will work together and justify their solutions.
page 3 of 4 Students will rate themselves on their student scale throughout the lesson. (Alternative if county and school require student scales; see attachment )
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
For students who may have difficulty reading the directions, teacher may assist in reading the directions and clarifying any tough vocabulary.
Teacher may also provide visual vocabulary cards to help the student understand the more difficult vocabulary words.
Extensions:
Alternate Activity:
Rather than using a balance to introduce the activity, the teacher could have students play the game of Tug-O-War to reinforce the concept of equal, same, or
balanced (when the Tug-O-War game results in a tie).
What do I do if my students "get it"?:
To extend the students' learning, the teacher could give individual students, or groups, their own balance to try and create equal equations.
For example: Say that there are 2 students who have proven they grasped the skill. Allow them to move to a quiet place in the classroom to continue working on
this concept. Give them their own balance to work with. Also, give them a bag of 100 snap cubes, paper, and a pencil.The first student will add cubes to the balance
and verbally say their equation aloud while their partner records the equation on the paper. The second student will then solve the equation on the paper and prove
their answer by demonstrating it on the balance. Students will switch roles and continue the game.
Suggested Technology: Computer for Presenter, Interactive Whiteboard, Overhead Projector, Microsoft Office
Special Materials Needed:
In order to complete this lesson, you will need:
A class set of dry-erase boards, markers, and erasers.
Approximately 10 balances
Approximately 10 bags of 100 snap cubes in each bag
Blank paper
Pencils
Further Recommendations:
It is recommended that student desks be set up into groups of 2 or 4.
Additional Information/Instructions
By Author/Submitter
This lesson incorporates the following Mathematical Practice Standard: MAFS.K12.MP.1.1 (Make sense of problems and persevere in solving them) because students are
solving equations.
SOURCE AND ACCESS INFORMATION
Contributed by: Nicole Ely
Name of Author/Source: Nicole Ely
District/Organization of Contributor(s): Orange
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.2.OA.1.a:
Description
Determine the unknown whole number in an equation relating four or more whole numbers. For example, determine
the unknown number that makes the equation true in the equations 37 + 10 + 10 = ______ + 18, ? – 6 = 13 – 4,
and 15 – 9 = 6 + .
page 4 of 4