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Exploration with True and False Equations CCSS.MATH.CONTENT.1.OA.D.7
Given numerical expressions of like and unlike values, students will use virtual tools and concrete manipulatives to explore equations and further their understanding of equality & the meaning of the equal sign.
What concepts or procedures are being explained or demonstrated in this lesson object?
Materials/Resources:

Interactive whiteboard displays: Essential Question, ‘I Can’ statements & True or False? Partner Equations worksheet

1 printed Partner Equations worksheet per team

True or False? Group Work (at Wizer.Me) on an interactive whiteboard

True or False? Exit Ticket (at Wizer.Me), assigned to students through Google Classroom or printed if paperpencil is required

Illuminations Pan Balance  Numbers on both the interactive whiteboard and team devices

Counters or cubes, enough for each team to have at least 20

1 iPad or Chromebook per team (ratio of 1 device for every 2 students)
Prerequisite Skills

Students can solve addition and subtraction expressions through 20 using concrete manipulatives, virtual tools/manipulatives and representational symbols (e.g., tallies, circles) on paper.

Students can compare one and two digit numbers, determining greater than, less than or equal to.

Students can define ‘true’ and ‘false’ in general but accurate terms.

This is not an introductory lesson for standard CCSS.MATH.CONTENT.1.OA.D.7. Students should have some experience with solving numerical expressions and comparing whether or not their values are the same. They should have some background knowledge of what the equal sign means, although they may display an incomplete understanding or some misconceptions. This lesson can be used to correct misconceptions, augment curricular units of equality or provide extra practice in mastering this standard.
Helpful (but not necessary) prior knowledge:

Previous experience working with virtual balances/scales, such as Illuminations Pan Balance  Numbers, and exploring balanced and unbalanced values (e.g., 9 vs. 3 and 9 vs. 9) with virtual manipulatives.

Previous experience with interactive worksheets on Wizer.Me.
Introduction/WarmUp:
Activate prior knowledge and engage (23 minutes)

Ask students to explain the difference between true and false. True statements are real facts that can be proven correct. False statements are pretend or not real and can be proven wrong. Restate student explanations using these terms embedded within the language they provided. Immediately correct misconceptions using these terms.

Present true or false statements about students in the class and/or items in the room. Ask students to give a thumbs up if the statement is true or a thumbs down if the statement is false. Examples of statements include:

Sam has red hair. (false)

Emma is in 3rd grade. (true)

We use pencils to write. (true)

We use our chairs to slide down the hill. (false)
Review learning goals (12 minutes)

Tell students that we will be practicing how to determine whether an equation or number sentence is true or false. Choral read the essential question from the board: “How can I decide if an equation is true or false?” Tell students that they will learn how to do this by practicing three things. Choral read the “I Can” statements from the board:

I can explain what the equal sign means.

I can solve number problems and compare the values on each side of the equal sign.

I can decide if equations are balanced (true) or not balanced (false).
Procedure/Activities:
Connect prior knowledge of true/false with the equal sign (810 minutes)

Tell students that we will review the statement, “I can explain what the equal sign means,” and that this is something they already know. Ask students to recall and explain what the equal sign means. Terms to reinforce are:

the same as

the same on both sides

the same values

balanced

tied
Restate student explanations using these terms embedded within the language students provide. Immediately correct misconceptions. Have students repeat information, emphasizing ‘the same as’ and ‘balanced.’

Display True or False? Group Work (at Wizer.Me) on an interactive whiteboard, scrolling to Part 1 Warm Up. Tell students that we will be comparing one number to one other number using the equal sign. We need to decide if these equations are true or false.

Choral read each equation in Part 1 using the phrase “is the same as” for the equal sign, then sort the equations into appropriate columns. For example, say, “32 equals 23 means 32 is the same as 23. Is this equation true or false?” If students struggle with this task, relate the numbers to something relevant such as M&M’s or dollars.

Frequently emphasize that the equal sign means “is the same as” and shows that both sides are ‘balanced.’
Explore equations with a partner (2025 minutes)

Tell students that they now will be working with a partner to solve equations and determine if they are true or false using counters or cubes and a virtual pan balance.

If they have not used this virtual tool before, display the Illuminations Pan Balance  Numbers on the interactive whiteboard. A link is provided directly from the True or False? Group Work display page after Part 1.. Demonstrate how you must click in the boxes to type the numerical expression for each side. Discuss the term ‘balanced’ as it relates to both sides having equal values. Show students the location of the sum or difference as well as the table where only balanced equations will appear. Point out the ‘reset balance’ and ‘reset table’ buttons if they need them.

Assign students to work areas with a partner, naming Partner 1 and Partner 2. Each team receives an iPad or Chromebook, counters or cubes, one pencil and one Partner Equations worksheet.

For each problem, Partner 1 will read the whole equation with the worksheet between the two students. Partner 1 then builds the value of each side with counters or cubes while Partner 2 builds the value of each side using the virtual pan balance. Partners compare the values they have calculated and decide together which values to record as well as whether the equation is ‘true’ or ‘false.’ Partner 1 records values for both sides and circles their ‘true’ or ‘false’ answer. If a discrepancy is found or if they cannot agree, they both are to rework their problem until their values match each other. Partners switch jobs after problem #6 so that each has a turn with both the concrete manipulatives and the pan balance.

If there is an odd number of students, create one group of 3. The third partner in that group will solve the equations by drawing symbols, such as tallies or circles, to represent the value of each side. This group will rotate every 4 problems so that each student has a turn at each job..

Circulate to monitor student engagement, team behavior and item responses. Provide ongoing, specific, positive feedback. Address misconceptions or errors immediately, asking guiding questions so that student teams discover and correct their own mistakes. See Notes/Reflection section for common misconceptions and anticipated student responses.

If any teams finish early, have them do this extension activity: Fix up & rewrite any of the ‘false’ equations so that they are true. They may use concrete or virtual manipulatives as well as representational drawings (e.g., circles, tallies) to prove their work.
Lesson Conclusion/Summary:
Summarize findings & review ‘I Can’ statements (810 minutes)

After 2025 minutes, have all teams return to the interactive whiteboard with their worksheets. Scroll to Part 2 of True or False? Group Work (at Wizer.Me). Part 2 includes a few of the equations found on the Partner Equations worksheet. Call on one team per equation to discuss their supporting evidence (i.e., values on both sides), then sort the equations into appropriate columns. Correct errors immediately if needed.

For at least one true and at least one false equation, have students use descriptive language in thinking aloud to problemsolve. Examples include:

“132=11 and 9+2=11. The value 11 on one side is the same as the value 11 on the other side, so this equation is balanced. This equation is true.’

‘5+5=10 but 102=8. The value 10 on one side is not the same as the value 8 on the other side, so this equation is not balanced. This equation is false.’ .

Emphasize the language in the last two ‘I Can’ statements as they relate to some of the equations. In other words, explicitly discuss how students solved number problems, compared values on both sides of the equal sign, decided it was ‘true’ if the values were the same (balanced) or decided it was ‘false’ if the values were not the same (unbalanced).
Exit Ticket & Extension Activity (810 minutes)

Students who were Partner 1 will generate true equations (not false) on the backside of the worksheet while students who were Partner 2 complete the True or False? Exit Ticket (assigned from Wizer.Me via Google Classroom or printed). This short quiz provides equations similar to the partner exploration activity but with different numbers. Students may not use concrete manipulatives or the virtual pan balance, but they may have blank paper on which to draw or work problems if needed.

Switch jobs when appropriate so that all students complete the Wizer.Me exit ticket and also have a chance to generate their own true equations.
Assessment: Formative / Summative
Formative Assessments

Circulate & evaluate student work during the partner activity, immediately correcting misconceptions and using guiding questions to allow students to detect and fix errors on their own. The goal is 100% response accuracy.

True or False? Exit Ticket & Student Examples of True Equations: Evaluate student responses, noting patterns in order to address common errors in subsequent lessons or with individuals./small groups.

Use all formative assessments to determine next steps:

Which students are ready to retest on CCSS.MATH.CONTENT.1.OA.D.7?

Which students need additional practice on the skills taught in this lesson?

Which students mastered skills in this lesson but demonstrate a need for further practice in different ways on CCSS.MATH.CONTENT.1.OA.D.7?
Summative Assessment

Retest students with curriculumbased math assessments from their assigned math program, similar to those used previously in which CCSS.MATH.CONTENT.1.OA.D.7 was identified as unmastered.
FollowUp Lesson(s):

If exit tickets or other assessments indicate that more practice is needed, this lesson can be repeated with different equations from a variety of sources (e.g., math workbooks, worksheets).

Ideas for future lessons to extend understanding of equality:

Focus on fixing up false equations to be true and comparing responses to show that this can be done in different ways. For example, 3+3=6+1 is false. It can be fixed up in many ways: 3+3=6+0, 3+4=6+1, etc.

Use concrete and/or virtual manipulatives to determine missing numbers in true equations (e.g., 4+5=__  1).

For the end of an equality unit or for students who demonstrate an understanding of this standard but need extended practice, these two EDpuzzle activities can be additional resources:
What was your experience, both successes and challenges, using this lesson object with your students?
Notes/Reflection:

Common misconceptions about equality include:

Thinking that the equal sign is an operator meaning ‘do the problem’ or ‘find the answer’ instead of understanding that the equal sign indicates a relationship between the two sides

Ignoring the equal sign altogether and just adding all of the numbers

Only solving one side of the equation

By design, this lesson was meant to provide additional practice with manipulatives and tools to close the math gap for older students who have not yet mastered CCSS.MATH.CONTENT.1.OA.D.7. As a result, students will catch on and demonstrate mastery at different rates. It is important to be flexible with the type of strategy students employ as long as they can discuss their work and supply evidence for their answers. For example, some students may not need concrete manipulatives beyond the first few problems and thereafter may choose to create representational drawings or recall known math facts to calculate values. Other students may need to record values under the numerical problems as they calculate so that they do not have to rely on their memory as they work each side.