Finding Solutions to Equations

8 teachers like this lesson
Print Lesson


SWBAT: • Define solution and substitution. • Use substitution to check whether a number is a solution. • Solve one-step equations.

Big Idea

Are the solutions to 30 – n = 15 and n – 30 = 15 the same? Why or why not? Students apply their knowledge to finding solutions to one-step equations.

Do Now

7 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students realize that although the variables, values, and operations are the same the solution to each of these equations is different.  I want students to see that in the first equation 30 – 15 = 15, so 15 must equal n here.  In the second equation if you substitute 15 for n, your answer does not equal 15.  Rather 45 – 30 = 15, so n must equal 45. 

Some students may use guess and check or substitution to find the values for n.   Other students may work backwards to find the value for n.  I call on students to share out their thinking and the way they arrived at their answers.  I do not explicitly teach students to use inverse operations to solve equations.  When I have done this in the past it has resulted in students memorizing (and often confusing) a procedure and losing sight of what they are actually doing.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others and MP7: Look for and make use of structure.


13 minutes

We review the vocabulary words together.  Students work independently on problems 1-4.  If they get stuck I encourage them to substitute one of the numbers in the answer box into an equation to see if it works.  I walk around and monitor student progress.  A common mistake is that students think that 2 to the 4 power is equal to 8.   Another common mistake is that students think that t = 12 in problem 1.  They think that 18 = t – 6 is the same as 18 – 6 = t.

When most students have completed their work on these 4 problems we come back together.  I present the common mistakes mentioned above as solutions to problem 1 and 2.  Students participate in a Think Pair Share to discuss whether or not they agree with me and why.  I call on students to share out their thoughts.  I push students to use substitution to prove that my answers are indeed incorrect.  Students are engaging in MP2: Reason abstractly and quantitatively and MP3: Construct viable arguments and critique the reasoning of others.


20 minutes


  • Before this lesson I print out 6.10 Engage NY Matching Cards for each student and cut them out.  I label each set with a number and place that number on the back of each card in the set.  Each set goes in its own envelope labeled with the set number.  That way if one piece is left out, it can be easily identified.
  • I Post A Key in the room showing the correct solution to each equation.

I tell students that they will be working independently to match an equation with a solution.  When they find a match, they record it in the table.  I remind students that if they get stuck they can look at their notes in the packet to remind them of strategies they can use.

As students work I walk around to monitor student progress.  I observe what strategies students are using and which equations are challenging for students.  I use these observations to help inform my questions in the closure.  Students are engaging in MP2: Reason abstractly and quantitatively, MP6: Attend to precision, and MP7:  Look for and make use of structure.

If students find their matches, they raise their hand.  I quickly scan their work.  If they are on track, I send them to check their work using the key.  If they successfully complete this work, they work on the challenge questions.

Closure and Ticket to Go

10 minutes

I use my observations to pose a question to students.  For instance, if I notice that many students struggled with p + 13 ¾ = 32 ¾ I ask students to participate in a Think Pair Share about how to find a solution.  I call on students to share out their thinking.  I ask students if they found their solution using a different strategy.  I want students to be exposed to multiple strategies for finding solutions to equations.

I pass out the Ticket to Go and the HW Finding Solutions to Equations.