Lesson Title: Introducing Two-Step Equations
Date: _____________ Teacher(s): ____________________
Course: Common Core Mathematics 7
Start/end times: _________________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which Mathematical
Practices do you expect students to engage in during the lesson?
7.EE.B.4a Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations
and inequalities to solve problems by reasoning about the quantities.
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational
numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying
the sequence of the operations used in each approach.
MP3:
MP4:
MP5:
MP7:
MP8:
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Lesson Launch Notes: Exactly how will you use the first
five minutes of the lesson?
Begin by playing a game called “I’m thinking of a number”.
Start with these questions or ones similar to them:
 I’m thinking of a number that when multiplied by 3, the
result is 36.
 I’m thinking of a number that when added to 5, the
result is 28.
 I’m thinking of a number that when you multiply by 2
and then add 1, the result is 29.
 I’m thinking of a number that when you add 1 and then
multiply by 2, the result is 40.
 I’m thinking of a number that when you divide by 4 and
subtract 2, the result is 9.
Lesson Closure Notes: Exactly what summary
activity, questions, and discussion will close the
lesson and provide a foreshadowing of tomorrow?
List the questions.



How can we isolate a variable in order to
determine its value?
How do you know what operations to use when
translating an equation from a word problem?
What key words help you to determine your
equation?
How can you be sure the solution to your
equation is correct?
Having an exit ticket at the end of each day will help
to monitor student understanding before moving on
to the next part of the lesson.
It is helpful to show these clues rather than just read them
out loud. Before discussing the answer to the questions,
give students a chance to think and write down their answer.
Students should also be writing down a proof about why
their answer is correct. Have students discuss the answer to
each question (think-pair-share) before moving on to the
next. This will help those students who are struggling to
catch on. By the end, students should realize that in order to
solve the problem, they need to work backwards and use the
inverse operation to determine the number. (Look for
evidence of MP8.)
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
1. Whole Group: Number Game: After discussing the strategy to solve each riddle in the number game, show
how to translate each of the problems you used into algebraic equations. Have students tell you how they were
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Introducing Two-Step Equations
Course: Common Core Mathematics 7
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
able to solve each problem in their own words and model their process on each equation. (Look for evidence of
MP4.)
2. Individual Practice: Number Game: Give three to four more examples of riddles from the number game. Ask
students to model the problem with an equation and then determine the solution to the problem. At this point, do
not be concerned if they are showing their work properly (subtracting or adding from both sides of the equation)
3. Whole Group: Human Balance Scale: Review the definition of equation with students. Remind them both
sides are to remain equal to each other at all times. Relate it to a balance scale they may have seen in science
class. For this activity, ask for eight volunteers. Draw an equals sign on the chalkboard and place four people
on one side and four people on the other. Ask students if the equation is balanced. Are there an equal number of
people on each side of the equals sign? Next, ask for two ‘special’ volunteers to act as variables. Hand each of
these volunteers a sheet of paper that says x. Rearrange your human equation so that it models the equation 2x +
4 = 8. Use the ‘Number Game’ riddle to describe this equation. I’m thinking of a number that when you multiply
it by 2 and add 4, you get 8. Ask students to translate this equation algebraically. Then, ask them what they
would do to solve this problem. When they tell you to subtract four, send four people back from both sides of
the equation. Model this on the board by subtracting four from both sides. Then write the equation 2x = 4.
Then when students say to divide by 2, ask if you divide both sides by 2, what will be left on each side of the
equation? Consider having each of the variables pair up with two of the people from the other side of the
equation to show that each x is equal to 2 people. (Look for evidence of MP4.)
4. Small Group: Modeling Equations with Manipulatives: Use this link:
http://learner.org/workshops/algebra/workshop1/index2.html for a description of solving equations with
manipulatives. Go to the bottom of the page and click ‘Lesson Plans.’ This will take you to two activities you
could use in your classroom. (Look for evidence of MP4 and MP5.)
5. Small Group: Word Problems: Numerous word problems have been provided with this lesson (See 7.EE.4a
Word Problems). In each case, students are asked to translate an equation from the word problem and then
solve. These types of activities are best done in small groups so students can work together and talk each other
through difficult problems. (Look for evidence of MP3.)
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student mastery? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened (and conceptual) understanding.
Students should be able to recognize, translate, and solve the equation that a word problem is describing. Students
with a deeper understanding should be able to write their two-step equation word problems.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Vocabulary: Equation, Inverse operation, variable
Connections: This lesson builds on what students learned in 6.EE.7 (one step equations) and will introduce solving
two-step equations in a non-procedural way.
Common Mistakes: Students will sometimes start by trying to divide or multiply to solve instead of adding or
subtracting first.
Resources: What materials or resources are essential for
students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
This website provides an explanation of using manipulatives
to solve equations as well as a real world problem involving
2 step equations with and without the distributive property:
http://learner.org/workshops/algebra/workshop1/index2.html
An assignment that consists of some problems where
the Number Game riddles are involved would be a
good assignment after day 1 of instruction. Consider
having the students translate the equation
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Introducing Two-Step Equations
Date: _____________ Teacher(s): ____________________
Here is a game students could practice with at home:
http://www.math-play.com/Two-Step-Equations-Game.html
Course: Common Core Mathematics 7
Start/end times: _________________________
algebraically and then solving to find the missing
number.
A matching activity where students need to match the
equation with the word problem or riddle would help
those students who are struggling with translating
equations. (Look for evidence of MP7.)
Students could be asked to develop their own twostep equations and solve them or create their own
word problems that would be solved with a two-step
equation.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Are students able to recognize which operation they should use first to solve an equation?
Can students translate a word problem into an equation?
Do students understand how to check their solution to be sure it is correct?
Do students understand how to apply algebraic equations when solving word problems?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.