This activity helps students to apply two-step equations to the real world.
Divide and Ride, by Stuart Murphy; ISBN 0064467104
Background for Teachers
This is a follow-up activity designed to extend your students'
knowledge of solving two-step equations through a review and real life
situations. Students should have an understanding of equality and
solving equations before attempting this lesson.
This lesson employs the skills of Bloom's Taxonomy, which include
three overlapping domains: the cognitive, psychomotor, and affective.
Bloom's Taxonomy aids these domains through steps of educational
objectives: knowledge, understanding, application, analysis, synthesis,
and evaluation, all of which are used in the situation cards portion
of this lesson. Bloom's is recommended for all curriculum areas to
enhance the thinking abilities of your students.
Invitation to Learn
Post this question on the board: Does algebra relate to "real life?"
Instruct students to jot down their responses in their math journals.
This question will be discussed at the end of the lesson.
- Have all students stand and pass out one Algepairs Card to
each. Starting anywhere in the room, have a student read
his/her card. The student who can complete that card should
read their card, and so on. Students should sit down when
finished and try to complete the problems as the cards are
read to stay engaged in the game.
- Redistribute cards and play again, or collect cards.
- Put students into groups of three and pass out one Situation
Card and calculator (optional) to each group. Cards are on
different colors to indicate whether they are easy (red), midlevel
(green), or challenging (blue). You may use these to vary
difficulty or to help specific students. Students must still show
all of their work if they use a calculator.
- Have students work cooperatively to understand the problem,
write an equation, and find the solution. They should each
be able to explain the solution to someone in another group.
For example, if a student has Situation Card 7, she should
understand that since baby-sitting pays $7.50 an hour and she
baby-sat for 4 hours that means she made $7.50 each of those
hours. The unknown is how much she made. 7.50 x 4 = $30
on Saturday night.
- If students finish early, ask them questions to extend their
thinking, or pass out another situation card not being solved by
- When all groups are finished, regroup students in threes with
each person from a different original group. Have them take
turns sharing their situation and equation then allowing the other students in the group to solve the problem using the
equation. Allow enough time for all students to share and
- Again regroup students into threes and instruct them to create
a situation of their own. They must have a variable and their
equation must be two steps.
- Use the finished situations and equations for sharing and/or
- Discuss the Invitation to Learn using ideas from the situation
cards and earlier discussion. Have students share any new ideas
in their math journals.
Strategies for Diverse Learners
- Pass out more than one Algepairs Card to your advanced
- Vary the levels of Situation Cards for advanced and special needs
- Have students write an essay to convince their peers that algebra
relates to real life.
- Read Divide and Ride, by Stuart Murphy, and have the students
create equations for the situations described.
- Go to futureschannel.com and click on Algebra in the Real
World to download videos displaying algebra in real world
situations. Could use this as a kick-off or follow-up to the
- Decide on a travel spot for a real or imaginary family vacation.
Determine at least 5 expenses (i.e. airline tickets, rental car, food, activity prices, etc.), create equations for each, and solve.
Based on your data, how much will the trip cost?
- Create a student edition of Algepairs Cards to play at home.
- Students should create their own algebraic situation, then write
an equation and solve.
- Informal assessment during Algepairs game and math
Martinie, S. (2003, October). Families ask: cooperative groups. Mathematics Teaching in the
Middle School, 9, 106-107.
More than 900 studies endorse the use of cooperative learning,
which improves student achievement, social skills, and motivation
and enthusiasm for math. Students learn and retain information better
in cooperative groups. Students are held responsible for their own
learning and build confidence and value in their own thinking.
Panitz, T. (2000). Using cooperative learning 100% of the time in mathematics classes
establishes a student-centered, interactive learning environment. ERIC Source (ERIC
ED448063). Retrieved December 3, 2006, from http://www.eric.ed.gov
Cooperative learning activities help to identify student
misconceptions and enable the teacher to focus on specific concepts.
Verbal, visual, and kinesthetic student learning styles are addressed.
The benefits of cooperative learning are indicated, including enhanced
critical thinking skills, better student-teacher relationships, and an
enjoyment of math classes.