The activities in this lesson will help students understand the concept of equal values. In addition, students will understand that an equation is a number sentence that shows relationships.
- Thinking MathematicallyIntegrating Arithmetic and Algebra in
Elementary School, by Thomas P. Carpenter, Megan Loef Franke,
and Linda Levi; ISBN 0-325-00565-6
- In the BalanceAlgebra Logic Puzzles Grades 4-6, by Lou Kroner
(McGraw-Hill); ISBN 0-7622-0551-2
- Equate The Equation Thinking Game,
http://www.lakeshorelearning.com; Item ZE511
- Math Equation Match-Ups,
http://www.lakeshorelearning.com; Item GG269
You can quite easily make your own worksheets for your students to
practice this skill.
Background for Teachers
Many students and adults are programmed to look for the answer at
the end of the problem when doing math. They have difficulty
understanding that math problems can be written in different forms. One
of the most difficult forms for students, and often their parents, to
understand is the equation. Students must be taught the concept of equal
values. They must also understand that an equation is a number sentence
that shows relationships, not just an operation. To become competent
with equations requires a lot of practice and review throughout the year.
Intended Learning Outcomes
2. Become mathematical problem solvers.
3. Reason mathematically.
Invitation to Learn
Pass out small candies to the students. Give different amounts to
each student, some one, some two, some five, some none. Ask students
if they were treated fairly. Why or why not? They should come up with
the idea that they did not get the same (equal) amount. Explain that you
will be working on math problems that require them to understand the
concept of equal value and making sure that all parts are worth the same
amounts. Pass out more candies so that each student gets five pieces.
Tell them that they will be allowed to eat them when they have shown
you they understand the math concept for the day.
- Invite two students to come up to the front of the class. Give one
student five candies in one hand and four candies in the other
hand. Give the other student four candies in one hand and none
in the other. Ask the class if you treated the two students fairly.
Why or why not?
- Ask students to figure out what you would need to do to make the
second students candies equal to the first students candies. They
should figure out that the second student needs five candies in
his/her other hand.
- Write the equation on the board to represent the candies.
5 + 4 = 4 + _____
- Review what the equal sign means and point out that the number
sentences on each side of the equal sign must have equal values.
- If students are still having difficulty grasping the concept of "equal value," try using a simple balance scale to visually show "equal."
Example: Put six cubes on one side and two on the other. Ask
how many cubes you need to add to make the scale balance.
Explain that when the scale balances, the weights (values) are
- Do a number of equations on the board or overhead to help the
students grasp the concept of different types of equations. Use
the operations they are familiar with. At the beginning of the year
use addition and subtraction, then as the year progresses you can
add multiplication, division, fractions, and decimals.
- Assign students to complete the Equations Review worksheet independently. Some students will struggle to understand
these. Let them work with a partner or form skill groups to work
- When students have had several experiences working with
equations you can assign equations as warm-ups/seat work. Give
students a challenge such as: How many equations can you
make where one side is ten? Give them a few minutes to work.
Allow time for them to share their favorite equationthe
discussion among the children about whether the equations are
true helps them develop their understanding of equations and
other math concepts.
- Write problems that need to be solved using an equation by using
facts from your science or social studies curriculum.
Send an Equations Review worksheet home and assign your
students to teach this concept to their parents. Ask their parents to
reply with a comment on how hard they thought it was to
understand this concept.
- Use ongoing assessments throughout the year by correcting the
students’ assignments and evaluating the types of mistakes they
are making. Reteach the difficult types of equations and continue
working on them on a regular basis.
- Teacher observation and interaction with students while they are
writing their lists of equations will provide the teacher with
information about how the students’ skills are developing and
provide opportunity for reteaching/correcting.