Summary: Students will use algebra tiles to help them evaluate algebraic expressions.
Main Curriculum Tie: Mathematics Grade 6 Strand: EXPRESSIONS AND EQUATIONS (6.EE) Standard 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. Materials:
 Algebra tiles
 Foam craft mat for each student
 Colored pencils
Additional Resources
The Algebra Lab: Middle School (Creative Publications)
Prentice Hall Middle Grades Math Tools for Success, Course 1, 2001.
Web Sites
Background For Teachers: Evaluating expressions is a concept used throughout all of algebra. The student
is required to replace a variable (unknown) with a given value and then evaluate
(calculate) the answer. There are many realworld situations in which this is
used, (e.g., If I order 3 CD’s at $17 apiece and add shipping and handling
charges, what will my final cost be?) We also come upon formulas that require
a value to take the place of an unknown variable. Students must follow the order
of operations in order to correctly evaluate algebraic expressions.
Using algebra tiles to introduce the evaluation of expressions helps students
to have a visual image of what is happening. They are actually replacing the
variable with a tile that represents a number. This should make the transition
to paper and pencil evaluations easier to understand.
Intended Learning Outcomes: 5. Make mathematical connections.
6. Represent mathematical situations. Instructional Procedures: Invitation to Learn
Discuss with students the fact that some jobs pay the worker a certain amount
per hour. For instance, babysitting may pay $2 or $3 per hour. Other jobs pay
per piece. Lawn mowing may pay $10 or $15 per lawn. In both situations, there
is always an unknown involved. In babysitting, one must know the number of hours
worked and in lawn mowing, one must know the number of lawns mowed. As soon
as we know that, we can calculate how much money we have earned.
Instructional Procedures
 Using the algebra tiles, demonstrate a variable expression and have students
model it with their tiles, (e.g., 3h to show $3 per hour of babysitting).
Have a student choose the number of hours they babysat (2 hours) and demonstrate
how each variable (h) is replaced with 2 “ones.” They will see
that 6 ones or $6 is the amount earned. Use the algebra tiles to manipulate
the same situation with lawn mowing at $10 per lawn. These are very simple
problems and most will immediately see the connection between the problem
and the algebra tiles.
 Continue working with algebra tiles making the problems increasingly more
difficult.
2x + 1, where x = 3
5b – 1, where b = 2
4 + 2t, where t = 4
Using 2 variables:
2x + 3y, where x = 3 and y = 4
3g  h, where g = 2 and h = 5
 While using the algebra tiles for each problem, make sure students write
down the expression and solve it with pencil and paper so that the transition
becomes easier.
Curriculum Integration
Meteorology—The temperature formula above (T = (n/4) + 37) is
fun for students when they learn that crickets actually chirp more times per
minute as the temperature rises. There are also formulas to convert from °C
to °F. °F = 1.8 x °C = 32, or °C = 1.8(°F – 32). Many
countries use the Celsius scale rather than the Fahrenheit scale for measuring
temperature.
Extensions: Extensions and Adaptations
Introduce some formulas and have students evaluate the formulas. For instance:
A = l x w (Area = length times width), where l
= 8 and w = 6.
P = 2l + 2w (perimeter = 2 times length + 2 times
width), where l = 3 and w = 2.
d = rt (distance = rate times time), where r = 60
mph and t = 2 hours.
T = (n ÷ 4) + 37 (Temperature (°F) =
number of times a cricket chirps in one minute divided by 4 plus 37), where
n = 100.
a = h ÷ n (batting average = number of hits
÷ number of times at bat), where h = 11 and n = 40.
Homework & Family Connections
Give the students the formula s = 3f – 24 (shoe size = 3 times foot length
in inches minus 24), which is used to calculate men’s shoe size. Assign
them to calculate the shoe size of 3 men in their family or among their friends
by measuring the length of the man’s foot in inches and calculating the
formula.
Assessment Plan: Have students evaluate the expression 2a + 3b for a = 2 and b = 5, showing
each step. Have them exchange their work with a partner. Next to each step,
the partner writes what operation was performed.
Author: Utah LessonPlans
Created Date : Sep 16 2003 10:46 AM
