Best Practice
Topic: Algebraic Expressions
Strategies
Activating: Word Splash
Organizing: Think Aloud
Comprehending: Problem Chart
Summarizing: Cartooning
Activating with Word Splash
Saphier, J. & Haley, M.A. (1993). Activators:
Massachusetts: Research for Better Teaching.
Activity structures to engage students’ thinking before instruction.
Purpose: This strategy is used to help students make predictive statements about how each of the
terms, phrases or ideas is related to one key concept, in this case, Algebraic Expressions.
Description: Prior to lesson, a word splash is a quick way to display a collection of key terms, phrases or
ideas that are related to the concept of adding, subtracting, multiplying and dividing algebraic
expressions that the teacher wants to cover during the lesson. The students’ task is to make predictive
statements about how each of the terms may relate to Algebraic Expressions.
Procedure:
1.
Place main idea, Algebraic Expressions on center of sheet. Surround this with words associated
with solving and simplifying Algebraic Expressions. Ask the question, “How can you help me
understand more how to solve and simplify Algebraic Expressions?”
a. Variables, solution, inverse operations, addition, subtraction, multiplication, division
(Properties of Equality), isolate variables, etc.
2. Students can add to the list.
3. Students will make predictive statements about how each of the terms relates to Algebraic
Expressions
Isolating variable
solution
addition
subtraction
Algebraic Expressions
Isolate variables
Inverse operations
division
multiplication
simplify
Organizing with Think Aloud
William, J. (2001). Improving comprehension with think-aloud strategies. New York: Scholastic Books.
Purpose: This strategy is used by teachers to model the thinking process required to complete specific
tasks- Algebraic Expressions, along with word problems.
Description: Think Alouds provide opportunities for teachers to model thinking processed by verbalizing
thoughts while solving and simplifying Algebraic Expressions.
Procedure:
1. Select an Algebraic Expression
2. Read prior to introducing to students in order to determine what your thinking process is for tackling
the problem.
3. As students follow along, read the expression aloud. Stop periodically to verbalize your thoughts,
questions, and strategic thinking to solve the problem.
4. Repeat with other Algebraic Expressions and word problems.
Variations on Think Aloud Constructions:
*Teacher to students
*Teacher leads think aloud with whole class assistance
*Student to teacher
*Students to students
Problems that could be used
*g – 4 = 13- I have to isolate the variable. I do this by using the inverse operation of subtraction,
which is addition. I add 4 to each side. 13 + 4 = 17. So, g = 17. Is this correct? How do I find
out? Since g = 17, I will then put 17 back in the problem. 17 – 4 should equal 13. It does, so I
am correct.
*20 = 7 + p- I have to isolate the variable. I do this by using the inverse operation of addition,
which is subtraction. I subtract 7 from each side. 20 – 7 = 13. So, p = 13. Is this correct? How
do I find out? Since p = 13, I will then put 13 back in the problem. 7 + 13 should equal 20. It
does, so I am correct.
* k/8 = 7- I have to isolate the variable. I do this by using the inverse operation of division,
which is multiplication. I multiply 8 to each side. 7 x 8 = 56. So, k = 56. Is this correct? How do
I find out? Since k = 56, I will then put 56 back in the problem. 56/8 should equal 7. It does, so I
am correct.
*5x = 35- I have to isolate the variable. I do this by using the inverse operation of multiplication,
which is division. I divide 5 on each side. 35 ÷ 5 = 7. So, x = 7. Is this correct? How do I find
out? Since x = 7, I will then put 7 back in the problem. 5 x 7 should equal 35. It does, so I am
correct.
* On Friday nights, a local bowling alley charges $5 per person to bowl all night. If Carol and her
friends paid a total of $45 to bowl, how many people were in their group? (5p = 45, p = 9, nine
people were in the group)
What information do I know? Alley charges $5 per person, Carol and friends paid a total of
$45, question is asking how many in group?
Comprehending with Problem Chart
Barton, M.L., & Heidema, C. (2002). Teaching reading in mathematics. 2nd Edition. Alexandria,
VA: ASCD
Purpose: These strategies are used to demonstrate the importance of showing how a problem
is solved.
Description: These strategies involve having students explain step by step how to complete a
particular activity, task, or solve a problem, and verbalize the reason or reasons for doing each
step. These strategies re-focus student concern from “Did I get the answer right?” to “How did I
get the answer?”
Procedure:
1. Select a sample problem and model how to use both the problem/process charts.
2. Have students create either a Problem/Process chart or the Five-Step Problem Solving graphic
organizer.
3. Have student complete the process portion of the graphic organizer.
4. Allow students time to share their processes in small or whole groups.
Problem
Process
Sample Problem
240/12= 20
12f = 240
f = 20
12 x 20 = 240
Describe exactly what you did. Be as clear as
possible.
First, I isolated the variable by performing the
inverse operation. I divided 240 by 12, which
is 20. I then put 20 back in the problem and
checked to see if it was correct.
Write directions for solving an Algebraic
Expression.
Isolate the variable. Use the inverse
operation. Solve. Check for correctness.
Problem
Sample Problem
Describe exactly what you did. Be as clear as
possible.
Write directions for solving an Algebraic
Expression.
Process
Five-Step Problem Solving
It costs $6 per ticket for groups of ten or more people to see a minor league baseball game. If
Albert’s group paid a total of $162 for game tickets, how many people were in the group?
1. Restate the problem
question:
How many people in the
group? _____________
2. Find needed data:
$6 per ticket for groups of 10. $162 total paid.
3. Plan what to do:
6 p = 162
___________________________answer___________________________
4. Find the answer:
Step 1
Step 2
Isolate the variable
Use inverse operation
P=?
p = 162/6, p = 27
Answer: 27 people in each group.
5. Check. Is your answer reasonable?
27 people each paid $6. Yes, this is
reasonable.
Step 3
Check: 6 x 27 = 1
1. Restate the problem
question:
____________________
____________________
2. Find needed data:
____________________________________________
3. Plan what to do:
__________________________________________________________
___________________________answer___________________________
4. Find the answer:
Step 1
Step 2
Answer: _________________________________
5. Check. Is your answer reasonable?
_______________________________
_______________________________
Step 3
Cartooning
Purpose: This strategy is used to summarize and review new learning while students get a
chance to be creative, humorous and engaged.
Description: Because cartooning forces the creator to be both humorous and reflective in just
one or two lines of text, this strategy is effective in helping students determine what
information to delete, substitute and keep.
Procedure:
1. After students have completed a unit or topic of study, introduce this strategy by sharing a
cartoon relevant to your topic of study.
2. Have students focus on what makes the cartoon meaningful.
3. Emphasize that the rule of cartoons follows Shakespeare’s sentiment that “brevity is the soul
of wit.”
4. Instruct students to complete a cartoon that will summarize their understanding of the topic
of study.
5. Have students create cartoons on chart paper or the cartooning frames and share their
products by displaying cartoons in the classroom.
* www.vocabularycartoons.com and
http://www.vocabularycartoons.com/teachersresources.aspx
by ________________________________________
by _____________________________________