Lesson Title: The Distributive Property
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.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions
with rational coefficients.
MP2:
MP3:
MP4:
MP5:
MP8:
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Look for and express regularity in repeated reasoning.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Examine each of the following area models. Write at
least two expressions to represent these products.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.
What happens when one of your factors has a
negative? What effect does the negative sign have on
the result?
Ask students to look back at the problems they solved
today and determine if any pattern or relationship can
be found. (The number on the outside of the
parenthesis multiplying by each term) If there is
time, this relationship can be discussed during the
closure or it could be discussed the following day.
(Look for evidence of MP8.)
(Use this as a pre-assessment to see if students are able
to use the commutative and associative properties as a
launch for the distributive property). (Look for
evidence of MP2 and MP3.)
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. Introduce algebra tiles to your students. Keep in mind that this will be a review for many of them, but
could be new to some. Consider doing this in the following ways:
 Provide physical algebra tiles to each student.
 Bring in computers and have the students use virtual algebra tiles.
 Prepare printable algebra tiles for your students.
2. Review what each tile represents.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: The Distributive Property
Date: _____________ Teacher(s): ____________________
Course: Common Core Mathematics 7
Start/end times: _________________________
(Michigan Virtual University, 2009)
3. Revisit the warm-up models. Show the expression 3(2+3). Have students identify which of the models
can be represented with this expression. Have students explain that 3(2 + 3) is equivalent to 3 groups
of 2 plus 3 groups of 3. Have students generate another equivalent expressions for this model (or one
of the other models).
4. Explain that this property can be extended to expressions with variables by creating a similar area
model. As a whole class and using the algebra tile mat, if you are using physical algebra tiles, have the
students organize the following expression as seen below. (Look for evidence of MP4 and MP5.)
2(3x+1)
(Michigan Virtual University, 2009)
5. Discuss the similarities between the way that you set up this expression and the ones in your warm-up.
The students should notice that placing one factor across the top and one along the side makes the
array. Ask the students to identify the two factors in the expression above.
6. Demonstrate how filling in the array results in the simplified expression.
6x + 2
(Michigan Virtual University, 2009)
7. Have students try additional examples in small groups, such as -3(x + 4).
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: The Distributive Property
Date: _____________ Teacher(s): ____________________
Course: Common Core Mathematics 7
Start/end times: _________________________
(Michigan Virtual University, 2009)
Ask students to predict how the negative number will change the result.
(Michigan Virtual University, 2009)
8. If your students are not prepared to complete similar problems independently, use the pass the problem
expressions to continue practicing as a large group.
Pass the Problem:
Print the attached problems. Group the class into 6 groups and give each group one problem.
Give them 2 min to create the answer on their algebra mat. After 2 min the groups will pass the
problem to the next group and receive their next problem.
9. If your students are ready to work independently, use the following activities to offer them additional
practice with building expressions. These activities can be used as whole group instruction or as centers
depending on the level of independence that your students demonstrate. (Look for evidence of MP4
and MP8.)
Matching:
Create enough sets of the matching cards for each partner to have one set. With a partner have
the students shuffle the cards and place them face down in an array. The object of the game is to
create more matches than your partner. A match consists of the expression and its representation
in algebra tiles.
What’s My Expression:
Put the students in partners. Round one: Player one creates an expression using algebra tiles
while Player B factors it out. It is important that the student making the expression knows the
answer so that they can tell their opponent whether or not they are correct. Round two: the roles
are reversed. This time Player B creates the expression while Player A is to factor it out.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: The Distributive Property
Date: _____________ Teacher(s): ____________________
Course: Common Core Mathematics 7
Start/end times: _________________________
Roll With It:
This activity requires 4 dice (three regular number cubes and one number cube with three sides
negative and three sides positive). The students roll the dice. One number rolled represents the
first factor. The second number represents the coefficient within the parentheses and the third
represents the constant of the second factor. If the 4th die rolled is a negative sign, the student
much choose if they will make the first factor negative, the coefficient negative, or the constant
negative. The student will then simplify the expression they created.
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 success? 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 will be able to explain how to find the product of expressions. The teacher will measure
understanding by circulating as students work through classroom activities and through class discussion.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Key Vocabulary: factor, coefficient, constant, algebra tiles, distributive property
Connections: Students will need to connect to their prior understanding of writing and solving equations
from 6.EE.3
Misconceptions: The students may have some difficulty working with and understanding the algebra tiles.
It will be important to reinforce the vocabulary throughout the lesson (especially coefficient, constant, and
factor).
Bibliography:
Michigan Virtual University. (2009). Virtual algebra tiles: Multiplication. Retrieved from
http://media.mivu.org/mvu_pd/a4a/homework/applets_multiplication.html
Teacher Vision. (2012). Algebra tiles. Retrieved from
http://www.teachervision.fen.com/algebra/printable/6192.html
Math.com. (2005). Algebra worksheet generator. Retrieved from
http://www.math.com/students/worksheet/algebra_sp.htm
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?
Copies of the Algebra Tile Mat
Computers
Virtual algebra tiles (Michigan Virtual University,
2009)
Printable algebra tiles (Teacher Vision, 2012)
Pass the Problem sheet
Algebra tiles manipulatives
4 number cubes (3 marked with numbers 1-6 and 1
The teacher will determine the appropriate homework
based on current student understanding.
Consider:
* Additional practice problems for students to solve
using cutout algebra tiles or virtual ones.
* If this is not discussed during the closure, ask
students to reflect on any patterns they saw during
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: The Distributive Property
Date: _____________ Teacher(s): ____________________
with 3 sides marked with a negative sign and 3
sides marked with a positive sign)
Course: Common Core Mathematics 7
Start/end times: _________________________
class today. Provide students with additional practice
problems to allow them to model the relationship that
exists between the number on the outside of the
parenthesis and the terms on the inside. (MP3)
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
Were my students able to create the expression accurately?
Once they had the expression, were they able to work through possible ways to simplify it?
Did I offer enough scaffolding while giving them enough room to develop their own understanding
independently?
Did I give my students the opportunity to persevere?
Did my students’ homework assignment show understanding of the Distributive Property?
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.