Lesson Title: Applying Properties to Multiply/Divide Rational Number Course: Common Core 7

Date: _____________ Teacher(s): ____________________ Start/end times: ___________________

Lesson Standards/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.NS.A.2 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and
divide rational numbers.
c. Apply properties of operations as strategies to multiply and divide rational numbers.

MP1: Make sense of problems and persevere in solving them.

Lesson Launch Notes: Exactly how will you use the Lesson Closure Notes: Exactly what summary activity,
first five minutes of the lesson? questions, and discussion will close the lesson and connect
big ideas? List the questions. Provide a foreshadowing of
Since this activity consists of four stations, the class tomorrow.
can be divided into four groups by providing each
student a card with a rational number computation After each group has rotated to every station, bring
problem to solve upon arrival. Students having the students together for a brief class discussion. Some
same numerical solution would join to form a group at possible questions/prompts are: What are some of the
a designated station. different models you used to help multiply and divide with
rational numbers? What are some ways to decide if an
answer is correct? What are some of the properties you
applied at the stations? Which station’s activities did you
enjoy the most? the least?

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.

Instructional Note: This activity consists of four stations. Each station should be numbered and have enough chairs
for the students in each group. Each station should also include the needed materials and the instructions for the
activity. Place the required materials at each station as well as having 10 x 10 grids, strips of paper, 2-sided chips,
number lines, and two colors of highlighters available to assist students with their computations. Although the
students will be working together, you may want to have the students record their individual answers to keep them
engaged and for future reference. You may want to assign roles – Reader, Materials Manager, Timekeeper,
Facilitator, etc. once the groups are formed using the Lesson Launch strips.

1. Have students form groups using the Lesson Launch Activity. Tell students that today they will be exploring
multiplication and division of rational numbers by participating in four different station activities. Inform
students that they will be visiting stations in their new groups and all station materials will be available at the
station. Students will have about 15 minutes at each station. Tell students to read the station directions carefully
and to be sure to return all materials as they were found.
2. Have students work through the following stations: (Look for evidence of MP2, MP3, and MP4.)
Station 1:
Have students find a set of cards and a penny at this station. They will use these to create multiplication and
division problems, involving rational numbers, by choosing two cards and writing them in the frames provided.
Then, they will flip the penny to determine the operation sign. If the penny lands “heads up”, students write a
multiplication sign between the boxes, or a division sign if the penny lands on “tails”. Have the students work
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Applying Properties to Multiply/Divide Rational Number Course: Common Core 7
Date: _____________ Teacher(s): ____________________ Start/end times: ___________________
together to solve the problem that they created and write it in the spaces provided once everyone agrees with the
answer. (Look for evidence of MP2, MP3, and MP6.)
Station 2:
Present students with two different answers to several problems. They will need to determine the correct answer
and explain why using objects, models, or other facts to support their decision (see ” Evaluating an Argument”
resource.)
Station 3:
Have students create expressions that require multiplication or division of rational numbers to solve, make up
accompanying story situations to illustrate on a comic strip frame, then solve the problems. (Look for evidence
of MP2 and MP4.)
Station 4:
Have students work in pairs, with members of their group, to play the game “War”. Have them cut apart a copy
of the cards, each of which contains a problem they must solve by using the distributive property with rational
numbers. Each student plays with ten cards. Have them flip one card over, then compute the answer to the
problem shown. The student whose answer has the higher value will take both cards. Have them repeat this
process until they have completed the problems on all cards. The player who has more cards at the end is the
winner. (Look for evidence of MP2, MP3, and MP6.)
3. Have students return to seats with completed activity sheets to assist them with recalling the activities. Lead a
whole class discussion, using the questions listed in the Lesson Closure Notes.

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.

The station activities provide students with opportunities to practice and apply their previous understandings of
operations with rational numbers. Student success will be measured by the accuracy of their computations, their
ability to create models to support their answers, and their ability to apply properties of operations in the context of
the station activities. Teacher observation while students are performing the station activities and during the
debriefing class discussion, along with the work shown on the activity sheets, will be used to provide evidence of
student mastery. The observations and written work required by the station activities, along with the debriefing
discussion should assist the teacher in assessing individual student understanding of this Standard as a continuum.

Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.

Vocabulary: rational numbers, properties of operations

Connections: extending understanding of multiplication with fractions to rational numbers, applying properties of
operations to multiplication and division of rational numbers

Anticipated misconceptions: students not able to generalize properties of operations from multiplication of
fractions to rational numbers (particularly the distributive property), difficulties interpreting products and quotients
of rational numbers in real-world contexts, difficulties justifying why an answer is correct using models

Resources: What materials or resources are essential Homework: Exactly what follow-up homework tasks,
for students to successfully complete the lesson tasks or problems, and/or exercises will be assigned upon the
activities? completion of the lesson?

Lesson Launch Cards – need to be cut apart/shuffled “This One Does Not Belong” Given sets of three
Station 1 – rational number cards, several pennies problems each, involving multiplication and division of
Station 2 –“ Evaluating an Argument” problems rational numbers, students will determine which
Station 3 – Comic Strip template expression in the set is not equivalent to the other two.
Station 4 – “War” Cards (scissors to cut apart) They will also create one set of three similar problems to
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Applying Properties to Multiply/Divide Rational Number Course: Common Core 7
Date: _____________ Teacher(s): ____________________ Start/end times: ___________________
Homework – “This One Doesn’t Belong” share tomorrow.

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?

Are students able to apply previous understandings to operations with rational numbers?
Are they able to create their own examples or models to support their answers to computation work?
Can students use a variety of strategies to solve the problems?
Are the students able to create expressions applying properties of operations as strategies to multiply and divide
rational numbers?

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 (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.