Parking Lot Multiplication
Students will be able to show their understanding of the commutative property of multiplication, both visually and in writing. Students will be able to make arrays to represent the commutative property of multiplication.
- Begin the lesson by asking your students to describe a parking lot, or to share what they notice/know about parking lots.
- Ask the class how cars are arranged in a parking lot. If not mentioned, talk about how parking lots have rows and columns, with space for cars to drive around and between.
- Tell students that today they will use cars in a parking lot to visualize and solve multiplication problems.
Explicit Instruction/Teacher Modeling(10 minutes)
- Explain to students that the focus of this lesson is on making comparisons of two multiplication problems that have something in common (the same numbers in different orders). For example: 3 x 4 and 4 x 3.
- Write an example of two multiplication problems on the board.
- Ask your students what they notice about these problems. Their answers may vary, which is okay—this is just to get them thinking.
- Tell students that there is a mathematical term for problems like these: commutative property of multiplication. Write this term on the board and explain that the commutative property of multiplication means that two numbers can be multiplied in any order.
- Ask students if they know what an array is. Remind them that an array refers to things that are arranged in a particular way. Draw an example of an array on the board for students to reference during the lesson.
Guided Practice/Interactive Modeling(15 minutes)
- Gather your students in a circle and model placing the cars in an array that matches the multiplication problems that you wrote on the board. For example: create an array with 3 rows and 4 columns, and an array with 4 rows and 3 columns.
- Tell students that these are arrays of cars, arranged like you might see them in a parking lot.
- Point to the two multiplication problems on the board, and ask students which car array matches which problem. Explain that, in a multiplication problem, the first number represents the number of rows, and the second number represents the number of columns.
- Ask students how many cars are in each array. Then, ask them how there can be the same amount in each array.
- Write written equations for each of the multiplication problems on the board. For example: 3 times 4 equals 12 and 4 times 3 equals 12.
- Explain that these two written equations represent the commutative property of multiplication, that the order of the cars does not change how many there are, but the array for each will look different.
Independent Working Time(20 minutes)
- Explain that students will now solve a Parking Lot Multiplication problem on their own, by cutting and arranging cars, like you all just did as a class.
- Pass out a copy of Parking Lot Multiplication Problem #1 worksheet and a copy of the Student Cars worksheet to each student. Give each student a pair of scissors and some glue.
- Instruct your class to cut out their car manipulatives. They will be using them to solve the Parking Lot Multiplication Problem #1.
- Tell students to make sure to get their arrays checked before they glue them down.
- Tell students that once they finish and get their work checked, they will work on Parking Lot Multiplication Practice Problems worksheet.
- Walk around and make sure students are able to make arrays and to check students before they glue their arrays. Once you've checked your students' work, give them a copy of the Parking Lot Multiplication Practice Problems to work on.
- Enrichment: Challenge your advanced students to create their own parking lot problems. Encourage them to draw a diagram of a parking lot and decide how to arrange the spaces for cars. If time allows, they could share their work with the rest of the class.
- Support: Gather students who are struggling to grasp this concept together in a small group. Using the car manipulatives, work on a few simple problems together, vocalizing your thought process with each step. Answer questions as they arise. Talking through the steps thoroughly will help students understand why they're getting the answers they are, and why the order of the numbers in a multiplication problem does not change the product.
- Formative Assessment: During the whole class discussions, at the beginning and end of the lesson, monitor student participation and understanding. Assess your students' initial understanding by how easily they complete Parking Lot Multiplication Problem #1.
- Summative Assessment: Use Parking Lot Multiplication Practice Problems worksheet to gauge whether students were able to show their understanding of the commutative property of multiplication by solving parking lot problems without using the cars, but actually drawing arrays.
- These assessments happen during the lesson, so the time reflects this.
Review and Closing(10 minutes)
- To wrap up, call students together. Write 15 cars on the board and ask for a student to come up and draw dots to show one possible arrangement for 15 cars. Have students describe the array using an equation. For example: 3 times 5 equals 15.
- Ask another student to draw an array to represent the commutative property of multiplication related to the first array. Have students describe the array, using an equation. For example: 5 times 3 equals 15.