Guided Lessons

# Multiplying with Arrays

Making mistakes helps us learn! Your students will flex their analytical muscles to pinpoint errors in multiplication problems using arrays. Use the lesson on its own or as support to Base Ten Arrays for Multi-Digit Multiplication.
This lesson can be used as a pre-lesson for theBase Ten Arrays for Multi-Digit MultiplicationLesson plan.

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This lesson can be used as a pre-lesson for theBase Ten Arrays for Multi-Digit MultiplicationLesson plan.

Students will be able to use an array to solve multiplication problems with two two-digit factors.

##### Language

Students will be able to analyze and correct a flawed multiplication problem using arrays and visual representations.

(4 minutes)
• Draw a simple array using dots or circles (e.g., 3 rows of 4 circles) on a piece of chart paper. Note: do not write any numbers or symbols near the array.
• Ask students to describe to a partner what they see. Invite a few students to share their observations. Record students' responses below the drawing of the array. Students may say they see an array or some circles in rows and columns. Affirm their responses.
• Explain that the circles drawn in neat rows and columns are called an Array. Write the word, along with its definition (an arrangement of objects, pictures, or numbers in columns and rows) on the chart paper. Tell students that in this case, this array was drawn to represent a multiplication problem 3 x 4By showing that when there are 3 rows of 4 circles, there is a total of 12 circles.
• Inform students that today they will play the role of multiplication experts and master the art of using arrays to represent and solve multiplication problems.
(7 minutes)
• Tell students that drawing an array is one way to visually represent multiplication. An array helps us to see the two Factors, or numbers that we multiply to get another number, that make up the Product, or answer to a multiplication expression. For example, in the multiplication sentence 4 x 5 = 20, the 4 and 5 are factors and 20 is the product. Write this problem on the board and label the factors and product. Then, draw an array to match it.
• Provide students with an example of a multiplication problem which uses an array. Display the following problem and read it aloud to students: "A marching band has a total of 45 members. For the upcoming parade, five members can fit on Main Street standing in a row comfortably with room for their instruments. How many rows of marching band members will there be?"
• Draw two lines which represent Main Street and five small dots in a row in between the two lines to show the first row of the marching band members. Show students how you draw five dots below the first row and continue filling in the rows until you get to the total of 45.
• Think aloud: "I know that there will be nine rows of marchers. This array shows that 4 x 9 = 45."
• Repeat this process with another problem. Show students this problem: "How many limes are there in total if I buy 4 bags of limes, each with 13 inside?"
• Model how you solve the multiplication problem by drawing an array of 4 rows and 13 columns of limes. Point out that an array can be represented using dots, circles, squares, stars, or any other objects or shapes. As long as they are in rows and columns, the array works and helps us to visually see how many total objects there are.
(10 minutes)
• Inform students that they will practise solving multiplication problems using an array.
• Write the following sentence stem and display it for students to see: "This array shows..."
• Distribute the Multiplication: Array Multiplication (Part One) worksheet to students and display a teacher copy.
• Review the sample problem with students and assign students into effective partnerships.
• Instruct them to first complete the worksheet independently by labeling the factors and product in each array. Then have them share their answers with their partner using the sentence stem above. Review the answers as a whole class when students have completed the worksheet.
(10 minutes)
• Tell students that now that they have mastered how to use arrays for multiplication, they will look at some multiplication problems that have mistakes or errors in the solution. Explain that when we correct mistakes in maths, we become better mathematicians because we have to analyze and think critically about what went wrong in the process of solving the problem. As we become aware of errors, we are more careful when we solve maths problems too.
• Show the following problem on the document camera and read it aloud:
• Problem: "My apartment building has a mini theater. There are 6 rows of 4 seats in the theater. How many people can fit in the theater?"
• Solution: draw an array with 5 rows of 4 dots and 1 row of 3 dots to equal a total of 23 seats.
• Model to students as you think aloud to consider if the answer is correct or not. Point out that the person who solved the problem simply left out one more seat in the last row, leading them to the incorrect answer of 23 when it should be 6 rows of 4 which totals 24 seats.
• Emphasize to students that they are taking on the role of detective to discover where and how the mistake happened.
• Distribute the Can You Spot the Mistake? worksheet to students and display a teacher copy. Read aloud the directions and have students work on the first problem with a partner. Review this problem as a whole class.
• Instruct students to complete the second and third problem independently. Provide students with sentence stems to help them explain: "In this problem, the mistake happened when.... To correct the mistake, I..."
• Invite a few students to share their explanations and corrections with the class once complete.

Beginning

• Pair beginning students with intermediate or advanced students, or those that speak the same home language (L1) for any independent work.
• Allow students to use home language resources such as bilingual glossaries or online dictionaries to look up the meaning of unknown terms.

• Have students elaborate further on the corrections they made to the flawed mathematical responses.
• Ask students to rephrase directions and explain in their own words the key concepts of this lesson to their peers.
• Give students more complex errors in the multiplication problems to correct.
(5 minutes)
• Hand out a whiteboard and marker to each student.
• Read aloud and display this problem and solution:
• Problem: "Megan wants to plant 9 rows of lettuce. She can fit 8 lettuce plants in each row. How many heads of lettuce will she have in all?"
• Solution: "Jack decided to add 9 and 8 to get the answer of 17. He claims that Megan will have 17 lettuce heads in all."
• Ask students to write on their whiteboard the mistake that Jack made, along with the correct way to solve the problem. Remind students to use an array to help them solve the problem.
(4 minutes)
• Have students share their whiteboards with each other in pairs.
• Call on a few of them to read their analysis of the multiplication mistake and the proper way to solve it.
• Ask students to reflect on why they think it is helpful to look at errors when learning maths. Use this sentence stem to help students discuss the reflection question: "It is helpful for me to look at errors in maths because..."