Multiplying fractions by whole numbers can be a challenging concept for students to understand. It is important to find engaging and interactive ways to teach this skill to students. One effective way to teach multiplication of fractions by whole numbers is to use arrays.

An array is a visual representation of the multiplication process and is particularly helpful for visual learners. Using arrays, students can see how the whole number is being multiplied by the fraction. It also helps them to understand the concept of proportionality.

Here are some activities that can be used to teach students how to multiply fractions by whole numbers using arrays:

**1. Create an array**

The first thing you can do is create an array on a chart paper or whiteboard. To create an array, draw a rectangle or square and divide it into equal parts. For example, if you’re multiplying 2/3 by 4, you can draw a rectangle and divide it into thirds vertically and halves horizontally. Then, shade in the equal parts.

**2. Fill the array**

After creating the array, you can have students fill it in with appropriate multiplication values. For example, for 2/3 x 4, students would fill in the array by counting two thirds vertically and four halves horizontally. So, they would shade in 2/3 of each vertical section and 4/2 or 2 of each horizontal section. Then, they can add up all the shaded sections to get the answer, which would be 8/3 or 2 2/3.

**3. Match the fraction**

Another activity that can be done with arrays is to match the fraction with its corresponding array. Prepare a set of fraction cards and array cards. Shuffle the cards and have students match the fraction card with its corresponding array card. This serves as a fun way for students to review fractions and arrays while reinforcing their learning of multiplication of fractions by whole numbers.

**4. Pictorial representation**

For this activity, students can work in pairs or groups to draw their own arrays and solve multiplication problems using them. Provide students with a set of multiplication problems involving fractions and whole numbers, and have them use their creativity to draw and solve using arrays. Then, have them present their arrays and solutions to the class. This activity encourages creativity and collaboration among students.

In conclusion, using arrays is a fantastic way to teach students how to multiply fractions by whole numbers. By providing students with visual aids and interactive activities, they will be able to grasp this tricky concept with ease. The activities outlined above are just a few examples of the many ways in which arrays can be used in the classroom, so don’t be afraid to get creative and experiment with different approaches.