Do your students need help understanding division? Arrays and equal groups are two visual models that can be used to help students understand division.
An array is a visual representation of a multiplication problem but it can also be used to show a division problem. Just look at the example below.
Jackson has 12 football cards. His album only has 3 pages left and he wants to place the same number of cards on each page. How many cards should he put on each page?
To solve the problem using arrays, draw 3 rows using counters. Continue drawing one in each row until you count up to 12. To find the quotient, count the number of counters in each row making sure that each row has the same number of counters.
So, to answer the problem, Jackson should put 4 cards on each page of his album.
Using arrays in solving division problems helps students see the relationship between multiplication and division.
Another concept that can be used to help students understand division is equal groups. Equal groups show that when you divide, they should have equal parts and each part should have the same size or same number. Just look at the example below.
Ms. Jones has 15 apples and 3 containers. She wants to place the same number of apples in each container. How many apples should she put in each container?
To solve the problem using equal groups, draw circles to show the number of groups, in this case, the containers.
In each circle, draw one counter each until you draw 15. To find the quotient, count the number of counters in each group and make sure that you have the same number in each group.
So, to answer the problem, Ms. Jones should put 5 oranges in each container.
By using equal groups, students will be able to understand that division is the process of breaking a larger number into smaller, equal parts.
Together, arrays and equal groups are great visual models to help students understand the meaning of division and how it relates to multiplication. These two models help visualize the problem and break it down into smaller parts. In turn, students can develop a deeper understanding of how division works.
Activities to Practice Division Using Equal Groups and Arrays
Here are some ways students can practice division using arrays and equal groups.
- Write a journal: Give students a problem to solve using arrays and equal groups. You can even let them write their own problems too!
- Use word problems: Give students division word problems and let them use manipulatives such as blocks to solve the problem.
- Observation: Let students look for arrays or equal groups that they see inside or outside the classroom, or even at home. Let them draw it and write a division equation for it.
- Use virtual manipulatives: If you need online manipulatives to make them more accessible to students, you can use this one.
- Use worksheets and online resources: Worksheets and online resources provide practice problems and interactive activities to help your students practice the skill. Here are some that you can use. (Note: These links will send you to my TPT store.)
By providing your students with constant practice, they will be able to have a deeper understanding of division and have a strong foundational skills.