The gateway to multiplication, the foundation to finding area…I introduce to you…ARRAYS IN MATH!
And let me just say that students LOVE arrays and you can spice up an array lesson with colorful manipulatives and repeated addition… you won’t find a more fun time than this!
Importance of Arrays in Math
Equal groups: A great place to start with equal groups is teaching students odd and even (2.OA.3). Students will understand the odd one out, showing that the groups are not equal.
Another bonus to starting with equal groups is that students practice counting by 2’s which will help them during repeated addition.
Repeated Addition: Allows students to practice finding the total in arrays quickly and efficiently and also sets them up for multiplication. Students may struggle with larger numbers or they may be ready to move toward multiplication when it comes to repeated addition. Read more about Repeated addition in this blog post.
Doubles Math Facts: Doubles math facts are repeated addition. By having a working memory of these facts students won’t be overwhelmed with the longer repeated addition sentences.
Use the carrot method Doubles practice can be done a variety of ways. I created a virtual math facts practice that includes a Google Slides deck for students to brush up on their doubles facts at home or during a math center. Click here to see it.
Ways to Teach Arrays in Math
Let them play! I mean, for sure I always give my famous speech, “Math tools not toys,” but giving them time to explore with manipulatives to build arrays without the pressure of getting the answer right or wrong.
Here are some steps to take to get array practice started in 2nd grade.
Step 1: Introduce equal groups
By giving students manipulatives to sort into groups it helps them really grasp the equal concept. Have students write the number of objects in each group. I like to have students start with groups of 2 because we have usually covered even and odd numbers by this time of the year.
Step 2: Introduce repeated addition: Check out this blog post all about repeated addition!
Step 3: Introduce columns and rows. Side to side and up and down. When students understand this key vocabulary they will be more successful in building accurate arrays.
Step 4: Creating equal rows or columns using manipulatives. Start with creating equal groups then putting them into rows or columns you give them. This is a great step for students to practice with their partners. They get a chance to use the vocabulary and work together to get results.
Examples and non-examples: Make cards or a slideshow with simple, clear examples of arrays vs not arrays. By showing students the equal numbers in each row and column.
Use inch-sized graphing paper to build arrays. Have students use manipulatives to build inside the squares gives them a starting framework providing the structure of the array.
Start with small arrays. Use 2’s and 3’s until students get the hang of it.
Instead of using manipulatives to create equal groups, tell students an amount and have them draw the amount into equal groups. This extends because they don’t have the manipulatives to shift around physically. They must think about it and using a writing tool to record their thinking.
Multiplication. There are always a handful of students who are ready for this, or they have an older sibling spilling the beans during homework time (love when this happens.) Usually, the best way to start is with the array, students showing the repeated addition and then showing them how the repeated addition relates to multiplication.
The pattern I start student with is usually, draw the array, write the repeated addition, write the multiplication sentence and then the students tell me why or how they are related.
How many Ways? Give them a number of manipulatives and have them record how many different arrays they can make. Students record what the array looks like, the repeated addition and multiplication. Numbers of object I like to use is 12, 10 and 8. (Also a great review of associative property).
Hopefully this helps you get started with arrays in 2nd grade!
P.S. Need some digital array practice with arrays and don’t know how to deal with the lack of manipulatives? Check out these Google Sides with moveable pieces.