|This one features six groups of five. I made it using a bingo dauber and a half sheet of card stock. I flash the card at students for a few seconds and ask them to show me when they know how many dots they saw. I then have students share either with a partner or with the whole class (or both!) how many they saw and how they know they are right. As we get more and more practice with these types of cards, I decrease the amount of time I show the card for.|
Student 1: I counted by 5's
Student 2: There are three groups of 5 on the top which I knew was 15 and three groups of 5 on the bottom which is another 15 and 15 +15 = 30.
When a student shares a strategy like this one orally, I might record these types of equations on the board.
6 x 5 = 3 x 5 + 3 x 5 = 15 + 15 = 30
This strategy uses the distributive property!
Student 3: Two groups of 5 is 10 and I saw 3 tens which is 30.
|This time the dots are arranged in an array. The equal groups become columns or rows. When I first start using array cards with students, I give them a few extra seconds to look at them. As they have more exposure, I decrease this amount of time. This card was made using colored dot stickers.|
Here are some strategies I might hear about the above card.
Student 1: I knew it was 15 because I saw three rows of 5. I counted by 5's, 5, 10, 15.
Student 2: I saw 5 groups of 3 and I counted by 3's.
Student 3: I saw 5+5+5=15
I have stacks of these cards in second and third grade classrooms and for use with intervention groups. There are so many things that can be done with them. They are quick, easy and inexpensive to make and after students have some exposure to them, they love making their own!
Are your students ready for division?Here is an example of how I would use one of these cards to get at division facts. Kids would have repeated exposure to these cards by the time I did this.
|This card was made using round mini-stickers. It was made by a student! The different colored stickers really help kids see the groups when the cards might not be perfect. Mini-stickers make is so you can have more groups and/or more dots in each group.|
Ready to work on factors?
Toward the middle of grade 3 when I am ready to introduce the idea of factors of a number, I might hold the card above and ask kids to predict what is on it. I will tell them I have 48 dots and ask them how they might be arranged. They will start brainstorming ideas like 2 groups of 24, 6 groups of 8, 4 groups of 12, etc. I record these on the board using multiplication notation and it becomes a natural way to introduce the idea of factors.
When kids need more work
I currently have a group of third grade students who are part of an intervention group who need continued work with the ideas and concepts that these cards present. I want them to have more exposure but at the same time, many of the cards are becoming to easy for the entire class. Recently I came up with an idea to give these kids a way to practice this independently or with a partner. It is working REALLY well.
|A small group of students looks at some models of different cards that have been used with the whole group. They are using these models and what they have experienced with these cards to create their own deck on index cards|
I met with this group one afternoon and after doing some of the cards from the half sheets of cardstock, I invited them to make their own deck of these types of cards. I gave them index cards, 1 inch binder rings, and markers. They looked at some of the models to get them started and created a pile of cards for their own use. When time was up, I used my super 3-hole punch to punch a hole in the corner of their entire deck. They placed the 1 inch binder ring through the hole and were ready to go.
I reviewed their decks after-school and added a few cards of my own making to each deck. Now these students all keep their decks in their math browse box (similar to the box many primary students have for reading full of just right books). When they have a chance during their regular math class, during transition times, or when their intervention group meets, they can pull them out and practice a similar routine that we have done repeatedly in the classroom by themselves or with a partner. It has been about 3 weeks now and their fluency with multiplication and concepts about multiplication facts have improved dramatically.
|Here is a student's card showing 4 groups of 7|
|A student makes some array models on her card|