Number Relationships (Combinations) with Five-ness and Ten-ness

Beginning in kindergarten children can learn and incorporate a sense of five and a sense of ten when looking at groups of objects to instantly know the quantity. Subitizing (see second video below) is when children can look at an arrangement of objects and know immediately how many are in the group without having to count them individually. We really want our students to have this instant recognition of quantity based on relationships to 5 and 10. Five frames and ten frames are a great way to create this understanding and also a great way for children to gain understanding of more and less or fewer.

The first video is Quick Images: Visualizing Number Combinations from Teaching Channel. It shows a kindergarten class looking at number combinations to eight using a ten frame with magnets. I love the conversations and the way the students explain their thinking. (There is a little hand gesture you may see the students and teacher use where their thumb and pinky are extended and the students rock their hands back and forth at each other. This is their signal that “I agree with what you are saying” (I love it!). It is a great confidence booster to the child who is speaking and sharing their thinking.)After you work with students a bit using this visualizing number combinations idea, I think you could easily start asking, the more and less/fewer questions. For example in the video when there are 5 magnets on the top and 3 on the bottom you could ask, “How many fewer than 10 is this number?” or “How many more do we need to get to 10?” or “How many more than five is this number?” This lesson also lends itself very well to a small group lesson.

The second video, Ten Frames Fact Practice, is more for 1st and 2nd graders using ten frames to learn number combinations to 18, but the idea is similar to those in the video above. They incorporate addition strategies based on five-ness and ten-ness, doubles, doubles-plus one, etc. Think about using these for small group instruction so that students can explain their thinking and strategies, or have them journal their thinking. You could make a card game for this by creating ten frame “cards” with all the combinations and have students draw two cards, tell the number combination total and then voice their strategy on how they arrived at the answer. Voicing their strategy to their playing partner is very important so that strategies get shared and students can see multiple entry points.

In addition to Number Sense Games and Random Dot Cards below, you will also find a PDF for a really great little booklet, Dot Card and Ten Frame Activities, from the Winnipeg School Division. It includes everything you need to make 20 dot card activities, 8 five-frame activities, and 14 ten-frame activities. Many of these activities would be great in work stations.

Suggested Reading: 

Elementary and Middle School Mathematics by John Van de Walle, the Developing Early Number Concepts and Number Sense chapter, Relationships Among Numbers 1 Through 10.

Literature Connections: Anno's Counting Book, The Very Hungry Caterpillar, Two Ways to Count to Ten


Teaching Channel Videos: