Illuminations: Concentration - Numbers
Curator: Kimberly Anglin
In this applet, students match whole numbers, shapes, fractions, or multiplication facts to equivalent representations. Practice with the clear panes or step up the challenge with the windows closed.
Grade Level: K - 2
PSSM Content Standard: Algebra and Geometry
CCSSM Content Standard: Kindergarten math - K: Counting and Cardinality, Geometry
Math Content: Count to tell the number of objects, Understand the relationship between numerals and quantity, Identify shapes
What is being learned? What mathematics is the focus of the activity/technology? Is relational or instrumental understanding emphasized?
Students learn different ways of representing numbers and shapes. Relational understanding is emphasized because students need to match the two different representations of numbers and they are unable to do so unless they know how each is equivalent. For example, 4x4 is equivalent to 20-4. It is unlikely that one could guess their way through this activity. However, instrumental understanding is possible if the student simply memorizes the number each card represents and does not relationally understand why each card actually represents that number. This is good for fluency but outside of the game, an instrumental understanding will only take them so far.
How does learning take place? What are the underlying assumptions (explicit or implicit) about the nature of learning?
The activity strengthens the student’s ability to recognize equivalent quantities. It is assumed that students know how to do each of the operations presented in this activity. The learning goals are explicitly defined and have similarities and differences depending on the game of concentration they are playing (numeral to object to word, product to sum or numeral, quotient to percent to numeral to fraction, etc.). They are similar because game is practicing a previously learned skill, increasing fluency and memorization. They are different because some are only numeral identification and others involve computation which, eventually, will become mental math.
What role does technology play? What advantages or disadvantages does the technology hold for this role? What unique contribution does the technology make in facilitating learning?
Technology in this activity sets up the concentration games, the number representations on each card and gives feedback to the student. It also has audio for the cards that have words written on them which is something a card game of concentration couldn't do. Another advantage of this technology is that it offers a variety of child-friendly, readily accessible concentration games that challenge students to strengthen their problem solving and math facts fluency. One disadvantage is that it does not offer any lessons so it’s not actually teaching the student anything. When the student matches the wrong cards, it doesn't give any feedback or representation as to why it was wrong. While it would be very difficult, it is possible for a student to guess their way through the game.
How does it fit within existing school curriculum? (e.g., is it intended to supplement or supplant existing curriculum? Is it intended to enhance the learning of something already central to the curriculum or some new set of understandings or competencies?)
This resource is directly aligned to the Common Core State Standards for Kindergarten Mathematics. It is intended to practice what is learned in class. It works best to have some sort of follow-up in class as well.
How does the technology fit or interact with the social context of learning? (e.g., Are computers used by individuals or groups? Does the technology/activity support collaboration or individual work? What sorts of interaction does the technology facilitate or hinder?)
The students will use this either individually or with a partner on the Smartboard. Students who work together can help each other and when students work alone, it is a good assessment of their knowledge of the topic.
Grade Level: K - 2
PSSM Content Standard: Algebra and Geometry
CCSSM Content Standard: Kindergarten math - K: Counting and Cardinality, Geometry
Math Content: Count to tell the number of objects, Understand the relationship between numerals and quantity, Identify shapes
What is being learned? What mathematics is the focus of the activity/technology? Is relational or instrumental understanding emphasized?
Students learn different ways of representing numbers and shapes. Relational understanding is emphasized because students need to match the two different representations of numbers and they are unable to do so unless they know how each is equivalent. For example, 4x4 is equivalent to 20-4. It is unlikely that one could guess their way through this activity. However, instrumental understanding is possible if the student simply memorizes the number each card represents and does not relationally understand why each card actually represents that number. This is good for fluency but outside of the game, an instrumental understanding will only take them so far.
How does learning take place? What are the underlying assumptions (explicit or implicit) about the nature of learning?
The activity strengthens the student’s ability to recognize equivalent quantities. It is assumed that students know how to do each of the operations presented in this activity. The learning goals are explicitly defined and have similarities and differences depending on the game of concentration they are playing (numeral to object to word, product to sum or numeral, quotient to percent to numeral to fraction, etc.). They are similar because game is practicing a previously learned skill, increasing fluency and memorization. They are different because some are only numeral identification and others involve computation which, eventually, will become mental math.
What role does technology play? What advantages or disadvantages does the technology hold for this role? What unique contribution does the technology make in facilitating learning?
Technology in this activity sets up the concentration games, the number representations on each card and gives feedback to the student. It also has audio for the cards that have words written on them which is something a card game of concentration couldn't do. Another advantage of this technology is that it offers a variety of child-friendly, readily accessible concentration games that challenge students to strengthen their problem solving and math facts fluency. One disadvantage is that it does not offer any lessons so it’s not actually teaching the student anything. When the student matches the wrong cards, it doesn't give any feedback or representation as to why it was wrong. While it would be very difficult, it is possible for a student to guess their way through the game.
How does it fit within existing school curriculum? (e.g., is it intended to supplement or supplant existing curriculum? Is it intended to enhance the learning of something already central to the curriculum or some new set of understandings or competencies?)
This resource is directly aligned to the Common Core State Standards for Kindergarten Mathematics. It is intended to practice what is learned in class. It works best to have some sort of follow-up in class as well.
How does the technology fit or interact with the social context of learning? (e.g., Are computers used by individuals or groups? Does the technology/activity support collaboration or individual work? What sorts of interaction does the technology facilitate or hinder?)
The students will use this either individually or with a partner on the Smartboard. Students who work together can help each other and when students work alone, it is a good assessment of their knowledge of the topic.