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Manipulatives for Developing Counting and Number Sense
Manipulatives for Developing Counting and Number Sense
Bears
Unifix cubes
Ten Square
Clear Chips
Chips
Base Ten Block
Pennies
Rocks
Candy
Other object that are around your house
Learning Progression: Counting and Beginning Number Sense
Learning to count seems so easy, right? You begin by singing number songs and counting objects. However, did you know there is a learning progression to counting and that success in mathematics begins with developing a sense of number through counting and quantity? Often I have TK-K teachers or parents tell me that their child can count to 20, and they can, which is excellent. They think that because the student can count to 20 that they understand what 20 means. This is not always true. They need to develop the understanding that 20 has a value. Counting from 1 to 10 or even 100 is helpful, but this skill alone is not the same as learning how to count. Students are great about saying number names. For example, you show the child a dice, and the student will say, “3” but then we ask them to count the dots to prove that there are six dots and they may say 1,3,2.. They may even count correctly but 1,2,3 but when asked to touch or move the objects, they may touch two at a time or keep counting when they already have counted all the items. The child is relating an image to a number but does not understand that the word six, represents a value of six. Learning to count is way more complicated then we think. It is important that we take time as teachers/parents to understand and develop the important skills of learning to count and number sense in our students. Graham Fletcher is kind of a math genius, so please take the to watch the video below. The video above will help you develop an understanding of the "Learning Progression".
Learning the Progress of Counting and Developing Beginning Number Sense Sequence
Subitization
In an effort to continue understanding the progress of counting and developing beginning number sense sequence, I will discuss subitizing. Subitization means “instantly seeing how many.” Seeing numbers in patterns and pictorial form is the foundation of strong number sense. Subitization is the root of the ability to see patterns, visualize numbers, understand the relationships between numbers, support operational fluency, and add and subtract mentally, all of which are essential math skills. There are two forms of subitization:
Perceptual Subitizing
Perceptual Subitizing
Perceptual subitizing is the ability to see two or three objects and immediately know the number. Students can subitize small groups of objects, typically up to 5, and state the number. This is an essential first step! This skill is often exhibited in children who recognize the number on a die, such as four or five. If your kiddo struggles with perceptual subitizing, you can use flashcards to model different representations of groups up to 5.
To build perceptual subitizing, you want to give students a lot of exposure to visual stimuli, such as patterns for three, four, and five or ten frames.
Conceptual Subitizing
Conceptual Subitizing
Conceptual subitizing is not only the ability to recognize a subgroup but also to recognize multiple subgroups and combine subgroups together. Such as two dots plus two dots equals four dots. Another example is seeing two fours on an eight domino. Children at first may only be able to subitize small numbers, but in time, they will be able to apply this knowledge to larger numbers and more abstract concepts.
Activities to Develop Subitization:
Activities to Develop Subitization:
Quick Image Arrays
Materials: Subitizations cards, a group of similar objects (rocks, bears, etc.), or dominoes.
Quickly shows the child a group (3 bears) or a subitization card (3 fingers) and then cover it up. See if they can tell you the number of objects. After they answer, count the objects to prove or disprove their answer 1,2,3. As they improve, you can add two groups of objects. Let's say you have a group of 3 bears and a group of 2 bears. Flash the object and see if they can tell you how many bears in all. Again, make sure you count the objects after.
Matching Game
You can also create several cards that have the same number but with different patterns. Then have students match numbers that are the same but in different patterns.
Which is Different
Same as above, but add a card that does not belong. Let's say you have 3 different representations of 2, add a card 3 card to see if they can identify the one that doesn't belong in the group.
Catch Me if you Can
Give each child a set of cards, one to ten in different patterns and have them spread them out on a desk or table. Then call out a number and see if they find the number quickly. You can time them and see if they can beat their previous time. This kills two birds with one stone because this helps develop a sense of time.
Ten Frames and Conceptualizing Addition
At first, place only the objects on the top row of the frame to see if the student can tell you the number. Then count the number to make sure it is correct. After they master 5, add to objects to the bottom frame. This also begins to develop the combination of ten, which I will explain in a different post.
For more cool ideas, visit Teachstarter
What is and Why is One-to-One Correspondence Important?
What is and Why is One-to-One Correspondence Important?
One-to-one correspondence is the ability to match an object to a corresponding number and recognize that the number has a value. Often young children count 1,2,3 but do not make the connection from the word number "five" to the number of objects in a given set. Developing one-to-one correspondence is extremely important.
Simply put, one-to-one correspondence is the most fundamental skill needed to do math. Without one-to-one correspondence, students will struggle in all areas of math. (see video below for more detail)
How to Teach One-to-One Correspondence
How to Teach One-to-One Correspondence
Here are some simple ways you can help support the development of one-to-one correspondence skills in your classroom or at home:
Count together with children as often as possible.
Move each object from one side to another as you say each number word aloud.
If the object cannot be moved, point or touch the items as you say each number word aloud.
Asking children questions such as, "How will you keep track of the objects you've already counted and which ones you haven't counted?"
Game and Activities that will help develop One-to-One Correspondence:
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