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Preschool Math Standards: Number Sense

7/9/2014

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Often people think of preschool math as nothing beyond counting and numbers. However, it is the teacher's duty to prepare each child for every field of mathematics. There are five main areas into which we group our standards: Number Sense, Geometry, Measurement, Sorting and Patterning, and Problem Solving.

This blog entry will cover the Academic Standards that fall under the Number Sense category.

While repeated exposure to activities/games that include these concepts is paramount to the child's understanding, it is important to understand that a young child may not "get" a particular concept until he is developmentally ready.
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Number Sense
Rote Counting -  Rote counting is the ability to name the number words in the correct sequence. 
One-to-One Correspondence - One-to-One Correspondence is the ability to pair one object with one number while counting objects (the child says "one" as she touches the first object, "two" as she touches the second object). A child may have one-to-one correspondence to seven or to seventy. The object is to build this until a child has one-to-one correspondence indefinitely.
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One-to-One Correspondence may also be practiced (without counting) by matching one object to one specified space. In the photo below on the left, a child is placing one bean into each section of an ice cube tray. In the photo on the right, the child is placing one cookie onto each square of his game board. 
Numeral Recognition - Numeral Recognition is the ability to visually recognize and name numbers.
Quantification - Quantification is the ability to answer "How many?"
Conservation of Number - Conservation of Number is the ability to understand that the number of objects does not change no matter how they are arranged. (In each of the photos below, there are ten chips. There are a different number of black vs. white chips in each photo, and although the chips are physically arranged differently, there are still ten chips in each photo.)
Comparing Sets - Comparing Sets is the ability to determine which set between two or more sets, has fewer, more or an equal number of objects.
Counting Forward - Counting Forward is the skill used when a child can begin at a given number and continue counting. For example, if a child rolls two dice (six and two) he may point to the first die and say "six" and then point to the second die and continue with "seven, eight".
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Inclusion - Inclusion is the skill used when a child must count out a given number of items from a larger set. If instructed "hand me three gems," the child will include three gems.
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Sequencing -  Sequencing is using a rule to order numbers, colors, or parts of a story.
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Number Sense is just one small part of preschool mathematics. We have broken Number Sense into nine standards:


Rote Counting
One-to-One Correspondence
Numeral Recognition
Quantification
Conservation of Number
Comparing Sets
Counting Forward
Inclusion 
Sequencing 


In our classroom, each lesson, game or classroom material has been intentionally planned and placed in the room to fulfill our Academic Content Standards. 
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Guessing and Counting

4/5/2014

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Estimation is a valuable skill in our world. We use it more often than we may realize. Contractors frequently use estimates, and I, personally, use my own "guesstimate" system to remain within budget while grocery shopping. 
Young children must be introduced to any math concept they will be expected to to understand - at a level that they can understand.
We placed six blocks around Sisi so the children could see about how much of her body those six blocks covered. The children were encouraged to guess how many blocks it would take to go all the way around her body. We decided that since we already used six blocks, our guesses would have to be a number higher than six.
For some children this is fairly easy; for others, this can be a difficult concept. When working with a difficult problem, we must decide what is known. 
For this problem, we know two things. 
1.) We know that our guess must be a number. We want to know how many blocks it will take. 
2.) We also know that it will take more than six blocks to go all the way around Sisi.
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Any guess that is within our knowns is praised as a good guess.  
For the next guessing activity, the children drew a long line on butcher paper and guessed how many crayons it would take to cover the whole line. 
It's important for children to have many different experiences with each new concept we are introducing. 
Estimation has a great deal to do with number sense and understanding the concepts how many, more, and less. In the instances pictured, it also pertains to the concept of measurement. 
Children with "off-the-wall" guesses will begin to guess more accurately as they gain more experience.
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Counting

3/18/2014

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Counting in preschool is interesting because it is actually more than just one skill.  
Rote counting: This is just counting (memorization), not necessarily counting objects.
One-to-one correspondence: This is the ability to pair one object with each number when counting. A child may have one-to-one-correspondence to seven, but not ten.
Numeral recognition: This is a visual skill.
When we teach new skills in preschool, we make a conscious effort to include methods that will benefit all our auditory, visual AND kinesthetic learners. 
For this activity, I took my group to the block area and showed them pictures of some very different types of structures (Big Ben, The Eiffel Tower, The Golden Gate Bridge, and The Pyramids of Giza). We discussed some of the differences, and then we talked about what architects do. 
"Architects get to design their own type of building. They plan and oversee the construction of their building. Today YOU get to be an architect and design any type of structure you want!"
The children were able to choose how many of each size block they wanted to use. When they were done building their structure, they graphed how many of each block they used. 
Now you can use it in your class, too! (It's available for FREE in our teacherspayteachers store - just click on the button below and you will be re-directed to our store.)
Teacherspayteachers
We also practiced counting in the block area by building a city skyline.
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If we don't find many DIFFERENT ways to practice counting, it gets really boring. Here the children are rolling a die and counting out fruit loops. Fun snacks make anything more exciting!
This is a Minute-to-Win-it Fruit Loop Race. The children were given one minute to stack as many Fruit Loops as they could on the kebab stick. 
This was a GREAT way to practice counting (and fine motor!) because they wanted to do it again and again.
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When the minute was up, we counted and compared how many Fruit Loops we were able to stack. 
We have this fancy foam pad to hammer these plastic nails into, but Styrofoam and golf tees work just as well. 
In the game "Get to Zero", everyone begins with the same number of gems. The players take turns rolling a die and then put that many gems into the container. With older children, on their last turn, they must roll the EXACT number to "Get to Zero" and win. I use a die with numerals on it so they can practice numeral recognition as well as counting. 
You'd think these children would be sick of numbers and counting by now - that's why we try to make it different every day!
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Skip Counting: Tens

3/15/2014

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One of the ways that we teach children to count by tens is through song. Any child can be taught to do this; it is simply memorization. There is not necessarily any mathematical understanding involved. 
This is why it's important for us to spend time working with groups of ten to give children the understanding of WHEN we CAN count by tens. 

Each child in my small group made a group of ten unifix cubes. When they were done, I asked how many cubes were in each stick. "Ten!" They shouted. 
"How do you KNOW?" I asked.

(Pause)
"Because we counted them...?" One girl responded. 

"Yes! Now that we know there are ten cubes in every group, we can count by tens!"
Each child got a turn to be the "teacher" and point while we counted. It's interesting - the first time we do this every year, the children's one-to-one correspondence goes down the drain. They haven't yet associated each separate number (ten, twenty, thirty) with a separate group of ten. They regain this quickly. It's quite fascinating to watch.
We made necklaces to get some practice recognizing the numbers and putting them in order. 
Again, we practiced making groups of ten.
The next day we found another fun way to practice making groups of ten. 
We practiced putting our numbers in order again, too. The more we practice, the easier it gets!
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Problem Solving and Expectations.

2/28/2014

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In 1989 NCTM (National Council of Teachers of Mathematics) developed a set of standards for mathematics as a framework to guide each state in developing mathematical standards. 

We  use these standards as part of the framework in creating our preschool math curriculum because these standards are established, research-based and designed by professionals “dedicated to improving the teaching and learning of mathematics” and “to ensure the highest quality mathematics education to all students”.

We had a very successful day solving word problems. The chocolate chip cookie cereal we used might have something to do with that! Today we were solving with manipulatives (the cereal), but soon we will begin to increase the children’s repertoire of problem solving techniques. I can't wait!
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Notice that each child has her own visible workspace. This is an often overlooked necessity when working with young children.  Studies have shown that high expectations produce higher accomplishment in the classroom, but we can not have high expectations without providing the materials the children need to meet our expectations. 


Example: If I had given everyone the chocolate chip cookie cereal without the "workspace", one child would have the cereal under her legs, one would have his behind him, one would have hers beside her,  one would have his cereal in front of three other students, and two might have their cereal in front of them.  By the time we got organized and found everyone's cereal, I would have lost their attention and there would be very little math problem solving. 


By using a visible workspace we have freed up our time and our minds for higher level thinking. 
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Pennies and Nickels, Oh My!

2/21/2014

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More ways to practice counting! 

Sometimes in Small Group, we open a “store”. These children are rolling a die to earn money. At the end of the round, they can exchange  pennies for a nickel, and go ‘shopping’.
This is one way that we practice counting and one-to-one correspondence. It also helps us learn (and remember) that a nickel is worth five pennies.

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    Wendy Joy Yohman
    Eleven years teaching experience
     at a small private  school. 
    Current preschool supervisor.
     Bachelor's Degree in 
    Psychology with an emphasis
     on educational kinesiology 
    (how different movements 
    activate certain areas of the 
    brain). 

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