Exploring Dice-Dot Patterns

The ability to quickly recognize the patterns on a die without counting each dot is important for young children.
 So today I played a game with a First Grader in which we each had 20 counters and 1 die.

The players take turns rolling the die and picking up as many counters as indicated on the die until all of the counters have been picked up. To pick up the last counter, the number on the die must match the number of counters remaining.  The first player that picks up (or slides the counters to the side of their pile) all their 20 counters is the winner.

While playing this game it is easy for the teacher to evaluate:
1) Can the child recognize the pattern on the die at a glance, or is it necessary for the child to count each dot before knowing the amount indicated on the die?
2) When counting their counters do they have one-to-one correspondence, and do they count using the correct sequence?

When we played the game the second time, I counted out my counters by two's instead of by ones. The First Grader followed my lead by counting her counters by two's also. So I learned something new about her again... that not only could she count by two's but she had the ability to utilize that pattern when picking up (or sliding over) her counters. To count out the number of 5, she slid the counters in this way:  2,2,1.

EXTENDING THE LESSON


I told the student that I wanted to know what she already knew about the patterns on dice.  I gave her 6 post-it notes and asked her to draw the pattern for each number on the post-it notes.  This is what she drew:

 

When I looked at  the post-it notes I could tell that the student had internalized the 6 patterns on the die, and could  tell you immediately without counting the value of each pattern.

 

If I was saving evidence of learning, I could save the six post-it notes, or a photo of her work.

 

Deborah



Common Core Standards Taught During Calendar Routine Activities

Here are the promised Calendar Cards to promote the Common Core Standard K.CC.5 that I am sharing with you. Just click HERE  and Here to go to my Google Docs file to download them.

This is the Common Core Standard:

Count to answer "How many?" questions about as many as 20 things arranged in a line, a rectangular array, or a  circle, or as many as 10 things in a scattered configuration.

How would I use them?

I would make a ringed set of laminated counting cards for each child in your class. Then, each day (they are numbered in the upper left hand corner of the card) the class would orally practice counting the hearts together. Then I would ask individual students about their strategy to count sets of objects when they are not lined up in a row (which is the easiest way for students to count objects).

The student would orally share their strategy. Lastly, I would call on one more individual student to try the strategy that was discussed by their classmate and orally recount the hearts of the day.

By doing this as a calendar routinue, the teacher is providing 31 opportunities for students to practice this Common Core Standard!

Deborah Devine

Common Counting Errors for 4 and 5 Year Old Children

 I've been working with my two-year old granddaughter on counting. (Can you say "Overachieving Grandma?") In this picture we are painting TWO monsters after reading "My Monster Mama Loves Me So." This book  is about the relationship between a monster and his mother. As the title suggests, the monster lists some of the reasons he knows his monster mama loves him. Those reasons include the monster mama baking cookies that are filled with bugs. (Doesn't that sound delicious??) All of the examples the monster gives are funny and heartwarming.

Given the fact that I have a passion for both my granddaughter and MATH, I started thinking about the problems children have when they learn to count.  I've been reading the book, "Mathematics Learning in Early Childhood: Path Toward Excellence and Equity", and I found a list of Common Counting Errors.
As a teacher, I found these words interesting:

"As with many physical activities, counting will improve with practice and does not need to be perfect each time. Teachers do not have to monitor children’s counting all of the time. It is much more important for all children to get frequent counting practice and watch and help each other, with occasional help and corrections from the teacher."

After reading Debbie Diller's book, "Math Stations" this quote provided even more support for the use of math stations at the early learning grades.

Just in case you are interested,below is a direct quote from this book about common counting errors:

"There are some common counting errors made by young children as they learn the various principles that underpin successful counting. Counting requires effort and continued attention, and it is normal for 4-year-olds to make some errors and for 5-year-olds to make occasional errors, especially on larger sets (of 15 or more for 4-year-olds and of 25 or more for 5-year-olds). Younger children may initially make quite a few errors. It is much more important for children to be enthusiastic counters who enjoy counting than for them to worry so much about errors that they are reluctant to count. If one looks at the proportion of objects that receive one word and one point, children’s counting often is pretty accurate. Letting errors go sometimes or even somewhat frequently if children are trying hard and just making the top four kinds of errors is fine as long as children understand that correct counting requires one point and one word for each object and are trying to do that. As with many physical activities, counting will improve with practice and does not need to be perfect each time. Teachers do not have to monitor children’s counting all of the time. It is much more important for all children to get frequent counting practice and watch and help each other, with occasional help and corrections from the teacher.

Very young children counting small rows with high effort make more errors in which their say-point actions do not correspond than errors in the matching of the points and objects. Thus, they may need more practice coordinating their actions of saying one word and pointing at an object. Energetic collective practice in which children rhythmically say the number word list and move down their hand with a finger pointed as each word is said can be helpful. To vary the practice, the words can sometimes be said loudly and sometimes softly, but always with emphasis (a regular beat). The points can involve a large motion of the whole arm or a smaller motion, but, again, in a regular beat with each word. Coordinating these actions of saying and pointing is the goal for overcoming this type of error. For variety, these activities can involve other movements, such as marching around the room with rhythmic arm motions or stamping a foot saying a count word each time.

Counting an object twice or skipping over an object are errors made occasionally by 4-year-olds and even by 5-year-olds on larger sets. These seem to stem from momentary lack of attention rather than lack of coordination. Trying hard or counting slowly can reduce these errors. However, when two counts of the same set disagree, many children of this age think that their second count is correct, and they do not count again. Learning the strategy of counting a third time can increase the accuracy of their counts. If children are skipping over many objects, they need to be asked to count carefully and don’t skip any.

Young children sometimes make multiple count errors on the last object. They either find it difficult to stop or think they need to say a certain number of words when counting and just keep on counting so they say that many. When they say the number word list, more words are better, so they need to learn that saying the number word list when counting objects is controlled by the number of objects. Reminding them that even the last object only gets one word and one point can help. They also may need the physical support of holding their hand as they reach to point to the last object so that the hand can be stopped from extra points and the last word is said loudly and stretched out (e.g., fii-i-i-ve) to inhibit saying the next word.

Regularity and rhythmicity are important aspects of counting. Activities that increase these aspects can be helpful to children making lots of correspondence errors. Children who are not discouraged about their counting competence generally enjoy counting all sorts of things and will do so if there are objects they can count at home or in a care or education center. Counting in pairs to check each other find and correct errors is often fun for the pairs. Counting in other activities, such as building towers with blocks, should also be encouraged."