Counting

How do I help my child with counting?

What's the big deal with counting?

Children need a lot of experiences counting things, to develop their number sense and their understanding of quantity. Many students who struggle with math in 3rd-5th grades did not have enough experiences in the early grades developing this sense for how much a quantity is: 7 vs. 70 vs. 700. Counting Collections is an activity we do weekly in the early grades which gives children those counting experiences, and is easy to replicate at home.

What are more mathematical benefits of counting collections?

My child can count to 100! Now what?

We tend to think about counting as a matter of knowing the sequence of numbers, but it’s so much more complex than that....

Children often learn rote counting (1, 2, 3) before they understand numbers represent quantity. A preschooler who can count to 100 from memory is not necessarily able to count 100 objects accurately, and may not have developed a sense for how much an amount really is.
Even if a child can count objects, knowing how many total objects there are in all is another developmental step.
Being able to look at items and know the quantity, without counting each item, is a sophisticated skill that requires practice through play.
Assigning symbols (numerals) to the amounts is another step.

Counting Collections is a powerful activity because it provides an opportunity for children to practice and apply all of these skills!

How do we do Counting Collections?

Step 1: Create a collection of objects for your child to count.

Anything works! How many depends on your child, but here is a rough guide:

Kindergarten: 20-120 or more (start with about 50)
1st grade: 30-300 or more (start with a little less than 100)
2nd grade: 100-1000 or more (start with a little less than 200)

Adjust up or down the next time you do the activity,

Step 2: Child counts to find out the number of things in the collection.

First, ask child to write down an estimate for how many objects they think are in the collection.

Allow child to count in a way that makes sense to them. Your child may count all of the objects one at a time, or might group them first into twos, fives or tens. Over time, children will become more efficient in their counting, but there is no need to push grouping until a child initiates it.

Khalid drew a circle to represent each ten.

Step 3: Record the count.

Ask child to write the total on their paper near where they wrote their original estimate. Then they draw a picture or diagram of how they counted. Children find many ways to record their counts.

How do I help my children while they are counting?

What to watch for while child is counting

Keeping track - does the child have a way to keep track of which items they have and haven't counted?
Organization: does the child count by ones, or does he organize the items into groups for efficiency?
One to one correspondence: Does the child match each object to a number while counting?
Cardinality - Early counters don't realize that the last number they say is the total of the whole group.
Teen numbers: Some children struggle with teen numbers - eg., they might skip 13.
Decade numbers: Students often stumble when counting from 29 to 30, 39 to 40, etc.
Counting past 100: Children take time to figure out the numbers from 99-120, as new patterns are introduced, especially 99-100 and 109-110.

What to do if a child is wrong or stuck

When we asked Kindergarten teachers what they would want parents to know about counting collections, they said,

"Please don't tell the kids answers or correct their mistakes too quickly!"

We want to build student independence and encourage them to fix their own mistakes. So start by trying:

Ask them to back up and count from an earlier number. Say: "Could you go back and count from 27 (10, 78, 99, etc.)"
Use a resource like a hundreds chart as a reference.
Ask a question to prompt thinking (see below)

A sampling of questions you might ask during Counting Collections

How do you know which items you have counted and which ones you have not counted?
What were you doing last time to keep track?
Why did you decide to put those into (cups of 15)?
What are you going to do with all those ones?
Why did you organize your objects in this way?
Can you count another way? Did you get the same or different answer?
I noticed you counted like this...

Some ways to extend counting collections

Below are questions you can ask your child to help them extend the counting to place value and problem solving. These questions range in level from Kindergarten to 3^rd grade, so use the questions that make sense to your child. Over-explaining doesn’t help! More experiences counting, with real objects and appropriate follow-up questions, does help….

How many would you have if I gave you 10 more objects? 100 more objects? 200 more objects?
How many would you have if I took away 10 items? 100 items?
How many would you have if you doubled your collection?
How many more objects would you need to have ____________ objects? (50, 60, 100, 1,000)

Do you think you and I can equally share all of these objects? Why?
If you and I shared all of these objects equally, how many would we each get? (Allow student to act out with the objects if they request.)

Continue the Counting.....

This is an activity which can be repeated twice a week or more, depending on your child’s interest. If your child finds it easy, increase the number of objects. If the number is too high, start with a smaller number.

Consider getting a notebook devoted to counting collections, with a new page for each time you do the activity.

Take a Counting Walk!

Walk around the block, or to the park, but beforehand choose an item to count: dogs, trees, red cars, etc. Decide on a strategy to keep track as you go. When you get home, write the total and make a representation of your count. OR¸ as you walk, estimate how many steps to the next tree, to the top of a hill, etc., then compare your estimate to the actual count.

Do you have a change jar at home?

Have your child count how many of each type of coin, or how many coin all together. Older students can figure out the total amount in dollars and cents. Likewise, your child could figure out how many books you have, how many spoons, etc….. you could do an inventory of your entire house!

Want to know more about counting?

Short Overview

This 3 minute video from UCLA gives a clear explanation of counting collections for parents.

Early Counting

This website from Stanford has videos of children at different stages of learning to count and more information on how children develop early counting .

Counting-Collections-Article.pdf

Article

This article gives a good introduction of counting collections.

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