Understand Numbers

Helping Kids Understand Numbers

Subitizing

What is that? 

You may have never heard the word, but you probably have observed it and certainly did it yourself as a child. In fact, you probably still draw upon the skill all the time.

Children gain the ability to see a few objects in one group, see a few in another group, and instantly combine the groups mentally for the total. For example, 7 is not simply 7. 7 is in fact 1 + 6, 2 + 5, 3 + 4, and so on. It can even be broken down further, for example 1 + 2 + 4. Or they see a group total, name it, but also mentally subtract a subset that is a different color to name the number of the other color. 

The role of the teacher is to take an implicit skill where children do it without conscious awareness of that ability and make it an explicit skill, as well as to provide experiences through activities and games to develop it further.

Subitizing:

• helps children develop a strong understanding of number sense, see the relationships between different numbers and groups of objects, which helps them to make sense of math problems and to solve them more easily.

• helps children to develop efficient counting skills and use their subitising skills to help them to keep track of where they are in the counting process, so they can count larger groups more quickly and accurately.  .

• is a skill that is used in many different areas of mathematics, including in addition and subtraction problems, multiplication and division problems and in geometry problems.

The skills involved in subitizing are an intrinsic part of life as a human. It was observed  and described in the early part of the 20th century and got its name in the 1950s. Research has confirmed its importance.

Find out more and get teaching resources here, here, and elsewhere. Search online if you would like to find videos or other materials on subitizing. Note: these resources are from outside sources so check with each site on whether materials are free or not.

Build Larger Numbers with Place Value Money

They need to be able to read those numbers with understanding of what their place value tells about the digits to read them correctly. They also need to be able to apply that to comparing quantities and ordering and compare numbers. 

Place value money is ideal for demonstrating building numbers up through 9 one dollar bills, and then when one more is added to make 10, needing to trade it for one $10. 

Teaching point: No 2-digit number can be written in one place value, so it has to be traded for the next higher bill. 

So then the next place value would be to build up to 9 $10s and 9 $1s (99), then add one more dollar bill and needing to trade the 10 $1s for 1 more $10. That would make ten $10s, triggering the need to then trade those for one $100. Likewise demonstrate the trades that need to be made — and written — when building from 999 to 1000. 

You can download a full set of place value money for whole numbers (ones, tens, hundred, thousands) here.

Building Decimal Numbers with Place Value Money

As with whole numbers, understanding the place value of decimal numbers can be developed by showing the number increasing by 1 cent (hundredth) to 9 cents, add one more for 10 cents and trade the 10 pennies for 1 dime. Continue adding pennies until they reach 10 again and trade for another dime. Be sure to show each step written, at least at the point of regrouping into dimes (0.09…add 1 cent…can't write ten in the hundredths place because it's a two digit number, so the 10 pennies must be traded for 1 dime 0.10; up to 9 dimes 9 pennies 0.99…add 1 penny and do the trade of the 10 pennies for the 10th dime, which must immediately be traded for a one ($1). 

By tying decimals to concrete objects, students gain a better understanding of quantity, making it easier to order and compare decimal numbers.

By the time students learn about thousandths, it should be sufficient to refer back to the example of hundredths, tenths, and so forth. There is no equivalent to thousandths in place value money. Nor are there any decimal equivalents in place value blocks.

Use place value charts with the decimal place value materials to represent written numbers as they construct and read aloud decimal numbers. Also use them to add or subtract them until students grasp the concept well. As students learn to order and compare decimal numbers, the charts can be of help.

Learners often get stuck on wanting to have a decimal equivalent of the ones place. A concrete way of showing it is impossible is to ask students to divide a $1 bill into "oneths" or by one. If they still try for that symmetry with whole numbers, they could count the decimal point as their "oneths" place. 

Place value charts for Grades 2 & 3, 4, 5, and 6 can be downloaded here. Please note that these charts are geared for both students who process the written word well and those who are better able to process numerals and would be confused by words. 

Reminder: When decimal numbers are read aloud the decimal point is read as "and." Often in earlier grades teachers accidentally read the comma in large numbers as "and." So it may take some unlearning for students to drop that habit and relearn to only use it in place of the decimal point.

Tie Money Models to Place Value Blocks

As the section on subitizing above suggests, being able to solve problems with numbers in a variety of different ways develops effective number sense and mathematical thinking. Place value blocks are a piece of that.