The Importance of Place Value in Primary

The importance of place value

I always start the school year with number sense. Why? Because it gives me a good indication of each student’s comfort with numbers. Number sense is the one strand that is always interwoven into other strands in mathematics. It is also the most telling predictor of a child’s success in math. If they have a good number sense – they can work flexibly and easily with numbers in most situations. If they don’t, I will have an idea of how to construct the rest of my lessons so that those students finish the year feeling more confident with numbers.

So what concept do most teachers start with? Place value. Place value is one of the hardest yet most important skills for primary students to master.

“Place value is the understanding that the same numeral represents different amounts depending on which position it is in.” (Charlesworth, 2012)

“The most critical period in this development occurs in grades pre-K to 2” (Van de Walle, 2014).

The understanding of place value follows this progression:

Level 1:        Initial concept of 10 (see 10 as ten units).

Level 2:        Intermediate concept of 10 (see 10 as a unit of ten ones but rely on
physical or mental models to do so)

Level 3:        Facile concept of 10 (easily work with units of 10 without the use of
                      models)

Place value development carries on through the elementary years by increasing the place value to build bigger numbers. But it is more than just knowing how to read big numbers; it is crucial to the learning of trading rules that underlie whole number operations. As a result, it is the most important building block for number sense.

Sadly, all too many children have a rote understanding of place value without truly understanding what different place values actually mean. They are not able to go back and forth between equivalent representations of the same number (i.e. 31 could be three groups of 10 and one 1or it could be 2 groups of 10 and 11 ones).

Introducing place value

Rory has just started kindergarten (my baby!!!!) and he has no understanding of place value (and nor should he!). He does have a good understanding of conservation of number though, meaning he understands that different arrangements of counters still mean the same number. To introduce him to place value, I did the following:

1)   I asked him which was larger 63 or 36 to see if he has any understanding of what he’s counting or place value. He didn’t. Interviewing children is a great way to gauge their ability and find out what they’re thinking and why.

2)   I gave him a bunch of unifix cubes (a great model to start with!) and asked him to count as high as he could. This is a great test for cardinality and one-to-one correspondence. Both he and I were surprised that he made it to 39 without any assistance!

3)   I asked him to now group the cubes into groups of 10 which he did easily. He quickly noticed if a group of 10 was incomplete (the benefit of a proportional model!).

4)   We finished by noticing that the number of groups of 10 corresponds to the place value in the number. This went way over his head, but I felt better for saying it!

If this were a classroom lesson, I would complete it with a comparison of one ten tower to one cube and engage the students in a discussion of what they notice.

Do’s and Don’ts for Teaching Place Value

So how do you teach something this important? Here are some do’s and don’ts

DO:

  • DO use proportional manipulatives (the hundreds should be bigger than the tens which should be bigger than the ones)
  • DO use many different manipulatives so the child doesn’t think PV can only be represented with one type (i.e. base 10 blocks, unifix cubes, paperclips, counters)
  • DO integrate PV teaching with estimation and computation tasks
  • DO integrate PV teaching with measurement tasks (and use different units to measure!)
  • DO work on PV skills throughout the school year (not just in September!)
  • DO question and assess students constantly to be sure they are really understanding the concepts and not just answering in a rote manner
  • DO engage students in composing and decomposing #’s in a wide variety of ways
  • DO allow children to invent their own computation strategies

DON’T:

  • DON’T give worksheets which encourage a rote understanding not a concrete understanding (i.e 6 tens and 4 ones is 64 in all.)
  • DON’T teach PV abstractly, tie it to a manipulative
  • DON’T rush into operations involving regrouping tasks i.e. borrowing and carrying (mental math rarely involves regrouping as a strategy) and you run the risk of students not conceptualizing place value
  • DON’T start computation with numbers that don’t require regrouping (i.e. 23 +45); otherwise students will think that 56 + 35 = 811
  • DON’T rely on one type of manipulative (i.e. base 10 blocks) or children will memorize that a rod is ten and a small cube is one without actually understanding how many ones make a rod
  • DON’T teach PV in isolation, make it rich by integrating it with other subjects (see the link below for suggestions)

A true understanding of place value doesn’t usually happen until the concrete stage of development (7-8 years old), but it doesn’t mean you shouldn’t provide lots of opportunities for its development. What can you do? COUNT EVERYTHING!!!!

Want more suggestions? Click here!

Back to top!

Feeling Peppy for Patterning!

The importance of patterns

Pattern

Peppy for patterning!

Young children are naturally drawn to patterns, but as a parent, you may wonder why exploring patterns is such a useful activity.

“Learning to look for, describe and extend patterns are important processes in thinking algebraically.” Van de Walle

Patterning is the process of discovering repetitions or regularities and can be explored used songs, movements, manipulatives, nature or behaviours. Patterns and relations are important for understanding the world around us. Much of our life revolves around a pattern: seasons, days of the week, set the table – clear the table, wash your hands – eat your snack, or my Personal favourite: the 3 P’s: Potty, Pull-ups, P.J.’s!

The stages of pattern development:

In pre-K: Children discover patterns (shapes, colours, routines, nature)
Grade K-1: Children learn about number patterns (odd vs. even, 2’s, 5’s, 0’s, the 100 chart)
Grade 2: Children extend patterns into operations (skip counting, adding 10 each time)
Grade 3: Children use patterns as a strategy for multiplication and division
Grade 4-5: Children use patterns to prepare for expressions, equations and functions
Grade 6: Children see algebra as the study of patterns and relations!

Repeating vs Growing Patterns

Now obviously your 3 year old isn’t about to study functions and relations, but the more exposure he or she has to interpreting patterns the better. Marilyn Burns suggests that even in the kindergarten years, we should be exposing our students to repeating and growth patterns to help students develop flexibility in their thinking. By mixing up the type of pattern you present, you are introducing them to problem-solving experiences that will aid in their development of numerical reasoning.

Having taught growing patterns to Grade 6 for years, I couldn’t imagine a 4 year old identifying a growing pattern. (A growing pattern happens when something is added each time).

I decided to present Rory with a growing pattern that could be represented by x+1. I was quite curious to see whether Rory would see the pattern, and was really impressed at his innate ability to solve it after only a few hints! Notice how I use the key questions listed below to engage him. I also use my voice in a rhythmic way to help him identify the growth pattern (“one fish, one bunny, two fishes, one bunny, etc.). Watch how he does!

How to start

Ideally you want to expose your child to as many different types of patterns as possible. This means use song, movements, nature, the world and of course manipulatives. For teachers, Van de Walle stresses the use of manipulatives instead of work sheets or drawings. Manipulatives allow for trial and error and reduce the fear of being wrong. If you are using worksheets to keep a record, you could always have the students record their work after.

When introducing your child to patterns, there are a few key questions to ask:

  1. Did you see a pattern?
  2. Tell me about this pattern (describe it)
  3. What is the pattern? How do you know?
  4. Can you predict what comes next?
  5. Can you extend the pattern for me?

Here’s a video of Rory being introduced to patterns. I started with an easy one using colours, then I tried a different modality (sound) and showed how it could be related to manipulatives. After some discovery time with repeating and growing patterns, I had him create his own. With each exploration, I kept those 5 questions in mind.

Feeling peppy about patterning? Click here for some activities!

Back to top!