Understanding Place Value

Understanding Place Value

One of the most important concepts that children need to understand deeply is the concept of place value.

Place value is much more than just locating hundreds, tens and ones and placing a value for each number.

For children to develop a deep understanding of place value they also need 

to understand that 10 is both 10 ones and 1 ten.

For example in the number 38. The value of the 3 in this number is 3 tens or 30 ones. 

In this activity, the children are using their hands/fingers to make the concept of place value visible. It is not about counting with your fingers one by one, but showing groups of tens and ones.

The children are representing different numbers by working together to show the groups of tens and ones.

Together the children represented the number 34: 3 tens and 4 ones
OR
34 ones.

Representing numbers visibly helps children to move beyond
counting one by one on their fingers.

This learning will be effectively applied when working with much bigger numbers in the 100's and 1000's. We need to know about the nature of numbers so that we can mentally manipulate any numbers, no matter how large.

Representing numbers using the blocks

The number expander

Using the interactive display to manipulate number blocks electronically.

Learning about suffixes

Why are suffixes so important?

Understanding the different types of suffixes, and how and why they are fixed to bases to create new words, is an important part of understanding how the English spelling system works.

In this activity we built a list of different suffixes by identifying them in words, from a variety of books. The children had to prove that the sufffix was a 'real suffix' by building a word sum to demonstrate their thinking.

For example: <action>

• In <*ac + tion>, <tion> is not a real suffix because <ac> is not a base (it doesn't hold any meaning); but
• in <act + ion>, <ion> is the real suffix because <act> is the base and holds the meaning.

When the children had gathered a number of real suffixes we played a game to show that there are two different types of suffixes.

As the children shared the suffixes they discovered, I sorted them into two groups. The children's task was to think about and reflect on why I had sorted them into these two groups. 

• One group of suffixes started with a vowel letter: <-ed> <-ing> <-er> <-y> <-ion> 
• The other group of suffixes started with a consonant letter: <-ment> <-th> <-ful>.

The children discovered there are vowel suffixes and consonant suffixes!

The vowel suffixes are often called 'interesting suffixes' because they might cause a change to a base:

love/ + ing--> loving

The consonant suffixes are often called 'boring suffixes' because they don't make any changes to the base:

love + ly --> lovely

We are gathering and proving different suffixes.

The children had to think about why some suffixes
were placed on the left column while others were placed
on the right column.

Here are some word sums for your family to work on together. Remember to think about any changes to the base!

love + ed --> 
move + ment -->
move + ing --> 
like + ly -->
like +ed -->
nice + ly -->

Near 20 - Maths Game

'Near 20'-A maths game to develop quick mental thinking!

How to play:

1. Use a deck of cards with numbers from 0-9.
2. Each player receives 5 cards. 
3. Each player chooses 3 of the cards to make a total as close to 20 as possible.
4. The players' score for the round is the difference between 20 and their combination.
5. At the end of each round the players discard the cards used and collect new ones for the next round.
6. The players keep a score of their differences on a 'Near to 20' recording sheet.
7. The lowest score after 5 rounds is the winner!

Maths games are fun and motivating and they provide many
opportunities to practise and consolidate important maths strategies.

Questioning, problem solving and reflecting are important skills
that are used throughout these games.
How can I choose a combination of numbers
that could be closer to 20?

Using effective mental strategies, like bridging to 10 and doubles,
strengthens children's deep understanding of
mathematical concepts.

You can play this game very easily at home by creating your own recording sheet and using numbers from a deck of cards. Ask your child to explain the game to you.

Understanding why maths learning looks different in the 21st Century is important for us to know. Please read this short article, published by the NCTM (National Council of Teachers of Mathematics) which describes some changes in maths teaching and learning.

Art - Charcoal Drawing

We used charcoal to do large scale portraits on paper. We experimented with different types of lines and smudging to get different effects. Our portraits are on display in the library.

I was drawing my teacher. I used charcoal as
 my drawing tool.

I drew my friend and my hands got black
because of the charcoal.

I made a picture with charcoal. I learned
that charcoal is similar to crayon but they
are black.

It is a Koala Man. He has big ears. 

It was my teacher's face that I drew with charcoal.

This is my charcoal drawing and I put the eye
on top of the nose. Funny...haha..

I drew a face of my best friend in the classroom.

A large scale portrait.

Lung Model

We made a working model of the lungs showing how the diaphragm pushes air from our lungs. We then wrote up a series of steps to make it.

Cow's Heart Dissection

What sort of apron do you wear in the kitchen?

We spent an afternoon dissecting a cow's heart and investigating the various parts we could find. We were able to see the valves, aorta, atrium, ventricles and the "heartstrings" which were really tough tendons. Enjoy the comments made by our students.

I was so curious of the cow's heart.

I am ready with my plastic gloves and glasses.

I looked at the cow's heart. It felt gross.

I wonder why there is a string stuck to the heart?

I will cut the heart..I felt a little bit scared.

I felt sick before dissecting the cow's heart because I thought there would be blood splashing.

Barrett has a theory that these words might be related.

I am so curious now...

This is what it looks like inside the cow's heart.

The heart is not soft. It is a muscle so it is hard.

In the end, we are drawing the heart. 

Estimation

The importance of estimation in maths cannot be stressed enough. Estimating is one of the most useful maths skills we can acquire. It relates to all sorts of different areas of maths – measurement, handling data, handling money, time, space, shape, number operations.  It allows us to make judgements about how much time, money, food, paint…we will need. If you are good at estimating it is a skill that you use on a daily basis in adult life – it saves time and sometimes money.

One of the best things about estimating is that we use our mathematical reasoning.  There are often several ways to come to an answer, none of which is wrong.  When a student comes up with an answer, we can ask them to explain, in words, their thought-process/reasoning.  It encourages problem solving.  Importantly, estimating allows us to check to see if our calculated answers are reasonable.Estimating often provides very rich and active maths. Why sit down and work out on a piece of paper how many beanbags you would need to fill up a bath, when you could experiment with how many beanbags it takes to fill up other things?

We asked three basic questions when trying to estimate the number of pencils we might have in a container.

1. What do we have to compare this to?
2. What methods could we use to estimate?
3. How can we check our estimate?

If we could find out what "ten" looked like it was easier to estimate the rest.

Counting by twos to get a group of ten.

Learning about the structure of English

We had a helper who showed us about how bases are important parts of words and are attached to prefixes and suffixes. This is really important when we begin to look at complex patterns in English.

Using the fist to represent a base.

We are learning how to commit words to long term memory by spelling the word sum aloud as we write it. We then write the word three times, each time spelling it aloud.

Now we will test our words.