A huge bonus of CONNETIX is that they can be used in so many ways for so many purposes. This includes playing and learning. There are endless opportunities to embrace CONNETIX in the classroom, whether it be in a traditional mainstream school, a Montessori setting, a home-schooling family or any other approach to education.
Let’s take a look at how CONNETIX can be used to explore fraction and decimal concepts suitable for ages 11 and 12 years.
Tip: Begin teaching fractions with squares and rectangles as they are easier to split into equal parts.
COMPARING FRACTIONS WITH THE SAME DENOMINATOR
When comparing and ordering fractions we can begin by creating fractions as a shape, using a new tile to show each part of the denominator (the bottom number) of the fraction. So, if we’re working on quarters, we would use four tiles. Then we can label each tile as its own quarter. For example, 1/4 2/4 3/4 4/4 .Now we can clearly compare which quarters are greater and smaller. Don’t forget you can use the < (smaller than) and > (larger than) symbols to integrate other concepts.
Extra activity
To make it more fun you could roll a dice three times to create two fractions. The first roll gives you your denominator for both fractions and the next two rolls gives you your numerators (the top number). Now you can create both fractions using your CONNETIX and then order and compare which is greater or smaller.
Activity tip: if you don’t have a die, try flipping a deck of cards or using dominoes.
ADDING AND SUBTRACTING FRACTIONS
If we’re exploring adding fractions with the same denominator, we can identify the denominator and create a rectangle with this amount. Think of this as a template. It can be helpfull to use the same colour for the template. For example, if our equation is 1/3+1/3, we can take three blue tiles as our template. Next, we can identify the numerators of each fraction and add this amount on top of our template using a different colour. So, we would take one purple tile, then a second purple tile and add them on top of our template. In total we can now physically see that we have 2/3. This is the same as drawing a shape and shading the parts that I’m sure we’re all used to; however, this is a different hands-on and interactive experience to mix up the learning in an engaging way.
Some kids might be tempted to add the 3+3 from the denominators but we can explore this misconception by creating each individual fraction in the equation. Then examine how we haven’t split our whole into eight parts, but rather how we have some quarters in each fraction that we are adding together.
If we are subtracting fractions with the same denominator, we can build our fraction with one color showing the amount of equal parts our fraction has been split into, just the same as before, creating a template. We can then place tiles of another color on top of the template to show how many we are starting with. Next, we can remove as many tiles as necessary to complete the equation.
Extra activities
To turn this idea into a game, grab a dice or some cards. Roll the dice three times or pull out three cards. Use one number as the denominator and the other two as the numerators, then write an equation, placing an addition or subtraction symbol in as well. Create the equation using CONNETIX and solve!
You could also write a range of fractions on your CONNETIX, then place them face down. Next, turn two tiles over and create an addition or subtraction equation. If you want a challenge, try flipping over more than two tiles for the equation.
FINDING THE FRACTION OF A QUANTITY (where the result is a whole number)
Fractions are another representation of division. Basically, one quarter can be represented as the fraction ¼ which is equal to 0.25. When exploring this concept why not get creative when finding the fraction of a quantity? Ask your learner to make a model of something they love; a train, a character of some sort, a ball run or maybe even a rainbow. Then ask them to collect a specific number of tiles. This number must be divisible by all the denominators you will use. Give them a specific set of instructions that they must follow to create their project. These instructions can include statements as a fraction or a numerical value where they must work out the fraction of tiles to use.
For example, ask them to collect 100 tiles.
The instructions state that:
- 1/5 must be a primary colour
- At least 2/8 need to be a four-sided shape
- 10 need to be orange
Your learner must work out the fraction or amount of each tile before they can get creative!
THE DECIMAL PLACE VALUE SYSTEM
When we begin to explore decimals, we are learning about a whole new world of numbers. Now, instead of always having perfect whole numbers in our place value system, we begin to explore the concept of a whole that can be split into smaller parts. During the first years of primary education students are taught about the place value system; with ones, tens, hundreds, thousands and so on labelled in different columns to organise the value that each digit represents. Decimals numbers are the exact same. The first digit after the decimal point tells us that our whole has been split into ten parts, and the digit in this column is how many we need to represent. For example, 0.2 is simply 2 out of ten parts (2/10) or two tenths. We can recreate our place value system using CONNETIX to give our learners a visual representation of what it will look like. In doing so, we begin to consolidate the idea that our number system is more than just whole numbers and where a digit sits after the decimal point has meaning.
REPRESENTING DECIMALS TO TENTHS OR HUNDREDTHS
We can use our CONNETIX to create decimals just as we would when creating visual representations on pen and paper. If we are representing a number that is one digit after the decimal place, create a rectangle with 10 squares. Again, we can use one colour for this template. Then take another colour and place the amount shown in the decimal on top of the template. For example, 0.4 shows that we are splitting our whole into tenths (the digit four is in the tenths column) so we would take ten tiles. Then we can take another colour and layer four tiles on top to recreate 0.4.
Where we move into two decimal places after the decimal point, this becomes a little tricky. Do we really want to pull out 100 tiles? If not, you can show your learner what happens when we split each of our tenths into ten parts. We can draw this onto our tiles and then we will see that we can easily make hundredths because splitting our ten tenths into ten parts each gives us 100 or hundredths. From here we can cover our template in a new coloured tile or colour over our template tiles. For example, 0.23 would look like this.
ADDING AND SUBTRACTING DECIMALS
With a solid understanding of the decimal places value system, we can now add and subtract decimals. I would suggest making the decimals first so learners can see what is happening when we add and subtract, especially when you move beyond one whole. A fun idea is to write a range of decimals on each of your CONNETIX, then turn them over facing downwards. Next, turn two tiles over and create an addition or subtraction equation. You can also try turning over more than two tiles for the equation or creating decimal numbers greater than one whole.
You might also like to create a 4×4 grid to play Connect 4. Each player writes their own decimals on each tile ranging from 0.1 to 1.2 (if using a six-sided dice). Then roll the dice, add or subtract the decimals together and whoever connects four tiles first is the winner!
CONVERTING BETWEEN FRACTIONS, DECIMALS AND PERCENTAGES
Once a learner has a solid grasp of fractions and decimals, percentages can be introduced. As we know percentages mean out of 100. This links easily to our knowledge of the decimal place value system and using division to work out the fraction of a collection.
You can ask your learner to create shapes, then identify the different fractions and decimals that have been created. They might like to use different colours to show the different fractions and decimals being made.
Extra activities
To allow children to be creative and think critically, ask them to create as many examples as possible where they can represent 50% by making different shapes. When they can confidently achieve this, ask them to move to other percentage amounts.
You might also like to write a range of equivalent fractions, decimals and percentages on your CONNETIX and have your learner match them. If you wanted to turn it into a game, flip the tiles upside down and play it as a memory game.
Another fun idea might be to play a game of bingo. Write a range of equivalent fractions, decimals and percentages on your CONNETIX and let children create their own bingo boards with these numbers. Stack the tiles up then flip them over one at a time and read it aloud. If the child has that number or its equivalent, they can cross it off their board. The aim of the game is to cross off all the tiles on their board.
CONNETIX are such an all-rounder resource! They can be used for endless hours of creative play but also for so many different maths concepts. In an education setting, children have a powerful learning tool that gives them a manipulable, hands-on experience where they are engaged and most importantly, having fun!
This blog post has been adapted from Connetix's website, you can read their original article in full here
