Woolworth's Teaching Decimals

At one of the EAL (English as an Additional Language) professional development workshops I attended last year, the speaker discussed how useful "junk mail" could be for teaching maths. She had us look at a flyer for a local grocery store and come up with different ways of how it could be used in our maths class. Going on this trend, I decided to use a Woolworth's flyer to create an application activity for decimal place value, addition and subtraction. 

 

I can always tell the success of a lesson based on the engagement level of the students in my class and throughout this activity, all students had their heads down and were working diligently with their partners. First, they were asked to find the prices of ten different items in the flyer. Next, they had to organise the items from the most expensive (number with the greatest value) to the least expensive (number with the lowest value). The third thing students had to do was purchase as many of the items as they could with a $10 budget. This required students to both add decimals to create a total and subtract decimals to see how much money was left in their budget. 

A very simple activity to create and students were able to improve their skills with ordering and comparing decimals as well as decimal addition and subtraction!

Creating 3D Shapes

As an application activity for 3D shapes, our maths class created their own 3D shapes with marshmallows and toothpicks. I was surprised with how talented my students were with quickly creating numerous 3D shapes. 

Once the students created their 3D shape, they had to identify the faces, edges and vertices of that shape. Each group had to create as many different 3D shapes as possible. This activity was extra engaging as all students were able to participate. A rich learning task where students could enter at their level allowed every student to participate and work together in a group. This task also allowed me to see which students were easily able to identify edges, vertices and faces, which students could identify them using concrete materials, and which students still needed additional help with this. 

At the end of the lesson, we were able to put our 3D shapes up on display and it was great to see how proud our students were of their work. 

The Day we Measured the Netball Court...

Usually I would be measuring a basketball court or a baseball diamond, but in Australia, we are measuring the netball court! For those outside of Australia who don't know what netball is (don't worry, I was in the same boat when I first arrived here), check this website out for more info: http://www.netball.asn.au/default.asp

So back to my lesson...Today we measured the netball court as part of our unit in measurement. 

Materials needed: 

A trundle wheel

A metre ruler

 

A measuring tape

A notebook and a pencil

First, in groups, students had to estimate what the perimeter of the netball court is in mm, cm, and m. This also tested their conversion skills. Next, they had to measure the court using each type of measuring equipment. 

It ended with students identifying which item (metre ruler, trundle wheel, measuring tape) was the best to use to measure the netball court and having to justify their choice with reasoning. We then compared our measurements and converted again between each unit of measurement. 

And students got some fresh air too!!!

Units of Measurement

Learning Focus: Estimating length and perimeter of objects of various sizes

As I've mentioned, my students love creating posters and seeing their work displayed. So today's activity catered to this learning style. Students were given the sheets below that had a number of different pictures of objects on it.

Their task was to create a chart and estimate which unit of measurement (mm, cm, m, or km) they would use to either measure the length of perimeter of each object. They had to cut out the picture and place it in the correct column of their chart. 

This task is related to the Concrete-Pictorial-Abstract approach of teaching maths as it falls directly under the pictorial. The lesson prior to this would have students estimating objects in front of them, and then they move to estimating objects based on a picture of the objects and thus need visualisation skills for this. The next lesson should be estimation based on simply seeing the name of the object without a picture.

Equivalent Fractions

Fractions are always a tricky thing to teach students and sometimes can be a hard concept for students to grasp, especially equivalent fractions. 

Again I like to teach equivalent fractions by using the concrete-pictorial-abstract approach. 

This is an activity for teaching equivalent fractions using the concrete approach to begin. In a small teacher focus group, I handed out a bunch of scrap paper to each student. 

I asked them first to fold the paper into half and shade in one half of the paper. That was easy. We left that paper alone and grabbed another sheet. I then asked the students to fold that paper into quarters. The instruction was then to shade in as many pieces of the sheet as needed to the same amount was shaded as the sheet for halves.

We repeated this activity for eighths. 

The picture on the left is the result of our little experiment. A few students soon caught on that 1/2, 2/4, and 4/8 all represent the same size and are therefore equivalent fractions. 

This was an exciting activity for me as a teacher as I didn't tell the students we were going to learn about equivalent fractions. Rather, I sat back, gave the instructions and watched the students draw their own conclusions about the paper in front of them. It was wonderful to see the "Ah-ha!" moment on their faces when they were able to make the connection. This will definitely be an activity repeated in the future.

Are you a Square?

I found this activity from New Zealand Maths and thought that my students might enjoy it as they love hands-on activities. It is called "Are you a Square" and is used for estimation and measurement of length and height. 

Students predict whether their body shape is landscape, portrait or square, based on their height and the measurement of their arms spanned out.

I modelled the activity to the students and then they were given the sheet to record their estimations and actual measurements.

First thing they had to do was make estimations. Then, they were to work with the students at their table to measure each others arm span and height with a piece of string first. Next they used the measuring tape to measure the length of the ribbon and get their accurate measurements. 

This activity took a whole one hour maths lesson and students stayed engaged throughout the whole session. One again, another hands-on maths activity that engaged students and allowed them to develop their estimation and measurement skills. 

This activity relates to the e5 model of instruction as it engages the students and allows them to explore this maths unit through an activity using concrete materials.

Fractions with Smarties

Once again when teaching in maths, I love working with concrete materials!!! They allow students to work hands-on with their learning and grasp a concept more easily than just trying to understand it on paper.

To begin our unit on fractions, I had students do an investigation with Smarties. Geeze, they were excited about that!

Students were placed into groups and given a package of Smarties. They then had to find the fractions of each colour in the box. 

For example: The fraction of red Smarties in the box is 5/40. 

I gave very little instruction to the students other than telling them they needed to find the fractions of each colour. This worked well as I was able to rove around and see the different strategies students used to find their fractions. Some groups sorted all the Smarties into each colour first, while others counted the total number of Smarties first. This was definitely an exciting investigation for the children but also a good diagnostic to see who grasped the concept of fractions.

Sharing in Division

The classic banana sharing activity! I have used this to teach division multiple times. When teaching any of the number operations (addition, subtraction, multiplication, division), I try to make sure that I am teaching the students many different strategies that they can use to solve equations. 

For basic division, the main strategies I teach are: sharing, inverse operations, and chunking/splitting. I always start with sharing as it is the simplest and most basic way to explain division. This activity is a concrete approach to teaching the sharing strategy.

Each student is given a worded division problem and pictures of bananas as their counters. They need to solve the problem by sharing their bananas between the amount of people in their problem to show how many bananas each person receives. 

In this example, the problem is the following:  

"There are 20 bananas in a bunch. Two people will share them. How many bananas will each person receive?"

This student cut out the twenty bananas from their bunch and split them between the two people to solve the problem. Although this seems like a very simple task, it is a great introduction into division and is an easy way for you, as a teacher, to identify whether the students in your class understand the concept of division through sharing. 

Probability Stations

A fun and exciting way to teach probability in maths. I ran a station activity with the students where they had to rotate and complete a sheet at each station using a different type of concrete material.

 Station #1: Conducting an experiment with a spinner.

Station #2:  Using a deck of cards to answer probability questions.

*Be sure to include an info sheet on cards i.e. 52 cards in a desk, 26 red cards (13 diamonds, 13 hearts), 26 black cards (13 spades, 13 clubs), each suit has the cards 1-10, Jack, Queen, King and Ace.

Station #3: Answering probability questions about a spinner with numbers and colours. 

Station #4:  Using marbles and dice to solve probability questions.

Ordering Fractions

In teaching maths, I find one of the best ways that students learn is through hands-on activities. 

"Concrete - Pictorial - Abstract" Approach to Maths 

Read this book by David Sousa to learn more about this approach. Essentially, the approach takes a unit of math and argues that students learn best by starting with working with concrete materials, moving to then using the strategy with a pictorial representation and finally moving to abstract problem.

This website has a wonderful example of this approach: http://www.loganschools.org/mathframework/CPA.pdf

The example is working with a worded problem relating to money.

Concrete: Students use play money to solve the problem.

Pictorial: Drawing out the problem with images of the money.

Abstract: Using the number operations to solve the problem.

So when I was teaching "ordering fractions with like denominators" to my class, I began with the concrete (using fraction pieces) and then moved to the pictorial (using flash cards). I combined concrete and pictorial by giving students a fraction flash card and having them arrange themselves to create a number line of fractions with the same denominator. Students were not allowed to speak to each other when arranging themselves so it ensured that the students all used their own knowledge to understand ordering of fractions. Having students move around to represent fractions is an excellent way of keeping students engaged and showing clear representations of fractions. It also allows students to stretch and have a change of pace from sitting down for an activity.

 For more information on the Concrete-Pictorial-Abstract approach, please read the following:
http://www.loganschools.org/mathframework/CPA.pdf
http://www.k8accesscenter.org/training_resources/CRA_Instructional_Approach.asp
http://fcit.usf.edu/mathvids/strategies/cra.html

Creating a Pie Chart with Sentence Strips

Our data...a little blurry from the IWB.

Pie charts... where do I begin? I find them very difficult to teach to children as they often understand and can analyse them, but struggle to create them. 

I tried this idea recently with my maths class for creating a pie chart. We used sentence strips to create a pie chart. For our example, it worked out that we were teaching fractions and graphing simultaneously and so we used data from our "Smarties" fractions activity to create a pie chart to represent that data.

The total number of Smarties was 40, so we began by dividing our sentence strip into 40 even pieces. Each piece was the width of our ruler.

Next, we coloured in the amount of each part of the pie chart. Thus, three pieces of the sentence strip were coloured brown to represent the three brown Smarties, six pieces coloured orange to represent the orange Smarties and so on.

The next step was to create our pie chart by putting the ends of the sentence strip together. The smaller the sentence strip, the easier this is so we had to get a little creative to keep the ends together.
Once the ends were together, we place our circle onto paper to trace our pie chart.

And finally, we used a ruler to create the divisions of the pie chart on our paper. A fun and creative way to create a pie chart! This is also a concrete way of creating pie charts. Following the Concrete-Pictorial-Abstract theory, we then moved on to creating pie charts on paper and then abstractly.