What are the chances?

We have been working on the Statistics and Probability section of the Maths curriculum in our Monday maths time. The curriculum statements for Grade 5 and 6 are in the images below.

Probability is the measure of how likely an event is.

We have sorted probability words, looked at a scale of probability and worked on collecting data about the chances of rolling numbers on a fair die. One of things that we discussed was how the results of our experiments could vary from the theoretical probability.

Die Challenge

We rolled a die and recorded our results for 12 rolls and each result was very different.

We then combined our results using a Google form and could see that the more results we gathered the closer these results came to the theoretical probability outcome of an equal 1 in 6 chance of rolling each number.

We would love to collect more data and ask that you have a go. Roll a fair die 12 times and record your results on our Google form. The graph should change over time as more results are recorded.

We have also written a list on our books in response to an open ended question that Mrs S put on the board.

Listing Outcomes

We needed to think about outcomes that have a 1 in 2 chance and give as many examples as we could. The outcomes we were thinking about were those in the middle of our probability scale as a 1 in 2 chance can also be described as 0.5 or 50% or 1/2. The outcomes are equally likely to occur.

What ideas could you add to our list? Please leave a comment sharing your thoughts.

Creating Spirolaterals

We are one week into Term 4. The last term at our school for our Grade 6 classmates. Time has flown by since the start of this year.

To start our term Mrs S found an interesting Maths challenge that mixed Maths and Art. We created some spirolaterals.

Spirolaterals using the 10 time table

Spirolaterals using the 10 time table

Spirolaterals are geometrical images that are created by repeating a simple rule. For our spirolaterals we explored the patterns in our multiplication tables. Mrs S found a blog post with a video and that was our introduction to creating spiral patterns by following a rule.

Multiples of 10 explanation

Firstly we needed to write down the multiples of the number we chose and then reduce all double digits to single digits to get our pattern of steps for the spiral. Each turn was 90 degrees and we needed to always turn in the same direction. This could be clockwise or anticlockwise.

For the multiples of 10 the steps started by moving 1 square and turning 90°, then 2 squares and turn 90°, 3 squares and turn 90° , 4 squares and turn 90° and so on until the largest part of the spiral at 9 squares before starting again with 1.

Below are some of our trials. Many of us are still working on finishing our patterns.

It all sounded easy but keeping track of the steps and turns needed lots of concentration.

What patterns have you noticed in the multiplication tables? Do you think that all the patterns in the multiplication tables will create a closed spiral pattern. Please leave a comment sharing your thoughts.

Let’s Collaborate

Earlier in the year Mrs Smith received an email from Miss Crowther and the children of 5/6 Team@UPPS. It let us know that she would be travelling to Tassie with some of their class on a school trip. She asked about spending a day with our class.

Map

© Google – Imagery © Terrametrics, NASA, Map data © 2015 Google

Oh, wow! What a great idea. We would get to meet some of the children we have exchanged Trading cards with and Mrs S would get to meet someone that she has only spoken with via email or Skype over the last four years.

The answer was definitely yes and the date was quickly added to the school calendar.

As the day drew closer Mrs S thought and thought and thought about what we could do. She felt that this would be a great day to collaborate in person so we were sorted into groups of 4. Each group had children from both schools. During the day we worked together and got to know each other as we created some tetrahedral kites.

Before we started with the kite making the 5/6 CS students gave the 5/6 UPPS students a tour of our school and found out a little about our guests.

Kite

Making the kites was a little tricky at first. To start we watched a video. Then we read through the instructions and worked out how to join six straws together with string to create a tetrahedron. Thank goodness for pieces of wire as this made threading the string through the straws a little easier. We learnt that tying good knots was important when repairs were needed on one kite which did not quite get out the door for the first test fly. All was good once some knots were retied.

15-IMG_0346

Working together gave us the opportunity to combine four small kite sections together to create a bigger tetrahedral kite. Our fickle weather made the first test fly of our kites a little troublesome but eventually all the kites were in the air. Take a look at our Animoto to the see the fun.

It was fantastic fun meeting our online buddies and creating kites, talking, flying kites, talking and playing games. The day flew by and then 5/6 UPPS headed off to see some more of our great state.

Have you worked together to create something? Have you flown a kite? Please leave a comment sharing your thoughts.

Term 3 Commences

50 degree angle Jimmie via Compfight

We have just had a lovely two week break from our classroom and we are now at the start of Term 3.

We will be having another busy term with class work, sport, music, the Grade 6 trip to Canberra and many other learning opportunities.

With Mrs S on Mondays we will continue to work at our understanding of angles before moving on to working with 3D shapes. To start our term we will need to refresh our memories about the maths vocabulary we use when measuring and caculating angles. There is a great review and introduction to angles video at Maths Antics.

Last term we created and measured obtuse, acute, straight and right angles. We used protractors and rulers to help us with our work. This term we will look at how we can use our knowledge about straight and right angles to work our angles with out needing to find a protractor to help us.

Have you calculated the measurement of an angle without a protractor? How might this be possible? Please leave a comment sharing your thoughts.

Creating Angle Fish

During Maths on a Monday with Mrs S we have been working on some posters about angles. Measuring and creating angles using a protractor is one of the content descriptors in the Year 5 Mathematics curriculum.

Angles Content Description Year 5

Mrs S found some inspiration on the internet via this blog and challenged us to create a poster with four quadrants that contained fish that represented different angles. We created Right Angle Fish, Acute Angle Fish, Straight Angle Fish and Obtuse Angle Fish. All of our fish needed to be correctly labelled, measured and marked. We need to extend the rays of our angles so that it was easy to use a protractor to measure the angle of each fish’s mouth.

Here are some of our finished posters.

Some of us are still a little confused about how to correctly measure our angles. Using a protractor can be a tricky as it contains two sets of numbers and we needed to be very careful to check that we used the correct set to measure our angles.

Have you used a protractor? What angles are missing from our poster? Why might we have avoided making fish for the angles that are missing? Please leave a comment sharing your thoughts.

Working on our Multiplication Facts

As part of our Maths this term we will be focusing on our understanding and recall of the multiplication facts. Quick recall of basic multiplication facts can help us to solve more complicated mathematical equations easily.

Mrs S has created a padlet with some links to help us become faster with our recall of multiplication facts.

There are some strategies that can help us when we are working on our multiplication facts. One of these could be called the Twin Rule. When we are multiplying two numbers it does not matter which way we write them the answer will be the same. 3 x 4 and 4 x 3 will both equal 12. The real name for this strategy is the Commutative Law.

What strategies do you use to understand and remember your multiplication facts? Can you recommend any other good websites for our class to use? Please leave a comment sharing your thoughts.

Order of Operations

Last week we did some work in Maths about BODMAS. The grade six Maths curriculum focuses on exploring the use of brackets and the order of operations to solve equations.

Order of operations

Curriculum statement from the Australian Curriculum for Year 6

 

When you have an equation like 10 – 3 x 2 which part of this do you solve first? Do you work out 10 – 3 first and then multiply the answer by 3 or do you work out 3 x 2 and subtract the answer from 10? The order of operations helps to make this decision easy.

Order of operations 1

Definition taken from the Australian Curriculum glossary

We created a diagram to help us remember the order in which we need to solve equations that contain more than one operator. First come brackets. Next is orders. Orders are exponents such as powers and roots. Next come division and multiplication. They rank equally so in our diagram we sat them side by side with an arrow to remind us that we go left to right. Last comes addition and subtraction. They also rank equally and left to right is important.

BODMAS

Our Order of Operations diagram

We used our new knowledge about brackets and order of operations to have a go at maths challenge where we were able to use only four 4’s, brackets and the operators + – x ÷ to create equations with as many different answers as we could. We also found a great game to play that helped us practise using our order of operations knowledge.

Have you had a go at the four 4’s challenge? What equations can you make? Please leave a comment sharing your thoughts.

24 Hour Time – Is It Confusing?

Day 311 - Take your Time

Christophe Verdier via Compfight

One of the Mathematics curriculum statements for Year Five is about comparing and understanding the differences between 12 hour and 24 hour time.

Curriculum statement

Mrs S found some research that had been conducted by McCrindle, a research company, where it stated 1 in 10 adults in Australia are confused by 24 hour time and cannot read it properly.

24 hour time, sometimes called military time, shows how many hours and minutes since midnight. 12 hour time splits the day into two sections. The first section runs from midnight to noon (the AM hours) and the second section runs from noon to midnight (the PM hours). The Math is Fun website has a great image comparing 12 hour and 24 hour times.

We may see 24 hour time on train, ferry or bus timetables and airlines use 24 hour time when listing flight departures and arrivals. It is used to avoid confusion about when an event is occurring as the numbers in a 24 hour period are all different when using 24 hour time.

If 12 hour time is used we see the same set of numbers used twice in a 24 hour period and need to see the AM or PM suffix to help us read the time correctly. The timeanddate website has some great information about AM and PM.

Mrs S found an online interactive that we can use to practise telling time and also to practise converting times between the 12 and 24 hour time systems. You might also like to have a go at Stop The Clock (12hr time) or Stop The Clock (24hr time) to brush up on your time telling skills.

Where have you used 24 hour time? When would it be better to use 24 hour time? Please leave a comment sharing your thoughts.

Solving Problems in Maths

Last week with Mrs S we used our maths knowledge to solve an open ended problem in Maths. An open ended problem has several or many correct answers.

When we first read an open ended maths problem we need to look for the maths terms that we must understand to be able to work out an answer. We also have to work out the steps we will take to record our answer so that we can demonstrate our knowledge to best of our ability.

In last week’s problem we needed to known about parallelograms and coordinates. After looking through our work Mrs S created some charts about parallelograms to put on our Maths wall. She combined our different suggestions into a definition of a parallelogram.

Definition

Our definition of a parallelogram.

Our Maths wall now has some different types of parallelograms on display. Each poster uses words and mathematical notations to help us remember these shapes.

Parallelogram

Parallelogram

rectangle

Rectangle – one special form of a parallelogram

rhombus

Rhombus – one special form of a parallelogram.

square

Square – one special form of a parallelogram.

 Have you solved any open ended maths problems? How did you show your understanding? Where might you see some parallelograms being used? Please leave a comment sharing your thoughts.

Exploring Cartesian Coordinates

On Monday we started some work on Cartesian coordinates with Mrs S. It gave us another opportunity to explore Scratch which uses Cartesian coordinates to locate sprites on the stage.

scratch stage

The Scratch stage showing the coordinates for locating sprites.

Cartesian coordinates allow us to give a precise location to an object on a grid or graph. We use a numbering system – (x,y) – to name the locations on a graph. The first number in the ordered pair is always on the horizontal axis and the second number is always on the vertical axis.

We used a grid that was the same size as the Scratch stage to draw our initials in the upper left quadrant and work out the coordinates of the points we would need to draw these using a sprite and the PEN commands in Scratch. For those who finished this challenge the next step was to translate, rotate and reflect our initials in the other quadrants of the Scratch stage. We are still working on our projects and have shared some of our unfinished ones via the Scratch website.

  

Have you played any games that use coordinates? Where and when would it be useful to use coordinates? Please leave a comment sharing your thoughts.