Concrete, Representational and Abstract

A few weeks ago I came across the blog Math Coach's Corner which really prompted me to consider how I can use the concrete and representational stages more in maths. It's because of this blog that I decided to have the kids use counters then draw pictures when working on their Maths Daily Puzzlers. Because of these stages, they are now writing number sentences which really correspond with the word problem. This skill can actually be very difficult at times and I think it will give them great preparation for when they start algebra.


Last week we had a math's test on graphing and interpreting data tables. One question asked, how much longer is Africa's Nile River than Australia's Murray River? I sat with two students today and they reattempted the question with my support and using our problem solving techniques.



We circled the pertinent data in the table (6700 km for Nile River, 2500 km for Murray River). They laid out counters, using 6 to show the Nile River and 2 to show the Murrary River. I used my pen to demonstrate that "how much longer" is the missing part (or the question mark part).





The girls then drew the problem using lines and labelling the length.

I suggested to the girls that they refer back to the counters and write a simple number sentence as a model. Once they did this, they had no problems looking at their drawing then writing the corresponding equation.

They were also able to apply their knowledge of inverse operations in order to solve it. Excellent job girls! Next stop - using counting on and other methods to solve such subtraction problems mentally!

I am more convinced than ever regarding the importance of using the concrete and representational stages when students are tackling challenging problems.

Last week we began a really interesting novel study. The novel in question is The Dragon Skateboard which is part our Rigby guided reading collection. It's a short but fun story, most students were able to read it in 30-45 minutes and it includes some great literary elements such as foreshadowing, strong characterisation and so on. The students also really enjoyed the characters and storyline.

The novel begins on Tate's birthday when he rips open his present to discover his parents had given him a skateboard. I asked the students, how did Tate feel about receiving a skateboard? (Happy, excited, etc) Does the author actually tell us that? Then how did you know?



The students used a circle map. In the middle they wrote a statement (Tate was happy to receive a skateboard) and outside it they wrote evidence from the text which supported this idea. It was a great activity for inferring. A few students wrote 'he ripped the wrapping paper off his present' or however the sentence goes and this led to an interesting discussing. Does this support the idea that Tate was happy to receive a skateboard since, at this point, he doesn't know it's a skateboard yet?



One of the standards in Year 5 English is understanding how an author uses words and vocabulary to develop ideas and points of views. So we took some of the phrases/sentences (A skateboard! He raced out to the driveway... and his heart beat a little faster) and the students had to write a different short scene. Here are two written by amazing students!

Take 1

Take 2 

(This is rough work that hasn't been edited. The students typed it straight onto their laptops then emailed it to me from their student email account so that we could practise email skills) 

Today we looked at the narrative structure and some examples of narrative naps. The students then mapped/graphed the plot line of The Dragon Skateboard. Some were more complex then others but the students clearly grasped the idea that tension built and the story included a multitude of events.
Next week we will start a character analysis of Tate, Jesse and Mandy (three of the characters) and some point-of-view activities. In the final activity the students will examine the cause and effect of choices made by Tate and evaulate the morality of said choices. The final part will be part of our RE assessment as we are learning about morality this term.
All in all, a very fun novel study!

Morning Rotation

I am a major fan of rotations in teaching! I have recently started up a Morning Rotation with my students. In the morning students come into the room then take out their laptop and morning work folder. The latter has their handwriting book, word sort, maths puzzler sheet, and a pencil and rubber.

The students start on handwriting while I take the roll, deal with questions, hand out marked work, etc etc. We then move into 3 x 10 minute rotations. I project the following slide to remind the kids where to move next. I only have girls in my class hence the flower names...!

Puzzlers: The groups are split according to their Daily Maths Puzzler level. I spend my time mostly with the group working on Puzzlers. At the moment we are using Concrete-Representational-Abstract for each puzzle. We use counters etc to show the concrete stage. The students then draw a representation. For the abstract stage, they write a number sentence. For the last stage, plenty of teaching moments regarding the Order of Operations pop up! The students are definitely enjoying these puzzlers and it will be interesting to track their progress over the year.

Partner Games: Students practise multiplication facts using their laptops or partner games. If they are already fluent (most of the class now - yeah!) they play mental games which mostly consist of adding and subtracting 2-3 digit numbers mentally. Most of my games are very simple, based on dice and playing cards. There are also some BLM games which I have made up including Bingo, Go Fish, I have/Who Has, etc.

WTW: Our school uses Words Their Way (which I love!). During this rotation the students sort their words. At the moment they then move into writing sentences or a blind sort/blind writing sort but maybe I will introduce games here too. From this week, I will be asking students to leave their sorts on their desk when they move to the next rotation so that I can check them over quickly.

After the rotation, we begin maths! Tomorrow we are starting Calendar Maths from Teaching in Room 6 and I can't wait!!