Division Using Different Strategies

To end my unit on division, I had students work through different word problems. They were quite good at understanding the problem but the challenge was that they had to use a variety of the strategies we learnt in class to solve the word problems. Here is some of their work:

 

In this example, this student showed how to solve division problems using sharing, inverse operations, and repeated addition.

Chapter Books for New Readers

This has always been a struggle for me and I know for many other teachers:

What texts do you give to students in your class who need extra assistance in reading or are EAL students? How do you select a text that is at their reading level but also at their interest level?

I did endless searching this year to find chapter books that caters to new and developing readers. And surprisingly there are excellent books out there that are chapter books and have a larger font, easier vocabulary and simple concepts but still interest students. 

Below are some examples that you can try to use in your classroom. And the best thing is that each book comes in a series, so if a student takes interest, there are more books to follow.

Series: My Weird School Daze                                       Series: Billie B Brown

            by Dan Gutman                                                    by Sally Rippin

 

Series: Nancy Drew and the Clue Crew                       Series: Boy vs. Beast

 by Carolyn Keene                                                          by Mac Park

          

Series: Zac Power                                               Series: The Go Girl Difference

by H.I. Larry                                                       by Chrissie Perry

 

Probability Statements

This activity comes from George Booker's book "Teaching Primary Mathematics"

In the early stages of our unit on probability, students were placed into mixed ability groups and given the following cards. Each card had a statement that could be made in reference to probability.

 

In groups, students had to place the cards on a probability scale in order from 100% chance to 0% chance. It was interesting to see their answers and how they interpreted the vocabulary on the cards. Especially "fat chance", as most students thought this meant a big chance. A great diagnostic tool as well. 

EAL Students in a Mainstream Class

I had a student in my class who was a part of the language centre and was a very new arrival to Australia. His English was extremely limited, and that is where I am faced with the challenge. How do you incorporate students with limited English into a mainstream class? If they've had the same amount of schooling in their native language, than they should be able to work at the same level as the other students who are native English speakers. 

Lucky for me, I have an Education Support staff that speaks/read/writes Turkish which is the language that this student spoke. She was so helpful and handy to have and we tried to ensure that he was doing the same/or very similar activities as the rest of the class. Although you want EAL students to learn English, it is still important that you use the native language in the beginning stages of English language acquisition.

For a deconstruction activity, my ES translated the writing into Turkish. Then, in working with the student, they wrote out each part of the deconstruction in Turkish and next translated it in English. This way, the student could understand each part of the information report and also know what that part was called in English.

Another example of this was in our integrated unit on the Olympics. The student completed a KWL chart, just like everyone else, but began in his language and then translated the words he knew into English with assistance. 

Teaching Division using Inverse

I often find division the hardest of the operations to teach simply because I think I struggle myself to simplify it for students. This time around I really tried to break it down and provide students with as many strategies as possible to help them understand the concept.

Our strategies included: vocabulary, sharing, repeated addition and repeated subtraction and we have now moved on to inverse operations.

Repeated addition and subtraction provided a great segway into inverse operations as students were able to make the connection between multiplication and division on their own. It is great when students can make these connections as you see the lightbulb switch in their head.

My students also love making posters in maths, so we rarely do worksheets and take a simple activity and turn it into a 5 star project. So here, I present to you, our inverse posters:

Developing a Character

One of the first things we worked on in narrative writing is the development of a character. I wanted students to come up with as many descriptive words they could use to describe personality and physical appearance. A wonderful idea that my team came up with was to present students with a picture of a person and have them develop a character based on that prompt. 

After finding a bunch of photos online, each student was given a picture. The pictures represented people of all ages, genders, races, religions etc. etc. 

Students had to describe the physical characteristics of the character in their photo. They then had to create a personality for this person, state the role (career) of the character, their challenge and achievements and whether or not they would like to be friends with them. 

It was crucial that students knew there was no right or wrong with this activity, and that it was their own character that they were creating. 

AWESOME activity!!! Please use this in narrative writing :)

Writing Ladder - Updated

For information report writing, I used a writing ladder which worked wonderfully!

For narrative writing, I have updated my writing ladder and it looks like this:

This time, I've made it look like a ladder and the students have to "climb" up the ladder as they progress through writing their narrative. 

Each students' name is placed on a little laminated card that they move up the ladder as they finish that part of their narrative writing. 

Our ladder steps from the beginning to the end are:

Plan, Develop the Characters, Set the Scene, Orientation, Complication, Resolution, Self Editing and Revising, Publishing, Group Editing

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!!!

Narrative Rubric

As you may remember (and if you don't, check out this post: Writing Unit Sequence, my writing sequence to begin a new writing genre always includes a rubric.

Here is the rubric jointly created by our class.

The students chose Structure, Creativity, Writing Process, Language Features, and Grammar and Spelling as the categories for a narrative rubric. 

Then working in small groups, they filled in what a 5*, 4*, and 3* and lower narrative would look like for each category. 

Once again, excellent collaboration between students. 

The creation of rubrics by the students is a part of the e5 Instructional Model, as it relates to the engage section of the model: "The teacher presents a purpose for learning, determining challenging learning goals, and making assessment and performance requirements clear."

Measurement Scavenger Hunt

A simple activity that focuses on estimation and measurement of length. 

Students were placed in mixed ability groups and each group was given the above worksheet. We ran this activity like a competition between groups. I had a big timer on the interactive whiteboard and when I said "go", each group had three minutes to come up with as many items that would measure to approximately 1cm. We repeated this for 10cm, 50cm, and 100cm/1m. 

This was a good activity to use as a diagnostic to evaluate students' estimation skills. It was also a fun way for students to work together as a team and share their ideas. They were able to develop their estimation skills also through teamwork. 

Once again, I found this activity from NZ Maths and modified it for my maths class.

Division Strategies

My post "Sharing in Division" is about an activity that I use often at the beginning of my unit on division to teach the strategy of "sharing". 

The next two strategies I teach in division are "repeated subtraction" and "repeated addition". My maths class loves hands-on activities so I am constantly thinking of different ways to teach lessons which will keep my students engaged. This strategy could have been taught simply by using a worksheet, but instead, I had students solve their division equations on a sentence strip using a number line.

This lesson was taught over two days, one for repeated addition and one for repeated subtraction. The simple fact of having students complete their number lines on a sentence strip, rather than on a piece of paper in their notebook caused students to stay engaged and focused (and also very excited) throughout this maths lesson. Another thing that is wonderful about my maths students is their excitement when they see their work displayed, hence students put in extra effort when they are completing a task that will be displayed.

For repeated subtraction, students were given a division equation and had to solve it using a number line. They began by drawing the line and started by placing the dividend on the right side. They then jumped backward by the amount of the divisor until they got to zero (hence, repeated subtraction). The number of jumps they made was the answer (quotient) to their division equation.

For repeated addition, students completed a number line again, however, this time they started on the left side of the number line at zero. They then proceeded to make jumps in the amount of the divisor until they reached the dividend amount. Again, the number of jumps they made was the answer (quotient) to their division equation.

 After teaching repeated addition, students made the realisation that "division is like multiplication" which was amazing as it segwayed perfectly into teaching the inverse operations strategy.

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.

Division Simplified

Here is a poster that I make with the children when we start our unit on division. 

It is crucial that students use the correct mathematical vocabulary but sometimes you need to break it down for the students to help them remember what the vocabulary means.

Keeping this poster up and showing 3 different ways to remember the formal algorithm. It is also very helpful for EAL (English as an Additional Language) students in a mainstream class to help them remember the correct mathematical vocabulary and to remember what the vocabulary means.

Somebody, Wanted, But, So, Then

SWBST as referred to by my students. One of the first summarising strategies on our success criteria.

Take any narrative and have students try to fill in a SWBST chart for their narrative. This was first shown to me by my colleague Shane and it works for all skills levels too. 

I've been explicitly teaching this strategy in my whole class focus lessons and it is used as a follow up task also. Here is a picture of our class poster that gets updated for each new narrative we read. 

We also completed this strategy on the interactive whiteboard:

Narrative Writing Goals

This is one the best parts of starting a new writing genre...

student self-evaluation and goal setting for their own writing

The idea behind this lesson is that students (especially in grade 6) are given greater ownership and accountability over their own work. By setting their own writing goals, they have achievable and visible goals set for their own writing.

To set our writing goals, students were given their pre-tests back and they had to use the rubric that we created as a class to mark their work. From that, they needed to choose the three areas that they felt they needed to improve upon from the rubric. These areas then were turned into writing goals. As a class, we shared our individual writing goals and  create a class list of the top goals.

The top goals selected by the students for narrative writing were:

1. Have a detailed plan

2. Include a title, orientation, complication, and resolution (and sometimes a cliffhanger)

3. Write in full paragraphs

4. Have lots of juicy language (descriptive and figurative)

5. Be CREATIVE (Is my story exciting to read?)

6. Use a range of punctuation correctly

They are along the left side of the poster. Then, when we work on our group editing session, students add their names (on sticky notes) to the box corresponding to the goal they achieved. They can then go back and revise to ensure they have achieved all these goals in their writing. Students love seeing their name beside each goal and really worked hard because of this.

This strategy relates to the e5 Instructional Model components of engage and evaluate.

- Engage: Teachers provide support for students to create and achieve their learning goals. 

- Evaluate: Students are able to evaluate their progress and achievements. (and in a visual format)

Banned Words for Narrative Writing

In hopes of making our narratives more exciting to read, the grade five/six teachers created a list of words that were banned from students narrative. There include: big, small, happy, sad, good and bad.

As a class, we created a massive list of synonyms that could be used in narratives instead of those words. I ran this activity as a competition for the best list between mixed ability groups. Each student in the group was given a specific tool they could use to add to their list: a thesaurus, Microsoft Encarta Dictionaries on their netbook, online thesaurus, Microsoft Word thesaurus, and one member writing the list.

And here, my friends, are the wonderful lists created by my wonderful students:

Summarising

A wonderful idea shown to me by my teaching and learning coach Mrs Kenely. Please check out her blog...she is fabulous!

For my unit on "summarising" (for those readers from Canada and the USA, "summarising" is spelt with an "s", not a "z" in Australia... yes, it took some getting used to) in reading, I created an anchor chart as seen below.

 

A nice clear visual for the students with a definition of summarising, a specific learning focus for my class, a success criteria based on strategies we will work on throughout the unit, and a summary of learning area for our share time. 

One of my favourite parts of the poster is the "Summary of Learning" section. At the end of each reading session, one student from each of my reading groups writes what they have learnt that day on a sticky note, presents it to the class and places it on our chart. These sticky notes can then be used for teacher formative assessments based on student self-evaluation. 

Narrative Deconstruction

Above is our joint deconstruction of a narrative titled "There's an Alien in My Bedroom". After completing our discovery charts, students had a fair idea of the various features and the structure of a narrative and were able to apply this knowledge to the narrative presented to them. This is all part of our writing sequence of lessons used to begin a new writing genre.

Pie Charts with Beads

This is a hands on way to teach students about the creation of pie charts. Similar to the activity with sentence strips, this one uses string and beads.


 

Students in groups were given a set of data and their task was to create a pie chart for it.

The first step was to identify what colour beads we would use for each category. As you can see on our data sheet, we coloured the category the bead colour. 

Next, we began putting on the amount of each category for the beads. One bead = one tally mark.

 This is what our string looked like after putting on the total amount of beads. We made sure that the amount of tally marks on the data set was the same amount of beads we had.
We then attached the end of our strings to create a circle. And ta-da...we had ourselves a pie chart.